The Study and Simulation of the Electron Transport Phenomena on Bulk Hg1-xCdx Te Based on an Ensemble Monte Carlo Method

Copyright: © 2013 Tahir HM, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.


Introduction
Mercury cadmium telluride (HgCdTe) is the material system of choice to fabricate high performance photovoltaic and avalanche detectors over the entire infrared spectral region [1]. Several groups have reported an exponential gain curve and extremely low multiplication noise in electron injected HgCdTe Avalanche Photodetectors (APDs) at temperatures in the range of 77 K to 260 K for a variety of cutoff wavelengths in the MWIR and LWIR bands [2,3]. These exceptional characteristics of HgCdTe APDs are indicative of the exclusive impact ionization of the electrons and of dead-space effects that tend to introduce order in the random impact ionization process, i.e., a historydependent gain mechanism [4,5]. The electron impact ionization process in HgCdTe becomes important at relatively small electric fields due to the high mobility of electrons and their low impact ionization threshold energy. The high gain at low bias and the low noise factor make HgCdTe APDs particularly well suited for several applications, including night vision, nondestructive control and medical imaging, multicolor focal-plane arrays (FPAs) for astronomy, and photon counting. Despite this interest, a complete description of the transport properties of HgCdTe alloys is still lacking, especially in the high-field regime. The low field mobility has been the only transport parameter that has been the object of extensive theoretical [6] and experimental [7,8] investigations. The electron drift velocity characteristic in CdTe as a function of temperature and electric field was measured by the transient-charge technique by Canali et al. [9] Borsari and coworkers [10] performed Monte Carlo calculations of electron transport in CdTe to investigate the negative differential mobility of this material, which was attributed to the randomizing effect of intervalley scattering rather than to the population of lower-mobility valleys [10].
The current demand growth of new components capable of operating at high power, high frequency, high temperatures and convergence towards miniaturization has lead to the development of new fields of nanotechnology based on II-VI semiconductor. Interest in nanostructures based on II-VI semiconductor narrow gap containing mercury (such as superlattices HgTe / CdTe) was due to their advantages over alloys with cadmium telluride Mercury (MCT: HgCdTe). The ternary alloy Hg 1-x Cd x Te is a semiconductor bandgap direct; in our work we are interested in the ternary compound

Model Description
The most important input to Monte Carlo transport simulation is the electronic structure of the material to be studied [11]. The electronic structures of the binary compounds CdTe and HgTe have been computed by using the Nonlocal Empirical Pseudo Potential Method (NL-EPM), while the ternary alloy HgCdTe has been studied by using NL-EPM within a disorder-corrected Virtual Crystal Approximation (VCA). The computed electronic structures, which take into account spin-orbit interactions, accurately replicate the available experimental data and ab initio information. Figure 1 shows the NL-EPM electronic structure of HgCdTe. The presence of secondary valleys at the L point (intervalley separation energy 1.37 eV) can be noticed. Besides the electronic structure, the carrier-phonon interaction at high energies is the critical piece of information to be evaluated in order to study the carrier dynamics at high fields and impact-ionization-related phenomena. Empirical fits to low-energy transport data are still used to determine the electron-phonon coupling constants, and these values are used for simulation beyond their expected range of validity. The lack of reliable information on the carrier-phonon interaction has always affected the ability to treat the impact ionization process. Scarce information is available on the electron-phonon deformation potentials in HgCdTe. Chattopadhyay and [12] suggested a theoretical value of 9.5 eV for the electron acoustic deformation potential in HgCdTe, adopting the value reported by Rode for CdTe [13]. To the authors' knowledge, no information is available for the whole deformation potential coefficients.
The electronic transport is always described by models based on the resolution of the Boltzmann equation who characterizes the modification of the particles state caused by various actions. Thus, including the charges transport in semiconductors, the Monte Carlo method is a statistical method, as a popular and effective mathematical tool for the study and analysis of the physical phenomena.
In this work we have to use a three valleys model of the conduction band, Г, L, X considered isotropic but not parabolic. Our model is developed considering the deformation potential of each considered valley, the energy gap structures, and the main scattering mechanisms in details. The concentrations of electrons in L and X valleys relative on the minimum Г are: Where E ΓL and E ΓX are the separation energies between Г-L and Г -X respectively.

Results
The number of electrons simulated is 20,000 electrons subject to different values of the electric field under different temperatures. The implementation of this model is made by taking the following steps: for each electron simulated, we associate with initial position and an initial wave vector, and using the process "self scattering"; we introduce a fictitious scattering which aims to establish a time distribution. The Monte Carlo model adopted in this work is used for calculating and retrieval features of electronic transport in the HgCdTe alloy in the transitional and stationary regime. The calculation is made for electric fields ranging from 0 to 50 KV for different values of temperature.
The average velocity is one of the key parameters to describe the behaviour of a compound. In our study we focus on the modulus of the velocity and the drift velocity is an average velocity of the course. Indeed, the electrons under the influence of thermal energy will have a random way, and therefore they have no path. But when subjected to an electric field their way is more random and the distance travelled is not zero.
After a collision the electron will have a zero velocity component in the direction parallel to the electric field, but the effect of thermal agitation that the electron back to speed, the electrons move in the opposite direction of the field.
In figure 2, we note that the drift velocity increases with the electric field and then it reaches a saturation value equal to 6.16.10 7 Cm/S, which corresponds to a critical electric field is 1.2 kV/cm. Thereafter, the drift velocity decreases with the field until it reaches a value of 7 10 1.08.
Cm S from an electric field equal to 14 kV/cm.
In figure 3, when the carriers are subjected to an electric field they will gain energy. We identify two phases, the energy of the three module valleys Γ, L and X. Once the electric field is applied, the energy of the carriers increases very rapidly to a maximum of energy which is 190 meV. After a very short period of time (about 10 -14 S), we see that the energy becomes constant.
In figure 4, we present the curves for different drift velocities in electric fields with time at 300 K. We note that the velocity exhibits a maximum for the strong fields. This is due mainly to the wide variation of angular momentum and energy relaxation as a function of electron energy, so the transient over shoot in velocity is typically observed when the applied electric field is quite high contribution to the critical field; the electrons can reach a maximum energy as the time is small compared to the energy relaxation. Figure 4 shows the shape of the electron drift velocity versus time for an electric field of 20 kV, and a concentration of 20 3 1e Cm − at 300 kV. This curve has four phases: • For t <0.2ρS the velocity increases linearly with time.
• For 0.2ρS < t <0.3ρS the velocity continues to grow but more slowly. There is a maximum of 7 1.910 / Cm well above the stationary value corresponding to the applied field, so there is a phenomenon of over speed.
• Between 0.3 and 2ρs, the velocity decreases rapidly to the steady state.
• In the last phase (t 7 10 0.9. . Cm S elocity remains unchanged, it is equal to the steady velocity When the electrons are subjected to fields largely varying in time, a phenomenon of over-speed appears. This phenomenon was often studied by many authors, which did not fail to underline the practical interest of this phenomenon, in particular on the level of the submicronic components. Figure 5 shows the variation of the drift velocity, energy carriers and the population in the three valleys Γ, L and X with the applied electric field for three different temperatures of the network (T=200 K, T=300 K and T=400 K), for a mole fraction of x=0.3 HgCdTe alloy studied.
At high temperatures, the thermal energy increases, the disorder in the material increases, which implies that collisions at temperature T=200 K with the lattice vibrations are less important than temperature T=300 K and T=400 K, by carriers that are subject to thermal agitation disrupts this low and less movement of the carriers.

Conclusion
Research in modeling devices are focused on developing analytical descriptions of the physical devices. In this study we addressed a number of issues related to the phenomenon of electron transport carriers in semiconductors II-VI and more precisely in the ternary alloy HgCdTe. We essentially used the program Monte Carlo simulation to describe the functioning of this complex system from the elementary laws governing the movement of electrons. The principle of this approach is to simulate the behavior of electrons in the conduction band using the statistical method of Monte Carlo.
The transient electron transport in the HgCdTe alloy was studied. The characteristics and properties of the material obtained by this model, compared on many experimental reference frames, are satisfactory and they inform us about electronic dynamics as well as the behaviour electric high and low fields and high temperatures of these materials. Furthermore, this results proves the usefulness of this technique as an excellent tool for analysis and simulation of electronic transport phenomena in the semiconductor material, unless the query what is the good definition of physical parameters material which are sometimes poorly understood.