Heavy-hole Effective Mass Research Articles

Normal incidence infrared photoabsorption in p-type GaSb/GaxAl1−xSb quantum wells

Absorption of infrared radiation at normal incidence from intervalence-subband transitions is investigated in p-type GaSb/Ga1−xAlxSb quantum wells. Normal incidence absorption is allowed in conventional p-type quantum wells due to the favorable properties of the p-like valence-band Bloch states and the heavy- and light-hole mixing. By using GaSb as the quantum-well material, which has the smallest heavy-hole effective mass of the commonly used III-V semiconductors, absorption can be further enhanced. We find that normal incidence absorption of 3000–6000 cm−1 can be easily achieved in these proposed quantum wells with well widths of 55–90 Å for the wavelength range of 8–12 μm and typical sheet doping concentrations of 1012 cm−2. This absorption strength is comparable to that in the intrinsic Hg1−xCdxTe detector. Strong absorption of normally incident radiation makes this structure a good candidate for infrared photodetection.

Theoretical study of photoresponse to pulsed radiation in n-InSb in the temperature range 77–300 K

The results of a theoretical simulation of a transient experiment in n-InSb in the temperature range 77–300 K, are reported. Minority carrier lifetimes for the three recombination processes, radiative, SRH and Auger, have been calculated at different temperatures using the temperature dependence of intrinsic carrier concentration,n i, and density of states effective mass of heavy holes,m d. It was found that around room temperature the lifetimes for the three processes become comparable and at higher temperatures the Auger lifetime becomes dominant. This fact was ignored in previous work where only SRH and radiative processes were considered in the calculation of effective lifetime. The present results of effective lifetime in n-InSb are in reasonably good agreement with the results obtained previously. The effect of higher time modes on the decay of photoresponse to pulsed radiation is discussed. An instantaneous time constant has been defined and its variation with time at different temperatures has been studied.

Monte Carlo simulation of charge-carrier behavior in electric fields

Monte Carlo simulation has been widely used to study charge-carrier transport in electric fields in GaAs, InP, Si and Ge at high frequencies. New physical ideas for solution of the problems important for solid-state devices for microwave and far-infrared applications are presented and discussed: overshoot of drift velocity, avalanche plasma instabilities, plasma-wave excitation by drifted electrons in GaAs, inversion of population of light and heavy holes in p-Ge, negative differential conductivity due to intervalley and optical-phonon scattering in GaAs and heavy-hole negative effective mass. They have opened new possibilities to develop semiconductor amplifiers and oscillators at frequencies 10 11−10 13 s −1. Some of the predictions are confirmed experimentally.

Electron transport and energy-band structure of InSb

Various n-InSb crystals, pure and Te doped, were prepared using the horizontal zone-refining technique. The electrical conductivity and Hall coefficient of these samples were measured as functions of temperature from 90 to 470 K. By self-consistently fitting the theoretical transport parameters to the experimental data, a set of parameters was refined and/or determined. They include the optical band-gap variation E0(T) = [0.235 − 3.2× 10−4T2/(220 + T)] eV, the heavy-hole effective mass m*hh = (0.20 ± 0.02)me, and the acoustic deformation potential Ed = (13 ± 1) eV. Various scattering mechanisms and impurity phenomena are also discussed.

Intrinsic absorption spectroscopy and related physical quantities of narrow-gap semiconductors Hg 1− xCd xTe

The intrinsic optical absorption has been measured for thin film samples made from bulk Hg 1− x Cd x Te with x ranging from 0.165 to 0.45 and at temperature from 4.2 to 300 K. The energy gap E g, momentum matrix P, effective mass of heavy hole and spin-orbit splitting have been obtained from fitting calculations of absorption curves. The temperature coefficient of energy gap versus composition and the energy gap versus composition and temperature have been derived based on the experimental results. The B-M shift, the Urbach absorption tail and the intrinsic carrier concentration n 1 are also discussed in this paper.

Resonant Tunneling of Holes in Si/Si1−xGex, Quantum Well Structures

EXTENDED ABSTRACT: We investigated resonant tunneling of holes in Si/Si1−xGex double barrier resonant tunneling (DBRT) diodes grown by MBE [1]. The aim of this study was an unambiguous identification of the quantum states involved In the two dominating resonances (Fig. 1), which have been observed by several groups [2],[3], [4]. For this purpose we calculated the transmission probabilities as a function of the well width by means of a transfer matrix method in a one-particle model [5]. The respective effective masses of heavy-holes (hh) and light-holes (lh) in the strained SiGe layers were calculated following Refs. (6) and [7], with appropriate strain corrections added according to Ref. (8); hh/lh mixing [9] was Introduced a posteriori. The calculated resonance positions are in reasonable agreement with experiments (Fig. 2), if the resonance at lower energy is attributed to a hh channel in the well, and the second resonance to a lh channel. Since only hh states are occupied in the emitter cladding layer at the temperatures (≈1.5K) studied, hh/lh coverslon due to the loss in rotational symmetry is involved in the second resonance.

Tunneling-induced optical nonlinearities in asymmetric Al0.3Ga0.7As/GaAs double-quantum-well structures.

A photoluminescence study of the optical response in asymmetric, double-quantum-well structures is presented. The results reveal the existence of strong nonlinearities that can be attributed to electron and hole tunneling through the barrier layer. These nonlinearities arise from the difference between the electron and heavy-hole effective masses. The band bending resulting from spatial charge separation has a strong influence on the measured photoluminescence intensities for peaks associated with transitions between the lowest-energy electron and hole subband states in each quantum well. The system is strongly perturbed by an anticrossing of the second- and third-order heavy-hole subbands. Establishment of the heavy-hole resonant tunneling condition is shown to influence the intensities of the quantum-well photoluminescence peaks strongly. An effective-mass model of the double-quantum-well system reveals how the strength of these effects depends on both interwell coupling and the degree of structural asymmetry. This model successfully predicts the heavy-hole anticrossing observed in photoluminescence.

Band structure parameters of Pb0.25Sn0.72Mn0.03Te semimagnetic semiconductors

Reflectivity spectra of Pb0.25Sn0.72Mn0.03Te samples were measured in the region of the plasma edge. The p-type samples with very high carrier concentrations (pH=2.2*1020-1.2*1021 cm-3) were studied at T=77 K. On the basis of the free-carrier dispersion theory, the experimental values of the susceptibility effective mass, the optical dielectric constant and the optical mobility were determined. Strong carrier concentration dependence of the plasma frequency and the hole effective mass was observed. The analysis of these dependences was made on the basis of a two-valence-band model. The parameters of the model, the energy gap, the effective mass of heavy holes and the energy separation between light- and heavy-hole-band edges, are determined and discussed.

Intrinsic carrier concentration in Hg1−xCdxTe

The effective mass of heavy holes has been determined on the basis of simultaneous analysis of the Hall coefficient and conductivity data obtained in the temperature region 100–300 K on well characterized p-type Hg1−xCdxTe (x≈0·2) samples. Its value is ≈0·7m0. The calculation of intrinsic carrier concentration for 0·19≦ x≦0·3 and 50 Kg ≦T≦ 300 K has been carried out using the above value of the effective mass of holes, Hansen's expression for the band gap and momentum matrix element from magneto-optical measurements.

Effective mass of holes in quaternary InGaAsP alloys lattice-matched to InP

Abstract Rapid growth of optical communications technology over the last decade is largely due to the development of InGaAsP/InP light sources and detectors whose operating wavelengths match the low-loss and low-dispersion windows of silica fibers. Proper design of such devices is, to a large extent, conditional upon the detailed knowledge of relevant material characteristics. In spite of intensive studies of InGaAsP quaternary alloy semiconductors prompted by their practical applications,1–4 there remain a number of important parameters for which only rough estimates are available. Such is the case of the heavy-hole effective mass, which is one of the least-known parameters even in the case of the binary InP.

Temperature dependence of intrinsic carrier concentration and density of states effective mass of heavy holes in InSb

From Hall measurements the temperature dependence of the intrinsic carrier concentration n i in InSb is determined between 200 K and the melting point of the compound (798 K). An empirical formula describing the temperature variation of n i is proposed. From the formula the temperature dependence of the density of states effective mass of heavy holes m d in InSb is determined. The effective mass increases from the minimum value of 0.37 m e at 225 K to a maximum value of 0.45 m e at 650 K. The obtained temperature variation of m d is smaller than found in earlier publications. The value of m d and its temperature dependence are also determined independently from the values of the valence band parameters and their temperature dependences. m d = 0.400 m e decreasing with temperature at the rate of about 10 −5deg −1 is obtained by this method. The discrepency of the results obtained by both methods is discussed and it is shown that the m d determined from the valence band parameters is more reliable. A by-product of the work is the determination of the valence band parameters which are: F = −97.8, H = −4.72 and G = −1.30.

Quantum-confined Stark effect in graded-gap quantum wells

Exciton states in AlxGa1−xAs graded-gap quantum well structures with an electric field perpendicular to the layer have been calculated. The calculations show that, for the ground-state heavy-hole exciton in this quantum well structure, the dependence of Stark shift and the oscillator strengths on the external electric field is quite different from the case of the usual square-shaped quantum well structure, whereas for the ground-state light-hole exciton there is no significant difference between these two quantum well structures. These results can be interpreted in terms of the difference between the heavy-hole effective mass and the light-hole one.

Determination of band offsets in AlGaAs/GaAs and InGaAs/GaAs multiple quantum wells

The determination of valence band offsets Qv by fitting the optical transmission spectra for AlxGa1−xAs/GaAs and InyGa1−yAs/GaAs multiple quantum wells (MQWs) is discussed. The valence band offset Qv is defined as Qv =ΔEv/(ΔEv+ΔEc), where ΔEv and ΔEc are the valence and conduction band discontinuities at the heterojunction. For AlxGa1−xAs/GaAs (Type I for both heavy holes and light holes, i.e., electrons, heavy holes, and light holes are located in the same layers) the energy separation ΔE between the first light and heavy hole subbands in the valence band is used to determine the valence-band offset Qv. In order to improve the precision, MQWs with narrow well widths and higher Al mole fraction x should be used. Further, the inclusion of coupling between the valence and conduction subbands in Kane’s three-band model is also essential. However, Qv is still not determined uniquely by the above energy difference ΔE. Different combinations of Qv and heavy hole effective masses mhh in GaAs can lead to the same ΔE. The forbidden transition E13h in a narrow well can be used to identify the actual values of mhh and Qv. [The designation Enmh(l) refers to the energy separation of the nth conduction subband and mth heavy (light) hole subband.] Following such a procedure, we find that Qv =0.33 and mhh =0.34 m0 for AlxGa1−xAs/GaAs MQWs (x<0.37). For InyGa1−yAs MQWs (Type I for heavy holes and Type II for light holes, i.e., both electrons and heavy holes are located in the same layers, but the light holes are in different layers), the transition energies between the conduction subbands and the light hole valence subbands are much better parameters to determine the band offsets in comparison with the transitions involving the heavy holes. Both the optical measurements and the calculations including the strain effect show that E11l between the first conduction subband and the first light hole valence subband in the MQWs with wider well widths is a sensitive enough parameter to determine the band offsets. By comparing with the optical measurements we obtained Qvh =0.30 and Qvl =−0.23 (Type II) (for 0.13<y<0.19) for the heavy hole and light hole valence band offsets, respectively.

Nonequilibrium electron transport in bipolar devices

The dynamics of nonequilibrium electron transport in bipolar devices have been investigated by calculating minority-carrier elastic and inelastic scattering rates as a function of energy for different majority-carrier concentrations in typical p-type III-V semiconductors. Scattering rates depend on the majority-carrier concentration and a constraint involving the ratio of electron and heavy-hole effective mass.

Effective mass of heavy holes in diamond-like semiconductors

Nonparabolicity of the heavy hole band in diamond-like semiconductors, which occurs within the framework of the three band model with the perturbation from the other bands taken into account to the Lowdin prucedure, is studied. A direct dependence of nonparabolicity on the band anisotropy (caused by the different effect of γ15c and γ12c bands) and the inverse dependence on the magnitude of the spin-orbit splitting is established. A connection between the effective mass of heavy holes and their energy is obtained, which is valid for the majority of diamond-like semicondactors, except for materials with very strong nonparabolicity of the band of silicon type.

Photoluminescence from AlGaAs-GaAs single quantum wells grown on variously oriented GaAs substrates by MBE

Photoluminescence (PL) measurements at low temperatures have been carried out for AlGaAs-GaAs single quantum well (SQW) structures grown on (100), (110), (111)B, (311)A and (311)B GaAs substrates by MBE. A mirror smooth surface was obtained under each optimal growth condition except for (111)B and (110) samples. The (110) surface is cloudy due to the columnar growth. PL results suggest that the height of column is in the order of 10 nm. The film on the (111)B surface consists of a lot of trigonal pyramids, which give a rather broad line width of PL peaks from a SQW compared with the (100) sample. The high optical quality for both (311)A and (311)B SQW's, which is comparable to that for (100) SQW's, is achieved in optimal growth conditions. PL study determines the heavy-hole effective mass of about 0.5 m 0 for the [311] direction.

Inter-band magneto-absorption in a Ga 0.47In 0.53As-Al 0.48In 0.52As quantum well

Transitions between the Landau levels of the N = 1 electron and heavy hole sub-bands have been observed in the inter-band optical absorption of a modulation doped Ga 0.47In 0.53As-Al 0.48In 0.52As multi-quantum well in magnetic fields up to 16T. Results are compared with the results of conduction band cyclotron resonance on the same sample to obtain measurements of both the electron and the heavy hole effective mass, and the results are compared with known values for bulk GaInAs. It is shown that the electron states at high energies are in good agreement with the predictions of three-band k . p theory. This is in contrast to the cyclotron resonance results, for which a substantial polaron correction is required.

Magneto-optics in GaAs-Ga1-xAlxAs quantum wells.

The interband photoconductivity of GaAs-${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As quantum wells has been studied in steady fields of up to 16 T, applied both parallel and perpendicular to the growth axis. In fields parallel to the growth axis, excitonic Landau-level transitions have been identified with Landau indices up to n=12 and energies up to 400 meV above the energy gap of bulk GaAs. Transition energies and diamagnetic shifts have been measured for both allowed (\ensuremath{\Delta}N even) and forbidden (\ensuremath{\Delta}N odd) subband exciton transitions, including a transition at high energy in the widest wells which we tentatively identify as involving a bound state in the spin-orbit split-off band. Landau levels are observed at fields as low as 2.5 T, permitting a determination of exciton binding energy from linear extrapolation. High-field results are fitted using a calculation of the binding energy of two-dimensional excitons as a function of magnetic field. It is found that the exciton binding energy obtained from fitting high-field results is slightly higher than that obtained from low-field measurements, giving exciton binding energies of 16--9 meV, for well widths from 22 to 110 A\r{}. The heavy-hole effective mass for motion in the plane of the layers is found to vary with well thickness, and this is explained by decoupling of the bands.

Photocurrent spectroscopic observation of interband transitions in GaAs-AlGaAs quantum wells under an applied high electric field

A technique using photocurrent spectroscopy under high electric field perpendicular to the heterointerface has been applied to characterize the interband transitions in 105 Å thick GaAs/125 Å thick AlGaAs multiple quantum wells (MQWs). The spectra from MQWs under high electric fields show various clear exciton peaks corresponding to forbidden transitions from heavy- and light-hole subbands to electron subbands. From both allowed and forbidden transition peaks, we determined the interband transition energies between the two lowest electron and four highest hole subbands, and the splitting energies of these suhbands. Our data are in excellent agreement with a finite-square-well calculation using a conduction band offset of 60% of the hand gap discontinuity, a heavy-hole effective mass of 0.34. and a light-hole effective mass of 0.12.

Theoretical study of hole transport in ZnSe

Hole mobilities in ZnSe were calculated by solving the Boltzmann transport equation by the variational method, with all major scattering mechanisms included. Valence-band state symmetries were accounted for, both intra- and interband scattering terms for light and heavy holes were included, and generalized Fermi–Dirac statistics were used throughout. Screening of polar optical phonon and ionized impurity scatterings was also included. The contributions of all component scattering mechanisms to the total hole mobility as a function of hole concentration at 300 and 77 K, have been calculated for the first time. The influence of the compensation ratio, and the concentration of ionized impurities on both the hole mobility and resistivity has also been calculated for the first time; these results are shown to facilitate rapid and direct evaluation of electronic materials quality. In addition, the theoretical model was used to calculate the temperature dependence of the hole mobility in ZnSe, which proved to be in excellent agreement with available experimental data, confirming the choice of scattering parameters. Ultimate limits for the hole mobility in ZnSe at 300 and 77 K were calculated to be about 110 and 2000 cm2/V s, respectively, given zero compensation. Finally a derivation of the heavy-hole effective mass in ZnSe is presented, which yields a value 0.60 m0.