Brazilian Journal of Physics, vol. 27/A, no. 4, december, 1997
227
The Role of Doping on the Ultrafast Transport
Transient in p-GaAs and n-GaAs
E. W. S. Caetano1 , E. A. Mendes1, R. N. Costa Filho1,
V. N. Freire1, and J. A. P. da Costa2
1: Departamento de Fsica, Universidade Federal do Ceara, Campus do Pici,
C. P. 6030, 60455-760 Fortaleza, Ceara, Brazil
2: Departamento de Fsica Teorica e Experimental, Campus Universitario,
Universidade Federal do Rio Grande do Norte, C. P. 1641,
59072-970 Natal, Rio Grande do Norte, Brazil.
Received February 2, 1997
A comparison is made between the role of doping on the ultrafast transport transient of
minority and majority carriers in p-GaAs and n-GaAs, respectively. During the evolution
towards the steady-state, both the drift velocity and temperature of the majority carriers
are higher than those of the minority carriers. It is shown that an increase of the doping
can preclude the existence of an overshoot eect in the drift velocity of the minority carriers
in p-GaAs, but not in that of the majority carriers in n-GaAs.
I. Introduction
The understanding of the dynamics and high-eld
transport of carriers in heavily doped semiconductors
is relevant to the design improvement of high-speed
bipolar ;and hetero-junction
bipolar transistors. High
doping 1018cm;3 has important eects on the carriers dynamics and transport properties in semiconductors. Experimental observations in p-GaAs showed
that: (i) the energy dissipation rate of its hot carriers increases with doping[1], and that the electron-hole
interaction is the key scattering mechanism to explain
this behavior[1;2] ; (ii) the enhancement of its minority
mobility depends on the level of doping[3;4]. In this
case, there are two controverse experimental results,
one showing a sharp valley in the measured mobility
around 11019cm;3 , with a factor of 2:7 increase in mobility when the doping is increased from 1 1019cm;3
to 8 1019cm;3[3] , and the other one where carbondoped GaAs presents a continual decrease in minority
electron mobility with increasing p-type doping[4].
Monte Carlo simulations have also highlighted the
eect of the electron-hole interaction on the steady-
state transport[5;6] and on the ultrafast relaxation[1;7]
of hot minority carriers in p-GaAs as a function of doping. In particular, Taniyama et al.[6] found for a given
electric eld intensity that the steady-state velocity and
temperature of majority carriers in n-GaAs are always
higher than that of minority carriers in p-GaAs. Alencar et al.[8] have studied the high-eld transport transient of minority carriers in p-GaAs using transport
equations for the energy and drift velocity in the approximation of momentumand energy relaxation times,
p and , respectively. They showed that a reduction
of the overshoot in the minority carrier velocity due to
the electron-hole interaction is obtained when the doping increases[8] . Later, Alencar et al.[9] have used the
same scheme to study the ultrafast relaxation of hot
minority carriers in p-GaAs.
Since the dierence in features of the carrier-carrier
scattering produces discrepancies in the steady-state
transient regime between the majority and minority
electron velocity and temperature in p-GaAs and nGaAs[7] , respectively, one can argue that this will also
be the case during the transient transport regime. In
Contact Author: V. N. Freire Tel: +55 (85) 288.9903, Fax: +55 (85) 287.2184, E-mail: valder@sica.ufc.br
228
E.W.S. Caetano et. al.
this theoretical work, a comparison is made between
the role of high doping on the ultrafast transport transient of minority and majority carriers in p-GaAs and
n-GaAs, respectively.
In Section II, the theoretical model used to the description of the ultrafast transport transient of carriers
in p-GaAs and n-GaAs is introduced, as well as the
electron scattering mechanisms that were considered,
and the way the numerical solutions of the transport
equations were obtained. The time evolution of the minority and majority electron drift velocity and temperature in p-GaAs and n-GaAs, respectively, is presented
in Section III. This work nishes in Section IV with the
presentation of the conclusions.
II. The transport model for p-GaAs and n-GaAs
was used previously in several problems to calculate
the transient behavior of the transport parameters in
semiconductors[8;13].
III. Results and discussions
The ultrafast transport transient of minority carriers in p-GaAs was studied. Doping concentrations
p = Na = 1:5 1017; 1:5 1018; and 1:5 1019cm;3
were considered, where Na is the acceptor concentration. Equivalent concentrations were used for the donor
doping during the calculations of the ultrafast transport
transient of majority carriers in n-GaAs. In both cases,
electric eld intensities of 3kV=cm and 9kV=cm were
considered.
Electrons are minority carriers in p-GaAs and majority carriers in n-GaAs. When high doping is considered, the main scattering mechanisms for these
doped semiconductors are the electron-optical and
the electron-acoustic phonon scattering, the electronelectron scattering, and the electron-hole scattering[10] .
They are used to the determination of the momentum
and energy relaxation times, p and , respectively,
that are present in the following transport equations:
dv = qE ; v ;
(1)
dt
m p ()
d = qvE ; ; 0 ;
(2)
dt
()
where v is the electron drift velocity; (= 3kB T=2) is
the average electron energy and T is the electron temperature; 0 is the thermal energy of the electron at the
lattice temperature Tl = 300K; kb is the Boltzmann
constant, q is the electric charge of the electron, and m
is its eective mass in GaAs; nally, E is the applied
electric eld. The coupled transport equations (1) and
(2) can be derived from the Boltzmann equation.
The time evolution of the electron drift velocity
and average energy in p-GaAs and n-GaAs is obtained
by solving numerically the coupled transport equations (1) and (2). The calculations of p and are
based on the steady-state relations between the electron drift velocity and energy with the applied electiric
eld as published by Taniyama et al.[6] . This scheme
Figure 1. Time evolution of the minority (solid) and majority (dotted dashed) carrier drift velocity in p-GaAs and
n-GaAs,
respectively, for doping concentrations of 1:5 1017 ; 1:5 1018 ; and 1:0 1019 cm;3 . The doped semiconductors are subjected to an electric eld of 3 kV=cm.
Fig. 1 depicts the time behavior of the electron
drift velocity in p-GaAs (vp - solid) and n-GaAs (vn
- dotted dashed) when the electric eld intensity is
E = 3kV=cm: For a given doping, the drift velocity vn
of the majority carriers is always higher than the drift
velocity vp of the minority carriers. When the doping
increases, the values of vn and vp are reduced (when
Brazilian Journal of Physics, vol. 27/A, no. 4, december, 1997
229
compared at the same instant of time) and the time
evolution of both to the steady-state becomes faster.
vn presents a very small overshoot eect only when the
doping is of 1:5 1017cm;3 :
Figure 3. Time evolution of the minority (solid) and majority (dotted dashed) carrier temperature in p-GaAs and
n-GaAs, respectively, for doping concentrations of 1:5 1017 ; 1:5 1018 ; and 1:0 1019 cm;3 . The doped semiconductors are subjected to an electric eld of 3 kV=cm.
Figure 2. Time evolution of the minority (solid) and majority (dotted dashed) carrier drift velocity in p-GaAs and
n-GaAs,
respectively, for doping concentrations of 1:5 1017 ; 1:5 1018 ; and 1:0 1019 cm;3 . The doped semiconductors are subjected to an electric eld of 9 kV=cm.
When the electric eld intensity increases to
9kV=cm, vn and vp can present an overshoot eect
(see Fig. 2). However, it becomes smaller when the
doping increases, and can even be eliminated if the
doping is high enough. In fact, one can see that vn
does not present an overshoot when the doping is of
1:0 1019cm;3 . One can observe in Fig. 2 that the
overshoot eect in the drift velocity of the majority carriers is always bigger and lasts more than the overshoot
eect in the drift velocity of the minority carriers.
The evolution of the electron temperature in both
p-GaAs (Tp - solid) and n-GaAs (Tn - dotted dashed)
subjected to an electric eld of 3kV=cm (9kV=cm) is
presented in Fig. 3 (Fig. 4). In both gures, for a
given doping the temperature Tn of the majority carriers is always higher than the temperature Tp of the
minority carriers . When the doping increases, both Tn
and Tp are reduced when compared at the same instant
of time.
To understand the above results, it is important to
remember that the carrier-carrier scattering becomes
more eective when the doping increases. Consequently, both the electron drift velocity and temperature are reduced when the doping increases, as was
shown in the Figs. (1-4). The drift velocity and temperature of the majority carrier is bigger than those of the
minority carriers because the electron-hole scattering is
more eective than the electron-electron scattering.
230
E.W.S. Caetano et. al.
Acknowledgements
V. N. Freire would like to acknowledge the partial
nancial support from the Fundac~ao Cearense de Amparo a Pesquisa (FUNCAP). This work has received
partial nancial support from CNPq and FINEP.
References
Figure 4. Time evolution of the minority (solid) and majority (dotted dashed) carrier temperature in p-GaAs and
n-GaAs,
respectively, for doping concentrations of 1:5 1017 ; 1:5 1018 ; and 1:0 1019 cm;3 . The doped semiconductors are subjected to an electric eld of 9 kV=cm.
IV. Conclusions
It was investigated the eect of high doping on the
time evolution of the drift velocity and temperature
of electrons in p-GaAs and n-GaAs, respectively, subjected to high electric eld intensities. During the evolution towards the steady-state, both the drift velocity and temperature of the majority carriers in n-GaAs
were shown to be higher than those of the minority carriers in p-GaAs . This was shown to occur for all the
electric eld intensities and level of doping. An overshoot eect can occur in both the drift velocities of
electrons in p-GaAs and n-GaAs if the electric eld intensity is higher enough, but it depends on the level of
doping. An increase on the doping can even eliminate
the overshoot eect in the drift velocity of the minority
carriers in p-GaAs, but not in the drift velocity of the
majority carriers in n-GaAs.
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