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  1. 1. F. Nofeli et al.Int. Journal of Engineering Research and Application ISSN : 2248-9622, Vol. 3, Issue 5, Sep-Oct 2013, pp.732-735 RESEARCH ARTICLE OPEN ACCESS Monte Carlo Simulation in InAsxP1-X, InAs and InP at High Field Application 1 F. Nofeli and 2M. Abedzadeh Fayzabadi 1 Physics Department, Khayyam Higher Education University, Mashhad, Iran 2 Physics Department, Payame Noor University, Fariman, Iran Abstract We study how electrons, initially in thermal equilibrium, drift under the action of an applied electric field within bulk zincblende InAsxP1-x, InAs and InP. Calculations are made using a non-parabolic effective mass energy band model, Monte Carlo simulation that includes all of the major scattering mechanisms. The band parameters used in the simulation are extracted from optimized pseudopotential band calculations to ensure excellent agreement with experimental information and ab-initio band models. The effects of alloy scattering on the electron transport physics are examined. For all materials, it is found that electron velocity overshoot only occurs when the electric field is increased to a value above a certain critical field, unique to each material. This critical field is strongly dependent on the material parameters. Key words: Non-parabolic; pseudopotential; alloy scattering; velocity overshoot. Improved electron transport properties are I. Introduction one of the main targets in the ongoing study of binary InP and InAs offer the pospect of mobilities comparable to GaAs and are increasingly being and ternary InP, InAs and InAsxP1-x materials. The developed for the construction of optical switches Monte Carlo technique has proved valuable for and optoelectronic devices. While GaAs has been studying non-equilirium carrier transport in arange of extensively studied [1-3], InAs and InP and alloy semiconductor materials and devices [6-7]. However, constructed from them like InAsxP1-x, have yet to carrier transport modeling of InP and InAs materials examined to the same extent. Alloys of InAs and InP has only recently begun to receive sustained attention, have unfortunately proved to be a difficult material to now that the growth of compounds and alloys is able work with in practice and very little experimental to produce valuable material for the electronics work on InAsxP1-x material and devices have been industry. In this communication we present Monte done because of technical problems in forming Carlo calculations of steady-state and transient Schottky contacts with sufficiently high barrier electron transport conditions in InP, InAs and potentials. Nevertheless some experimental work has InAsxP1-x. We demonstrate the effect of injection been done on other types of InAs and InP field-effect energy and electric field on the transient electron transistor, most notably MISFETs [4-5], and there is transport. The differences in transport properties are every reason to be optimistic that some form of analyzed in terms of important material parameters. heterojunction under the gate may well overcome the Our current approach employs a one-dimensional problem of the low barrier. ensemble Monte Carlo technique to investigate 732 | P a g e
  2. 2. F. Nofeli et al.Int. Journal of Engineering Research and Application ISSN : 2248-9622, Vol. 3, Issue 5, Sep-Oct 2013, pp.732-735 steady-state and transient electron transport in InP, III. Results InAs and InAsxP1-x. However, the momentum space treatment is three dimensional, and the scattering Figure 1 shows the simulated velocity-field events consider all three dimensions. Specifically, characteristics of zincblende InAs, InP, InAs0.2P0.8 our model includes the three lowest valleys of the and InAs0.8P0.2 semiconductors at 300 K, with a conduction band with non-parabolicity. background doping concentration of 1017 cm-3, and with the electric field applied along one of the cubic II. Model details axes. The simulations suggest that the peak drift Our ensemble Monte Carlo simulations of velocity for zincblende InAs is 3.4 ×105 ms-1, while electron transport in zincblende InP, InAs and that for InP, InAs0.2P0.8 and InAs0.8P0.2 are about InAsxP1-x are similar to those of Arabshahi et al  2.3 ×105 ms-1, 2.5×105 ms-1 and [8-9]. As indicated earlier, a three-valley model for respectively. At higher electric fields, intervalley the conduction band is employed. optical phonon emission dominates, causing the drift In order to calculate the electron drift velocity for large electric fields, consideration of 3.2×105 ms-1, velocity to saturate at around 1.5 ×105 ms-1 for all materials. conduction band satellite valleys is necesasry. The first-principles band structure of zincblende InAs, 3.5 InAs InP and InAsxP1-x predicts a direct band gap located 3.0 satellite valleys at the X point and at the L point. In -1 our Monte Carlo simulation, the  valley, the three InAs0.8P0.2 InAs0.2P0.8 2.5 5 Drift velocity ( 10 ms ) at the  point and lowest energy conduction band equivalent X valleys, the four equivalent L valleys, are represented by ellipsoidal, nonparabolic dispersion relationships. We assume that all donors InP 2.0 1.5 1.0 GaAs 0.5 are ionized and that the free-electron concentration is 0.0 equal to the dopant concentration. For each 0 500 1000 1500 2000 2500 3000 Electric field ( kV/m ) simulation, the motion of ten thousand electron particles are examined, the temperature being set to 300 K, and the doping concentration being set to 1017 cm-3. In the case of the ellipsoidal, Figure 1: Calculated steady-state electron drift velocity in bulk zincblende InAs, InP, InAs0.2P0.8 non-parabolic conduction valley model, the usual and InAs0.8P0.2 using non-parabolic band models at Herring-Vogt transformation matrices are used to room temperature. map carrier momenta into spherical valleys when particles are drifted or scattered. Electrons in bulk The calculated drift velocities apparent from material suffer intravalley scattering by polar optical, figure 1 are fractionally lower than those that have non-polar optical and acoustic phonons scattering, been calculated by Adachi et al. [14-16], who intervalley phonons, and ionised impurity scattering. assumed an effective mass in the upper valleys equal Acoustic scattering is assumed elastic and the to the free electron mass. The threshold field for the absorption and emission rates are combined under onset the equipartition approximation, which is valid for conduction band valleys is a function of the lattice temperatures above 77 K. Elastic ionised intervalley separation and the density of impurity scattering is described using the screened states in the satellite valleys. Coulomb potential of the Brooks-Herring model. The valley occupancies for the , X and L valleys are of significant scattering into satellite electronic illustrated in figure 2 and show that the inclusion of 733 | P a g e
  3. 3. F. Nofeli et al.Int. Journal of Engineering Research and Application ISSN : 2248-9622, Vol. 3, Issue 5, Sep-Oct 2013, pp.732-735 the satellite valleys in the simulation is important. Significant intervalley scattering into the satellite 1.0 InAs0.2P0.8 InAs0.8P0.2 1.0 valleys occurs for fields above the threshold field for Gamma-valley each material. This is important because electrons 0.8 Electron occupancy (%) which are near a valley minimum have small kinetic energies and are therefore strongly scattered. It is apparent that intervalley transfer is substantially larger in InAs over the range of applied electric fields shown, due to the combined effect of a lower  effective mass, lower satellite valley separation 0.8 0.6 0.6 X-valley 0.4 0.4 0.2 energy, and slightly lower phonon scattering rate 0.2 within the  valley. L-valley 0.0 We have also examined transient electron 0 1000 0.0 3000 0 2000 1000 Electric Field (kV/m) transport in bulk InAs, InP, InAs0.2P0.8 and 2000 Electric Field (kV/m) InAs0.8P0.2 semiconductors. The transient response of electrons in these materials are compared in figure Figure 2: Fractional occupation of the central  and 3 for fields up to 1600 kVm-1 strengths. In InAs, we satellite valleys of zincblende InAs, InP, InAs0.2P0.8 find very little or no overshoot occurs below the and InAs0.8P0.2 as a function of applied electric threshold field of field using the non-parabolic band model at room 400 kVm-1. As the electric field strength is increased to a value above the threshold temperature. field, overshoot begins to occur. As the field strength In InAs, the velocity overshoot initially is increased further, both the peak overshoot velocity increases more rapidly with increasing electric field increases and the time for overshoot relaxation due to the lower  valley effective mass. For decreases. example, at 1600 kVm-1, the maximum overshoot velocity for InAs is about 8×105 ms-1, whereas for 1.00 InP, InAs0.2P0.8 and InAs0.8P0.2 it is about 4×105 1.00 InAs Gamma-valley 0.80 Gamma-valley 0.80 ms-1, 5×105 ms-1 and 7×105 ms-1, respectively. It is found also that for the same value of the electric field above the threshold value, the electron drift velocity 0.60 X-valley 0.60 X-valley is always smaller in InP, InAs0.2P0.8 and InAs0.8P0.2 than in InAs. 0.40 0.40 0.20 0.20 5.0 InAs0.2P0.8 8 InAs0.8P0.2 7 L-valley L-valley 1000 2000 Electric Field (kV/m) 3000 0 1000 2000 Electric Field (kV/m) 6 3000 5 0 1600 kV/m 4.0 0.00 800 kV/m -1 0.00 Drift velocity (10 ms ) Valley occupancy ratio (%) InP 5 3.0 4 2.0 400 kV/m 3 2 1.0 1 0.0 0 0 2 4 6 8 Time ( ps ) 10 12 0 2 4 6 8 10 12 14 16 18 Time ( ps ) 734 | P a g e 3000
  4. 4. F. Nofeli et al.Int. Journal of Engineering Research and Application ISSN : 2248-9622, Vol. 3, Issue 5, Sep-Oct 2013, pp.732-735 [5] 5 -1 Drift velocity (10 ms ) (1983) 400 kV/m 800 kV/m 1600 kV/m InP 4 -1 5 Whitehouse, Electron. Lett., 18, 534 (1982) [6] 2 C. Moglestue, Monte Carlo Simulation of Semiconductor Devices, 1993, Chapman and Hall 0 0 Drift velocity (10 ms ) D. C. Cameron, L. D. Irving, C. R. 2 4 6 8 10 12 [7] 10 InAs 8 C. Jacoboni and P. Lugli, The Monte Carlo Method for semiconductor and Device 6 Simulation, 1989, Springer-Verlag 4 [8] 2 H. Arabshahi, M. R. Benam and B. Salahi, Modern Physics Letters B., 21, 1715 (2007) 0 0 2 4 6 8 10 12 [9] Time ( ps ) H. Arabshahi, Modern Physics Letters B., 21, 199 (2007) Figure 3: A comparison of the velocity overshoot [10] effect exhibited by InAs, InP, InAs0.2P0.8 and B. E. Foutz, L. F. Eastman, U. V. Bhapkar and M. Shur, Appl. Phys. Lett., 70, 2849 InAs0.8P0.2 semiconductors as calculated by our (1997) Monte Carlo simulation. The donor concentration is [11] 1017 cm-3 and the temperature is 300 K. U. V. Bhapkar and M. S. Shur, J. Appl. Phys., 82, 1649 (1997) [12] IV. Conclusions J. D. Albrecht, R. P. Wang and P. P. Ruden, K F Brennan, J. Appl. Phys. 83, 2185 (1998) Electron transport at 300 K in bulk [13] zincblende InAs, InP, InAs0.2P0.8 and InAs0.8P0.2 have been simulated using an ensemble Monte Carlo simulation. Using valley models to describe the E. O. Kane, J. Phys. Chem. Solids, 1, 249 (1957) [14] S. Adachi, GaAs and Related Materials, Bulk semiconducting and Superlattice electronic bandstructure, calculated velocity-field characteristics are in fair agreement with other calculations. Thevelocity-field characteristics of the materials show similar trends, reflecting the fact that all the semiconductors have satellite valley effective densities of states several times greater than the central  valley. References [1] K. Brennan, K. Hess, J. Y. Tang and G. J. Iafrate, IEEE Trans. Electron Devices, 30, 1750 (1983) [2] N. Newman, T. Kendelewicz, L. Bowman and W. E. Spicer, Appl. Phys. Lett., 46, 1176 (1985) [3] N. Newman, V. Schilfgaarde, T. Kendelewicz and W. E. Spicer, Mater. Res. Soc. Symp. Proc., 54, 443 (1986) [4] D. C. Cameron, L. D. Irving, C. R. Whitehouse, Thin Solid Films.,103, 61 735 | P a g e