Volume-dependence of phonon frequencies and mode Grüneisen parameters for Si and Ge

The volume-dependence of phonon frequencies for Si and Ge is studied using higher-order perturbation and local Heine-Abarenkov model pseudopotential. The obtained mode Grüneisen parameters at atmospheric pressure are in good agreement with the experimental data. The mode Grüneisen parameters obtained for the Raman, TO, LO and LA modes increase slightly with decreasing volume. The other TA mode Grüneisen parameters decrease strongly as function of the volume strain, and give important contribution to the anharmonic properties of Si and Ge. The pressure dependence of phonon frequencies for Raman and some modes at the zone boundaries are estimated over the whole region of the compressed volume before the pressure induced covalent-metallic phase transition.     

Calculation of the lattice dynamical properties of Ge

The lattice dynamical properties of Ge are studied employing a frozen phonon approach within an ab initio density-functional pseudopotential formalism. Using the atomic number, atomic mass, and crystal structure as the only input information, we calculate phonon frequencies and mode Grüneisen parameters at Γ and X and the third-order anharmonic parameter for the zone center optical mode. The results are in excellent agreement with available experimental data. An analysis of various energy contributions to the TA (X) mode shows that the proper inclusion of the exchange-correlation energy is crucial for accurate microscopic studies of lattice dynamics.     

Grüneisen parameter and thermal expansion of V3Si and V3Ge

The Grüneisen parameter and lattice thermal expansion of the A-15 compounds V₃Si and V₃Ge at room temperature are evaluated on the basis of the method due to Brugger and Fritz [1] from the third order elastic constants reported earlier [2]. The calculated values are compared with available experimental values and are found to fit satisfactorily.     

Mode grüneisen parameters for long-wave phonons under pressure of Si and Ge

The elastic stiffness constants under pressure of Si and Ge are studied theoretically using the higher-order perturbational formalism and the local Heine-Abarenkov model pseudopotential, and the mode Grüneisen parameters for long-wave phonons are estimated as a function of the compressed volume. The results obtained for atmospheric pressure are in good agreement with the experimental data. The long-wave LA mode Grüneisen parameters decrease slightly as the volume is reduced by compression. The TA mode Grüneisen parameters show a large decrease as function of the volume strain, and become negative near the covalent-metallic phase transition. The volume-dependences of the long-wave mode Grüneisen parameters are useful in the study of the anharmonic properties of Si and Ge.     

Pressure dependence of the zone edge TA phonons in silicon

The sharpest peak in the 2TA second order Raman spectrum of Si has been measured as a function of hydrostatic stress up to 6 kbar. This peak is assigned to overtones of two phonons near the X point of the Brillouin zone. The Grüneisen parameter of the TA (X) phonon so obtained (? 1.4) is considerably larger than that obtained in model calculations including up to second order neighbors (～?0.6). From this discrepancy the necessity of including anharmonic forces between further neighbors is concluded.     

Thermal expansion coefficient of GaAs and InP

The temperature dependence of the thermal expansion for GaAs and InP is investigated theoretically using the experimental pressure derivatives of elastic stiffness constants and phonon frequencies. The linear correlation between the transverse acoustical mode Grüneisen parameter γ^X_TA and the metallic transion pressure P_t obtained by Weinstein is not satisfied for GaAs and InP, but the observed thermal expansion of GaAs is well reproduced. In addition, the linear expansion coefficient of InP is predicted theoretically as a function of temperature. Then, the phonon dispersion curves of GaAs and InP at their covalent-metallic transition pressures are quantitatively shown.     

GexSi1-x合金中的键长及其对电子能带结构的影响

采用经验紧束缚理论，以类似闪锌矿结构的晶体模型模拟Ge_xSi_1-x合金，根据总能最小原则计算了Ge_xSi_1-x合金中的键长及点阵常数．同时以紧束缚方法计算了原子位置发生弛豫前后的电子能带结构，并与虚晶近似下的计算结果进行了比较．计算结果表明，Ge_xSi_1-x合金中的键长基本上与合金组分无关，各自接近于Ｇｅ，Ｓｉ晶体中的键长，与广延ｘ射线吸收精细结构（ＥＸＡＦＳ）测量结果符合得 关键词：     

Pressure induced lattice anomalies in pnictides

Hydrostatic pressure Raman and synchrotron XRD measurements at room temperature have been carried out on a series of NdFeAsO_1−xF_y (Nd1111) oxypnictides in order to investigate pressure-induced lattice modifications. The synchrotron XRD data indicate that there is an increased deviation of the lattice constants from smooth pressure dependence in the superconducting compound, in close agreement with the results from SmFeAsO_1−xF_x (Sm1111), although the effect is less pronounced in Nd1111. As in Sm1111 the hydrostatic pressure Raman measurements show that the A_1g mode of the rare earth atom deviates from the linear pressure dependence. Anomalous pressure dependence and a hysteresis is observed in the phonon width of the phonon modes. The calculated Grüneisen parameter for the Nd phonon is very similar to the corresponding value for SmFeAsO_1−xF_x compound and it does not vary with substitution. For the As mode it has a lower value indicating a stiffer phonon with the increased ion size. In connection with the XRD measurements the Raman data show a sudden increase of the pressure-induced lattice anomalies close to doping where the compounds become superconducting.     

Phonons in Si3Ge1 and Si1Ge3 short-period superlattices

Oscillatory spectra and single-phonon state densities are calculated in the Keating atomic interaction model for the ultrathin superlattices Si₃Ge₁ and Si₁Ge₃. Fundamental features of the superlattice phonon spectra and their relationship to the spectra of Si and Ge crystals are analyzed. Conditions required for oscillation localization in the interface region are studied and the role of the Si-Ge bond in formation of interlayer oscillations is considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii. Fizika, No. 8, pp. 40–44, August, 1993.     

Effect of the composition of the solid solution on the high-temperature microhardness of SiGe heteroepitaxial layers grown on Ge and Si substrates

The effect of the composition of epitaxial layers (ELs) of the Si_xGe_1?x solid solution grown on Ge and Si substrates on their microhardness and the length of dislocation rosettes forming around indentations is studied at a homologous temperature 0.5T_melt for each composition. For the Si_xGe_1?x/Ge (0≤x<0.15) and Si_xGe_1?x/Si (0.85<x≤1) ELs, the dependences of the microhardness and the length of dislocation rosettes on the solid-solution composition are nonmonotonic. The nonmonotonic change in the plasticity of the ELs is most likely caused by hardening of the solid solutions in a certain composition range due to their spinodal decomposition with the formation of clusters and disperse precipitates.     

Si–Si optical phonon behavior in localized Si clusters of Si<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Ge<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript> alloy nanocrystals

Raman spectra acquired from Si _x Ge_1−x -nanocrystal-embedded SiO₂ films show dependence of the Si–Si optical phonon frequency on Si content. The frequency upshifts, and peak intensity increases as the silicon concentration increases. For a given Si content, the frequency remains unchanged with annealing temperature. Spectral analysis and density functional theory calculation reveal that the optical Si–Si phonon is related to the formation of localized Si clusters surrounded by Si/Ge atomic layers in the Si _x Ge_1−x nanocrystals and the intensity enhancement arises from the larger cluster size. The synergetic effect of surface tensile stress and phonon confinement determines the Si–Si optical phonon behavior.     

Effect of surface segregation on the sharpness of heteroboundaries in multilayered Si(Ge)/Si1−x Gex structures grown from atomic beams in vacuum

The main reasons for composition intermixing in the vicinity of heteroboundaries in an Si(Ge)/Si_1?x Ge_x heterosystem grown by the molecular beam epitaxy method are considered. The proposed model explains all the experimentally observed peculiarities, such as the clearly manifested asymmetry of the solid solution profile in layers, and demonstrates the noticeable erosion of the composition profile at the boundaries even in the absence of the surface segregation effect. It is shown that the surface segregation in the Ge/Si_1?x Ge_x system may play a positive role, leading to an increase in the profile steepness of the Si_1?x Ge_x layer near the boundaries.     

Electronic structure of SixGe1−x semiconductor solid solutions

The electronic structure of Si_xGe_1?x solid solutions is studied by means of a semi-ab initio method without involving the virtual crystal approximation. The calculations are performed on large cubic cells of the diamond lattice which contain a total of 64 Si and Ge atoms homogeneously distributed in different compositional ratios. The basis functions and the potentials used in the calculation give good band structures of elemental Si and Ge respectively. The calculated variation of band gap with x is in agreement with optical experiment: the two linear curves of gap vs concentration have different slopes at high and low x values with a crossing-over at about x=0.28. The band gaps are direct for xε (0, 0.28) and indirect for x ≥ 0.28. The density of states (DOS) of the solid solution can be very well approximated by the weighted average of the bulk Si and Ge DOS. There is a very slight charge transfer of about 0.05 electron per atom from Si to Ge.     

四方晶系应变Si空穴散射机制

基于Fermi黄金法则及Boltzmann方程碰撞项近似理论, 推导建立了(001)弛豫Si_1-xGe_x衬底外延四方晶系应变Si空穴散射几率与应力及能量的理论关系模型, 包括离化杂质、声学声子、非极性光学声子及总散射概率(能量40 meV时)模型. 结果表明: 当Ge组分(x)低于0.2时, 应变Si/(001)Si_1-xGe_x材料空穴总散射概率随应力显著减小. 之后, 其随应力的变化趋于平缓. 与立方晶系未应变Si材料相比, 四方晶系应变Si材料空穴总散射概率最多可减小66%. 应变Si材料空穴迁移率增强与其散射概率的减小密切相关, 本文所得量化模型可为应变Si空穴迁移率及PMOS器件的研究与设计提供理论参考.     

Effect of the Ge content on the Schottky barrier height in structures based on Si1 − x Ge x solid solution

The subject of investigation is the influence of the Ge content on the Schottky barrier height in Au-p-i-n/Al structures based on Si_{1 ? x} Ge _x (0 < x < 0.26) solid solutions grown by electron-beam floating-zone melting. In Au-i-Si_{1 ? x} Ge _x , Au-αGe/Si(Li), Au-αGe/Si, and Au-n-Si_{1 ? x} Ge _x structures, the height of the barrier is about 1 eV, which exceeds the average value of this parameter for silicon available in the literature. It is shown that an excess Ge concentration in the near-surface region of the Si_{1 ? x} Ge _x crystal causes self-passivation of the surface, which leads to a rise in the barrier height. In the Au-i-Si_{1 ? x} Ge _x structures, the Schottky barrier height increases from 0.97 to 1.03 eV as Ge content x increases from 0 to 0.11.     

生长在Si(001)衬底上应变合金层GexSi1-x的光学性质

采用经验的紧束缚方法对生长在Si(001)衬底上的应变合金Ge_xSi_1-x的光学常数进行了计算。应变对电子能带结构的影响,通过紧束缚参数随键角方向余弦的变化以及键长按经验的标度定则的变化而进行计算。其中标度指数根据对Ge和Si的畸变势常数的实验值进行拟合而确定。计算介电常数虚部时出现的动量矩阵元,根据对Ge和Si的介电常数虚部的实验曲线拟合而决定。列出了当x=0.2和1时的光学常数——介电常数虚部ε₂、折射率n、吸收系数α和反射率R的计算结     

Electronic structure,mechanical and optical properties of ternary semiconductors Si1-xGexC (X = 0, 0.25, 0.50, 0.75, 1)

The electronic structure of silicon carbide with increasing germanium content have been examined using first principles calculations based on density functional theory. The structural stability is analysed between two different phases, namely, cubic zinc blende and hexagonal phases. The zinc blende structure is found to be the stable one for all the Si_1-xGe_xC semiconducting carbides at normal pressure. Effect of substitution of Ge for Si in SiC on electronic and mechanical properties is studied. It is observed that cubic SiC is a semiconductor with the band gap value 1.243?eV. The band gap value of SiC is increased due to the substitution of Ge and the band gap values of Si _0.75 Ge _0.25 C, Si _0.50 Ge _0.50 C, Si _0.25 Ge _0.75 C and GeC are 1.322 eV, 1.413 eV, 1.574 eV and 1.657?eV respectively. As the pressure is increased, it is found that the energy gap gets decreased for Si_1-x Ge_xC (X?=?0, 0.25, 0.50, 0.75, 1). The elastic constants satisfy the Born – Huang elastic stability criteria. The bulk modulus, shear modulus, Young’s modulus and Poisson’s ratio are also calculated and compared with the other available results.     

Nanocrystal growth of single-phase Si1−xGex alloys

We present the formation of single-phase Si_1−xGe_x (x=0.2, 0.4, 0.6, and 0.8) alloy nanocrystals dispersed in a SiO₂ matrix. The studied samples were prepared by co-sputtering with excess Si_1−xGe_x in SiO₂ of approximately 33 at%. Upon heat treatment, crystallization of Si_1−xGe_x alloys was examined by using X-ray diffraction and high-resolution transmission electron microscopy measurements. Single structure of face-centered cubic nanocrystals in a space group Fd-3m was concluded. The average nanocrystal size (from 2 nm to 10 nm) and the lattice constant a of the single-phase Si_1−xGe_x nanocrystals were found to increase with the Ge composition parameter x. Density functional theory-generalized gradient approximation calculation showed the replacement of Ge into the Si sites and vice versa.     

The hydrostatic pressure derivatives of the elastic constants of indium and an indium cadmium alloy

The hydrostatic pressure derivatives of the elastic stiffness constants of indium and indium-3.4 at.% cadmium alloy single crystals have been obtained from pulse echo overlap measurements of the dependence of ultrasonic wave velocities upon pressure. The softest zone centre acoustic phonon mode in indium is a shear mode propagating k along the [101] direction rather than that (k[110], e[11?0]) which drives the ferroelastic phase transition in the indium-cadmium alloys. The derivative δ((C₁₁ – C₁₂)/2)/δP is positive, accounting for the stability of the fct structure of indium under high pressure. Using the quasiharmonic, anisotropic continuum model the acoustic mode Grüneisen parameters have been calculated and are discussed in terms of mode softening. The high temperature limiting value$\text{\$}\text{?}$γ_H (= 2.56) of the mean acoustic mode Grüneisen parameter is found to be close to the thermodynamic Grüneisen parameter γ^th (=2.5).     

On the spectral frequency distribution of translational vibrations in a face-centered cubic lattice of the C60 fullerite

The spectral frequency distribution g(ω) of translational lattice vibrations in the face-centered cubic phase of the C₆₀ fullerite at T = 300 K is calculated by the superposition method. The contribution from the translational vibrations to the heat capacity C _V of the C₆₀ fullerite and the x-ray characteristic temperature gJ_R entering into the exponent of the Debye-Waller factor are determined using the calculated frequency distribution g(ω). The results of the calculations are in good agreement with experimental data. It is noted that the librational and intramolecular lattice vibrations observed in the C₆₀ fullerite do not contribute significantly to the temperature-induced decrease in the x-ray diffraction intensity at T = 300 K. The Grüneisen parameters γ_mod calculated from the x-ray diffraction data are consistent with the thermodynamic Grüneisen parameters γ_lat at temperatures T ≤ 80 K but substantially exceed those at T ≈ 300 K. New x-ray diffraction experiments are proposed for independently determining the anomalously large negative values of the parameter γ₀, which is actually an orientational analog of the Grüneisen parameter.