Optical-phonon Deformation Potentials Research Articles

Electron-phonon deformation potential interaction in core-shell Ge-Si and Si-Ge nanowires

We settle a general expression for the Hamiltonian of the electron-zone-center optical phonon deformation potential (DP) interaction in the case of nonpolar core-shell cylindrical nanowires (NWs). On the basis of a long-range phenomenological continuum model for the optical modes and by taking into account the bulk phonon dispersions, we study the size dependence and strain-induced shift on the electron-phonon coupling strengths for Ge-Si and Si-Ge NWs. We derive analytically the DP electron-phonon Hamiltonian and report some numerical results for the frequency core modes and vibrational amplitudes. Our approach allows for the unambiguous identification of the strain and confinement effects on the optical phonons at the $\ensuremath{\Gamma}$ point. We explore the dependence of mode frequencies, phonon amplitudes, and hole-DP scattering rate on the spatial symmetry and the structural parameters of these core-shell structures, which constitute a basic tool for the characterization and device applications of these novel nanosystems.

Measurement of phonon pressure coefficients for a precise determination of deformation potentials in SiGe alloys

AbstractFor an effective use of Raman scattering as strain characterization tool in SiGe nanostructures a precise knowledge of the phonon deformation potentials (DPs) is strictly necessary. The optical phonon DPs can be determined by means of Raman scattering measurements from the cleaved edge of a biaxially strained SiGe alloy layer grown pseudomorphically on silicon and subsequently capped. Due to uncertainties in the literature values of the unstrained phonon frequencies it turns out that the desired degree of accuracy is only attained by complementing the Raman measurements from the edge with that of the hydrostatic pressure coefficient of the optical phonons. For that purpose we have grown by molecular beam epitaxy up to seven partially strained Si1–x Gex alloys on Si spanning the entire compositional range and measured the dependence on hydrostatic pressure of the frequency of the Ge‐like, Si‐like and mixed Si–Ge optical modes. After correcting for the pressure dependent biaxial stress induced by the Si substrate on the alloy layer and taking into account the dependence on alloy composition of the bulk modulus we obtain a fairly constant value of the Grüneisen parameter around 1.0 for all three optical modes in the whole range of Ge contents. We also determined the strain shift coefficients for the three modes, which are essentially independent of Ge content between 0.4 and 1. Our results are in very good agreement with recentcalculations of the SiGe phonon deformation potentials using a modified Keating model, which settles the longstanding issue about the large discrepancies between results from different experiments. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Electron capture by quantum wells in an internal electric field

We have investigated the electron capture times by a single quantum well, taking into account the influence of the built-in electric field due to the piezoelectric effect as in GaN/AlxGa1−xN and GaAs/InxGa1−xN structures. Theoretical carrier capture is calculated by considering a variational electron wave function inside the quantum well and a linear combination of the Airy functions above the quantum well. It is shown that the scattering rate by the optical-phonon deformation potential exhibits a smoothly decreasing function with increasing electric field. This effect is due to the shift of the bound state to lower energies and to the electron heating due to the electric field in the quantum well. This result is quantitatively in agreement with both Monte Carlo simulations and previous experimental measurements.

Crystal Data, Photoconductivity and Carrier Scattering Mechanisms in CuIn5S8 Single Crystals

The X-ray diffraction has revealed that CuIn 5 S 8 is a single phase crystal of cubic spinel structure. The value of the unit cell parameter for this crystal is 1.06736 nm. The crystal is assigned to the conventional space group Fd3m. The photocurrent is found to have the characteristic of monomolecular and bimolecular recombination at low and high illumination intensities, respectively. The electrical resistivity and Hall effect of CuIn 5 S 8 crystals are measured in the temperature range of 50-400 K. The crystals are found to be intrinsic and extrinsic above and below 300 K, respectively. An energy band gap of ∼1.35 eV at 0 K, a carrier effective mass of 0.2 m 0 , an acceptor to donor concentration ratio of 0.9, an acoustic phonon deformation potential of 10 eV and a nonpolar optical phonon deformation potential of 15 eV are identified from the resistivity and Hall measurements. The Hall mobility data are analyzed assuming the carrier scattering by polar optical phonons, acoustic combined with nonpolar optical phonons, and ionized impurities.

Monte Carlo studies of ohmic hole mobility in silicon and germanium: Examination of the optical phonon deformation potential

Monte Carlo methods which have been widely used for studying high field electron and hole transport, so far have not been applied to the complex problem of Ohmic hole transport. We present a versatile generalization of the Monte Carlo approach for Ohmic hole mobility studies and apply it to pure silicon and germanium. In particular, we examine the role of the optical phonon deformation potential d0 in controlling the temperature dependence of the mobility.

STUDY OF OPTICAL-PHONON DEFORMATION POTENTIALS ON Λ-AXIS FOR III-V COMPOUND SEMICONDUCTORS

The study of optical-phonon deformation potentials (ODP*s) versus wavevector on 1111A-axis in Brillioun zone for nine III-V compound semiconductors is carried out systematically, based on ab initio LMTO-ASA band calculation within the frozen-phonon approximation model. The ODP*s d30(∧),d10(∧,val) and d10(∧,con) obtained from the calculation are presented.

Ab initio calculations of optical phonon deformation potentials in diamond and zinc-blende semiconductors

Ab initio calculations of optical-phonon deformation potentials (ODP's), i. e., d0, d30, d10 (val) and d10 (con) for sixteen semiconductors were carried out systematically. The calculations are based on the LMTO-ASA band-structure method within the framework of the frozen-phonon approximation model, in which the displacement of empty sphere is considered to match its atomic sphere partners. We have compared the d0 values obtained by several different theoretical calculation methods and studied the main factors affecting them. It is pointed out that the two different models (rhombohedral strain model and frozen-phonon model) for calculations will lead to different results of d0.

Theoretical calculation of the optical-phonon deformation potentials on the Lambda axis in the Brillouin zone for tetrahedral semiconductors

In this paper, the ab initio calculations of optical-phonon deformation potentials (ODPS) d30, d10(val) and d10(con) on the Lambda axis in the Brillouin zone for 12 elemental and compound semiconductors are reported. This work is based upon the density-functional theory LMTO ASA band-structure method with a frozen-phonon model. The ODP values as functions of the k-points and their material dependences have been investigated.

Optical-Phonon Deformation Potentials in Diamond-Structure Crystals: ab initio LMTO-ASA Calculation

The optical-phonon deformation potentials of C, Si, Ge and Sn are calculated by LMTO-ASA approach within the frosen-phonon approximation. The comparisons between our results and those of several present theoretical calculations and experiments demonstrate that our calculation model is reasonable.

Electron mobility in InAs1−xSbx and the effect of alloy scattering

The significance of alloy scattering on the electron mobility of InAs1−xSbx is studied in detail. Since little experimental data are available for the InAs1−xSbx compound, calculations of the electron mobility of the binary InAs and InSb semiconductors are first evaluated from the average momentum relaxation times, 〈τm〉 of the individual mechanisms (comprising ionized and neutral impurities, acoustic phonon deformation potential and piezoelectric, optical phonon deformation potential and polar) so that they can be compared to available experimental results. Having ensured that the calculated data are in good agreement with the experimental results in these binary compounds, the electron mobility of the ternary, InAs1−xSbx as a function of x at 77 K and 300 K is calculated by introducing an alloy scattering term. At 77 K, for a total doping concentration of ≂1017 cm−3, the electron mobility of InAs1−xSbx is limited by ionized impurity scattering and alloy scattering is insignificant. However, for doping concentration of ≂1015 cm−3, alloy scattering is found to be the most significant process from about x=0.1 to 0.8. At 300 K the alloy scattering reduces the total electron mobility from between a few percent at x=0.15 to a maximum of about 11% for x=0.60. It is observed that alloy scattering is greatest at x=0.15 but it still is about 11% of the total electron mobility at this composition. The alloy mobilities at 77 K for x=0.6 and x=0.15 are 1.28×106 cm2 V−1s−1 and 7.96×105 cm2 V−1s−1, respectively. The mobilities at x=0.60 are further evaluated as a function of the doping carrier concentration at 77 and 300 K. It is found that alloy scattering becomes increasingly significant for lightly doped semiconductors at low temperatures.

Comment on "Ab initio pseudopotential calculations of optical-phonon deformation potentials in zinc-blende semiconductors"

A recent paper [B.S. Wang et al., Phys. Rev. B 39, 12 789 (1989)] reports results of careful pseudopotential calculations of optical-phonon deformation potentials in GaAs and GaP. We point out that the comparison to other theoretical calculations is complicated due to confusion of notation and definitions.

FIRST PRINCIPLE STUDY OF OPTICAL-PHONON DEFORMA-TION POTENTIALS ON Λ-AXIS FOR GaAs AND AlAs

Ab initio calculations of optical-phonon deformation potentials (ODP)d30, d10 (val) and d10 (cond) on Λ-axis in Brillioun zone for the compounds GaAs and AlAs are reported. The study is based on a frozenphonon model and using the LMTO-ASA method with a frozen-potential approximation, in which the displacement of the empty sphere was considered +o match its atomic sphere partners. The validity of our method and results have been verified with the aid of calculations for wave-vector dependence of the ODPs on Λ-asix, the numerical test to the expressions about d0 VS d30 and d10 VS d10 (val) near Γ point and an extensive comprison with various calculations as well as the experiment.

STUDY OF OPTIC AL-PHONON DEFORMATION POTENTIALS IN Ga1-xAlxAs

The optical-phonon deformation potentials (ODP's) of the tranary compounds Ga1-xAlxAs have been calculated by LMTO-ASA band structure technique combining with a virtual crystal approximation and a frozen-phonon model. The ODP's as a function of the Al composition x has been predicted. We find that the ODP's d0,d30,d10(val)and d10(cond) can be expressed as a quadratic equation of the compositions. Among them a small bending parameter is only connected with the d0 vs x, showing it to be a nearly linear dependence. The computational results also show that the d10(val) will equal to the d10(cond) at x≈0.65. So the ratio d30/d10 should be divergent at that composition. This fact implies that the contribution of the two-band term to the Raman tensor of the first-order resonance Raman scattering for energy gap E1-E1+△1 can be neglected at that composition in Ga1-xAlxAs. The reliability of our calculation results has been verified by using the relationship between the ODP's.

Resonance Raman scattering in HgTe: TO-phonon and forbidden-LO-phonon cross section near the E1 gap.

In this paper we present Raman intensity variation of the TO phonon and the forbidden LO phonon in HgTe. We evaluate the optical-phonon deformation potentials near the ${E}_{1}$ gap (${d}_{10}^{5}$=24 eV and ${d}_{30}^{5}$=20 eV). The differences that arise as a consequence of the inverted band structure of HgTe are discussed and it is shown that the standard macroscopic formalism for Raman susceptibility for the TO-phonon mode in terms of linear susceptibility can be applied to HgTe also. Investigation of forbidden-LO-phonon intensity reveals that impurity-induced scattering is dominant and interband electron-phonon scattering has to be explicitly included to account for its variation with laser wavelength.

Resonance Raman scattering in InSb: Deformation potentials and interference effects at the E1 gap.

This paper presents a reevaluation of the optical-phonon deformation potential constants near the ${E}_{1}$ gap of InSb. The absolute values of the deformation potentials ${d}_{1}$,${0}^{5}$ and ${d}_{3}$,${0}^{5}$ are obtained from a measurement of the Raman efficiency for allowed LO-phonon scattering and a fit of previous uniaxial-stress experiments by using new ellipsometric data for the optical susceptibility. The signs of the deformation potentials are deduced from a study of the interference between the amplitudes for forbidden and allowed LO-Raman scattering. The values obtained are ${d}_{1}$,${0}^{5}$=-16.2\ifmmode\pm\else\textpm\fi{}4 eV and ${d}_{3}$,${0}^{5}$=32.9\ifmmode\pm\else\textpm\fi{}8 eV. The study of the interference also provides information about the relative weight of different sources of forbidden LO-Raman scattering.

Cathodoluminescence efficiency of binary compound phosphors

A theoretical treatment is given of binary compound cathodoluminescence efficiency on the basis of the statistical model treating the branching process of ionization scattering and phonon emission. Energy loss mechanisms of hot electrons in semiconductors are quantitatively examined using Penn’s model assuming an optical phonon deformation potential and polar-mode electron-phonon interactions. The quantum yield of e-h pairs is calculated with three parameters, the band-gap energy Eg, and two loss parameter constants Sd and Sp which are determined completely in terms of material parameters including Eg, the mass density, the lattice constant, the covalency, the optical phonon frequency, and dielectric constants. The material characterization of efficient phosphors is discussed in terms of empirical correlations between cathodoluminescence efficiency and the physical constants. Dependence of efficiency on the crystal structure of the phosphor host is particularly noticeable. Comparisons are made with previous work.

Calculation of optical- and acoustic-phonon—limited conductivity and Hall mobilities forp-type silicon and germanium

Optical- and acoustic-phonon---limited mobilities for $p$-type silicon and germanium have been calculated, without the relaxation-time approximation, from solutions of the full Boltzmann equation. The valence-band dispersions are obtained from Kane's $6\ifmmode\times\else\texttimes\fi{}6 \stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}$ Hamiltonian. Hole-phonon transition rates are calculated using the deformation-potential theory with one adjustable parameter for hole---optical-phonon interaction strength which is fitted to mobility data at room temperature. This represents the first such calculation for silicon. Very good agreement is found between experiment and theory for both mobilities in silicon and for the conductivity mobility in germanium. The agreement between experiment and theory for the Hall factor in Ge is better than 20%, which may still be improved upon with more reliable deformation-potential parameters. However, the agreement is better than that attained by earlier calculations. The fitted values of the hole---optical-phonon deformation potentials are within bounds of independent estimates for their values. It may therefore be concluded that the deformation-potential theory is well suited for quantitative modeling of phonon-limited mobilities.

Alloy scattering potential in p-type Ga1−xAlxAs

The two-band transport model is expanded in order to analyze the Hall mobility of p-type III–V compound semiconductors. Using this model, the drift and the Hall mobilities can be calculated separately. The alloy scattering as an additional scattering mechanism in alloy semiconductor systems is assumed and the Hall mobility of p-type Ga1−xAlxAs is analyzed. By comparing the theoretically calculated Hall mobility with the reported Hall mobility data of high purity p-GaAs, the acoustic phonon deformation potential and the optical phonon deformation potential were found to be 7.0 and 11.5 eV, respectively. Theoretical calculations showed that the acoustic and nonpolar optical phonon scattering are more prominent than the polar optical phonon scattering at 300 K in the entire Al compositional range. The alloy scattering potential was determined comparing the theoretically calculated values with the Hall mobility of liquid phase epitaxial p-type Ga1−xAlxAs. Best agreement in the compositional variation at room temperature and the temperature variation was found with the alloy scattering potential of 0.7 eV.

Theoretical analysis of optical-phonon deformation potentials in semiconductors

A method to compute the electronic and structural properties of semiconductors self-consistently is applied to analyse the electron-phonon interaction in these crystals. The authors have calculated the optical-phonon deformation potentials along the symmetry directions in Si, Ge and GaAs. Their results confirm the previous ones obtained in more simplified approaches. Quantitative discrepancies with experimental data suggest what must be the next step to be taken in the theoretical effort.

Theory of optical-phonon deformation potentials in tetrahedral semiconductors

A nonlocal pseudopotential theory of the optical-phonon deformation potentials in 11 diamond and zinc-blende semiconductors is presented. The one-phonon deformation potentials associated with the major conduction- and valence-band states at the $\ensuremath{\Gamma}$, $L$, and $X$ point are calculated. The effect of the spin-orbit interaction on the optical deformation potentials is examined in detail. The published experimental data are compared both to one another and to the present theory. In addition, an analytical linear combination of atomic orbitals (LCAO) model is developed which predicts the optical deformation potentials for any tetrahedral semiconductor in a simple yet accurate way. The optical deformation potentials are presented for 37 semiconductors. The LCAO model also yields an analytical expression for the optical deformation potentials in terms of the observed optical gaps of the semiconductors.