Ab initio calculations of the forbidden Bragg reflections energy spectra in wurtzites versus temperature

Thermal-motion induced (TMI) scattering is caused by the influence of atomic displacements on electronic states in crystals and strongly depends on temperature. It corresponds to dipole-dipole resonant x-ray scattering, but is usually accompanied by dipole-quadrupole scattering. The phenomenological theory supposes the dipole-quadrupole term to be temperature independent (TI). As a result, the transformation of the energy spectra with temperature observed experimentally in ZnO and GaN corresponds to the interference between the TMI and TI terms. In the present paper the direct confirmation of this theoretical prediction is given. Ab initio molecular dynamics was used to simulate the sets of atomic sites at various temperatures followed by quantum mechanical calculation of resonant Bragg reflection energy spectra. The results of simulation are in excellent coincidence with experimental energy spectra of forbidden reflections and confirm the earlier phenomenological conjecture about the interference between the TI dipole-quadrupole and TMI dipole-dipole contributions to the resonant atomic factor.     

Resonant "forbidden" reflections in magnetite

Resonant x-ray scattering was used to investigate electronic fluctuations of the octahedral iron atoms in magnetite. We measured the (002) and (006) "forbidden" x-ray diffraction reflections permitted by the anisotropy of the iron anomalous scattering factor. The energy and azimuthal angle dependencies of these reflections, and the polarization analysis, are shown and discussed. The results clearly show p and d iron empty states ordering in magnetite at room temperature. Moreover, the octahedral iron atoms are electronically equivalent in a time scale lower than 10(-16) sec. Therefore, magnetite should be considered as an itinerant magnet and not as a fluctuating mixed valence material.     

Ab initio simulation of resonant forbidden reflections in Ge crystals

Forbidden reflections are observed in the case of diffraction of synchrotron radiation with wave-lengths close to the absorption edges in crystals. A new method for calculating the intensity of thermal-motion-induced (TMI) forbidden reflections is proposed in this paper. It includes two stages: simulation of instantaneous thermal atomic displacements using ab initio molecular dynamics and subsequent quantum-mechanical calculations of the resonance scattering amplitude for various configurations. This procedure is used to calculate the temperature dependence of the 600 reflection intensity for Ge. The proposed method for simulating forbidden TMI reflections is suitable for any crystal structures and can explain many results so far obtained using synchrotron.     

Effect of electron–phonon interaction on surface states in wurtzite nitride semiconductors under pressure

A variational theory is proposed to study the electronic surface states in semi-infinite wurtzite nitride semiconductors under the hydrostatic pressure. The electronic surface state energy level is calculated, by taking the effects of the electron–Surface–Optical–phonon interaction, structural anisotropy and the hydrostatic pressure into account. The numerical computation has been performed for the electronic surface state energy levels, coupling constants and the average penetrating depths of the electronic surface state wave functions under the hydrostatic pressure for wurtzite GaN, AlN and InN, respectively. The results show that electron–Surface–Optical–phonon interaction lowers the electronic surface state energy levels. It is also found that the electronic surface state energy levels decrease with the hydrostatic pressure in wurtzite GaN and AlN. But for wurtzite InN, the case is contrary. It is shown that the hydrostatic pressure raised the influence of electron–phonon interaction on the electronic surface states obviously. The effect of electron–Surface–Optical–phonon interaction under the hydrostatic pressure on the electronic surface states cannot be neglected, in specially, for materials with strong electron–phonon coupling and wide band gap.     

Anisotropic resonant X-ray scattering: Beauty of forbidden reflections

Experimental results and their theoretical explanation are reviewed for fundamentals of anisotropic resonant X-ray scattering. Resonant scattering depends on X-ray polarization, i.e. the scattering reflects anisotropic environment of atoms in crystal. The polarization anisotropy in atomic scattering can excite the forbidden Bragg reflections. Studying this type of forbidden reflections we can distinguish electronic orbitals of specific symmetry. This method is very useful for studying local electronic states in crystal. We reveal detailed property of the anisotropic scattering, effect of quadrupole transition, thermal motion, magnetic scattering and so on. Especially successful examples are given in detail: observation of phase of the scattering factor, the hybridization of states with different parity, local chirality of atom in centrosymmetric crystals, thermal-motion-induced resonant reflections, etc.     

Raman spectroscopy of optical phonons as a probe of GaN epitaxial layer structural quality

We report on Raman scattering measurements of all Raman-active phonons in wurtzite and zinc blende structure GaN epilayers grown on GaAs (001), GaAs (111)A, and GaAs (111)B oriented substrates by means of molecular beam epitaxy (MBE). Raman spectra are taken from these epilayers at room temperature and 77 K in backscattering geometry. The measured values of the phonon frequencies are in agreement with other studies and with lattice dynamic calculations of phonon modes in GaN zinc blende and wurtzite structures. We show that crystal quality is much better in samples grown on GaAs (111) substrates than in samples grown on GaAs (001) substrates. The observation of disorder-activated modes gives information about sample quality. Comparison of the spectra from different thickness epilayers shows that the GaN is more highly disordered close to the substrate, particularly for the (001) substrates. Received 16 July 1999     

纤锌矿相GaN空穴输运特性的Monte Carlo模拟研究

用全带多粒子Monte Carlo方法模拟纤锌矿相(Wurtzite)GaN空穴输运特性的结果. 用经验赝势法计算得到能带结构数据. 模拟包含了声学声子散射，光学声子散射，极性光学声子散射，压电散射，电离杂质散射及带间散射等散射机理. 计算得到了空穴沿3个主要对称方向上的空穴平均漂移速度和平均能量与电场强度的关系曲线，室温下漂移速度呈现饱和特性. 在所研究的电场范围内，最大平均漂移速度约为6×10⁶cm s^-1，最大空穴平均能量约为0.12eV, 这些值均比电子的相应参数低很多. 还给出了空穴的扩散迁移率与杂质浓度关系的模拟结果. 关键词： 蒙特卡罗 氮化镓 输运特性 能带结构     

Electron-phonon interaction effects on the surface states in wurtzite nitride semiconductors

A variational approach is used to study the surface states of an electron in a semi-infinite wurtzite nitride semiconductor. The surface-state energy of the electron is calculated, by taking the effects of the electron-surface optical phonon interaction and structure anisotropy into account. The numerical computation has been performed for the energies of the electronic surface states as a function of the surface potential V₀ for wurtzite GaN, AlN, and InN, respectively. The results show that the electron-phonon interaction lowers the surface state energy. It is also found that the energies of the electronic surface-state in wurtzite structures are lower than that in the zinc-blende structures by hundreds of meV for the materials calculated. The influence of e-p-interactions on the surface state of electron cannot be neglected.     

GaN layers with different polarities prepared by radio frequency molecular beam epitaxy and characterized by Raman scattering

GaN layers with different polarities have been prepared by radio-frequency molecular beam epitaxy (RF-MBE) and characterized by Raman scattering. Polarity control are realized by controlling Al/N flux ratio during high temperature AlN buffer growth. The Raman results illustrate that the N-polarity GaN films have frequency shifts at $A_{1}$(LO) mode because of their high carrier density; the forbidden $A_{1}$(TO) mode occurs for mixed-polarity GaN films due to the destroyed translation symmetry by inversion domain boundaries (IDBS); Raman spectra for Ga-polarity GaN films show that they have neither frequency shifts mode nor forbidden mode. These results indicate that Ga-polarity GaN films have a better quality, and they are in good agreement with the results obtained from the room temperature Hall mobility. The best values of Ga-polarity GaN films are 1042 cm$^{2}$/Vs with a carrier density of 1.0$\times $10$^{17}$~cm$^{ - 3}$.     

Coupling between spin and orbital degrees of freedom in KCuF3

We present the results of resonant x-ray scattering experiments on KCuF3. Structurally forbidden reflections, corresponding to magnetic and 3d-orbital long-range order, have been observed. Integrated intensities have been measured as a function of incident energy, polarization, azimuthal angle, and temperature. The results give evidence for a strong coupling between orbital and spin degrees of freedom. The interplay between magnetic and orbital order parameters is revealed by the temperature dependence of the intensity of orbital Bragg peaks.     

Application of X-ray resonant diffraction to structural studies of liquid crystals

Liquid crystals are soft materials that combine the fluidity of disordered liquids and the long range orientational or positional order of crystalline solids along one or two directions of space. X-ray scattering is widely and generally successfully used to investigate and characterize the microscopic structure of most liquid crystals. In many cases however, the Bragg reflections are forbidden by special symmetries of the unit cell and the low dimensional structure of the liquid crystalline phases are out of reach of conventional X-ray experiments. We show in this paper that this problem can be overcome by resonant scattering of X-rays as it reveals the anisotropy of the tensor structure factor. We review various examples in which the restored forbidden reflections reveal unambiguously the hidden structure of liquid crystalline phases. Moreover, we show that in some cases, a fine analysis of the polarization of the Bragg reflections enables one to discriminate between different structural models. These studies solved long standing questions about biaxial liquid crystal structures and provided new insights into physical phenomena such as supercritical behaviour or commensurate-incommensurate transitions.     

Radiative life time of an exciton confined in a strained GaN/Ga1-xAlxN cylindrical dot: built-in electric field effects

The binding energy of an exciton in a wurtzite GaN/GaAlN strained cylindrical quantum dot is investigated theoretically.The strong built-in electric field due to the spontaneous and piezoelectric polarizations of a GaN/GaAlN quantum dot is included.Numerical calculations are performed using a variational procedure within the single band effective mass approximation.Valence-band anisotropy is included in our theoretical model by using different hole masses in different spatial directions.The exciton oscillator strength and the exciton lifetime for radiative recombination each as a function of dot radius have been computed.The result elucidates that the strong built-in electric field influences the oscillator strength and the recombination life time of the exciton.It is observed that the ground state exciton binding energy and the interband emission energy increase when the cylindrical quantum dot height or radius is decreased,and that the exciton binding energy,the oscillator strength and the radiative lifetime each as a function of structural parameters (height and radius) sensitively depend on the strong built-in electric field.The obtained results are useful for the design of some opto-photoelectronic devices.     

GaN结构相变、电子结构和光学性质

运用第一性原理平面波赝势和广义梯度近似方法,对纤锌矿结构和氯化钠结构GaN的状态方程及其在高压下的相变进行计算研究,分析相变点附近的电子态密度、能带结构和光学性质的变化机制.通过状态方程和焓相等原理得到GaN从纤锌矿到氯化钠结构的相变压强分别为43.9 Gpa和46.0 Gpa;在相变的过程中,GaN由典型的直接带隙半导体转变为间接带隙半导体材料;氯化钠结构GaN相比于纤锌矿结构,介电函数主峰值增强,本征吸收边明显往高能方向移动,氯化钠结构GaN在低能区域的光学性质差于纤锌矿结构.     

Energy of a Polaron in a Wurtzite Nitride Finite Parabolic Quantum Well

The effects of electron-phonon interaction on energy levels of a polaron in a wurtzite nitride finite parabolic quantum well （PQW） are studied by using a modified Lee-Low-Pines variational method. The ground state, first excited state, and transition energy of the polaron in the GaN/Al0.3Ga0.7N wurtzite PQW are calculated by taking account of the influence of confined LO（TO）-like phonon modes and the half-spaee LO（TO）-like phonon modes and considering the anisotropy of all kinds of phonon modes. The numerical results are given and discussed. The results show that the electron-phonon interaction strongly affects the energy levels of the polaron, and the contributions from phonons to the energy of a polaron in a wurtzite nitride PQW are greater than that in an A1GaAs PQW. This indicates that ehe electron-phonon interaction in a wurtzite nitride PQW is not negligible.     

Anisotropy of atomic bonds formed by p-type dopants in bulk GaN crystals

The anisotropy of atomic bonds formed by acceptor dopants with nitrogen in bulk wurtzite GaN crystals was studied by means of linearly polarized synchrotron radiation used in measurements of X-ray-absorption spectra for the K-edgeof Mg and Zn dopants. These spectra correspond to i) a single acceptor N bond along the c-axis and ii) three bonds realized with N atoms occupying the ab-plane perpendicular to the c-axis. The Zn dopant formed resonant spectra similar to that characteristic for Ga cations. In the case of the Mg dopant, similarity to Ga cations was observed for triple bonds in the ab-plane, only. Practically no resonant structure for spectra detected along the c-axis was observed. The absorption spectra were compared with ab initio calculations using the full-potential linear muffin-tin-orbital method. These calculations were also used for determination of the bond length for Mg–N and Zn–N in wurtzite GaN crystals and show that introducing dopants causes an increase of the lengths of the bonds formed by both dopants. Extended X-ray-absorption fine-structure measurements performed for bulk GaN:Zn confirmed the prediction of the theory in the case of the Zn–N bond. Finally, it is suggested that the anisotropy in the length of the Mg–N bonds, related to their larger strength in the case of bonds in the ab-plane, can explain preferential formation of a superlattice consisting of Mg-rich layers arranged in ab-planes of several bulk GaN:Mg crystals observed by transmission electron microscopy. Within the sensitivity of the method used, no parasitic metallic clusters or oxide compounds formed by the considered acceptors in GaN crystals were found. Received: 1 March 2001 / Accepted: 19 September 2001 / Published online: 20 December 2001 / Published online: 20 December 2001     

Temperature dependence of the structure factor anisotropy in vanadium metal from γ-ray diffraction experiments

The temperature dependence of the structure factor anisotropy in V metal has been measured over the range from 70 to 800 K by means of Bragg scattering of 0.03 Å γ-radiation for the pairs of reflections 330/411 and 442/600. The low temperature data agree well with earlier X-ray scattering results by Diana and Mazzone [1] and confirm a deformation of the 3d charge distribution in the solid which points toward the nearest neighbours in the bcc lattice. At higher temperatures the anharmonic motion towards the next-nearest neighbours first cancels the effect of the electronic anisotropy and finally dominates the measured structure factor anisotropy for the 442/600 pair of reflections.     

钎锌矿相GaN电子高场输运特性的Monte Carlo 模拟研究

应用全带多粒子Monte Carlo模拟方法,研究了钎锌矿相GaN 材料电子的高场输运特性. 模拟中利用了基于第一性原理总能量赝势方法计算得到的纤锌矿GaN的能带结构数据. 用Cartier的方法,计算碰撞电离散射率. 计算得到了电子平均漂移速度和电子平均能量与电场的关系曲线. 电离系数的分析表明当电场强度大于1 MV/cm时,才会有明显的碰撞电离发生,量子产额的分析表明当电子的能量大于7 eV时,量子产额随能量增加迅速增大. 研究了在0—4 MV/cm电场强度范围内电子在各导带的分布,低场下电子全部位于 关键词： 碰撞电离 高场输运 能带结构 Monte Carlo模拟     

纳米晶粒团聚GaN纳米线A1(LO) Raman峰的非对称展宽

氮化镓(GaN)是一种直接带隙Ⅲ～Ⅴ族半导体化合物,具有较宽的禁带宽度(Eg=3.4eV),较高的热稳定性,以及抗辐照等特性[1-4],是制备近紫外和蓝光光电子器件、高速微电子器件的理想材料.制备低维纳米结构,研究其物理性质既是理解低维量子现象的要求,也是未来纳米电子器件发展的需要.近年来,很多小组已经通过不同的方法成功地制备出GaN纳米棒、纳米线等一系列一维材料.这些方法包括碳纳米管辅助的方法[5]、电弧放电的方法[6]、激光刻蚀的方法[7]、升华法[8]、高温分解法以及化学气相沉积(CVD)[9-15].其中CVD方法以其制备过程简单,制备材料晶…     

Interband transitions and electronic Raman continuum in systems with strong inelastic scattering: Applications to YBa2Cu3O7-δ

We consider a model for the electronic Raman continuum which takes into account strong inelastic scattering and interband transitions. Calculations are based on four-vertex Raman scattering diagrams (Kawabata formalism) within the RPA for Coulomb interaction and the ladder diagram Bethe-Salpeter equation for the vertex. We apply this method to an analysis of the nature of the electronic Raman continuum in the normal state of the high-T _c superconductor YBa₂Cu₃O₇. In numerical calculations we take into account all the self-energy effects and make simulations for vertex corrections assuming that inelastic scattering is due to electron-phonon interaction. Theab-plane polarized continuum contains a large contribution from interband processes and does not depend strongly on temperature and inelastic scattering strength. The in-plane anisotropy is determined by interband transitions rather than by anisotropy of the Fermi surface. The ZZ continuum contains only weak contribution from interband transitions. It can be crudely described within a single band model with inelastic scattering and is strongly dependent on the relaxation rates of inelastic scattering. The nature of the oxygen-deficiency dependence of the Raman spectra is also commented upon.     

Spin-orbit coupling and crystal-field splitting in the electronic and optical properties of nitride quantum dots with a wurtzite crystal structure

We present an sp ³ tight-binding model for the calculation of the electronic and optical properties of wurtzite semiconductor quantum dots (QDs). The tight-binding model takes into account strain, piezoelectricity, spin-orbit coupling and crystal-field splitting. Excitonic absorption spectra are calculated using the configuration interaction scheme. We study the electronic and optical properties of InN/GaN QDs and their dependence on structural properties, crystal-field splitting, and spin-orbit coupling.