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Temperature and doping dependencies of hot electron transport properties in bulk GaP, InP and [Ga.sub.0.5][In.sub.0.5]P.


The study of electron transport in semiconductors at high electric fields has reached an important stage in the last few years. Nowadays the microscopic transport model based on the Monte Carlo method seems to be adequate for studying of electronic transports characteristic in bulk and semiconductor devices (Fischetti and Laux, 1991; Izuka, 1990). In this paper we deal with electron transport in bulk of GaP, InP and [Ga.sub.0.5][In.sub.0.5]P which can used in design and analysis of electronic device performance in various condition (Besikci, 2000).

Because of high mobility and high saturation velocity, InP has become an attractive material for electronic devices of superior performance among the III-phosphates semiconductors (Ghani, et al, 2003). Therefore study of the electron transport in group III-phosphates is necessary. GaP possesses an indirect band gap of 0.6 eV at room temperature whereas InP and [Ga.sub.0.5][In.sub.0.5]P have a direct band gap about 1.8 eV and 1.5 eV, respectively (Martienssen, 2005; Vurgaftman, 2001).

In this article, the transport properties of bulk group III-phosphates in the temperature range from 300 to 600 K and in the applied electric field range from 0 to 500 kV/cm will be discussed. Simple, analytic expressions for the temperature and ionized impurity concentration dependences of high-field drift velocity are then proposed for incorporation into the group III-phosphates (Arabshahi, 2008; Arabshahi, et al, 2008;). High-field transport properties in these materials are dominated by band structure effects, i.e, electron transfer to satellite valleys of the conduction band, which lead to a peak and a subsequent decrease in the drift velocity with increasing electric field. Here, the temperature dependence of this phenomenon is examined and the drift velocity peak is characterized in terms of an analytic expression (Carlo Jacoboni, 1983).

This paper is organized as follows. Details of the conduction band parameters and the employed simulation model which is used are presented in section 2, and results for simulation carried out are interpreted in section 3.

2. Simulation model

An ensemble Monte Carlo simulation has been used to investigate the electron transports in bulk semiconductors. This program simulated the trajectories of ten thousand quasi-particles as they move through the material under the influence of external forces and subject to random scattering events.

In order to calculate the electron drift velocity for large electric fields, consideration of conduction band satellite valleys is necessary (Yu, Carbona, 2001). One of the main inputs of the model is the energy band structure. The first-principles band structure of InP and [Ga.sub.0.5][In.sub.0.5]P predicts a direct band gap located at the [GAMMA] point and lowest energy conduction band satellite valleys at the X point and at the L point. In our Monte Carlo simulation, the [GAMMA] valley, the three equivalent X valleys, and the four equivalent L valleys were represented by spherical, non-parabolic, analytical effective mass expressions of the following form (Foutz, B.E., L.F. Eastman, 1997; Bhapkar, U.V. and M.S. Shur, 1997; Albrecht, J.D., R.P. Wang, 1998),

E(k)[1 + [[alpha].sub.i]E(k)] = [h.sup.2] [k.sup.2]/2[m.sup.*] (1)

Where [m.sup.*] is effective mass at the band edge and [[alpha].sub.i] is the non-parabolic coefficient of the i-th valley. Nonparabolic coefficients are obtained according to the Kane (1957) model as

[[alpha].sub.i] = 1/[E.sub.g] [1 - 2[m.sup.*]/[m.sub.0]][1 - [E.sub.g][DELTA]/3([E.sub.g] + [DELTA])([E.sub.g] + 2[DELTA]/3)] (2)

Where Eg is the band-gap energy and ~ is the spin-orbit spilling. The band structure and material parameters necessary for calculating the scattering probabilities used in the present Monte Carlo simulation are given in table 1 and 2.

The Monte Carlo model includes polar optical, acoustic phonon, ionized impurity and non-polar inter-valley phonon scattering which are the most important mechanisms that affect on the electron motion in the material (Jacoboni, 1989; Ridley, 1993).

3. Simulation results and discussion

Average electron energy as function of applied electric field has depicted in figure 1 for temperatures up to 600K. Many aspect of electron behavior which has influenced by an external electric field, can be explained by this figure. It is clearly see that energy curves demonstrate a higher monotonic increasing with increasing of external field at first. After this region, the energy only increase slowly with increase of electric field, this feature is due to the electron transfer from the [GAMMA] valley to L and X valleys. The mean energy initial rise is due to the dominant contribution of the acoustic scattering mechanism until it reaches to a certain threshold value about 10, 100 and 2 kV/cm for InP, GaP and [Ga.sub.0.5][In.sub.0.5]P, respectively. This increase is due to the quasi-elastic nature of the acoustic scattering and ionized impurity scattering (Jacoboni, 1989). With increasing electric field more than the threshold fielded, the electrons have not enough energy to make the inter-valley scattering. Beyond this value, the optical scattering mechanisms play a drastic role rather than acoustic and ionized impurity scattering. Since this process is inelastic, electron energy curves have sensitive variation in its slope; in fact it does not increase as fast as increasing in initial fields.


Figure 2 shows the velocity-field characteristic in bulk InP, GaP and [Ga.sub.0.5][In.sub.0.5]P at room temperature and with a background doping concentration of [10.sup.16] [cm.sup.-3]. As can be seen, velocity-field characteristic exhibit a peak for InP and [Ga.sub.0.5][In.sub.0.5]P at about 2.3 x [10.sup.5] and [1.sup.x] [10.sup.5] [ms.sup.-1], respectively. The velocity-field curves typically present a decrease of the electron velocity, when the electric fields increase above the threshold value. This effect is due to the transfer of electrons from central [GAMMA] valley with low energy state and high mobility to higher valley with high energy state and low mobility. GaP has an indirect band gap and at lower electric fields, so electrons occupied X satellite valley at first; so it is expected that its velocity-field curves does not have a peak. At higher electric field, inter-valley optical phonon emission dominates causing the drift velocity to saturate at around 0. [6.sup.x] [10.sup.5] [ms.sup.-1]. Also we present experimental result for velocity-field characteristic of GaAs and InP in room temperatures. It is seen that our simulated results are in fair agreement with other results (Brennan et al. 1983).


Figure 3 shows the calculated electron drift velocity as a function of electric field strength for temperatures of 300, 450 and 600 K. The decrease in drift mobility with temperature at low fields is due to increased intra-valley polar optical phonon scattering whereas the decrease in velocity at higher fields is due to increased intra and inter valley scattering.


It can be seen from the figure that the peak velocity also decreases and moves to higher electric field as the temperature is increased. This is due to the general increase of total scattering rate with temperature, which suppresses the electron energy and reduces the population of the satellite valleys. This latter effect is apparent from the fact that the electron population in the [GAMMA] valley increases with temperature as shown in figure 4.


The importance of electron inter-valley transfer at high electric fields can be clearly seen in Fig. 4. In this figure the electron valley occupancy ratio for different materials is plotted. It is obvious that the inclusion of satellite valleys in the simulations is important. Significant electron transfer to the upper valleys only begins to occur, when the field strength is very close to the threshold value. Electrons ,which are near a valley minimum, have small kinetic energies; therefore they have strongly scattered. It is apparent that inter-valley transfer is substantially larger in InP over the range of applied electric fields shown, due to the combined effect of a lower [GAMMA] effective mass, lower satellite valley separation energy, and slightly lower phonon scattering rate within the [GAMMA] valley. As can be seen, lowest valleys in conduction band in GaP are locate at X Point then electrons scattered to next lowest energy satellite valleys ([GAMMA] and L valleys) with increase of electric field.

Figure 5 shows how the velocity-field characteristic of InP, [Ga.sub.0.5][In.sub.0.5]P and GaP materials change with impurity concentration at 300 K. It is clear that with increasing donor concentration, there are reduction in the average peak drift velocity and the threshold field because of increasing scattering rate events. The results show the trend expected from increased ionized impurity scattering is in good general agreement with recent calculations by other workers (Brennan et al. 1983; Newman, N., T. Kendelewicz, 1985; Newman, N., V. Schilfgaarde, 1986).


4. Conclusions

Electron transport at different temperatures in bulk GaP, InP and [Ga.sub.0.5][In.sub.0.5]P have been simulated using an ensemble Monte Carlo simulation. Using valley models to describe the electronic bandstructure, calculated velocity-field characteristics show that the inter-valley transitions in high electric fields play an important role in these materials. The inter-valley transitions lead to a large negative differential conductance. We have also shown that impurity concentration does not effect the electron transport properties in GaP semiconductor; therefore, GaP devices are expected be more tolerant to self-heating and high ambient temperature device modeling.


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(1) A. Mokhles Gerami, (1) H. Rahimpour Soleimani, (2) H. Arabshahi and (3) M.R. Khalvati

(1) Department of Physics, Guilan University of Rasht, Rasht, Iran

(2) Department of Physics, Ferdowsi University of Mashhad, Mashhad, Iran

(3) Department of physics, Shahrood University of Technology, shahrood, Iran

Corresponding Author: A. Mokhles Gerami, Department of Physics, Guilan University of Rasht, Rasht, Iran
Table 1: Important band parameters used in our simulation for
GaP, InP and [Ga.sub.0.5][In.sup.0.5]P (Martienssen, 2005;
Vurgaftman, I. and J.R. Meyer, 2001; Newman, N., 19860.

                Valle     Egap(eV   [m.sup.*]    Nonparabolicity

GaP             [GAMMA]   2.24      0.3          0.2
                L         2.76      0.64         0.06
                X         2.0       0.17         0.15
InP             [GAMMA]   1.35      0.07         0.7
                L         0.6       0.3          0.5
                X         0.75      0.6          0.15
[Ga.sub.0.5]    [GAMMA]   1.92      0.10         0.45
[In.sub.0.5]P   L         0.125     0.24         0.001
                X         0.217     0.61         0.069

Table 2:  Material parameter selections for GaP, InP, and
[Ga.sub.0.5][In.sub.0.5]P (Martienssen, 2005; Vurgaftman, I. and
J.R. Meyer, 2001; Newman, N., 19860.

                                        GaP             InP

Density [rho]([kgm.sup.--3])            4138            4810
Longitudinal sound velocity
  vs([ms.sup.--1])                      5850            5300
Low-frequency dielectric constant
  [[epsilon].sub.0]                     11.1            12.4
High-frequency dielectric constant
  [[epsilon].sub.~]                     9.11            9.55
Acoustic deformation potential D(eV)    3.1             8.3
Polar optical phonon energy (eV)        0.051           0.06
Energy gap (eV)                         2.24            1.35
Intervalley                             deformation     potentials
Intervalley phonon energies             51              29


Density [rho]([kgm.sup.--3])            4470
Longitudinal sound velocity
  vs([ms.sup.--1])                      4330
Low-frequency dielectric constant
  [[epsilon].sub.0]                     11.75
High-frequency dielectric constant
  [[epsilon].sub.~]                     9.34
Acoustic deformation potential D(eV)    7.2
Polar optical phonon energy (eV)        0.046
Energy gap (eV)                         0.217
Intervalley                             111

Intervalley phonon energies             10
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Title Annotation:Original Article
Author:Gerami, A. Mokhles; Soleimani, H. Rahimpour; Arabshahi, H.; Khalvati, M.R.
Publication:Advances in Natural and Applied Sciences
Article Type:Report
Geographic Code:7IRAN
Date:Sep 1, 2009
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