# Mobility of electrons in Hg1−xCdxTe

01 Mar 1974-Journal of Applied Physics (American Institute of Physics)-Vol. 45, Iss: 3, pp 1463-1465

TL;DR: In this article, an iterative solution of the Boltzmann equation incorporating the twomode nature of the polar optical scattering and the nonparabolicity of the conduction band was proposed.

Abstract: Electron mobility in semiconducting Hg1−xCdxTe at room temperature has been calculated in the range 0.2 ≤ x ≤ 1.0 by an iterative solution of the Boltzmann equation incorporating the two‐mode nature of the polar optical scattering and the nonparabolicity of the conduction band. The effects of the deformation potential acoustic, ionized impurity, and electron‐hole scattering have also been considered. The calculated results agree with the measured values to within a factor of 2 for x = 0.6 and 0.4, whereas for x = 0.2, 0.8, and 1.0 the agreement is within a factor of 1.4.

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TL;DR: In this article, a full-band Monte Carlo model was developed for understanding the carrier multiplication process in HgCdTe infrared avalanche photodiodes based on a realistic electronic structure obtained by pseudopotential calculations and a phonon dispersion relation determined by ab initio techniques.

Abstract: A full-band Monte Carlo model has been developed for understanding the carrier multiplication process in HgCdTe infrared avalanche photodiodes. The proposed model is based on a realistic electronic structure obtained by pseudopotential calculations and a phonon dispersion relation determined by ab initio techniques. The calculated carrier–phonon scattering rates are consistent with the electronic structure and the phonon dispersion relation, thus removing adjustable parameters such as deformation potential coefficients. The computation of the impact ionization transition rate is based on the calculated electronic structure and the corresponding wavevector-dependent dielectric function. The Monte Carlo model is applied to investigate key performance figures of long-wavelength infrared (LWIR) and mid-wavelength infrared (MWIR) HgCdTe avalanche photodetectors such as carrier multiplication and noise properties. Good agreement is achieved between simulations and experimental results. The multiplication process in LWIR (λc = 9.0 μm at 80 K) and MWIR (λc = 5.1 μm at 80 K) devices is found to be initiated only by electrons, as expected from excess noise measurements. This single-carrier multiplication behavior can be traced back to the details of the computed valence-band structure and phonon scattering rates.

39 citations

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TL;DR: In this paper, the role of nine different scattering mechanisms (ionized impurity, polar and non-polar optical, acoustic, dislocation, strain field, alloy disorder, neutral impurity and piezoelectric) in limiting hole mobilities in p-type Hg1−xCdxTe crystals was analyzed.

Abstract: In this paper, we analyze and discuss the roles of nine different scattering mechanisms—ionized impurity, polar and nonpolar optical, acoustic, dislocation, strain field, alloy disorder, neutral impurity, and piezoelectric—in limiting the hole mobilities in p-type Hg1−xCdxTe crystals. The analysis is based on obtaining a good fit between theory and experiment for the light and heavy hole drift mobilities by optimizing certain unknown (or at the most vaguely known) material parameters such as the heavy hole mobility effective mass, degree of compensation, and the dislocation and strain field scattering strengths. For theoretical calculations, we have adopted the relaxation time approach, keeping in view its inadequacy for the polar scattering. The energy dispersive hole relaxation times have been drawn from the published literature that take into account the p-symmetry of valence band wave functions. The temperature dependencies of multiple charge states of impurities and of Debye screening length have been taken into account through a numerical calculation for the Fermi energy. Mobility data for the present analysis have been selected from the HgCdTe literature to represent a wide range of material characteristics (x=0.2–0.4, p=3×1015–1×1017 cm−3 at 77K, μpeak≅200-1000cm2V−1s−1). While analyzing the light hole mobility, the acoustic deformation and neutral impurity potentials were also treated as adjustable. We conclude that
• the heavy hole mobility is largely governed by the ionized impurity scattering, unless the strain field or dislocation scattering below 50K, or the polar scattering above 200K, become dominant;
• the light hole mobility is mainly governed by the acoustic phonon scattering, except at temperatures below 30K where the neutral impurity, strain field and dislocation scattering also become significant;
• the intervalence scattering transitions make negligible impact on the heavy hole mobility, but virtually limit the light hole mobility;
• the alloy disorder scattering does not dominate in any temperature region, although it exercises some influence at intermediate temperatures;
• the heavy hole mobility effective mass ratio mhh/mo∼-0.28–0.33 for crystals with x<0.4; and
• the light hole band deformation potential constant is ∼12 eV.

23 citations

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TL;DR: In this article, a simple Monte Carlo model is developed for understanding the multiplication process in HgCdTe infrared avalanche photodiodes and the impact of physical and technological parameters.

Abstract: A simple Monte Carlo model is developed for understanding the multiplication process in HgCdTe infrared avalanche photodiodes and the impact of physical and technological parameters. A good agreement is achieved between simulations and experimental measurements of gain and excess noise factor. In both cases, an exponential gain and extremely low noise-F ~ 1 for multiplication gains up to 1000-were observed on 5.1-mum cutoff devices at 77 K, indicative of a single carrier impact ionization. A comparison study is presented to explain the effect of different combinations of scattering processes on the avalanche phenomenon in HgCdTe.

23 citations

### Cites background or methods from "Mobility of electrons in Hg1−xCdxTe..."

...5 eV [29], the volumic mass ρ to 7000 kg/m(3), and the sound velocity vs to 3000 m · s−1 in Hg0....

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...studied electron transport in HgCdTe using the relaxation time approximation method [29]–[31] or MC simulations [32]–[34]....

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TL;DR: In this article, experimental measurements of concentration and mobility for as-grown Hg 1-x Zn x Te, and after "stoichiometric" annealing, are presented.

Abstract: Experimental measurements of concentration and mobility for as-grown Hg 1-x Zn x Te, and after “stoichiometric” annealing, are presented. Experimental mobility values are compared with calculated ones. Results on the kinetics of p-to-n conversion are also given.

22 citations

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TL;DR: In this article, the random element isodisplacement (REI) model has been modified to include the polarization field, thereby enabling it to predict the long-wavelength longitudinal optic frequencies of a mixed crystal.

Abstract: The random-element-isodisplacement (REI) model has been modified to include the polarization field, thereby enabling it to predict the long-wavelength longitudinal optic frequencies of a mixed crystal. A criterion has been obtained to determine whether a given mixed crystal will exhibit "one-mode" or "two-mode" behavior. Under certain conditions the modified REI (MREI) model may also be made to work for mixed crystals with one-mode behavior. The so-called "virtual-crystal model" applicable to this type of crystals becomes a special case of the MREI model. Given the properties of the "pure" end-members $\mathrm{AB}$ and $\mathrm{AC}$, the MREI model then can determine whether $A{B}_{1\ensuremath{-}x}{C}_{x}$ is going to display one-mode or two-mode behavior, and can predict the concentration dependence of the TO and LO modes. A large number of examples of both types of mixed crystals is given.

375 citations

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Bell Labs

^{1}TL;DR: In this paper, the drift mobilities of the five direct-gap III-V semiconductors GaAs, GaSb, InP, InAs, and InSb are presented as a function of temperature.

Abstract: The electron drift mobilities of the five direct-gap III-V semiconductors GaAs, GaSb, InP, InAs, and InSb are presented as a function of temperature. Polar-mode, deformation-potential acoustic, and piezoelectric scattering are included, as well as nonparabolic conduction bands and the corresponding electron wave functions. The drift mobility follows exactly from the assumed model by a simple iterative technique of solution which retains all the advantages of variational techniques without, however, the need for excessive mathematical detail. Piezoelectric scattering is shown to be considerable in GaAs for temperatures below 100 \ifmmode^\circ\else\textdegree\fi{}K. The agreement between theory and experiment for GaAs is satisfactory.

295 citations

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TL;DR: In this article, the electron distributions were solved for the coupled Boltzmann equations of the GaAs under a set of approximations that are fair for fields around the beginning of the negative-differential-resistance region, but should be quite good at higher fields.

Abstract: We have solved the coupled Boltzmann equations for the electron distributions in ${\ensuremath{\Gamma}}_{1}$ and ${X}_{1}$ minima of GaAs under a set of approximations that are fair for fields around the beginning of the negative-differential-resistance region, but should be quite good at higher fields. Intervalley, polar and other relevant intravalley scattering processes have been included. Nonparabolicity of the central minimum has been taken into account. The effect of space-charge scattering has also been considered. From the distributions, we have calculated as functions of field the average drift velocity, the variation of the valley populations, diffusion constants, and mobilities in each of the valleys, etc. The validity of the principal approximations made, such as neglect of the ${L}_{1}$ minima, is discussed. The present experimental situation is examined, and some tentative explantations are offered for the large differences between the various measurements of drift velocity versus field.

242 citations

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TL;DR: RefReflection spectra of CdxHg1-xTe single crystals with 0 ≤ x ≤ 0.54 were measured in the spectral region from 1000 cm −1 to 25 cm−1 at 77 K and 300 K as discussed by the authors.

Abstract: Reflection spectra of CdxHg1-xTe single crystals with 0 ⩽ x ⩽ 0.54 were measured in the spectral region from 1000 cm−1 to 25 cm−1 at 77 K and 300 K. They were analyzed by Kramers-Kronig integrations. The mixed crystals show two transverse optical modes. Their frequencies vary regularly with respect to the alloy composition. For x < 0.34 an additional reflection band was observed around 100 cm−1 which depends strongly on temperature. It is tentatively attributed to a two-phonon subtractive process LO-TA.

160 citations