The document describes a Monte Carlo simulation of electron transport properties in InAsxP1-x, InAs, and InP semiconductors at high electric fields and room temperature. It finds that electron velocity overshoot only occurs above a critical electric field that is material dependent. The simulation includes non-parabolic bands and scattering mechanisms. It calculates drift velocities and finds InAs has the highest peak velocity followed by InAsxP1-x alloys then InP. Occupancy of satellite valleys increases with field strength more substantially in InAs. Transient transport shows larger overshoot velocities and faster relaxation in InAs compared to other materials.

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
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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
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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
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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
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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
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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 )
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10
12
0
2
4
6
8
10 12 14 16 18
Time ( ps )
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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
www.ijera.com
[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
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