Probing the last scattering surface through the recent and future CMB observations

12Enhancing Light Coupling with Plasmonic Optical Antennas289Fig.12.18Raman spectrum of the1M2,2 -cyanine enhanced by the localized surface plasmon resonance of the bow tie structure,comparing with the Ag/Cr substrate treated with1mM2,2 -cyanine solutions.to treat the nanopatterned region and that of the solution treating the reference.The EF s for different parameters of bow tie structure have been plotted in Fig.12.19, which shows enhancement of106–107in Raman signal.This short example outlines the use of the optical antenna–bow tie array as SERS substrate to study the effect on Raman scattering intensity of2,2 -cyanine molecules situated on these structures.Our study suggests that Raman scattering process can indeed be tuned by the geometry and loading of the bow tie antennas, which shows good potential of optical antenna used as SERS substrate.Fig.12.19The enhancement factor of different-sized bow ties fabricated on different substrates.290Jun Xu,Anil Kumar,Pratik Chaturvedi,Keng H.Hsu and Nicholas X.Fang 12.5SummaryHarvesting and confining light using plasmonic nanoantennas represent an interest-ing frontier of metamaterial research.The convergence of RF and optical device designs will bring revolutionary changes in highly compact and integrated pho-tonics for photon energy conversion,adaptive sensing,and image processing.We expect many inspirations from RF metamaterial research to be transformed on the study of optical antennas and this could bring a profound impact to thefield of nanophotonics.Acknowledgments The authors are grateful for thefinancial supports from the Defense Advanced Research Projects Agency(grant HR0011-05-3-0002),Office of Naval Research(grant N00173-07-G013),and National Science Foundation(grant CMMI-0709023).Cathodoluminescence ex-periments were carried out in the Frederick Seitz Materials Research Laboratory Central Facilities, University of Illinois,which are partially supported by the U.S.Department of Energy under grants 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reduce the memory requirement and CPU time for the matrix solution.Numeri-cal results and computational complexity analysis have shown that the AIM solver can significantly reduce the computational cost while maintaining a good accuracy. Inspired by the periodicity of SRR,the ASED-AIM,a new adaptive integral ap-proach based on accurate sub-entire-domain method,has been proposed to solve the electromagnetic scattering by large-scalefinite periodic arrays,especially the LHM structures like SRR.Several results are shown to demonstrate the efficiency of the method in solving periodic structures.Additionally,further computational time saving scheme for calculating the near-zone interaction matrix has been pro-posed.Both2-D and3-D periodic structures can be solved by this fast solver with impressive efficiency and accuracy.In the last section of this chapter,a novel rect-angular patch antenna was specifically designed using planar-patterned LHM con-cepts.This new antenna has demonstrated to have left-handed characteristics.It is shown to have great impact on the antenna performance enhancement in terms of the bandwidth significantly broadened and also in terms of high efficiency,low loss,and low VSWR.A good agreement is achieved between the simulation and measured results.This new antenna designed has strong radiation in the horizontal direction within the entire working band,which is desirable for some special applications. Joshua Le-Wei Li∗,Ya-Nan Li and Li HuDepartment of Electrical and Computer Engineering,National University of Singapore,10Kent Ridge Crescent,Singapore119260.∗e-mail:lwli@.sgT.J.Cui et al.(eds.),Metamaterials,DOI10.1007/978-1-4419-0573-413,293 c Springer Science+Business Media,LLC2010294Le-Wei Li,Ya-Nan Li and Li Hu Key words:Method of moments,split-ring resonator,adaptive integral method, electricfield integral equations,hybrid volume surface integral equations,ASED-AIM,finite periodical structure,scattering,RCS,LHM antenna,wideband,high gain,horizontal radiation,planar LHM,RF application.13.1Adaptive Integral Method(AIM)for Left-Handed Material(LHM)SimulationLeft-handed material(LHM)[43],which is also known as negative index material (NIM),represents a material of simultaneous negative permeability and permittivity. Typical LHMs,such as split-ring resonator(SRR)structure[41],are composed of a large array of periodical elements of dielectric body and conducting patches which usually require considerable computational costs during numerical simulation.Pre-vious researchers have often used the method of moments(MoM)[18]to carry out numerical simulations and have proven its reliability and accuracy.Among sev-eral fast solvers which are developed based on MoM,the adaptive integral method (AIM)[3,23,13]is one of the very efficient solvers which can tremendously reduce the memory requirement for LHM structures like SRR and accelerate the matrix-vector multiplications in the iterative solution procedure.13.1.1Hybrid Volume–Surface Integral Equation(VSIE)andMoM for SRRsFor SRR structures,both the dielectric substrate and the metal layer have induced currents and therefore contribute to scatteredfield to the total electromagnetic(EM)field.So,we need to adopt hybrid volume–surface integral equations(VSIE)to characterize thefield.In the dielectric region V,by taking the scatteredfield from both the surface current and the volume current into consideration,the total electricfield becomesE(r)=E i(r)+E s V(r)+E s S(r),r∈V,(13.1) where E(r)represents the totalfield in region V,E i(r)denotes the incidentfield, while E s V(r)and E s S(r)stand for the electricfields scattered by volume elements and surface elements in region V,respectively.Since the SRR structure consists of a very thin metal layer and dielectric body where the thickness of the metal layer can be considered to be almost0,the tangen-tial components of total electricfield vanishes on conducting surface:n×E i(r)=− n×E s V(r)− n×E s S(r).(13.2)13Antenna Design Using Metamaterials and Fast Solver295Equations(13.1)and(13.2)are known as the electricfield integral equations (EFIE)as they involve only electricfield.The EFIE is suitable for structures with open conducting surface.Inside the dielectric region V and on the surface S of con-ducting body,the incident wave induces a volume current J V and a surface current J S.The induced volume and surface currents can generate scattered electromagnetic field as follows:E sΩ(r)=−jk0η0AΩ(r)−∇ΦΩ(r),Ω=S or V,(13.3) where the magnetic vector potential is defined asAΩ(r)=ΩJΩ(r,r )g(r,r )d r ,Ω=S or V,(13.4)while the electric scalar potential is defined asΦΩ(r)=−η0jk0Ω∇ ·JΩ(r,r )g(r,r )d r ,Ω=S or V,(13.5)where g(r,r )=e−jk0|r−r |4π|r−r |,η0=μ0ε0,and k0denotes the wave number of back-ground medium(free space in this SRR investigation).The volume of dielectric material and surface of conducting body of SRR are meshed into tetrahedral elements and triangular patches,respectively.These basis function elements are used because of theirflexibility to model arbitrarily shaped3-D objects.The volume and surface currents are expanded using different vector basis functions.For surface elements,it is convenient to use the planar triangular basis functions or the Rao–Wilton–Glisson(RWG)basis functions[37]to expand the equivalent surface electric current.As for volume elements,similarly,we can apply the Schaubert–Wilton–Glisson(SWG)basis functions[39]to expand the equivalent volume electric current,that is,J S=N S∑n=1I S n f S n,(13.6a)J V=jωN V∑n=1˜ε(r)−ε0˜ε(r)I V n f V n=jωN V∑n=1κ(r)I V n f V n,(13.6b)whereκ(r)=˜ε(r)−ε0(r)denotes the contrast ratio and˜ε(r)represents the perme-ability of a tetrahedron element.After substituting above equations into the EFIE,we apply the Galerkin’s MoM testing procedure.Then,the integral equations are converted into a linear equationsystem written as¯Z VV¯Z V S¯Z SV¯Z SSI VI S=E VE S,(13.7)296Le-Wei Li,Ya-Nan Li and Li Hu where the vectors I V and I S represent the expansion coefficients of volume currents and surface currents,respectively.The excitation vector can be computed usingE V m=V mf V m·E i(r )d r ,(13.8a)E S m=S mf S m·E i(r )d r .(13.8b)The elements of the block matrices in Eq.(13.7)can be computed using the formulas shown below:Z VV mn=V mf V m f V n˜εd r−ωk bηbV mf V mV nκf V n g(r,r )d r +∇k2bV n∇ ·κf V ng(r,r )d r,(13.9a)Z V S mn=jk bηbV mf V m·S nf s n g(r,r )d r +∇k2bS n∇ ·f S n g(r,r )d rd r,(13.9b)Z SV mn=−ωk bηbS mf S m·V nκf V n g(r,r )d r +∇k2bV n∇ ·κf V ng(r,r )d rd r,(13.9c)Z SS mn=jk bηbS mf S m·S nf S n g(r,r )d r +∇k2bS n∇ ·f S n g(r,r )d rd r,(13.9d)whereκdenotes a constant value within the tetrahedron and can be taken out fromthe integration:∇·κf V n=κ∇·f V n+∇κ·f V n.(13.10)The second term given by the above equation in(13.10)is∇κ·f V n=I V n(κ+n−κ−n),on the common face t;0,elsewhere.(13.11)13.1.2Formulations for AIMThe matrix-vector multiplication implemented inside the AIM solution procedure can be summarized using the following four steps[14]:•to project the sources distributed on the basis functions onto the regular grid by matching their vector and scalar potentials at some given test points to guarantee the approximate equality of their farfields;•to evaluate the potentials at other grid locations produced by these grid-projected sources by a3-D convolution;•to interpolate the grid point potentials onto the testing functions;the projec-tion and interpolation operators are represented by sparse matrices,and the13Antenna Design Using Metamaterials and Fast Solver297 convolution can be carried out rapidly using discrete fast Fourier transforms (FFTs);and•to compute the near-field interactions directly and remove the errors introduced by the far-field operators.To employ the AIM,the object is enclosed in a rectangular grid and then re-cursively subdivided into small rectangular grids.In order to use the FFT to ap-proximate the far-zone interaction,we need to transfer the SWG and RWG basis functions into the Cartesian grids.It is noted that by using vector identity and di-vergence theorem,the∇operator in Eq.(13.9a)can be shifted and operated on the testing functions[37,39].Hence,we can denoteγn to represent any one of the com-ponents{f S,κf V,∇·(κf V)}and express all the matrix elements in Eq.(13.9a)in the following unified form:Z mn=αmαnγm(r)g(r,r )γn(r )d r d r.(13.12)The transformation functionγn(r)can be approximated as a linear combination of Dirac delta functions,i.e.,γn(r)≈ˆγ(r)=(m+1)3∑u=1Λnuδ(r−r ),(13.13)where m represents the expansion order,whileΛnu denotes the expansion coeffi-cients ofγn(r)and it can be determined using the multipole expansion or far-field approximation[23].The multipole expansion method is applied based on the crite-rion that the coefficientsΛnu produce the same multipole moments of the original basis function for0≤{m1,m2,m3}≤M:αnγn(r)(x−x0)m1(y−y0)m2(z−z0)m3d r=(m+1)3∑u=1(x nu−x0)m1(y nu−y0)m2(z nu−z0)m3Λnu,(13.14)where the reference point r0=(x0,y0,z0)is chosen as the center of the basis func-tion.The far-field approximation method matches the farfields produced byγn(r) andˆγn(r)on a unit sphere,and it thus obtains the expansion coefficients.Once the transformation function has been determined,the matrix elements can be approxi-mated asZ mn=(m+1)3∑v=1(m+1)3∑u=1Λmv g(r v,r u)Λnu.(13.15)By using the transformation function,now we are able to compute the two com-ponents in the matrix-vector multiplications in Eq.(13.7)with298Le-Wei Li,Ya-Nan Li and Li HuZ far=ΛgΛT,(13.16a)Z near=Z MoMnz−Z far,(13.16b) where Z near denotes the matrix containing only the direct interaction of neighbor elements andΛrepresents the basis transformation matrix of the elements.The matrix g is Toeplitz and this enables the use of FFT to compute the3-D convolution efficiently.Hence we can represent the matrix-vector multiplication asZI=Z near I+Z far I=Z near I+Λℑ−1ℑ{g}·ℑ{ΛT I},(13.17)whereℑ{•}andℑ−1{•}stand for the FFT and its inverse FFT,respectively. 13.1.3Numerical Results of AIM SimulationFirst,we work with a row of SRR structures(three inclusions placed side by sidealong the y-direction).The geometry and dimensions of this kind of inclusions areshown in Fig.13.1.The width of all metal strips is0.25mm,the thickness of di-electric is0.254mm,and the dimension of each side of the square is3.3mm.Therelative permittivity of dielectric material is set to beεr=1.05in the simulation.We characterize the scattering cross section(SCS)[45]of one row of three elements andplot it versus frequency in Fig.13.2.It can be seen that the resonant frequency ofthis SRR design is15.80GHz.Fig.13.1The front-side and back-side views of SRR unit cell inclusion.Then,at this resonant frequency,the propagation characteristics of electromag-netic wave in a LHM sample placed in the free space are analyzed.It is a LHM slabcomposed of many rows of inclusions shown in Fig.13.1.The3-D view of this slabis depicted in Fig.13.3.The space distances of the inclusions denoted,respectively,by d x,d y,and d z in the x-,y-,and z-directions,are all3.3mm.In total,54SRRelements are aligned into18rows along the x-direction and3columns along the13Antenna Design Using Metamaterials and Fast Solver299Fig.13.2Scattering cross section versus frequency for a row of three SRR inclusions.Fig.13.3LHM slab composed of SRRs and wires with two different incidences of waves in the reference frame.y-direction.In order to show that our AIM algorithm is suitable for this structure, the slab is illuminated by two different plane waves propagating in the y-direction, as shown in Fig.13.3.Then,the RCS of this SRR slab in each case is checked. Actually,SRR requires the incident electricfield E i in parallel with the plane of the ring(the y–z plane)to lead to the maximum magnetic resonance.In other words, the rings are not supposed to be placed on the H-k plane[21].That is to say,if E i is perpendicular to the plane of rings(incident is Case<2>in Fig.13.3),the RCS must be very small and the whole structure becomes an ordinary scatterer which does not acquire negative refractive index.Figures13.4and13.5show the E z and RCS values when the incident waves are of polarizations in Case<1>and Case <2>,respectively.It can be seen from Figs.13.4and13.5that when the electricfield is parallel in polarization with the plane of the ring the incident power can be transmitted to the other side of the LHM slab,which satisfies the property of LHM.When the electric field is perpendicular to the ring plane,however,there is neither magnetic resonance nor negative refractive index.300Le-Wei Li,Ya-Nan Li and Li HuFig.13.4E z(r,t)and RCS values due to the slab when the incident wave of Case<1>in Fig.13.3 at15.8GHz is considered.Fig.13.5E z(r,t)and RCS values due to the slab when the incident wave of Case<2>in Fig.13.3 at15.8GHz is considered.By using the fast solver,the adaptive integral method,we can significantly reduce the simulation time and hardware requirements:a direct solver of the MoM requires O(N3)operations to solve the equation and an iterative solver requires O(N2)op-erations in each iteration,while solvers require O(N2)memory to store the matrix elements.However,the computational complexity for the AIM is only O(N1.5log N) and O(N log N)for surface and volume scatterer objects,respectively.13.2ASED-AIM for LHM Numerical SimulationsIn the previous section,we have applied the AIM for numerical characterization of split-ring resonators(SRRs).It is noticed that for these structures,the inclusions are usually arranged periodically.Besides the typical LHM(such as SRR),many other designs like frequency selective surfaces and photonic crystals also have periodic-ity.Thus,a new adaptive integral approach based on an accurate sub-entire-domain method can be used in the electromagnetic simulation of large-scalefinite periodic13Antenna Design Using Metamaterials and Fast Solver 301array.It is a further acceleration procedure as compared with the existing AIM.This approach,referred to as the ASED-AIM,is also developed based on volume–surface integral equations and is able to solve problems associated with composite metal-lic and dielectric materials in a much faster and more efficient way of desirable accuracy.13.2.1Formulations for Hybrid VSIE and ASED-AIM The VSIE equations involved here are formulated as follows:E i (r )=E (r )−E s (r ),r ∈V ,(13.18a)E i (r ) tan =−E s (r )|tan ,r ∈S .(13.18b)V olume equivalent electric current J V (r )and surface equivalent electric current J S (r )are related to total electric field E (r )and scattered electric field E s (r )viaJ V (r )=j ωκD (r )=j ω(ε−ε0)E (r ),r ∈V ,(13.19a)E s (r )=−j ωμ0V g (r ,r )J V (r )dV −j ωμ0 S g (r ,r )J S (r )dS +∇j ωε0 Vg (r ,r )∇ ·J V (r )dV +∇j ωε0 S g (r ,r )∇ ·J S (r )dS ,(13.19b)where g (r ,r )=e −jk |r −r |4π|r −r |denotes the free space Green’s function,μ0and ε0are free space permeability and permittivity,respectively,εstands for the permittivity in the dielectric object,and κ=ε−ε0εrepresents the contrast ratio.For simplicity,herein we consider 2-D large-scale periodic structures.The 3-Dperiodic problem can be analyzed in the same fashion.Based on the ASED method,we can first solve a small problem with nine cells for 2-D periodic structures.Then,the resultant solution is used to construct the basis function for each cell for solving the whole problem in the next stage.If there are M unknowns for each cell and N 0=N x N y cells,the total number of unknowns will be MN 0.But the number of unknowns has been greatly reduced to N 0via the ASED.For the p th cell,in order to ensure the normal continuity of surface current in the metallic surface,surface currents can be expanded asJ S p =N S ∑m =1I S p m f S p m .(13.20)In order to ensure the normal continuity of electric flux density inside the dielectric objects,D can be expanded as302Le-Wei Li,Ya-Nan Li and Li HuD p=1jN V∑m=1I V pmf V pm.(13.21)Thus,volume currents can be expanded asJ V p=N V∑m=1I V pmκf V pm,(13.22)where f S pm and f V pmdenote RWG and SWG basis functions associated with the m thsurface and volume basis functions of the p th cell,respectively.N S is the number ofthe RWG basis function and N V is the number of SWG basis function.I S pm and I V pmare the coefficients to be solved.Thus,electric current for the p th cell can be written asJ p=J S p+J V p.(13.23) The total current for the nine-cell problem can be written as the sum ofJ=9∑p=1J p.(13.24)Then,the Galerkin MoM procedure is used to test the VSIE and to obtain the following matrix equation:[Z pm q n ][I qn]=[V pm],(13.25)where p m denotes the m th testing function in the p th cell and q n stands for the n th basis function in the q th cell.After solving the nine-cell problem,we can obtain the nine types of cell basis functions and use them to solve the entire problem.Now,thecurrent can be rewritten asJ=N0∑p=1j p J p,(13.26)where j p denotes unknown coefficients to be solved for.The cell impedance matrix elements can be written asZ C pq=M∑m=1M∑n=1I pmZ pm q nI qn.(13.27)Although there are N0cells for the whole domain,there are only nine types of basis functions.The nine types of basis functions can be mapped to the whole domain, as shown in Fig.13.6.When N0is large,we can use the AIM to accelerate the solution process.We should combine the ASED with the AIM to solve large-scale periodic structures.The basic idea of AIM is to calculate the far-zone interaction via projecting the basis functions to,and interpolating potentials from,grid space associated with each basis function while the near-zone interactions are directly calculated.Since the free space Green’s function is translational invariant and the13Antenna Design Using Metamaterials and Fast Solver303Fig.13.6Mapping of ASED basis functions.(a)Nine-cell problem and(b)the entire problem. calculation is made based on grid space,so the FFT can be used and it can greatly reduce the memory requirement and computational ing the conventional AIM,the matrix-vector multiplication is written asZ·I=V·H·P·I+Z near·I,(13.28) where V stands for the interpolation matrix,H denotes the Green’s function matrix, and P represents the projection matrix.It follows the four steps in the conventional AIM,which were described in the previous section and are shown in Fig.13.7.For the far-zone interaction,the impedance matrix elements can be approximated asZ pm q n ≈˜Z pm q n=∑s∑tV msH ms n tP nt,(13.29)where∑denotes summation of all the contributions from the grids associated with the basis functions.Thus,for cell interaction in the far zone,we haveZ Cpq=∑m∑nI pmZ pm q nI qn≈∑m∑s∑n∑tI pmV msH ms n tI qnP nt=V Cp·Hpq·P Cq,(13.30)where V C and P C denote the interpolation and projection matrices for cell basis functions and they can be written asV Cp=∑m∑sI pmV ms,(13.31a)P Cq=∑n∑tI qnP nt.(13.31b)。

a rXiv:as tr o-ph/72282v49J un28Gen.Relativ.Gravit.manuscript No.(will be inserted by the editor)Paper in honor of Bahram Mashhoon’s 60th birthday.,(2) RR 2R ′.(3)The density ρ(r,t )is in general an arbitrary function of r and t ,and the integration time-independent function M (r )is defined asM (r )≡4πR (r,t )0ρ(r,t )R 2dR =4πρ(r,t )R 3,(4)where r,(5)brings the metric into the formds 2=−c 2dt 2+a 2 1+a ′ra2=G a 3,(7)where we have introduced ρc (r )≡6M (r )2 13,a (r,t )= 33(t −t n (r ))23ρc r 3,(9)where ρc is a constant[2].To adapt this metric to observational data we need to know the backward light cone,the luminosity distance,the corresponding Hubble parameter,the deceleration parameter,the jerk,and the equation of state parameter w .We start with the radial light rays.The null geodesic corresponding to radially inward rays is given bycdt =−R ′(r,t )dr.(10)dz =cdz =−R′(r,t(r))RorH R′=˙R′H(z′),(14) we invert it to defineH(z)= d1+z −1.(15)Note that in our structured FRW model this definition corresponds to the Hubble parameter of the FRW background outside the past light cone.There-fore,in general,we may have three different definitions of the Hubble param-eter.It has been shown,however,that in the case of glued LTB to FRW along a null hypersurface the three definitions coincide[13].A numerical compari-son is given in section4.4and Fig.14The associated deceleration parameter is then defined asq(z)=−1+ 1+z dz,(16) and the effective state parameterw≡23d(1+z)3/2 .(17)In addition,we may define the jerk as in a FRW universe[25,26]:j=˙¨aa)−3=(a2H2)′′3rt′n,(20)˙R′=0−→t=tn −16t′n+3rt′′n.The sign of t′n,as it may be seen from the above relations,plays an important role in the discussion of the singularities.Taking note of these singularities, we will construct our model such that none of the singularities is on the light cone and all of them are far from the region where the LTB metric is effective.nL .For the sake of simplicity we rename from now on r′as r.Our coordinate r is now dimensionless and scaled by the inhomogeneity scale nL.But note that we may use r for the comoving coordinate or the scaled version of it interchangeably according to the context it is used!Now,for the bang time to have the desired property,we may write it in the following general form:t n=αr ),(21)where p and q are polynomials in their arguments having no constant and linear term.The time factorαis another constant of the model in addition to inhomogeneity parameter n.It is obvious that for r≪1the bang time approaches a constant,in fact zero for q=0,and for r≫1it approaches a constant,zero again for p=0,meaning that for large r we have effectively FRW metric again.Note that large r will corresponds in our case to redshifts bigger than1.To see the cosmological effects of polynomials like p(r)we restrict it to powers of up to r4.On the other hand,it is easily seen that large powers of1r2+1(22)t n=α1+r2suggested in[28].We will see that the bang time,(24)r4+r2+1where r is scaled to nL.We will alternatively use the comoving coordinate r in the scaled form or not,and the reader may simply see from the context which one is meant.The constantαhas the dimension of time.We have, therefore,two model parameters n andαto be determined by observation. Fig.9shows t n as a function of the redshift z,using(11).We have plotted r and R as a function of z in the same diagram to see the coordinate,or redshift for which our LTB metric is essentially FRW.Obviously,the value z≈1,corresponding to r≈10and t≈2α,is the boundary of transition from LTB to FRW.The inhomogeneity scale r≈10,or roughly1000Mpc, corresponds to the physical length≈1Mpc at the time of the last scattering for z≈1100.Although the transition point is at a relatively small z,we can follow the effect of inhomogeneity up to the last scattering surface at z≈1100.The bang time is zero almost everywhere,except in our vicinity. Therefore,if the inhomogeneity has any effect,it must show up at our time, in accordance with the cosmological coincidence.Now,for this bang time(24)we havet′n|r=0=0.(25) Therefore,we do not expect any weak singularity at the origin[28].In fact, for the LTB domain with this bang time,we have no singularity at all,as it is shown in Fig.3.Vanishing of R′′at the light cone and its vicinity indicates a maximum of R′for t=const.which reflects a feature of expanding layers. No invariant of the metric has a singularity within the domain of our interest. The singularity t=3t n which appears in the Kretschman invariant is well outside the region of our interest as shown in Fig.3.We have also plotted in Fig.5,R′as a function of r for somefixed values of time to have a better understanding of variation of the LTB metric function.Note the behavior of R′near its maximum values where R′′vanishes and compare it with Fig.3. The behavior of the LTB scale factor R/r and the metric function R′,for the sake of comparison the FRW scale factor for the CDM case(α=0)as a function of z,is depicted in Fig.10.The density as a function of redshift is also plotted in Fig.11and Fig.12for different ranges of z.p(r)χ2(for182SNe Ia)CDM1700ΛCDM(ΩΛ=0.7)393p(r) and we put n=1,α=1017s,t0=3.9×1017s.Different bang times t n having a wide range of free parameters(i.e.αand n)enables us to get bestfit luminosity distances,and likelihoods as in the other models like LCDM.Of course,we need to compare the results of our model with other cosmological data to choose the most suitable bang time and the acceptable range of its free parameters.At this stage,we found out thatαshould be approximately1017s for any bang time t n.Looking at the density contrast,we can estimate the inhomogeneity factor as well(see section4.4).Table2shows the best parameters for different bang times using SNe Ia data(GOLD samples):α(r2+1)−1 1.1 2.2188α(r4+1)−1 1.0 2.2212α(r4+r2+1)−1 1.0 2.9198or˙R′Rα(×1017s)nTable3Density contrast for t n and different parameter values.(15)we used to define the effective Hubble parameter may also differ from the other two definitions.It is interesting,however,to note that all three defini-tions coincide if the LTB metric is matched exactly to FRW metric along the light cone,as has been shown in[13].The requirement of the exact matching leads to a definite bang time,which could be calculated numerically.In fact, what we have done is the inverse problem:we have been looking for a suitable bang time mimicking the exact matching.What we have achieved is a bang time which leads almost everywhere,for the redshift values1100<z<0.03, to the equivalence of all three Hubble parameter,i.e.to an exact matching. The actual problem of requiring exact matching andfinding out the bang time is subject of a future work.Using relations(15)and(16),we have plotted in Fig.14the different Hub-ble parameters.For comparison,we have also plotted H−values for CDM and LCDM models in the homogeneous FRW universe models(α=0).Note the peculiar z−dependence of the Hubble parameters for z<0.5.There we observe a decrease of the Hubble parameter up to a value of about50and increase again to the present value of about70.This behavior may be par-tially due to the deviation of H R from H=H R′[3].The effective deceleration parameter,as defined in(16),is plotted in Fig.16 for t n1,used in our SFRW model.It shows the effective deceleration for dif-ferent n−values.For z≫1all models almost coincide and have q=1/2. They,however,differ from each other for small z.Negative deceleration is almost typical for all of them.Fig.18shows the deceleration parameter for t n.4.4Density contrastLet us now look at the density contrast within the LTB domain.At any time, the density contrast within the LTB domain defined above is given byδmax−δminδ=r2+1,(α=1017s,n=1).The solid line curve shows the shell focussing area R=0at t=t n.On this curve both R′and R′′are singular.Here,one can easily see that one of these singular points lie on the light cone.This singular point maybe avoided if we restrict the value of n to be less than0.2or choose another bang time t n(r).The shell focussing singularity crosses the light cone at z−values well above the last scattering surface which is outside the range of applicability of our model,although it may also be avoided using suitable inhomogeneity parameter.The dash-dotted green curve corresponds to Kretschman singularity(t=3t n(r)).,(α=1017s,n=1).All singularitiesr4+r2+1are well inside the curve t=3t n(r).The˙R′singularity points(corresponding to t=t n−1,n=1,α=1017s) r4+r2+1。

关于星星的使命英语作文Title: The Mission of Stars。

Stars, those celestial beacons scattered across the vast expanse of the night sky, hold within them a mission far beyond mere illumination. Their purpose transcends the boundaries of our understanding, weaving a narrative that spans the realms of science, mythology, and human imagination.Firstly, stars serve as luminous guides, illuminating the dark canvas of the night sky and offering direction to travelers and explorers since time immemorial. Sailors navigate the seas, guided by the steady pulse of distant stars; travelers in deserts and forests find solace in the constellations above, charting their course by their shimmering light. In this way, stars fulfill a practical role, aiding humanity in its quest for discovery and exploration.Beyond their navigational significance, stars possess a profound symbolic importance in cultures around the world. They are often emblematic of hope, inspiration, and the eternal cycle of life. For centuries, humans have looked to the stars for guidance in times of uncertainty, seeking meaning in their patterns and constellations. From the ancient civilizations of Mesopotamia and Egypt to the modern era, stars have inspired myths, legends, and religious beliefs, shaping the cultural fabric of societies across the globe.Moreover, stars play a pivotal role in the cosmic drama of creation and destruction. Born from the turbulent depths of stellar nurseries, they are the crucibles where matteris forged into elements essential for life. Through the process of nuclear fusion, stars generate energy and light, illuminating the cosmos and seeding the universe with the building blocks of planets, moons, and life itself. Yet, in their final act, stars meet their demise in spectacular fashion, exploding into supernovae and scattering their elemental remnants across the cosmos, enriching the cosmic landscape with the raw materials of future generations ofstars and worlds.In the realm of science, stars are invaluable laboratories for the study of astrophysics and cosmology. Astronomers peer through telescopes, unraveling the mysteries of stellar evolution, probing the depths of black holes and quasars, and deciphering the origins of the universe itself. Stars serve as cosmic beacons, offering insights into the fundamental forces that govern the cosmos and shaping our understanding of the universe's past, present, and future.Yet, perhaps the most profound mission of stars lies in their ability to evoke a sense of wonder and awe in the hearts and minds of humanity. Gazing up at the night sky, we are reminded of our place in the vast expanse of the cosmos, humbled by the sheer magnitude of space and time. Stars inspire us to dream, to question, and to explore, igniting a curiosity that drives us ever onward in our quest for knowledge and understanding.In conclusion, the mission of stars transcends theboundaries of the tangible and the intangible, weaving a tapestry of meaning and significance that stretches across the cosmos. From guiding lost travelers to inspiring the loftiest aspirations of humanity, stars embody the wonder and mystery of the universe, reminding us of our shared connection to the celestial dance of creation and destruction. As we gaze upon the glittering tapestry of the night sky, let us remember the timeless mission of stars and the profound role they play in shaping our lives and our understanding of the cosmos.。

大气科学系微机应用基础Primer of microcomputer applicationFORTRAN77程序设计FORTRAN77 Program Design大气科学概论An Introduction to Atmospheric Science大气探测学基础Atmospheric Sounding流体力学Fluid Dynamics天气学Synoptic Meteorology天气分析预报实验Forecast and Synoptic analysis生产实习Daily weather forecasting现代气候学基础An introduction to modern climatology卫星气象学Satellite meteorologyC语言程序设计 C Programming大气探测实验Experiment on Atmospheric Detective Technique云雾物理学Physics of Clouds and fogs动力气象学Dynamic Meteorology计算方法Calculation Method诊断分析Diagnostic Analysis中尺度气象学Meso-Microscale Synoptic Meteorology边界层气象学Boundary Layer Meteorology雷达气象学Radar Meteorology数值天气预报Numerical Weather Prediction气象统计预报Meteorological Statical Prediction大气科学中的数学方法Mathematical Methods in Atmospheric Sciences专题讲座Seminar专业英语English for Meteorological Field of Study计算机图形基础Basic of computer graphics气象业务自动化Automatic Weather Service空气污染预测与防治Prediction and Control for Air Pollution现代大气探测Advanced Atmospheric Sounding数字电子技术基础Basic of Digital Electronic Techniqul大气遥感Remote Sensing of Atmosphere模拟电子技术基础Analog Electron Technical Base大气化学Atmospheric Chemistry航空气象学Areameteorology计算机程序设计Computer Program Design数值预报模式与数值模拟Numerical Model and Numerical Simulation接口技术在大气科学中的应用Technology of Interface in Atmosphere Sciences Application海洋气象学Oceanic Meteorology现代实时天气预报技术（MICAPS系统）Advanced Short-range Weather Forecasting Technique(MICAPS system)1) atmospheric precipitation大气降水2) atmosphere science大气科学3) atmosphere大气1.The monitoring and study of atmosphere characteristics in near space as an environment forspace weapon equipments and system have been regarded more important for battle support.随着临近空间飞行器的不断发展和运用,作为武器装备和系统环境的临近空间大气特性成为作战保障的重要条件。

银纳米粒子制备及SERS检测福美双王斌;张莉【摘要】柠檬酸钠还原法制备银纳米颗粒.通过紫外-可见吸收光谱(UV-Vis),X-射线衍射佼(FEXRD)和场发射扫描电子显微镜(SEM)对银纳米颗粒光学性质、结构和形貌进行表征,并用纳米粒度及Zeta电位分析仪测定其粒径分布.利用结晶紫作为探针分子表征了银纳米颗粒的SERS性能.利用表面增强拉曼光谱技术对农药福美双进行了检测.结果表明,银纳米颗粒粒径均匀,分布在35～45 nm之间.银纳米颗粒作为SERS活性基底,具有很好的效果；同时,对农药福美双有很好的检测效果.【期刊名称】《宿州学院学报》【年(卷),期】2014(029)001【总页数】4页(P90-93)【关键词】柠檬酸钠法;银纳米颗粒;SERS;福美双【作者】王斌;张莉【作者单位】安徽理工大学化学工程学院,安徽淮南,232001;宿州学院自旋电子与纳米材料安徽省重点实验室培育基地,安徽宿州,234000;宿州学院自旋电子与纳米材料安徽省重点实验室培育基地,安徽宿州,234000【正文语种】中文【中图分类】O614.1221974年，Fleischmann等发现在粗糙的银电极上对吡啶的拉曼增强信号[1]，此后，表面增强拉曼光谱(SERS)迅速发展成为一种简单快速的痕量分析检测技术之一，在环境分析、化学、生物、医药等领域得到广泛的应用[2-3]。

研究发现，除常见的贵金属材料Au、Ag和Cu外，半导体材料TiO2和ZnO2等也有SERS增强效果，但多以Au和Ag效果最佳。

表面增强拉曼光谱具有较高的灵敏性和独特的指纹效应等特点，已成为近10年来研究的热点之一[4]。

随着纳米材料的兴起和发展，研究开发了具有高活性的SERS金属纳米颗粒溶胶、膜、复合材料等。

SERS增强机理的研究与SERS活性基底的制备是人们广泛关注的问题。

SERS增强的机理有电磁增强和化学增强，主要以电磁增强为主[5-6]。

通过激发贵金属表面的表面等离子体(SP)产生局部电磁场来实现电磁增强，调控贵金属材料的形状(如颗粒、棒、线、花状、立方体、三角、六面体、核壳材料[7-8]等)和大小以改变金属表面的电磁场分布，实现金属表面不同程度的电磁增强。

J.Phys.D:Appl.Phys.31(1998)2653–2710.Printed in the UK PII:S0022-3727(98)68952-XREVIEW ARTICLEGrowth and applications ofGroup III-nitridesO AmbacherWalter Schottky Institute,Technical University Munich,Am Coulombwall,D-85748Garching,GermanyReceived18February1997,infinal form15June1998Abstract.Recent research results pertaining to InN,GaN and AlN are reviewed,focusing on the different growth techniques of Group III-nitride crystals andepitaxialfilms,heterostructures and devices.The chemical and thermal stability ofepitaxial nitridefilms is discussed in relation to the problems of depositionprocesses and the advantages for applications in high-power and high-temperaturedevices.The development of growth methods like metalorganic chemical vapourdeposition and plasma-induced molecular beam epitaxy has resulted in remarkableimprovements in the structural,optical and electrical properties.New developmentsin precursor chemistry,plasma-based nitrogen sources,substrates,the growth ofnucleation layers and selective growth are covered.Deposition conditions andmethods used to grow alloys for optical bandgap and lattice engineering areintroduced.The review is concluded with a description of recent Group III-nitridesemiconductor devices such as bright blue and white light-emitting diodes,thefirstblue-emitting laser,high-power transistors,and a discussion of further applicationsin surface acoustic wave devices and sensors.1.IntroductionGroup III-nitrides have been considered a promising system for semiconductor devices applications since1970, especially for the development of blue-and UV-light-emitting diodes.The III–V nitrides,aluminium nitride (AlN),gallium nitride(GaN)and indium nitride(InN), are candidate materials for optoelectrical applications at such photon energies,because they form a continuous alloy system(InGaN,InAlN,and AlGaN)whose direct optical bandgaps for the hexagonal wurtzite phase range from 1.9eV forα-InN and 3.4eV forα-GaN to 6.2eV forα-AlN.The cubic modifications have bandgaps in the range from 1.7eV forβ-InN and 3.2eV for β-GaN to 4.9eV forβ-AlN(figures1and2)[1–6]. Other advantageous properties include high mechanical and thermal stability,large piezoelectric constants and the possibility of passivation by forming thin layers of Ga2O3 or Al2O3with bandgaps of approximately 4.2eV and 9eV.The spontaneous and piezoelectric polarization(in the wurtzite materials)and the high electron drift velocities (2×105m s−1[7])of GaN can be used to fabricate high-power transistors based on AlGaN/GaN heterostructures. In addition,AlN is an important material with a variety of applications such as passive barrier layers,high-frequency acoustic wave devices,high-temperature windows,and dielectric optical enhancement layers in magneto-optic multilayer structures[8,9].Very informative reviews of the growth techniques and structural,optical and electrical properties of Group III-nitrides and their alloys have been presented by Strite et al[10,11].A good overview of applications of Group III-nitride based heterostructures for UV emitters and high-temperature,high-power electronic devices is provided in[12]and[13].This review focuses on the development of the different growth techniques successfully applied to the deposition of Group III-nitride epitaxial films and heterostructures,such as chemical transport and metalorganic chemical vapour deposition(MOCVD), sputtering and molecular beam epitaxy(MBE).The quality of state-of-the-art material and its application for optical and electronic devices are discussed in detail in order to point out possible limitations,promising developments and future trends.Thefirst systematic effort to grow InN,GaN and AlN by chemical vapour deposition or sputtering processes took place in the1970s in order to characterize the optical and structural properties of thinfilms.At that time, neither metalorganic precursors containing In or Al with electronic grade purity,plasma sources for nitrogen radicals compatible with MBE systems,nor substrate material with reasonably good thermal and lattice matches to the nitrides were available.The InN and GaN material had large concentrations of free electrons,presumed to result from oxygen impurities and intrinsic defects,and the structural quality of the AlNfilms was not good enough for optical0022-3727/98/202653+58$19.50c 1998IOP Publishing Ltd2653OAmbacherFigure 1.Bandgap and bowing parameters of hexagonal (α-phase)and cubic (β-phase)InN,GaN,AlN and their alloys versus lattice constant a 0[1–6].or electronic applications.Primarily,the development of MOCVD and plasma-induced molecular beam epitaxy (PIMBE)over the last eight years has led to a number of recent advances and important improvements in structural properties.2.Crystal structure,polarity and polarization of InN,GaN and AlNIn contrast to cubic III–V semiconductors like GaAs and InP with the zincblende structure,the thermodynamically stable phase of InN,GaN and AlN,is the hexagonal wurtzite structure (α-phase).Beside the α-phase,a metastable β-phase with zincblende structure exists and a cubic high-pressure modification with NiAs structure was observed for pressures above 25kbar in the case of AlN [14].Because the α-and β-phases of Group III-nitrides only differ in the stacking sequence of nitrogen and metal atoms (polytypes),the coexistence of hexagonal and cubic phases is possible in epitaxial layers,for example due to stacking faults.The hexagonal crystal structure of Group III-nitrides can be described by the edge length a 0of the basal hexagon,the height c 0of the hexagonal prism and an internal parameter u defined as the anion–cation bond length along the (0001)axis.Because of the differentcations and ionic radii (Al 3+:0.39˚A,Ga 3+:0.47˚A,In 3+:0.79˚A[15]),InN,GaN and AlN have different lattice constants,bandgaps and binding energies as shown in table 1[16,17].Both wurtzite and zincblende structures have polar axes (lack of inversion symmetry).In particular,the bondsinFigure 2.Experimental results of bandgaps of hexagonal Group III-nitrides versus lattice constant c 0at room temperature [1–6].Table ttice constants,bandgaps and binding energies of hexagonal InN,GaN and AlN.Wurtzite,300K AlN GaN InN a 0(˚A)b 3.112 3.189 3.54c 0(˚A)b 4.982 5.185 5.705c 0/a 0(exp.)b 1.6010 1.6259 1.6116c 0/a 0(calc.)a 1.6190 1.6336 1.6270u 0a0.3800.3760.377a Bohr (˚A)a 5.814 6.04 6.66E B (M–N)c (eV)b2.882.201.98a From [16].b From [17].cM =In,Ga or Al,N =nitride.the 0001 direction for wurtzite and 111 direction for zincblende are all faced by nitrogen in the same direction and by the cation in the opposite direction.Both bulk and surface properties can depend significantly on whether the surface is faced by nitrogen or metal atoms [18,19].The most common growth direction of hexagonal GaN is normal to the {0001}basal plane,where the atoms are arranged in bilayers consisting of two closely spaced hexagonal layers,one with cations and the other with anions,so that the bilayers have polar faces.Thus,in the case of GaN a basal surface should be either Ga-or N-faced.By Ga-faced we mean Ga on the top position of the {0001}bilayer,corresponding to [0001]polarity (figure 3).Ga-faced does not mean Ga-terminated;termination should only be used2654Growth and applications of GroupIII-nitridesFigure3.Different polarities(Ga-and N-faced)of wurtzite GaN.to describe a surface property.A Ga-face surface mightbe N-terminated if it is covered with nitrogen atoms,butwithoutflipping the crystal it will never be N-faced.Itis,however,important to note that the(0001)and(000¯1) surfaces of GaN are inequivalent(by convention,the[0001]direction is given by a vector pointing from a Ga atom toa nearest-neighbour N atom).It has been reported that high-quality epitaxial GaNfilms deposited by MOCVD on c-plane sapphire substratesgrow in the(0001)direction with Ga-faced surfaces,whileMBE growth commonly occurs in the(000¯1)direction, yielding an N-facedfilm[20–22].Polar faces are known to have very marked effectson growth in binary cubic semiconductors.For example,growth along the Ga-faced{111}direction of GaAs isknown to be slow and has the tendency to produce planarsurfaces,whereas growth of the As-face is fast and rough[23].Similarly,Ponce et al found that the smooth sideof bulk single crystal platelets corresponds to the Ga-face(0001)whereas the N-face(000¯1)is much rougher[20].In the following we will discuss the influence ofspontaneous and piezoelectric polarization on the physicalproperties of Group III-nitrides.This class of polarization-related properties is obviously important for devices(section9)because the electricfields influence the shapeof the band edges and the carrier distribution insidenitride-based heterostructures.Therefore spontaneousand piezoelectric polarization can influence the radiativerecombination in light-emitting devices as well as theelectrical properties of the transistor structures discussedin detail later.Wurtzite is the structure with highest symmetrycompatible with the existence of spontaneous polarization[16,24,25]and the piezoelectric tensor of wurtzite hasthree independent nonvanishing components.Therefore,polarization in these material systems will have both aspontaneous and a piezoelectric component.Becauseof the sensitive dependence of spontaneous polarizationon the structural parameters,there are some quantitativedifferences in polarization of the three nitrides studied here.The increasing nonideality of the crystal structure going Table2.Spontaneous polarization,piezoelectric and dielectric constants of AlN,GaN and InN.Wurtzite AlN GaN InNP SP(C m−2)−0.081−0.029−0.032e33(C m−2) 1.46a0.73a0.97a1.55b1c0.65d0.44ee31(C m−2)−0.60a−0.49a−0.57a−0.58b−0.36c−0.33d−0.22ee15(C m−2)−0.48b−0.3c−0.33d−0.22eε119.0b9.5fε3310.7b10.4fa From[16].b From[26].c From[27].d From[28].e From[29].f From[30].from GaN to InN to AlN(u0increases and c0/a0decreases (table1)),corresponds to an increase in spontaneous polarization.In the absence of external electricfields,the total macroscopic polarization P of a solid is the sum of the spontaneous polarization P SP in the equilibrium lattice and the strain-induced or piezoelectric polarization P P E.Here we consider polarizations along the(0001)axis, because this is the direction along which standard bulk materials,epitaxialfilms and heterostructures are grown. Spontaneous polarization along the c-axis is P SP=P SP z (the direction of spontaneous polarization is determined by the polarity;the direction of the piezoelectric polarization depends on the polarity and whether the material is under tensile or compressive stress)and piezoelectric polarization can be calculated by using the piezoelectric coefficients e33 and e13(table2)asP P E=e33εz+e31(εx+εy)(1) where a0and c0are the equilibrium values of the lattice parameters,εz=(c−c0)/c0is the strain along the c-axis, and the in-plane strainεx=εy=(a−a0)/a0is assumed to be isotropic.The third independent component of the piezoelectric tensor,e15,is related to the polarization induced by shear strain and will not be discussed.To give an example of the possible influence of polarization on the physical properties of nitride-based heterostructures,we calculate the electricfield caused by polarization inside a Ga-faced Al x Ga1−x N/GaN/Al x Ga1−x N quantum well.We assume that the GaN is grown pseudomorphically on the AlGaN(a(GaN)=a(AlGaN))2655O AmbacherTable3.Experimental and calculated values of the piezoelectric constants and bulk modulus for wurtzite and zincblende Group III-nitrides.AlN GaN InNGPawurtzite exp.a calc.b exp.c calc.b exp.d calc.bC11345396374367190223C12125137106135104115C131201087010312192C33395373379405182224C44118116101951048B201207180202139141zincblende calc.e calc.b calc.e calc.b calc.e calc.bC11304304296293184187C12152160154159116125C4419919320615517786a From[31].b From[32].c From[33].d From[34].e From[35].and that screening effects due to free carriers and surface states can be neglected.The lattice constants a and c of the GaN layer are decreased and increased respectively,due to the biaxial compressive stress which becomes larger with increasing Al content of the AlGaNfilm.The relation between the lattice constants of the hexagonal GaN is given byc−c0 c0=−2C13C33a−a0a0(2)where C13and C33are elastic constants(table3). Using equations(1)and(2)the amount of piezoelectric polarization in the direction of the c-axis can be determined byP P E=2a−a0a0e31−e33C13C33.(3)The strain of the pseudomorphically grown GaN can be calculated using Vegard’s law(linear interpolation of the lattice constants of relaxed Al x Ga1−x N from the values for GaN and AlN:a(x)=(−0.077x+3.189)˚A(table1)), leading toP P E(GaN)=0.0163x C m−2(4) and a total polarization ofP(GaN)=P SP(GaN)+P P E(GaN)=(−0.029+0.0163x)C m−2.(5) The polarization generates an electricfield E(GaN)inside the GaN layer:E(GaN)=−P(GaN)ε(GaN)ε0=(3.6×106−2.1×106x)V cm−1(6) whereε(GaN)(table2)andε0are the dielectric constants of GaN andvacuum.Figure4.Polarization(spontaneous,piezoelectric and total polarization)of a relaxed Al x Ga1−x N and a pseudomorphic on top of Al x Ga1−x N grown GaN layer versus Al content x. The interface chargeσis caused by the different total polarizations of the GaN and the AlGaNfilm.The AlGaN is assumed free of strain and therefore the piezoelectric polarization equals zero.The total polarization of the AlGaN can be described by a linear approximation between the spontaneous polarization of GaN and AlN:P(AlGaN)=P SP(AlGaN)=(−0.029−0.052x)C m−2.(7)A charge density at the GaN/AlGaN interfaces,σ(GaN/ AlGaN),is caused by the different polarizations of GaN and AlGaN:±σ(GaN/AlGaN)=P(GaN)−P(AlGaN)=±0.068x C m−2.(8) The spontaneous polarization,piezoelectric polarization and interface charge density of GaN embedded in two Al0.15Ga0.85N layers are determined to be−0.029,0.0025 and±0.0025C m−2respectively.(For AlGaN/GaN/AlGaN heterostructures with different Al content x,seefigure4.) The electricfield caused by polarization effects can reach a strength of3×106V cm−1.The modification of the band edges due to spontaneous polarization and piezoelectricfields inside the GaN layer can have a significant influence on the optical properties (figure5).Due to the Stark and Franz–Keldysh effects, the effective bandgap of GaN will be red-shifted and the recombination probability of electron hole pairs will be decreased because of the spatial separation of electrons and holes[36,37].These physical effects thus change the energy of the electroluminescence out of GaN or InGaN2656Growth and applications of GroupIII-nitridesFigure5.Conduction and valence band edges of a pseudomorphic grown AlGaN/GaN/AlGaN(x=0.15)andGaN/InGaN/GaN(x=0.06)heterostructure.The arrows indicate schematically the radiative recombination of an electron and a hole,which is red-shifted in comparison to the bandgap energy due to the Stark effect.quantum wells and the recombination rates of carriers inside a Group III-nitride based laser structure(section9.5).The strong electricfields can also enhance electron or hole accumulation at AlGaN/GaN interfaces(figure5).This effect can be used in heterostructurefield effect transistors, as discussed later in section9.3.At which interface (lower or upper)of a AlGaN/GaN/AlGaN heterostructure electrons or holes are confined depends on the polarity of the material.In respect of polarization effects,the Group III-nitrides exhibit unusual properties.The piezoelectric constants have the same sign as in II–VI compounds,and opposite to those of III–V compounds.The absolute values of the piezoelectric constants are up to ten times larger than in conventional III–V and II–VI compounds.In particular the constants e33and e31of AlN are larger than those of ZnO and BeO[38],and are therefore the largest known so far among the tetrahedrally bonded semiconductors.The spontaneous polarization(the polarization at zero strain) is also very large in the nitrides.That of AlN is only about three tofive times smaller than in typical ferroelectric perovskites[39].For these reasons,the spontaneous and piezoelectric polarization of hexagonal Group III-nitrides can have a much larger influence on the electrical and optical properties of devices than in other III–V compounds. Finally it should be mentioned that free carriers with a concentration above1018cm−3,charged defects or compensation of surface charges by adsorbates can reduce the polarization-induced electricfields and have to be considered in a detailed analysis of polarization-related effects.3.Thermal properties and stabilityThe primary methods of obtaining crystal material rely on growing epitaxial layers on different substrates at high temperatures.Unfortunately,the different coefficients of thermal expansion between substrate and nitride introduce residual stress upon cooling.These induced stresses can cause additional structural defects and piezoelectricfields and will influence the optical and electrical properties of films and devices.The determination of thermal expansivity is not only related to other thermal properties(thermal conductivity, specific heat)but can also yield parameters pertinent to2657OAmbacherFigure ttice constant and c /a ratio versus temperature.other basic properties,like the temperature dependence of the band gap [2].The value of the thermal expansion coefficient depends on many parameters,such as defect concentration,free carriers,and strains,and the published values are somewhat scattered.The thermal expansivities perpendicular and parallel to the c -axis in hexagonal material are usually different.The lattice parameters and the thermal expansion coefficient have been measured to intermediate temperatures for AlN,GaN and once for InN [30,40–46].The increase of the lattice constant a and the thermal expansion coefficients of hexagonal InN,GaN and AlN with increasing temperature measured by different groups are shown for comparison in figures 6and 7.As the lattice constants a and c increase,the c/a ratio of the lattice constants becomes smaller with increasing temperature.The experimental data of the lattice constants and thermal expansion coefficients for AlN and GaN are in good agreement with the theoretical calculations of Wang and Reeber (figure 7)[47].The calculated thermal expansion coefficients of AlN,GaN and InN at 100K are 1.3×10−8K −1,1.2×10−6K −1and 2.4×10−6K −1for a 0and −5×10−8K −1,1.1×10−6K −1and 2.8×10−6K −1for c 0.At 600K,these values become 5.3×10−6K −1,5×10−6K −1and 5.7×10−6K −1for a 0and 4.4×10−6K −1,4.4×10−6K −1and 3.7×10−6K −1for c 0.Below 100K the thermal expansion coefficient of AlN was calculated to be negative.Above 600K up to the decomposition temperature (discussed below),the thermal expansion coefficients gradually increase by up to 25%.The lattice constants,binding energy and decomposi-tion temperature of Group III-nitrides have important con-sequences for the thermal stability of nitride-baseddevices.Figure 7.Thermal expansion coefficients parallel (α(c ))and perpendicular (α(a ))to the c -axis versus temperature.The relatively large range of uncertainty and the limited number of experimental data concerning nitrogen diffusion,the temperature dependence of the nitrogen flux from a ni-tride crystal surface and the nitrogen pressures necessary to stabilize a GaN melt are due in part to the very high melt-ing points T M and N 2equilibrium pressures of the Group III-nitrides.Recently,the thermal stability of InN was investigated at N 2pressures extending up to 18.5kbar [48].It was shown by differential thermal analysis that,over the whole investigated pressure range (0.1–18.5kbar),rapid decomposition of InN occurs above (710±10)◦C.Trainor and Rose [49]observed dissociation of thin InN films at 500◦C and 1bar N 2.Guo and Kato [50]observed a change of the reflective high-energy electron diffraction (RHEED)pattern of InN single crystal films when the temperature was raised above 550◦C.They concluded that the crystals decomposed to In and N 2above that temperature.MacChesney et al observed the equilibrium partial pressure of N 2over InN to be 1bar at 800K,increasing exponentially with 1/T to 105bar at 1100K [51](figure 8).The first study of the thermal stability of GaN was made by Johnson et al [52].More recently Sime and Margrave [53]investigated the evaporation of GaN and Ga metal in the temperature range 900to 1150◦C at 1atm pressure of N 2,NH 3and H 2,while studying the formation and decomposition equilibria.They determined the heat of evaporation and proposed the existence of [GaN]x polymers in the gas phase.Thurmond and Logan [54]chemically measured the partial pressure ratios which2658Growth and applications of GroupIII-nitridesFigure8.Equilibrium N2pressure over the MN(s)+M(l) systems(M=In,Ga or Al),and melting points T M from high-pressure experiments and theoretical calculations [48–60].exist in a(H2+NH3)gas mixture streaming over Ga and GaN.They determined the equilibria both in the case of formation and decomposition of GaN.Lorenz and Binkowski[55]observed the decomposition at given temperatures by measuring the time dependence of the increase in N2pressure.An extensive study on the thermal stability of GaN at high temperatures and pressures up to60kbar has been performed by Karpinsky et al[56], using a gas pressure technique and a tungsten carbide anvil cell.In the high-pressure range,the p(1/T)curve strongly deviates from the linear dependence proposed by Thurmond and Logan(figure8),but there is good agreement in the Gibbs free enthalpy with G0=(32.43T−3.77×104)cal/mol for GaN synthesis.The value of enthalpy H0of−37.7kcal/mol is in good agreement with the value estimated by Madar et al[57].Resistively heated graphitefilaments were used by Class[58]to evaluate the melting behaviour and temperature of AlN.The melting of AlN was observed at 2750–2850◦C,at nitrogen pressures of100and200bar. Slack and McNelly[59]calculated N2pressures over AlN in equilibrium with liquid Al to be1,10and100bar at 2563◦C,2815◦C and3117◦C respectively.The melting temperatures for different nitrides were evaluated by Van Vechten[60]with the use of a semi-empirical theory for electronegativity,concluding that the melting point of AlN is close to3487K.Figure8summarizes the results of the theoretical calculations and experiments described above, including the meltingtemperatures.Figure9.The partial pressure of mass28amu(N+2,CO+, C2H+4)versus effusion or decomposition temperature T E. The decomposition of InN,GaN and AlN is observed above 630◦C,850◦C and1040◦C respectively[61].To quantitatively determine and compare the thermal stability of thinfilms,the desorption and decomposition of polycrystalline InN deposited at550◦C,and epitaxial GaN and AlN grown at950◦C and1050◦C were measured by heating the samples in vacuum and recording the partial pressure of relevant gases using a quadrupole mass spectrometer[61].For a known heating routine,the desorption spectra can be analysed tofind the binding energies of various desorbed species as well as the thermal stability of the sample[62].Figure9shows the partialpressure of mass28amu(N+2,CO+,C2H+4)versus effusion or decomposition temperature T E.The nitrogen partial pressure increases exponentially above T E=630◦C, 850◦C and1040◦C for InN,GaN and AlN respectively, illustrating that the decomposition temperature in vacuum is much lower than the melting point.To determine the effective decomposition activation energy more precisely, the nitrogenflux was calculated from the measured nitrogen pressure.The rate of nitrogen evolution (N)is equal to the rate of decomposition,and the slope of ln[ (N)] versus1/T(figure10)gives the effective activation energy of the decomposition in vacuum E MN.The decomposition rate equals the desorption of one monolayer every second( (N)=1.5×1015cm−2s−1)at795,970 and1050◦C,and the activation energy of the thermally induced decomposition is determined to be E MN=3.5eV (336kJ mol−1), 3.9eV(379kJ mol−1)and 4.3eV (414kJ mol−1)for InN,GaN and AlN respectively(table4). This indicates temperature limits for high-temperature or high-power devices.2659OAmbacherFigure 10.Nitrogen flux or desorption rate for InN,GaN and AlN in the temperature range of decomposition.The rate of N evolution is equal to the rate of decomposition and the slope of ln[ (N)]versus 1/T gives the effective activation energy E MN of the decomposition in vacuum [61].Table 4.Density ρ,melting point T M ,decomposition temperature T E and activation energy E MN of thedecomposition of InN,GaN and AlN (p <10−6mbar).ρaT M a T E b E MN b(g cm −3)(K)(◦C)(kJ mol −1)AlN 3.2934871040414GaN 6.072791850379InN6.812146630336a From [17].bFrom [61].In connection with the thermal stability of hexagonal nitrides,the thermally activated nitrogen self-diffusion should be mentioned.Nitrogen diffusion is a fundamental transport process in Group III-nitrides.In general,self-diffusion processes in wide-bandgap semiconductors or insulators are more complex than in metals [63].This is due to the large variety of native defects,different possible charge states of defects,and to the much larger effects of small concentrations of defects on the Fermi level position [64].Diffusion processes also play an important role in device fabrication and the thermal stability of high-power devices [65].Diffusion of dopants is utilized to engineer p–n junctions and transistor structures [66].In other cases,diffusion can be destructive to delicate structures due to the transport of dopants from thin layers into the adjacent layers or thesubstrate.Figure 11.Arrhenius plot of the measured nitrogen self-diffusion coefficient in hexagonal GaN,obtained at temperatures between 770and 970◦C.The diffusion coefficients were calculated from the concentration depth profiles determined from SIMS signals of 14N (opensquares),15N (open circles),14N 2(full squares)and 15N 2(full circles).The line represents a least-squares fit to the measured data.In III–V compounds,diffusion measurements are difficult to perform because of the high partial vapour pressure of the Group V elements and the dependence of native defect species and concentrations on stoichiometry.Goldstein [67]and Palfrey et al [68]diffused radioactive 72Ga into bulk GaAs to study Ga self-diffusion.The measurement of the depth profile of 72Ga was realized by mechanical sectioning and determination of the radioactivity.Within the temperature range investigated,the authors reported activation enthalpies varying between 2.6and 5.6eV.Wang et al [69]grew and studied an isotopically tagged 69GaAs/71GaAs heterostructure.Upon heating between 800and 1225◦C under an As-rich condition,the Ga diffusion coefficient D was determined by secondary ion mass spectrometry (SIMS)to be D(Ga )=(43±25)cm 2s −1exp[(−4.24±0.06)eV k −1BT −1]over six orders of magnitude in D .In analogy to that experiment,nitrogen self-diffusion was studied by using Ga 14N/Ga 15N/Ga 14N (500/500/500nm)isotopic heterostructures grown on c -plane sapphire by PIMBE [70].Concentration profiles of nitrogen isotopes after annealing were measured using SIMS.The activation enthalpy and entropy of nitrogen self-diffusion were obtained by analysing the diffusion length measured for annealing temperatures between 7702660。

Calibration Techniques for Millimetre-wave On-wafer S-parameterMeasurementsXiaobang Shang*, Jian Ding#, Nick Ridler*, Christopher Buck#, Mike Geen#*National Physical Laboratory, Teddington, TW11 0LW, UK#Filtronic Broadband Limited, Sedgefield, County Durham, TS21 3FD, UK Emails:*********************.uk,***********************,******************.uk,*******************************,***********************I. SummaryAccurate characterisation of S-parameters (scattering parameters) at chip level is of great importance to the development of next generation electronic devices. Such measurements are usually carried out on a Vector Network Analyzer (VNA), subject to an on-wafer calibration. Calibration techniques play a key role in determining the accuracy of on-wafer measurements. This paper is intended to provide an overview of conventional calibration techniques, including TRL (Thru, Reflect, Line), Multi-Line TRL,SOLT (Short, Open, Load, Thru), LRM (Line, Reflect, Match), and LRRM (Line, Reflect, Reflect, Match). Advantages and limitations of these different calibration techniques are discussed briefly and summarised. This paper also gives an insight into important factors that influence on-wafer measurement quality. These factors include design of calibration standards, testing environment (boundary and nearby structures), probes pitch sizes, etc.II. Conventional Calibration Techniques for Planar MeasurementsMost RF and microwave probes are designed to have probe tips suitable for probing on coplanar waveguide (CPW) structures. Fig. 1 shows the typical CPW ground-signal-ground (GSG) probe tip configuration. Calibrations using reference devices in the on-wafer domain are usually performed prior to further on-wafer measurements so as to remove the systematic and drift errors from measurement results. Basic calibration standards include OPEN, SHORT, LOAD, and THRU, as shown in Fig. 2, with each having electrical characteristics that are very different from each other, which is preferable for the calibration. These standards are however not ideal, due to parasitic capacitance or inductance, see Fig. 2. Such parasitic capacitance and inductance associated with standards need to be taken into account when performing an on-wafer calibration to the probe tips.Probe manufacturers usually specify calibration coefficients obtained using a commercial Impedance Standard Substrate (ISS).(a) (b)Fig. 1. (a) Illustration showing signal excitation at coplanar GSG probe tips [1]. (b) Photograph of the GSG probes tips of the D-band (110-170 GHz) probes at NPL. These probes have a pitch size of 100 µm.Fig. 2. Typical calibration standards with parasitic capacitance and inductance. [1]SOLT TRLLRM LRRMMTRLFig. 3. Diagrams of five conventional on-wafer calibration techniques.Fig. 3 illustrates five conventional on-wafer calibration techniques using these basic standards. These are briefly described below [1].•SOLT requires rigorous definitions of calibration standards. SOLT is robust, as long as all calibration standards are perfectly known. Calibration coefficients for standards are defined for a particular probe placement, therefore the resulting SOLT calibration is relatively sensitive to probe placement errors that are inherent in microwave probing.•TRL requires minimal knowledge of electrical behaviour of standards. The reference plane is usually set at the centre of the THRU standard. REFLECT standard can be either SHORT or OPEN, but identical reflects are required on both ports. LINE standard (with electrical phase around 20° ~ 160° at test frequencies) provides information about the characteristic impedance of the CPW transmission line. Each LINE standard can only cover a limited frequency range, hence multiple lines are required for broadband measurements.•Similar to TRL, characteristic impedance of LRM is determined by the MATCH standard (equivalent to an infinitely long reflectionless line). The reference plane is set at the middle of the LINE standard. REFLECT standard can be either SHORT or OPEN, however it should again beidentical on both ports. LRM does not need knowledge about parasitic capacitance of OPEN or parasitic inductance of SHORT. However, the behaviour of the MATCH needs to be well understood.•Reference plane of LRRM is usually set at the middle of LINE. REFLECT does not require known OPEN or SHORT, however it must be equal at both ports. MATCH standard could have known resistance and unknown inductance (assumed constant with frequency). MATCH inductance is calculable using OPEN. LRRM requires one MATCH standard, whereas LRM needs two. LRRM requires the same set of standards as SOLT but requires less information about the standards.This can give better results than SOLT and is less sensitive to small errors in probe placement. •Multi-Line TRL (MTRL), developed by NIST, has become established as a reference calibration technique. MTRL involves multiple lines and uses all lines, to some extent, at all frequencies.Varying weighting is applied to all the LINE data to resolve the problem of band breaks of conventional TRL.It is important to understand strengths and limitations of each calibration technique. Table I gives a comparison between these techniques. Note that the optimum calibration technique depends on the exact measurement requirements. Verification standards can be used to compare different calibration techniques.Table I: Comparison between conventional calibration techniques. [1]There are two common calibration approaches:•Probe tip calibration using ISSs (off-wafer) + de-embedding using additional on-wafer structures (optional)•On-wafer calibration using standards fabricated on the same wafer as the Device Under Test (DUT).III. TRL Calibrations Using Different Reflect StandardsTRL is a popular on-wafer calibration method, with the minimal requirement on prior knowledge of the standards. In addition, the desired reference plane for calibration can be set the same as the DUT. Therefore, TRL is ideally suited to on-wafer measurements for DUTs with the same reference plane and lead structure.A TRL calibration was applied to the measurement of some D-band (110-170 GHz) integrated circuits. The circuits and the TRL calibration standards were fabricated on the same GaAs substrate with a thickness of 50 µm. Two sets of TRL standards were produced, and the layout of one set of these standards is shown in Fig. 4 (a). The first set has launches from the GSG pads to the reference plane of 300 µm length (i.e. L=300 µm), the second set has 100 µm long launches. The launches should besufficiently long so that the microstrip mode can be fully established by the time it gets to the reference plane. EM full wave modelling of the launch can be carried out to calculate the optimum length. On the other hand, the launch length should be no greater than λg/8 [2], otherwise the LINE standard would behave like a λg/2 resonator and bring in resonance to the transmission response. In this work, the 100 µm long launches fulfil this requirement, and the 300 µm long launches are considerably longer than λg/8.For TRL calibration, the REFLECT standard can be either a SHORT or OPEN. In this work, both types of circuits have been implemented and utilised for de-embedding the raw measurement results of the verification device.The measurement was carried out at NPL on a manual probe station. The setup shown in Fig. 4 (b) was used to obtain uncorrected raw data for the TRL calibration standards and the DUT (verification line). This was then postprocessed by implementing the four different TRL calibrations (i.e. L=100 µm or 300 µm, and OPEN or SHORT as REFLECT standard). This approach minimises the uncertainty due to contact repeatability. The corrected results are shown in Fig. 5. It was found that better agreement with the physical structure of the verification line was obtained using the 100 µm launches because the 300 µm calibration set yielded transmission responses close to 0 dB at the high end of the frequency band which does not agree well with theory. The processed results using calibrations with different REFLECT standards are also shown in Fig. 5. There is not any noticeable difference between the results based on SHORT and OPEN.(a)(b)Fig. 4. (a) Diagram of the TRL calibration standards fabricated on the same wafer as the devices.(b) Test setup at NPL, for D-band on-wafer measurements.Fig. 5. Measurement results of the verification line subject to TRL calibrations using 4 different sets of standards (i.e. L=100 µm or 300 µm, and OPEN or SHORT as REFLECT standard).IV. Impact from Neighbouring StructuresFor on-wafer measurements, the probe shadow region should be kept free of structures, to avoid coupling between probes and the nearby structures surrounding the DUT or calibration standards, as shown in Fig. 6. Otherwise, there will be noticeable dips (or resonances) in the measured transmission responses, regardless of the calibration techniques employed. This is also discussed in detail in [3] and [4].The impact from neighbouring structures has also been studied in [5]. Full wave simulations have been carried out for a microstrip line with a short microstrip line nearby. The modelled structures together with the simulation results are shown in Fig. 7. It can be observed that the frequencies of these dips in the transmission responses are related to the lengths of the neighbouring lines. More dips could occur in the transmission responses if there were more than one neighbouring structures. This would degrade the accuracy of measurement and calibration.Fig. 6. Illustration diagram showing the probe shadow, where couplings between the probes and neighbouring structures may exist. This figure is reproduced from [4].mFig. 7. Simulated S21 of a microstrip line together with a nearby short microstrip line with three different lengths Lm. The frequency of dip in S21 response changes when Lm varies from 600 µm to 1400 µm. This figure is reproduced from [5].Fig. 8 (a) shows the layout of TRL calibration standards for on-wafer measurements at E-band (60-90 GHz). A line was measured after TRL calibration, and there is a dip (resonance) in the measured S21 response, as shown in Fig. 8 (b). Similarly, the measured S11 of an OPEN exhibits an unwanted resonance, whereas the S22seems normal, as can be observed from Fig. 8 (c). This is due to the calibration standards being too close to each other, resulting in coupling and parasitic from the neighbouring structures underneath the probes. To address this problem, the metal layer was removed from some areas of the calibration standards, as shown in Fig. 8 (d), so that the probe coupling to neighbouring structures was considerably reduced. A TRL calibration based on these modified standards was performed and the same devices measured. The corrected results are given in Fig. 8 (b) and (c). The unwanted resonances have been eliminated. This demonstrates that the calibration standards need to be properly separated on the wafer and no other standards or test structures should be underneath the probes during the calibration and measurement.The impact from neighbouring structures on on-wafer measurements can also be reduced by utilising special probe-to-pad transition, as shown in Fig. 9 (a). The closed and shielded probe-to-pad design has proved to be very effective, in terms of suppressing the influence from crosstalk, higher-order modes and neighbouring structures. This is demonstrated at D-band (110-170 GHz), using a set of calibration standards and DUTs that are placed close to each other on the same wafer, as shown in Fig. 9 (c). Both the closed and shielded probe-to-pad design and the conventional design [see Fig. 9 (b)] have been implemented and measured. The former offered better performance and greater consistency in results from different organisations, as described in detail in [6].(a)(b)(c)(d) Fig. 8. (a) Layout of the TRL calibration standards for on-wafer measurement at E-band (60-90 GHz). (b) Measured S 21 responses of the Line subject to two calibrations, one using the original calibration standards, and the other using the modified standards with metal selectively removed. (c) Measured S 11 and S 22 responses of the OPEN, subject to two different calibrations. (d) Photographs showing the modified calibration standards after selectively removing metal from some areas. Purple rectangles indicate the standards used during the TRL calibration.Metal removed Metal removedMetal removedS 21, d BRed curve : Original standardsBlue curve : Modified standardsRed curve : Original standardsBlue curve : Modified standardsS 11 S 22Fig. 9. A set of CPW calibration standards and DUTs fabricated on a 50 µm thick wafer. Two different types of probe-to-pad transitions are shown. (a) Closed and shielded pad configuration, capable of offering lower crosstalk, less higher-order mode interference, and less neighbouring effects. (b) Direct probing contact configuration without any special probe-to-pad design. (c) Layout of the calibration standards and DUTs only. Both types of probe-to-pad transitions were implemented and characterised. This figure is reproduced from [6].V. Testing Boundary ConditionsAt millimetre-wave frequencies, the testing environments (e.g. boundary conditions) have a significant impact on measurement quality. Fig. 10 shows the experiment setups for the same device that was placed on two different types of sample holders, one is a Cascade absorber holder (PN 116-344) and the other is glass. Their corresponding return loss performance can be found in Fig. 11, in which the response without sample holder under the substrate is also given for comparison. It is evident that the absorber holder has reduced the ripples in the measured responses effectively. These ripples are introduced by unwanted spurious modes usually excited at frequencies higher than 50 GHz [7]. If the device is placed on a metallic chuck, a small fraction of the signal can propagate as microstrip modes in that the chuck acts as the ground plane. The absorber holder is capable of suppressing these modes and ultimately reducing the ripples. Note that the DUT is effectively a different structure (electromagnetically) with and without the absorber. Therefore, boundary conditions need to be specified during measurement comparisons.The absorber effectively acts like a lossy boundary during measurements, which has an impact on the loss and relative phase constants as well as the characteristic impedance of the CPW lines [8]. This may result in an inaccurate definition of the calibration reference impedance at high frequencies. More discussions on this topic can be found from [8], which reports on a detailed investigation into different boundary conditions and their impacts on calibration accuracy. Note that there is still active research in the testing boundary conditions, particularly at millimetre-wave and terahertz frequencies. Fig.10. Photographs of two different experiment setups with different boundary conditions.On glass On absorber Device Under Test(c)Fig. 11. Measured S 11 of the DUT with different experiment setups shown in Fig. 10.VI. Other Considerations for Planar MeasurementsThere exist many other factors that impact the accuracy of on-wafer measurements, these factors include design of CPW, probes with different pitch sizes, contact repeatability [9], cross-talk between probes [10], etc. This section includes a brief discussion on the first two factors. The investigation was carried out by colleagues across Europe and was described in detail in [3] and [4].Design of CPWMeasurement quality also depends upon the design of CPW, particularly the ground width and the ground-to-ground spacing. Dips may occur in the transmission responses (i.e. S 21 and/or S 12), as shown in Fig. 12, and this is attributed to radiation from the CPW and the ground plane. Full-wave simulations indicate that the total CPW width (W tot ) determines the frequency where the dip occurs, and the ground-to-ground spacing influences the significance of the dip behaviour [4], as shown in Fig. 12 (b) and (c). Minimizing ground-to-ground spacing is helpful in terms of eliminating the dips.Fig. 12 (d) exhibits the relationship between the CPW width and the dip frequency. To avoid the appearance of such dips, the recommended total CPW width can be calculated as follows [11].W tot < 2×cf max ×√2×(εr −1)where c is the velocity of light in free-space, εr is the relative permittivity of substrate, and f max is the upper frequency limit. There is excellent agreement between this equation and the full-wave simulation results, as shown in Fig. 12 (d).On metalchuck: ripplesOn glass: no ripplesOn absorber:no ripplesFrequency (GHz) S 11 (d B )(a)(b) (c) (d)Fig. 12. (a) Illustration diagram of the CPW. The total CPW width, W tot, equals to W g+S+W+S+W g.(b) Simulated transmission response as a function of frequency, for different CPW ground width W g. (c) Simulated transmission response as a function of frequency, for different ground-to-ground spacing S, whilst maintaining a characteristic impedance of 50 Ω and a width W tot of 1000 μm. (d) Relationship between W tot and dip frequency. The orange line was extracted from full-wave simulations whereas the blue line was plotted using the equation. These figures are reproduced from [4].Probes with different pitch sizeProbes of different pitch sizes can result in noticeable difference in on-wafer measurement results. Fig. 13 shows the error-corrected measured transmission responses of an attenuator using GGB probes with two different pitch sizes (100 µm versus 150 µm). The experiment was performed at PTB in a closely controlled environment, with the same measurement setup, calibration structures, chuck material (testing boundary), and the same operator. It can be observed from Fig. 13 that, there exists a systematic deviation for frequencies above 50 GHz, this can be attributed to the difference in probe geometries. It is expected that probes from different vendors could lead to even larger deviations in S-parameter results.Fig. 13. Influence of probe pitch width (blue – 100 µm, red – 150 µm) on transmission measurement of an attenuator. This figure is reproduced from [3].VII. ConclusionsThis paper has briefly reviewed conventional calibration techniques for on-wafer measurements. Some recent research activities in on-wafer measurements, at millimetre-wave frequencies, have been reviewed. Other considerations, e.g. repeatability of calibration, definition of reference plane, test environment, parasitic mode effects, etc, have not been covered in this paper. However, these also play an important role in the on-wafer measurement quality and should be taken into account for precise measurement.AcknowledgementsThis work was supported in part by the EMPIR research projects 18SIB09 TEMMT and 14IND02 PlanarCal, and in part by the Innovate UK Project 103438. The EMPIR initiative is co-funded by the European's Horizon 2020 research and innovation programme and the EMPIR Participating States.References[1] E. Lourandakis, “On-wafer microwave measurements and de-embedding”, Artech House, 2016[2] TRL calibration, online publication: https:///encyclopedias/trl-calibration[3] “Best Practice Guide for Planar S-Parameter Measurements using Vector Network Analysers”,EMPIR 14IND02 PlanarCal, 2018. DOI: https:///10.7795/530.20190424B[4] “Guidelines for the design of calibration substrates, including the suppression of parasitic modesfor frequencies up to and including 325 GHz”, EMPIR 14IND02 PlanarCal, 2018. DOI: https:///10.7795/530.20190424A[5] V. Krozer, R. Doerner, F. J. Schmückle, N. Weimann, W. Heinrich, A. Rumiantsev, M. Lisker, B.Tillack, "On-wafer small-signal and large-signal measurements up to sub-THz frequencies," 2014 IEEE Bipolar/BiCMOS Circuits and Technology Meeting (BCTM), Coronado, CA, 2014, pp. 163-170. DOI: 10.1109/BCTM.2014.6981306[6] R. Lozar, M. Ohlrogge, R. Weber, N. Ridler, X. Shang, T. Probst, and U. Arz, "A ComparativeStudy of On-Wafer and Waveguide Module S-Parameter Measurements at D-Band Frequencies," in IEEE Transactions on Microwave Theory and Techniques, vol. 67, no. 8, pp.3475-3484, Aug. 2019. DOI: 10.1109/TMTT.2019.2919538[7] G. Fisher, “A Guide to Successful On Wafer Millimeter Wave RF Characterisation,” onlinepublication: https:///upload/cmc_upload/All/OnWaferMillimeter.pdf[8] A. Rumiantsev, R. Doerner and E. M. Godshalk, "The influence of calibration substrate boundaryconditions on CPW characteristics and calibration accuracy at mm-wave frequencies," 2008 72nd ARFTG Microwave Measurement Symposium, Portland, OR, 2008, pp. 168-173. DOI:10.1109/ARFTG.2008.4804293[9] R. G. Clarke, C. Li and N. M. Ridler, "An intra-laboratory investigation of on-wafer measurementreproducibility at millimeter-wave frequencies," 2017 90th ARFTG Microwave Measurement Symposium (ARFTG), Boulder, CO, 2017, pp. 1-6. DOI: 10.1109/ARFTG.2017.8255866 [10] C. Liu, A. Wu, C. Li and N. Ridler, "A New SOLT Calibration Method for Leaky On-WaferMeasurements Using a 10-Term Error Model," in IEEE Transactions on Microwave Theory and Techniques, vol. 66, no. 8, pp. 3894-3900, Aug. 2018. DOI: 10.1109/TMTT.2018.2832052 [11] F. Schnieder, T. Tischler and W. Heinrich, "Modeling dispersion and radiation characteristics ofconductor-backed CPW with finite ground width," in IEEE Transactions on Microwave Theory and Techniques, vol. 51, no. 1, pp. 137-143, Jan. 2003. DOI: 10.1109/TMTT.2002.80692611。

Shading and Lighting• Shade objects so their images appear three-dimensional • Light-material interactions • Phong modelWhy we need shading• Suppose we build a model of a sphere using many polygons and color it with glColor. We get something like• But we wantShading• Why does the image of a real sphere look likeScattering• Light strikes A– Some scattered – Some absorbed• Some of scattered light strikes B• Light-material interactions cause each point to have a different color or shade • Need to consider– – – – Light sources Material properties Location of viewer Surface orientation– Some scattered – Some absorbed• Some of this scattered light strikes A and so on1Rendering Equation• The infinite scattering and absorption of light can be described by the rendering equation– Cannot be solved in general – Ray tracing is a special case for perfectly reflecting surfacesGlobal Effectsshadow• Rendering equation is global and includes– Shadows – Multiple scattering from object to objectmultiple reflection translucent surfaceRay Tracing SceneLocal vs Global Rendering• Correct shading requires a global calculation involving all objects and light sources– Incompatible with pipeline model which shades each polygon independently (local rendering)• However, in computer graphics, especially real time graphics, we are happy if things “look right”– Exist many techniques for approximating global effects2Light-Material Interaction• Light that strikes an object is partially absorbed and partially scattered (reflected) or refracted • The amount reflected determines the color and brightness of the object– A surface appears red under white light because the red component of the light is reflected and the rest is absorbedLight SourcesGeneral light sources are difficult to work with because we must integrate light coming from all points on the source• The reflected light is scattered in a manner that depends on the smoothness and orientation of the surfaceSimple Light Sources• Point source– Model with position and color – Distant source = infinite distance away (parallel)Surface Types• The smoother a surface, the more reflected light is concentrated in the direction a perfect mirror would reflected the light • A very rough surface scatters light in all directions• Spotlight– Restrict light from ideal point source• Ambient light– Same amount of light everywhere in scene – Can model contribution of many sources and reflecting surfacessmooth surfacerough surface3Phong Model• A simple model that can be computed rapidly • Has three components – Diffuse – Specular – Ambient • Uses four vectors – To source – To viewer – Normal – Perfect reflectorIdeal Reflector• Normal is determined by local orientation • Angle of incidence = angle of reflection • The three vectors must be coplanarr = 2 (l · n ) n - lLambertian Surface• Perfectly diffuse reflector • Light scattered equally in all directions • Amount of light reflected is proportional to the vertical component of incoming light– reflected light ~cos θi – cos θi = l · n if vectors normalized – There are also three coefficients, kr, kb, kg that show how much of each color component is reflectedSpecular Surfaces• Most surfaces are neither ideal diffusers nor perfectly specular (ideal reflectors) • Smooth surfaces show specular highlights due to incoming light being reflected in directions concentrated close to the direction of a perfect reflectionspecular highlight4Modeling Specular Reflections• Phong proposed using a term that dropped off as the angle between the viewer and the ideal reflection increasedIr ~ ks I cosαφ φ shininess coef reflected incoming intensity intensity absorption coefThe Shininess Coefficient• Values of α between 100 and 200 correspond to metals • Values between 5 and 10 give surface that look like plasticcosα φ-90φ90• Ambient light is the result of multiple interactions between (large) light sources and the objects in the environment • Amount and color depend on both the color of the light(s) and the material properties of the object • Add ka Ia to diffuse and specular termsreflection coef intensity of ambient lightAmbient LightLight Sources• In the Phong Model, we add the results from each light source • Each light source has separate diffuse, specular, and ambient terms to allow for maximum flexibility even though this form does not have a physical justification • Separate red, green and blue components5Material Properties• Hence, 9 coefficients for each point source– Idr, Idg, Idb, Isr, Isg, Isb, Iar, Iag, IabAdding up the ComponentsFor each light source and each color component, the Phong model can be written as I =kd Id l · n + ks Is (v · r )α + ka Ia For each color component we add contributions from all sources• Material properties match light source properties– Nine absorbtion coefficients • kdr, kdg, kdb, ksr, ksg, ksb, kar, kag, kab – Shininess coefficient αModified Phong Model• The specular term in the Phong model is problematic because it requires the calculation of a new reflection vector and view vector for each vertex • Blinn suggested an approximation using the halfway vector that is more efficientThe Halfway Vector• h is normalized vector halfway between l and vh = ( l + v )/ | l + v |6Using the halfway angle• Replace (v · r )α by (n · h )βExample• β is chosen to match shineness• Note that halfway angle is half of angle between r and v if vectors are coplanar • Resulting model is known as the modified Phong or Blinn lighting model– Specified in OpenGL standardOnly differences in these teapots are the parameters in the modified Phong modelComputation of Vectors• • • • l and v are specified by the application Can compute r from l and n Problem is determining n For simple surfaces n is can be determined but how we determine n differs depending on underlying representation of surface • OpenGL leaves determination of normal to application– Exception for GLU quadrics and Bezier surfacesRay Tracing Algorithm• References– Glassner, Andrew (Ed.) (1989). An Introduction to Ray Tracing. Academic Press – Shirley, Peter and Morley Keith, R. (2001) Realistic Ray Tracing,2nd edition. A.K. Peters – Free ray tracing program POV-Ray at – Siggraph 2005 course notes • Introduction to Real-Time Ray Tracing– Many graphics books…7。

剑桥雅思听力原文－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－T e x t 1 Section 1Man: Hello,this is Land Transport information at toronto Airport.Woman: Oh,good morning,I’m flying to toronto Airportnext week, and I need to get to a town called um,Milton.Cpould you tell me how I canget there?Man: Milton,did you say? Let me see. I think that’s about 150 miles south-west of here .In fact it’s 147 miles to be exact, so it’ll take you at least –say ,three to four hours by road.the Greyhound.Woman:Oh, that doesn’t sound too bad.especially if it*ll take me straight to the hotel.Man:But you do need to reserve a seat.Woman:OK. Is it possible to make a booking right now? Through you?Man:Sure.Man: OK.I just have to fill this form out for you. So what date do you want to book this for? Woman:The 16th of Octobler –oh,no,sorry.that’s my departure date. I arrive on the 17th, so book it for then,please.Man: So, That’s the Toronto Airport Shuttle to Milton.And this is for just one person or…? Woman: yes, just me, please.Man:Right. And you said your excepted time of arrival was 11:30? So if I book your Shuttle for after 12:00-let’s say, 12:30 that should give you plenty of time to, you know, collect your baggage maybe grab a coffee?Woman:Yeah, that sounds fine, as long as we land on time!Man: Well,we’ll take you flight details so you don’t need to warry too much about that. Now. what about the fare? What sort of ticket do you want? One way or…？Woman:Yes,that’ll be fine, provided I can book the return trip once I’m there.Man:No problem – just allow a couple of days in advanced to make sure you get a seat. And what’s you name, please?Woman:Janet, Janet Thomson.Man:Is that Thompson spelt with a “p”?.in the We’ve upgraded all these Spanish sites, and improved them considerably from their original three-star ratingWe believe our holidays offer superb facilities for the whole family. Parents who want their children to be fully occupied for all or part of the day can take advantage of our children’s activities. These are organised by our well-qualified and enthusiastic staff. Each day kicks off a sports match, perhaps football, or volleyball, followed by an hour of drama for everyone. This may include singing or dancing, mime or other activities. In the afternoon, there’s a different art activity for each day of the week including a poster competition or model making. What’s m ore, our sites are truly child-friendly, and, with this in mind, we operate a no-noise rule in theevenings. Children’s evening activities usually finish at 9:30, or occasionally 10, and from 10:30 holiday-makers are expected to be quiet in the areas where there are tents.We want nothing to go wrong on a PS Camping holiday, but if it does, we also want all customers to be insured. If you haven’t organised an annual insurance policy of your own you’ll need to take out the low-cost cover we offer and we require that you arrange this when you take your holiday reservation.There are many advantages to choosing PS Camping, and to recommending it to others. As a regular customer. You’ll be kept informed of special offers. And your friends can benefit from ten per cent off their holiday, or book a luxury tent for the price of a standard one. In return, we’ll send you a thank-you present, which you can choose from a list of high-quality items.When it comes to our tents, these are equipped to the highest standard. We really do think ofin Philip:Yes, I did. On the positive side, exposure to such diversity helps encourage creativity which is generally an asset to a company. But unfortunately individual difference are also the rootof conflict between staff and they can lead to difficulties for management, which can sometimes be serious.**********************************************Tutor:Thanks,philip. So now I guess the two main things to remember here are to identify individual talent and then to utilize it. So Janice, you were looking at identifying different talents in workers Do you think this is easy for managers to do?Janice:Well,currently teamwork is in fashion in the workplace and in my opinion the importance of the individual is generally neglected. What managers should be targeting is those employees who can take the lead in a situation and are not afraid to accept the idea of responsibility.Tutor:That’s true. Janice but unfortunately many managers think the entire notion of encouraging individuality amongst their staff is far too hard.Janice:Yes. That may be true but I think one of the most important tasks of managers is to consider the needs of the individual on one hand and group co-operation and conformity on the other. It requires creative thinking on the part of management to avoid tension.Tutor:So Janice, what kind of people do you think companies should be looking for?Janice Well, it has to start from the very beginning when companies are looking for new employees. When the personal department is choosing between applicants they need to look for someone who’s broken the mould and can think for themselves. Instead, people making these decisions often ues a range of psychological tests to see if a person is a problem solver, or will do as they’re told. I’m not convinced these qualities are actually the most important.This is the first seninar in preparation for our archaeological fieldwork in Namibia, we are fantastically luck to have received partial research funding for this trip from our Institute, so I shall expect 200% attention and participation from you all. First in this seminar, I’m going to give a brief introduction to contemporary research on rock art, and in the seco nd part I’m going to give you some do’s and don’ts for our fieldwork trip in April – so please listen very carefully.I’m first going to focus on the interpretation of rock art in Namibia, we are very fortunate to be going to an area where you can find some of the most important sites in the entire world. And I hope to show you how easy it is foe everyone to make mistakes in looking at cultures which are different from our pwn – the first and most important lesson we have to learn.In Namibia there are both paintings and engraving –that’s where the surface of the rock is cut out. Many of the engravings show footprints of animals and most scholars used to think that the purpose of these was simple and obvious. This r ock art was like a school book with picture to teach children about tracks whick belonged to which animal – giraffe, lion and so on.But there were some mysteries. First, when you look at a typical Namibian painting or engraving, you see the tracks are repeated, there are dozens of tracks for t he same animal. You’d expect just one clear illustration if the reason – the aim – was to teach tracking.Now there were two more problem, why are some of the engraving of animals very accurate as you’d expect – all clearly identifiable- and others quite unrealisticAnd another mystery – some of these unrealistic animals – that*s in the engravings – seem to be half human. Some, for example, have got human faces, Many reaearchers now think that theseAnd lastly please don’t even move rocks or branches to take photographs – you should leave the site intace –I’m sure I can rely on you to do that..Well,That’s about all I want to say before today’s first discussion, but if you have any question please ask them now –and don’t forget you’ll find some fascinating information aboutworld-wide sites on the Internet. Right, first question then?Text 2Section 1Woman: Hello… motor insurance department …Man: Oh hello… I’d like to ask about insurance for my car.Woman: Yes, of course. I’ll just take a few details. What’s your name?Man: Patrick Jones.Woman: And your addrss?Man: It’s 27 Bank Road.Woman: 27 Bank Road. Is that in Greendale?Man: Yes.Woman: And what’s your daytime phone number?Man: My work number is 730453.Woman: And could ask what your occupation is?Man: Dentist.Woman: OK… now a few details about your car… What size is the engine?Man: It’s a Hewton Sable.Woman: Social use (murmuring). Will you be using it to travel to work？Man: Yes… sometimes.Woman: …Anything else?Man: No. that’s it…Woman: And finally… when would you like to start the insurance？Man: I’ll need it from the 31st of January.Woman: Right… Mr Jones… I’m getting a couple of quotes coming up on the computer now… and the best bet looks like being with a company called Red Flag. Man: Yeah.Woman: And that comes out at ＄540 per year…Man: Well … that seems OK… it’s quite a bit lower than I’ve been paying up to now…Woman: Great… so would you like me to go ahead with that?Man: Sure… why not?Woman: How would you like to pay?Section 2Thank you for calling the Tourist Line. There are many different ways of getting round the city and we’d like to suggest some you may not have thought of.How about a city trip by boat? Thare are four main stopping points – from west to east: atop A Green Banks, stop B City Bridge, stop C Roman Landing and atop D Newtown.You can find the main booking office at stop A.The first boat leaves at 8 a.m. and the last one at 6:30 p.m. There are also many attractions youInterviewer: Now my first question is about the choice of location for the centre. Why Christchurch? Was it because of the climate?Doctor: Well, actually New Zealand is the second closest country to Antarctica and Christchurch isoften used on Antarctic expeditions.Interviewer: Right. So it’s because of where we are… coupled with our historical role. So tell us – what is the main purpose of the centre?Doctor: Well…we have two complementary roles. One is as a scientific base for expeditions and research and the other is as an information centre.Interviewer: Tell ue something about the role as a scientific base.Doctor: We’re able to provide information about what scientists should take with them to the South Pole – for example, the centre contains a clothing warehouse where expeditions are supplied with suitable clothing for the extreme conditions.Interviewer: I suppose you need a bit more than your normal winter coat!Doctor: yes, exactly and then there’s also the specialist library and mapping services. Interviewer: Right. And which countries are actually located at the centre?Doctor: Well…the centre houses research programmes for New Zealand, for The United States as well as for Italy…there*re even a US post office at the American airforce base here. Interviewer: Really?And what does the v isitor’s centre offer?Doctor: Well, since very few people will ever experience the Antarctic first hand, the visitors* centre aims to recreate the atmosphere of Antarctica. There’s a mock camp site where you canDoctor: Well, as far back as the 19th century, when eleven nations organised an international event.Interviewer: When was that exactly?Doctor: In 1870. And it was called the Polar Research Metting. And then, Not long after that, they organised something called the First International Polar Year.Interviewer: And that took place when exactly?Doctor: Over two years from 1882 to 1883. But it wasn’t until the 1950s that the idea of an international treaty was proposed. And in 1959 the Treaty was actually signed. Interviewer: What do you see as the main achievements of the treaty?Doctor: Well, firstly it means that the continent is reserved for peaceful use.Interviewer: That’s Article a, isn’t it?Doctor: Yes…Interviewer: That’s impor tant since the territory belongs to everyone.DOCTOR: yes but not as important as Article 5, which prohibits any nuclear explosions or waste disposal.Interviewer: Which is marvellous. Well, I’m afraid we’re going to have to stop there because I’m afraid w e’ve run out of time. Thanks for coming along today and telling us all about the centre and its work.Section 4My topic is handedness – whether in different sports it is better to be left – or right-sided or whether a more balanced approach is more succes sful .I’m left-handed myself and I actually–STUDENT：Oh，good morning ,Is this…er… room number 26?AGENT：Yes，that's rightSTUDENT：So ls this the Student Job Centre?AGENT：It certainly is．How can I help you?STUDENT：Well，actually I’m looking for a job -a part-time Job, Do you haveanything available at the moment?AGENT：Ah．Yes… Are you a registered student?I`m afraid this service isonly available to full-time studentsSTUDENT：Yes… I am I'm doing a degree in Business Studies．Here's mystudent cardAGENT：Which year are you in?STUDENT：Well… I've been at uni for four years but I'm in the Third Yearbecause I took last year off.AGENT：Right… well，let's just have a look at what positions are available at The moment There's a Job working at the reception desk at the SportsCentre，for three evenings a week that's Wednesdays ,Thursdays andFridays.STUDENT：That sounds 1ike fun but unfortunately I have evening lectures- sothat's not possible ,I’m afraid Is th ere anything during the day? AGENT：OK．That's no good then .Um .What about cleaning ? There's aposition for a cleaner at the Child Care Centre.thing.STUDENT：Well．I speak some JapaneseAGENT：Right I’ll make a note of that Now- let's see what else is availableWhat do you think of administrative work? There is a position for anOffice Assistant at the English Language CentreSTUDENT：That sounds interesting.AGENT：It's for 3 days a week—Monday , Friday and Saturday mornings．Interested?STUDENT：Mmm, I was hoping to have Saturdays free . But I need the work so… can you tell me what the job Involves?AGENT：Yes, sure. It says here that you'll be required to deal with studentenquiries and answer the phone.STUDENT：I’m su re I can handle all that without a problemAGENT：Great Well，would you like me to arrange an interview for you ? Say,Friday morning，around ten?STUDENT：Could we make it a bit later ? Unfortunately , I've got something to doat ten、Would that be OK?AGENT：Not a problem , How about eleven thirty ? Hope it works out for youAnitaSTUDENT：Me too . And thanks for all your help.However , you will need to be extremely fityou’re interested in coming with us . You have plenty of time to get into shape．You will be sleeping in tents so you must have quite a bit of equipment with you but you will be helpedby local assistants .Your bedding and so forth will be carded by them . We ask that you only walk with a small rucksack with needs for the day .I don’t think I've really said enough about the mar vell ous area you’ll be walking in . Let's havea look at some of the sights you’11 be seeing Apart from these spectacular snow-covered peaks and valleys, there are marvellous historic villages．The area has been famous for centuries for making beautiful carpets , although recently there has been a trend to moveinto weaving blankets and wood carving The people are extremely friendly and welcoming . We deliberately keep the parties small in size to minimize disruption to people and landscape .I hope that there are still some people interested . I will be distributing leaflets at the end where you call find out more information，but just for the moment I’ll outline the itinerary, the main highpoints of the holiday．Obviously , you’ll start by flying out to Kishba ，the capital city , on Day One．After a couple of days to acclimatize yourself , you’ll start the trek on Day Three walking through the enormous Katiba Forest which will take the whole of the day．Day Four takes us higher up，going through the foothills past a number of villages and visiting a school for the disabled in Sohan . Then you have a rest day ,that's Day Five ,before going to the spectacular Kumi Temple with twelfth-century carvings ,set in a small forest bya lake and that's Day Six，the highlight for many．We stay near there for Day Seven because then comes the hardest day ,walking through very mountainous country ,but culminating in a swim in the Parteh Falls , This is the highest waterfall in the region . Day Nine is much easier,whole kilometres down in the water．It stays at this depth for about 10days and is carried around by the currents which operate in the oceanat this level . During this time it's possible for it to cover quite largedistances but the average is fifty kilometresSTUDENT 2：So what is it actually recording ?SIMON：Well at this stage nothing．but as it rises to the surface it collects allsorts of data，most importantly variations in salinity ,that's salt levelsand the changes In temperature，a bit like underwater weather balloons”then when it gets back to the surface all the data it's collected isbeamed up to the satellite . After about five hours on the surface thefloat automatically sinks , beginning the whole process again STUDENT 1：What happens to the data?SIMON：Well the information Is transferred direct to onshore meteorological stations．．．like our one in Hobart．．．and within four hours thefindings can be on computers and they can be mapped and analysed．STUDENT 2：You say you're building models of the world's ocean systems buthow're they going to be used，and more importantly , when? SIMON：Some of the data has already helped in completing projects . Forexample，our understanding of the underlying causes of El Niňoevents is being confirmed by float data Another way we’re using floatdata is to help us to understand the mechanics of climate change，likeSECTION 4Good morning everyone . Today's lecture forms part of the Hospitality and Tourism module Last week 1 looked at the economy end of the hotel business；this week I'm going to discuss The luxury end of the market . Let's consider the following scenario. . .You wake up in the middle of the night in a strange hotel miles away from home , disoriented most probably from jet lag，when even the most expensive surroundings can seem empty and dispiriting . You have paid a great deal of money to stay in this first—class hotel with its contemporary technology ,but according to recent research carried out by an international travel and public relations company , all is not well . The research suggests that even the mostopulent，luxurious hotels seem to have underestimated the most basic needs of their customers-be they travelling for work or pleasure：the need to feel at home in surroundings which are both familiar and inviting .Do these findings , however apply only to hotels situated in particular areas ? Is it possible that the external environment can affect a guest's well-being ? The company's research covered a whole range of different hotel types , both independent hotels and those which are part of large chains . They investigated chic so-called boutique hotels in the heart of downtown business districts，stately mansions located in the depths of beautiful countryside ,and plush hotels built at the edge of tropical beaches surrounded by palm trees and idyllic blue ocean And the research concluded that what was outside the hotel building simply didn't matter．This is a fascinating revelation and those of you hoping to move into careers in the travel andPopular. . .Test 4SECTION 4OFFICER：Yes ,what can I do for you?SUTDENT：My friend Is in homestay … and she really enjoys it… so I'd like tojoin a family as wellOFFICER：Okay ,so let me get some details What's your name?SUTDENT：My name is Keiko YuichiniOFFICER：Could you spell your family name for me? SUTDENT：It's … Yuichini that's Y_U—l—C—H—I—N．I_ OFFICER：And your first name?SUTDENT：It's Keiko．K．E-I—K—O感谢阅读，欢迎大家下载使用！。

这就是浩瀚的宇宙英语作文这就是浩瀚的宇宙。

The Universe: A Vast Realm of Wonders。

Introduction:The universe, with its boundless expanse and unfathomable mysteries, has captivated the human imagination for millennia. From ancient civilizations gazing at the stars to modern astronomers probing the depths of space, our fascination with the cosmos knows no bounds. In this essay, we will embark on a journey through the vastness of the universe, exploring its wonders and contemplating our place within it.The Cosmos: A Celestial Tapestry。

The universe is like a magnificent tapestry, woven from the fabric of space and time. It is home to billions ofgalaxies, each containing billions of stars, as well as countless planets, moons, asteroids, and other celestial bodies. From the fiery furnaces of newborn stars to the icy depths of distant exoplanets, the cosmos is a realm of staggering diversity and beauty.The Scale of the Universe。

GIWAXS: A powerful tool for perovskite photovoltaicsChenyue Wang 1, Chuantian Zuo 2, Qi Chen 1, †, and Liming Ding 2, †1MIIT Key Laboratory for Low-dimensional Quantum Structure and Devices, Experimental Center of Advanced Materials, School of MaterialsScience and Engineering, Beijing Institute of Technology, Beijing 100081, China2Center for Excellence in Nanoscience (CAS), Key Laboratory of Nanosystem and Hierarchical Fabrication (CAS), National Center forNanoscience and Technology, Beijing 100190, ChinaCitation: C Y Wang, C T Zuo, Q Chen, and L M Ding, GIWAXS: A powerful tool for perovskite photovoltaics[J]. J. Semicond., 2021,42(6), 060201. /10.1088/1674-4926/42/6/060201The power conversion efficiency (PCE) for perovskite sol-ar cells (PSCs) now reaches 25.2%[1]. However, the perovskite materials have complex compositions and variable phases,calling for suitable characterization techniques to investigate the underlying operation and degradation mechanism. Graz-ing-incidence wide-angle X-ray scattering (GIWAXS) plays an important role in studying perovskite materials. GIWAXS data are generally two-dimensional diffractograms containing dif-fraction rings of different crystal planes. Grazing-incidence small-angle X-ray scattering (GISAXS) is similar to GIWAXS,while it has a longer detection distance than that of GIWAXS (Fig. 1(a))[2]. GISAXS enlarges the observable spatial range up to 10–100 nm and reduces the measurement sensitivity of crys-tallization, and it is mainly used to determine the morpho-logy of bulk-heterojunction films in nanoscale [3, 4]. Compared to GISAXS, GIWAXS is more popular in perovskite study. This technique has several advantages as follows: (1) high signal-to-noise ratio (SNR) and sensitive structural resolution; (2) no-contact and nondestructive probing; (3) abundant structural in-formation; (4) depth resolution; (5) in-situ observation. Here,we discuss two applications of GIWAXS, i.e., the crystallograph-ic information at steady state, and the in-situ measurement to probe the temporal information. As an important structur-al parameter of perovskite films, crystallographic orientation affects the optoelectronic properties and materials stability.The 2D GIWAXS diffractogram presents the Debye-Scherrer ring for certain crystallographic plane, enabling characteriza-tion of structural orientation of perovskite films. The orienta-tion degree for crystal planes can be obtained quantitatively according to the diffraction rings along the azimuth by using Herman’s orientation function.Quasi-2D perovskites receive attention due to their vari-able structures, tunable composition, and relatively high stabil-ity. The insulating organic long-chain cations in quasi-2D per-ovskites can block carrier transport. Suitable crystal orienta-tion can enhance the carrier transport in 2D perovskites, thus improving device performance. GIWAXS measurements give in-formation about crystal orientation, it can also tell the stack-ing manner of grains at different depths, which is essential for understanding the crystallization mechanism. For ex-ample, by using GIWAXS, Choi et al. found that the nucle-ation and crystallization of BA 2MA 3Pb 4I 13 perovskite occurs at the gas-liquid interface during annealing, which results in the vertical alignment of 2D perovskite crystals (Fig. 1(b))[5]. They further regulated the solvent and cation to prepare highly ver-tically orientated 2D perovskite films [6]. Rafael et al. found that the intermediate solvent complexes provide building blocks in the formation of 2D perovskites according to GI-WAXS measurements [7].High-quality 3D perovskites tend to make strong orienta-tion at certain azimuth angle. GIWAXS results can be used to evaluate the crystallization quality of 3D perovskite thin films.The results can also be used to guide the process optimiza-tion, as well as to clarify the relationship between crystallo-graphic orientation and device performance. Zheng et al. regu-lated the preferential orientation of perovskite crystals and im-proved the interfacial carriers transport in the corresponding devices by substituting A-site alkali metal cations [8].Recently, residual strain was observed in perovskite films due to the mismatch of the expansion coefficients for the sub-strate and perovskites, which influences the operational stabil-ity and efficiency of perovskite solar cells. Microscopically, the residual stress within the film results from a biaxial stretch-ing of the perovskite lattice in in-plane direction. The shift of corresponding diffraction peaks at different azimuthal angles reveals the lattice tilting and stretching. By depth-resolved GI-WAXS, Zhu et al. observed a gradient strain in FA-MA per-ovskite films (Fig. 1(c)). The performance of PSCs was im-proved by reducing lattice mismatch of the crystals [9]. Wang et al. replaced A-site cations on the perovskite surface by us-ing OAI post-treatment, forming a “bone-joint” configuration,reducing surface residual stresses and thus improving humid-ity and thermal stability of PSCs [10].In-situ measurement is attractive in perovskite research.It provides a rapid approach to track microstructural changes in perovskite materials, including the crystallization and aging processes. It is the key to unravel the kinetics process of perovskite materials. The formation process of perovskite crystals is not fully understood yet. The film formation pro-cess includes liquid-film gelation stage and crystallization stage. Many studies have shown that the orientation and phase structure of perovskite are already established during gelation stage. The quality of the perovskite precursor film (gel) significantly affects the final perovskite film. In-situ GI-WAXS provides information for the composition evolution during spin-coating process. It also provides guidelines for pre-paration conditions, such as spin speed and time, dripping time of anti-solvent, etc. Amassian et al. have conducted a series of in-situ GIWAXS studies on perovskite. They ob-Correspondence to: Q Chen, ***********.cn ; L M Ding, ***************Received 22 MARCH 2021.RESEARCH HIGHLIGHTS Journal of Semiconductors(2021) 42, 060201doi: 10.1088/1674-4926/42/6/060201phase to sol–gel state, and investigated the effect of precurs-or spin-coating time on PSCs performance [11]. They revealed that Cs + and Rb + cations were able to stabilize the sol–gel state and suppress the phase separation during spin-coating (Fig. 1(d))[12, 13].GIWAXS can also be used to study the crystallization pro-cess during thermal annealing. Using the peak area integ-rated by the Debye-Scherrer ring of GIWAXS, all the phase con-tents of perovskites and their evolution during annealing can be deduced, which illustrates the phase transition from inter-mediate phase to perovskite phase. The activation energies for perovskite formation can be determined by using Arrheni-us equation.Perovskite degradation caused by humidity and heat lim-its the commercialization of PSCs. In conjunction with the mois-ture and temperature controller, the aging process of devices under different conditions can be monitored by GIWAXS.Through depth-resolved characterization, the physical and chemical reactions at different positions can be deduced by combining with other characterizations, which will reveal the degradation mechanisms. Kelly et al. performed systematic in-situ GIWAXS studies on perovskite degradation. They ob-served that MAPbI 3 films decomposed to a hydrated intermedi-ate phase with PbI 64– octahedra in a humid environment [14].To further investigate the performance and structure changes of PSCs under humidity, they developed a humidity control-ler in conjunction with I–V measurement system (Fig. 1(e)).The results revealed that the decrease of performance res-ults from the electrode corrosion, rather than perovskite de-composition (Fig. 1(f))[15].In summary, GIWAXS has been widely used to reveal the relationship between perovskite crystal structure and device performance. In-situ GIWAXS can be used to track the crystalliz-ation process and decomposition process of perovskites. This method can help us to develop stable and efficient per-ovskite solar cells.AcknowledgementsThis work was supported by National Natural Science Foundation of China (21975028, 22011540377), Beijing Muni-cipal Science and Technology Project (Z181100005118002),and Beijing Municipal Natural Science Foundation (JQ19008).L. Ding thanks the National Key Research and Development Program of China (2017YFA0206600) and the National Natur-(d)(f)1.61.20.80.400.5Max.Min.12111098T i m e (s )T i m e (s )q (nm −1)765412111098q (nm −1)7656H3C2H4300200100Solvate Disordered colloidsSolvate Disordered colloids30020010012111098q (nm −1)7654121110+ 5% Cs98q (nm −1)76541.0Q xy (Å−1)1.52.0GIWAXS GISAXSz xy k iq xzq xy≈0.1 m ≈ 2.0−5.0 mq zqαion mp-TiO 2 substrate interface—preferential orientationTensile-strain lm50 nm 200 nm 500 nm31.69531.68031.66531.6501.00.80.6N o r m a l i z e d p a r a m e t e r s0.40.2000.5 1.0 1.5 2.0 2.5 3.0Time (h)3.54.0 4.55.0 5.56.0(110)I sc V oc FF PCECarrier gasWater bubblersMass ow controllersSynchrotron X-ray beamSamplechamberKaptonwindowSource-measure unitCCD area detector0.250.50sin 2φ0.752θ (°)k fk fαfαfI−V dataψχψFig. 1. (Color online) (a) Schematic diagram of GIWAXS and GISAXS. Reproduced with permission [2], Copyright 2017, John Wiley & Sons Inc.(b) Schematic diagram of the formation of vertically orientated 2D perovskite. Reproduced with permission [5], Copyright 2018, Nature Publish-ing Group. (c) Gradient strain at different depths in perovskite layer. Reproduced with permission [9], Copyright 2019, Nature Publishing Group.(d) Time-resolved GIWAXS for precursor films with and without K + during spin-coating. Reproduced with permission [13], Copyright 2019, Elsevier Inc. (e) Humidity control set-up. (f) Time-dependence for MAPbI 3 (110) peak area and device performance parameters. (e) and (f), reproduced with permission [15], Copyright 2018, American Chemical Society.2Journal of Semiconductors doi: 10.1088/1674-4926/42/6/060201al Science Foundation of China (51773045, 21772030, 51922032, 21961160720) for financial support. ReferencesYoo J J, Seo G, Chua M R, et al. Efficient perovskite solar cells via im-proved carrier management. Nature, 2021, 590, 587[1]Schlipf J, Müller-Buschbaum P. Structure of organometal halide perovskite films as determined with grazing-incidence X-ray scat-tering methods. Adv Energy Mater, 2017, 7, 1700131[2]Rivnay J, Mannsfeld S C B, Miller C E, et al. Quantitative determina-tion of organic semiconductor microstructure from the molecu-lar to device scale. Chem Rev, 2012, 112, 5488[3]Richter L J, DeLongchamp D M, Amassian A. Morphology develop-ment in solution-processed functional organic blend films: An in situ viewpoint. Chem Rev, 2017, 117, 6332[4]Chen A Z, Shiu M, Ma J H, et al. Origin of vertical orientation in two-dimensional metal halide perovskites and its effect on photo-voltaic performance. Nat Commun, 2018, 9, 1336[5]Chen A Z, Shiu M, Deng X, et al. Understanding the formation of vertical orientation in two-dimensional metal halide perovskite thin films. Chem Mater, 2019, 31, 1336[6]Quintero-Bermudez R, Gold-Parker A, Proppe A H, et al. Composi-tional and orientational control in metal halide perovskites of re-duced dimensionality. Nat Mater, 2018, 17, 900[7]Zheng G, Zhu C, Ma J, et al. Manipulation of facet orientation in hy-brid perovskite polycrystalline films by cation cascade. Nat Com-mun, 2018, 9, 2793[8]Zhu C, Niu X, Fu Y, et al. Strain engineering in perovskite solar cells and its impacts on carrier dynamics. Nat Commun, 2019, 10, 815[9]Wang H, Zhu C, Liu L, et al. Interfacial residual stress relaxation in perovskite solar cells with improved stability. Adv Mater, 2019, 31, 1904408[10]Munir R, Sheikh A D, Abdelsamie M, et al. Hybrid perovskite thin-film photovoltaics: In situ diagnostics and importance of the pre-cursor solvate phases. Adv Mater, 2017, 29, 1604113[11]Wang K, Tang M C, Dang H X, et al. Kinetic stabilization of the sol–gel state in perovskites enables facile processing of high-effi-ciency solar cells. Adv Mater, 2019, 31, 1808357[12]Dang H X, Wang K, Ghasemi M, et al. Multi-cation synergy sup-presses phase segregation in mixed-halide perovskites. Joule, 2019, 3, 1746[13]Yang J, Siempelkamp B D, Liu D, et al. Investigation of CH3NH3PbI3 degradation rates and mechanisms in controlled hu-midity environments using in situ techniques. ACS Nano, 2015, 9, 1955[14]Fransishyn K M, Kundu S, Kelly T L. Elucidating the failure mechan-isms of perovskite solar cells in humid environments using in situ grazing-incidence wide-angle X-ray scattering. ACS Energy Lett, 2018, 3, 2127[15]Chenyue Wang got his BS from University ofScience and Technology Beijing in 2018. Nowhe is a MS student at Beijing Institute of Tech-nology under the supervision of Professor QiChen. His research focuses on perovskite sol-ar cells.Chuantian Zuo received his PhD in 2018 fromNational Center for Nanoscience and Techno-logy (CAS) under the supervision of ProfessorLiming Ding. Then he did postdoctoral re-search at CSIRO, Australia. Currently, he is an as-sistant professor in Liming Ding Group. His re-search focuses on innovative materials anddevices.Qi Chen holds BS and MS degrees of TsinghuaUniversity, and received his PhD degree fromUniversity of California, Los Angeles (UCLA). In2013–2016, he worked as a postdoc at Califor-nia Nanosystem Institute (CNSI), UCLA. Nowhe is a full professor at Beijing Institute of Tech-nology. His research focuses on hybrid materi-als design, processing and applications in opto-electronics.Liming Ding got his PhD from University of Sci-ence and Technology of China (was a joint stu-dent at Changchun Institute of Applied Chem-istry, CAS). He started his research on OSCsand PLEDs in Olle Inganäs Lab in 1998. Lateron, he worked at National Center for PolymerResearch, Wright-Patterson Air Force Base andArgonne National Lab (USA). He joined Kon-arka as a Senior Scientist in 2008. In 2010, hejoined National Center for Nanoscience andTechnology as a full professor. His research fo-cuses on functional materials and devices. Heis RSC Fellow, the nominator for Xplorer Prize,and the Associate Editors for Science Bulletinand Journal of Semiconductors.Journal of Semiconductors doi: 10.1088/1674-4926/42/6/0602013。

A Method of Material Design for Systematic Absence of X-ray DiffractionHuan-hua WangInstitute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049Tel.: 86-10-88235994; Fax: 86-10-88236229; E-mail: wanghh@AbstractMaterials with systematic absence of x-ray diffraction peaks are desirable for conducting some special researches using x-ray diffraction or time-resolved x-ray scattering. This paper proposes a method for designing this kind of materials. It utilizes solid solution to reduce the structure factor of a selected reflection to zero by choosing proper components and their contents to let the reflection amplitudes from different atomic layers in the unit cells of the solid solution cancel each other completely. This method on how to select a solid solvent and how to calculate its content was illustrated using SrTiO3 as an example. A solid solution Sr1−x Ca x TiO3 with a systematic absence of the (001) diffraction can be designed, and the value of x is determined to be x = 0.54 using an iteration calculation process. This result was verified by the experimental XRD pattern of a Sr0.46Ca0.54TiO3 sample.Key words: systematic absence, x-ray diffraction, material design, perovskitePACS: 61.06.cp; ; 81.20.-n1.IntroductionSystematic absence (or extinction) is a common phenomenon in x-ray crystallography. It occurs when the structure factor is zero, due either to the centring of the lattice or to the presence of glide or screw symmetry elements. Systematic absences have important applications in x-ray diffraction (XRD) experiments, such as allowing to identify lattice type or at least to narrow greatly the number of possible space groups of a structure studied by diffraction [1]. But most compound crystals, such as the representative perovskite oxides SrTiO3, BaTiO3, PZT, (La,Ca)MnO3, YBa2Cu3O7-δ and LiNbO3, exhibit no systematic absences.Fig. 1 Structure and the two termination layers of ABO3 perovskite oxideMaterials with systematic absence of specific diffraction peaks are needed for solving some special problems in many XRD experiments or time-resolved x-ray scattering (TRXRS) experiments [2-4]. One example is using XRD to solve the unknown structure of an ultrathin film whose metastable phase cannot exist independently in bulk state. In this situation, a substrate with both equally symmetric lattice and systematic absence of the corresponding diffraction peaks is highly desirable. Another example is probing the growth unit of perovskite oxide thin films via TRXRS. This problem isvery important to atomic engineering due to the importance of this material family both in science and in technology. Scientists hope to control the termination layers of thin films and interface layers of heterojunctions in order to fabricate oxide optoelectronic devices with atomic-scale accuracy. As depicted in Figure 1, a simple ABO 3 perovskite thin film has two kinds of terminated layers, the AO-layer (A layer) and the BO 2-layer (B layer). It usually terminates with the B-layer at the top surface, but not always [5]. The attempt to control the terminated layers necessitates monitoring a possible -A-B-A-B- growth manner, whose weak TRXRS signal is hardly measurable due to the existence of a much stronger diffraction peak from the co-existed -AB-AB- (i.e. unit cell by unit cell) growth mode and from the already-existed thin film. So materials with systematic absence of specific diffraction peak whose position overlaps with the diffraction position of the A-layer lattice and the B-layer lattice are preferable.In this paper, a general method of designing this kind of materials was proposed. The idea and calculation procedure were demonstrated through an example. Preliminary experiment results confirmed the applicability of the proposed method. This method can be used to study many important problems via XRD and x-ray scattering (XRS).2. Basic Idea and MethodThe basic idea of designing a systematic absence material is utilizing a solid solution to reduce the structure factor of a selected reflection to zero by selecting a proper ratio of the components to let the reflection amplitudes from the different atoms in the average unit cell of the solid solution cancel each other completely. Take ABO 3 perovskite as an example to elucidate this idea: If we want the (001) diffraction to be systematically absent, the reflection amplitudes from the AO-layer and from the BO 2-layer can be adjusted to equal through doping a solid solvent. The two equal amplitudes are out of phase by π and thus cancel each other completely due to destructive interference. So (001) systematic absence is achieved.Now let me use SrTiO 3 as an example to illustrate how to select a proper solid solvent, and how to determine the component contents to make the (001) peak to be systematically absent.A. Selection of a solventThe structure factor for SrTiO 3 (001) can be written as ()()()()()()Q f Q f Q f r Q i Q f Q F O Ti Sr j jj −−=⋅⋅=∑r r r exp . where Q r is the scattering vector, θλπsin 4==Q Q r , and f is the atomic scattering factor. For the (001) diffraction, ****c c l b k a h G Q hkl r r r r r r =++==.In terms of the fact that f reduces to the electron numbers of the scatters at 0=Q , we can roughly judge that ()()()0>−−Q f Q f Q f O Ti Sr . Therefore, to make ()0=Q F r , a fraction of Sr ions should be substituted for an element with a smaller atomic order number, or a friction of Ti for an element with a larger atomic order number. Further considering the solubility of the components, they should have the same lattice type and close lattice constants. So CaTiO 3 (cubic, 3.827 Å) or SrMoO 3 (cubic, 3.975 Å) can be selected as the solvents to synthesize Sr 1-x Ca x TiO 3 (SCTO) or SrTi 1-y Mo y O 3 (STMO) solid solutions, respectively. Both solid solutions have cubic lattices because the tolerance factors of CaTiO 3, SrMoO 3 and SrTiO 3 are either very close or equal to 1. They have been synthesizedalready [6,7].B. Determination of the stoichiometry of the solid solutionAfter the solvent of SrTiO 3 has been selected, Sr 1-x Ca x TiO 3 for example, the next step is to determine the correct component content x. To make SCTO (001) systematically absent,()()()()()()01=−−⋅+⋅−=Q f Q f Q f x Q f x Q F O Ti Ti Sr SCTO r(1).The value of x cannot be directly obtained from this equation, because the four atomic scattering factors, which are dependent on x through Q = c*, are actually unknown either. However, an iteration method can be used to get the correct value of x following the following procedure.First, an approximate value of x can be obtained using the atomic scattering factors at Q=0. Substituting the electron numbers of Sr 2+ (36), Ca 2+ (18), Ti 4+ (18) and O 2− (10) into Equation (1),36 (1− x) + 18 x − 18 − 10 = 0andx = 4/9According to Vegard’s law, the average lattice constant of the cubic solid solution is approximately equal toa = 3.905 (1−x) +3.827 x = 3.8703 (Å).So the reciprocal lattice constant c* and the scattering vector Q can be calculated asQ = c* = 2π/asin θ/λ = Q/4π = 0.1292 Å−1Then the atomic scattering factors Mo Ti Sr f f f ,, and O f can be evaluated from the analytical approximation [8]()()[]c b a f j j j +−⋅=∑=241/sin exp /sin λθλθ (2) where the fitting coefficients a j , b j and c can be obtained from International Tables for X-ray Crystallography . Table 1 lists the related ones used here, where the parameters of O − instead of O 2− were used for the calculations with a error of about 0.55%. Substituting them into Equation (1), one gets a new x value:x ≅ 0.54061146Table 1 Coefficients for analytical approximation to the scattering factors excerpted from InternationalTables for X-ray Crystallography , Vol. 3.a 1b 1 a 2b 2 a 3 b 3 a 4 b 4c Ca 2+ 15.6348 −0.0074 7.95180.6089 8.4372 10.3166 0.8537 25.9905 −14.875Sr 2+ 18.0874 1.4907 8.1373 12.69632.5654 24.5651 −34.193 0.0138 41.4025Ti 4+ 19.5114 0.178847 8.23473 6.670182.01341−0.29263 1.5208 12.9464 −13.28 Mo 5+ 21.0149 0.014345 18.0992 1.0223811.46328.7809 0.740625 23.3452 −14.316O − 4.1916 12.8573 1.639694.17236 1.5267347.0179 −20.307 −0.01404 21.9412Revising a and Q using the new x value, one obtainsa=3.8628 Åsinθ/λ = Q/4π = 0.1294 Å−1Solving Equation (1) for x using these new values, one obtains an updated new value of x:x ≅ 0.54079512Use this updated x value and repeat the above steps, one getsx ≅ 0.54079512Within the error of practical experiments, the value of x doesn’t change any more. So the designed material is Sr0.46Ca0.54TiO3.A small error in the above calculation is resulted from the using of the analytical parameters of O− instead of that of O2−. Now we can use the real atomic scattering factor of O2− for the last step calculation above. By plotting the atomic scattering factor versus sinθ/λ curve of O2− using the values at several points given in International Tables for X-ray Crystallography, one obtains().01294389f≅ 7.26352−ORepeat the above step using this real atomic form factor, we obtainx = 0.5388495 ≅ 0.54So the compound is Sr0.46Ca0.54TiO3.C. Possible errorsIn an actual experiment, several sources of error can result in incomplete extinction of the (001) peak: (1) There existed weighing error of the raw powders; (2) The powders absorbed humidity during weighing, especially for TiO2 powder; (3) The raw materials are not perfectly pure; (4) The largest error comes from the deviation of the lattice constants of the solid solution from the linear Vegard’s law. The former three errors can be reduced low enough by careful operations. The forth error can be corrected by using the actual lattice constant of the solid solution. The lattice constants of the cubic Sr1-x Ca x TiO3 compounds have been given by Durst e t al. in Reference [6], but they are not used in this study because of their large errors. n fact, the right stoichiometry of the solid solution can be obtained by tuning its component ratio through experiments.Using the same procedure, the stoichiometry of SrTi1-y Mo y O3 was determined to be SrTi0.498Mo0.502O3.3.Experiment Results and DiscussionTo verify the proposed method, Sr0.46Ca0.54TiO3 was synthesized by sintering a compressed disk of mixed SrCO3 (99.99%), CaCO2 (99.99%) and TiO2 (99.99%) powders. The disk was sintered at 1200 °C for 40 hours, and then was reground into powders for XRD measurements. Fig. 2 shows the Cu Kα1 XRD pattern of Sr0.46Ca0.54TiO3. It can be seen from Fig. 2 that the relative intensity of the (001) peak greatly reduces compared with that of SrTiO3. The intensity ratio of (001) and (110), I001/I110, is 12% for SrTiO3 but only 0.015% for the Sr0.46Ca0.54TiO3 powders. It can also be seen that the XRD peaks of SrO, CaO and TiO2 are relatively weak, indicating that the raw materials were not uniformly mixed and thus the reaction was incomplete. Further uniform mixing and re-sintering should be performed.Fig.2 The θ-2θ scan XRD pattern of Sr 0.46Ca 0.54TiO 3 solid solutions after sintering at1200 °C. The intensity ratio, I 001/I 110, is reduced to ~0.015% Fig.3 The θ-2θ scan XRD pattern ofSr 0.46Ca 0.54TiO 3 solid solutions after regrinding and re-sintering at 1460°C. The (001) peak is systematically absent.So the powder was re-grounded for 6 more hours, compressed into a disk, and re-sintered at 1460°C for another day. The XRD pattern of the resulted solid solution was shown in Figure 3. It is obvious that the (001) diffraction peak is absent now, despite a small part of unreacted CaO and TiO 2 remained in the solid solution, possibly because unreacted CaO and TiO 2 had already formed separated grains and could not contacted and reacted with each other. This result indicates that this design method works.4. ConclusionA general method for designing materials with systematic absence was proposed. It uses solid solution to adjust the reflection amplitudes from different atomic layers in a unit cell and make them to cancel each other. The doping solvent can be selected according to the formula of the structure factor at Q = 0. The stoichiometry of the solid solution can be calculated using an iteration process. The applicability of this method has been experimentally verified.AcknowledgementsFinancial support from Institute of High Energy Physics, Chinese Academy of Sciences is acknowledged (under Contract H75463AOU2). The author thanks Professor Joel D. Brock and Dr. Darren Dale for their discussions.References:[1] X-ray Diffraction , B.E. Warren, Dover, New York, 1990.[2] A.Fleet, D. Dale, Y . Suzuki, J. D. Brock, Phys. Rev. Lett. 94, 036102 (2005).[3] J. Z. Tischler, G . Eres, B. C. Larson, C. M. Rouleau, P. Zschack, D. H. Lowndes, P. Zschack, Phys.Rev. Lett. 96, 226104 (2006).[4] J. D. Ferguson, A. R. Woll, G . Arikan, D. S. Dale, A. Amassian, M. W. Tate, J. D. Brock, Mater. Res.Soc. Symp. Proc. 1034, 1034-K10-20 (2008)[5] H. Tabata, K. Ueda, T. Kawai, Mat. Sci. Eng. B 56, 140 (1998).[6] G . Durst, M. Grotenhuis, A. G . Barkow, J. Am. Ceram. Soc. 33, 133 (1950).[7] L. H. Brixner, J.Inorg. Nucl. Chem. 15, 356 (1960).[8] Elements of Modern X-ray Physics, J. Als-Nielsen and D. McMorrow, Wiley, New York, 2001.。