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An ensemble Monte Carlosimulation is used to compare high field electron transport in bulk InAs, InP and GaAs. In particular, velocity overshoot and electron transit times are examined. For all materials, we find 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, about 3 kV/cm for InAs, 10 kV/cm for InP and 5 kV/cm for the case of GaAs, We find that InAs exhibits the highest peak overshoot velocity and that this velocity overshoot lasts over the longest distances when compared with GaAs and InP. Finally, we estimate the minimum transit time across a 1 μm InAs sample to be about 2 ps. Similar calculations for InP and GaAs yield 6.6 and 5.4 ps, respectively. We find that the optimal cutoff frequency for an ideal InAs based device ranges from around 79 GHz when the device thickness is set to 1 μm. We thus suggest that indium arsenide offers great promise for future high-speed device applications. The steady-state and transient velocity overshoot characteristics are in fair agreement with other recent calculations.

InAs and InP substrates are one of the promising materials systems for optical communication devices, very high frequency applications and quantum dots (QDs) infrared photodetectors [1,2]. Compared to the InAs/GaAs pair, InAs/InP has a smaller 3.2% lattice mismatch, resulting in the formation of relatively larger QDs. Despite these advantages, because the anions are different in InAs/InP unlike the InAs/GaAs case, complex interface reactions during the growth of the heteroepitaxial layers, such as As/P exchange reaction or as carryover due to the switching of group V sources, make it difficult to grow highquality QD layers and to control their properties [

In order to calculate the electron drift velocity for large electric fields, consideration of conduction band satellite valleys is necessary. The first principles band structure of zincblende InAs, InP and GaAs predicts a direct band gap located at the Γ point and lowest energy conduction band satellite valleys at the X point and at the L point. In our Monte Carlo simulation, the Γ valley, the three equivalent X valleys, the four equivalent L valleys, are represented by ellipsoidal, non-parabolic dispersion relationships of the following form [6-8]:

where, is effective mass at the band edge and is the non-parabolicity coefficient of i-the valley. For each simulation, the motion of 20.000 electron particles is examined, the temperature being set to 300 K and the doping concentration being set to 10^{17} cm^{−3}. The scattering mechanisms included within the simulation are: acoustic phonon scattering, the equivalent and nonequivalent inter-valley non-polar optical phonon scattering, polar optical phonon scattering, ionized impurity scattering, piezoelectric scattering. Band edge energies, effective masses and non-parabolic are derived from empirical pseudopotential calculations.

The principle of this method consists in following the behavior of each electron submitted to an electric field , in real space and the waves vectors space [4-11], for that:

a) We have associated for each carrier which we want to simulate the trajectory, an initial wave vector and an initial vector position.

b) We have used the procedure “self-scattering”. It consists in building a distribution of time following a law whose expression is simplified by the introduction of a fictitious interaction to the null effects known as “selfscattering” [

c) With each of the time step we know, for each carrier, its wave vector and that position at the instant where the measurement begins. Then for a carrier noted “”, we know:

d) We accomplish a coasting flight of duration, so we will have:

e) We look for if there was an interaction during the interval of time by pulling at the fate of a random number:

- If there was no interaction, the state of the carrier is not modified;

- If there was interaction, we place the interaction at the instant and one seeks after the shock by drawing lots from a random number, its state is defined now by [12,13]:

^{17} cm^{−3}. The simulations suggest that the peak drift velocity for zincblende InAs is 3.22 × 10^{7} cm∙s^{−1} while that for InP and GaAs are about 2.5 × 10^{7} cm∙s^{−1} and 2.3 × 10^{7} cm∙s^{−1} respectively. At higher electric fields, intervalley optical phonon emission dominates, causing the drift velocity to saturate at around 1 × 10^{7} cm∙s^{−1} for all materials.

The average carrier kinetic energy as a function of electric field is shown in

This difference can be understood by considering the Γ valley occupancy as a function of field (

lower satellite valley separation and reduced phonon scattering rate within the Γ-valley. The valley occupancy for the Γ, X and L valleys is illustrated in

We have also examined transient electron transport in bulk InAs, InP and GaAs semiconductors. The transient responses of electrons in these materials are compared in

In InAs, very little or no overshoot occurs below the threshold field of 3 kV/cm. As the electric field strength is increased to a value above the threshold field, overshoot begins to occur. As the field strength is increased further, both the peak overshoot velocity increases and the time for overshoot relaxation decreases. In InAs, the velocity overshoot initially increases more rapidly with increasing electric field due to the lower Γ valley effective mass. For example, at 20 kV/cm, the maximum overshoot velocity for InAs is about 10 × 10^{7} m∙s^{−1}, whereas for InP and GaAs it is about 3.74 × 10^{7} m∙s^{−1} and 5.35 × 10^{7} m∙s^{−1} respectively. It is found also that for the same value of electric field above the threshold value, the electron drift velocity is always smaller in InP and

GaAs than in InAs.

the average electron velocity reaches steady-state very quickly with little or no velocity overshoot. It is suggested that in InAs, 3 kV/m is the critical field for the

onset of velocity overshoot. As mentioned above, 3 kV/m also corresponds to the peak in the velocity-field characteristic associated with InAs. Steady-state Monte Carlo simulations suggest that this is the point at which significant upper valley occupation begins to occur, as shown in

In

displaced. Eventually, however, steady-state conditions are achieved, and the electron drift velocity settles to its steady-state value. It is noted that for a given displacement, L, that there exists an optimal applied electric field strength that will minimize the corresponding time to transit, τ. For L set to 1 μm, from

Noting that the cutoff frequency for a device,

where τ is the time of transit [

In this paper, steady-state and transient electron transport results, corresponding to the III-V semiconductors, InAs, InP, and GaAs, were presented, these results being obtained from our Monte Carlo simulations of the electron transport within these materials. Steady-state electron transport was the dominant theme of our analysis. Using valley models to describe the electronic bandstructure, calculated velocity-field characteristics are in fair agreement with other calculations. The velocity-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 Γ valley. Finally, transient electron transport and velocity overshoot in InAs, InP, and GaAs are examined.

For all materials, we find 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, about 3 kV/cm for the case of InAs, 10 kV/m for InP and 5 kV/cm for GaAs. We find that InAs exhibits the highest peak overshoot velocity and that this velocity overshoot lasts over the longest distances when compared with InP and GaAs. We found that the optimal cutoff frequency for an ideal indium-arsenide based device ranges from around 79 GHz when the device thickness is set to 1 μm. We thus suggest that indium arsenide offers great promise for future high-speed device applications. The steady-state and transient velocity overshoot characteristics are in fair agreement with other recent calculations.