46
The European Physical Journal Applied Physics
The analysis given by Oldwig Von Roos [10] has some This method uses experimental EBIC data for the deter-
similarities with Donolato, since he used the Fourier tech- mination of bulk minority carrier diffusion length and sur-
niques to resolve the continuity equation with appropriate face recombination velocity in the case of PN junction or
boundary conditions. He showed that the Donolato series Schottky barrier diode. The validity of the EBIC expres-
converge much more slowly than the integral equations.
Akamatsu et al. [11] used the Monte Carlo method
to compute the generated electron- hole pair distribution
and the electron beam induced current in order to deter-
mine the minority carriers diffusion lengths. They have
treated different GaAs samples: an homogeneous Schot-
tky diode, a liquid-phase-epitaxial Schottky diode and an
homostructure P-N junction with different doping levels.
They have shown that the diffusion length of minority car-
riers is deduced from the experimental measurements near
the junction for slightly doped semiconductors (transport
properties), but far from the junction the measured cur-
rent is produced by the multiple process of the reabsorbed
recombination radiation. This additional current become
also important near the junction in the case of highly
doped semiconductors and for high incident electron beam
accelerating voltage.
Farvacque and Sieber [12] have proposed a physical
model of the EBIC contrast due to a dislocation perpen-
dicular to the surface in the case of N-type GaAs samples.
This physical approach takes into account the diffusion of
minority carriers a well as the physical properties of the
dislocations. The authors proved that the contribution of
the recombination at the dislocation in the depletion layer
to the total EBIC contrast is important either at low ac-
celerating voltages, especially if the doping level of the
semiconductor is low, or at high accelerating voltage.
Daniel et al. [13] have used the cathodoluminescent
mode of the scanning electron microscope to deduced from
experimental data the diffusion length of minority carri-
ers, the normalized surface recombination velocity, opti-
cal absorption coefficient, dead layer thickness and a con-
stant which combines the instrumentation constant and
the quantum efficiency of radiative recombination in the
case of three GaAs devices with different doping levels.
Ong et al. [14] have proposed a model for the calcula-
tion of the induced current due to an electron beam with
an extended generation source given by:
sion is verified by the use of 3-D computer simulation.
In a previous paper [15,16], we have developed a
model for the calculation of the induced current due
to an electron beam with an extended generation pro-
file in the case of a Silicon doped Au/InP Schottky
diode and in the case of a sulphur doped ternary com-
pound (Ga0.7Al0.3As:N+/Ga0.7Al0.3As:P), prepared by
the MOVPE method. The plane of the junction is per-
pendicular to the surface and the electron beam scans the
surface perpendicular to the depletion layer (along the x-
axis). By measuring the steady-state electron beam in-
duced current (EBIC) as a function of the beam-junction
distance, current profiles are obtained, from which the mi-
nority carrier diffusion length and the surface recombina-
tion velocity are deduced.
In this paper, a 2-D generation rate model is applied
for the calculation of the collected induced current within
the plane PN junction. Our results are compared with
experimental ones. Then, we have focused our attention
to determine the diffusion length of the excess minor-
ity carriers and the optical self-absorption coefficient of
the material components generated by the electron beam
from the experimental data. The surface recombination
velocity is calculated from both the van Roosbroeck and
Bresse model and from our proposed model, in the case
of a Schottky diode Au/GaAs obtained by the MOVPE
method. A comparative study between these models is
then presented.
2 Theoretical study
We will investigate the case of a vertical junction silicon
doped Schottky diode Au/GaAs. The incident electron
beam is centred at x0 normally to the surface. The junc-
tion is parallel to the beam (Fig. 1).
The electron beam scans the cleaved surface of the
sample along the x-axis. The excess minority carrier den-
sity created within the region p is a solution of the steady-
state continuity equation:
Z
λ(x, y, z)
x
L
I =
kx2
e− dx dy dz
(3a)
g
V
∆n(x, z)
1
Dn
2
where V is the generation volume, k is the proportionality
constant, λ(x, y, z) is the generation function distribution
of the extended source and g is the total generation rate
satisfying the relationship:
∇ [∆n(x, z)] −
= −
g(x, z)
(5)
Ln2
that satisfies the boundary conditions associated to this
physical model:
Z
∂∆n
g =
λ(x, y, z)dx dy dz.
(3b)
z = 0, Dn
z = h, Dn
= VS∆n
(Neuman equation) (6a)
V
∂z
∂∆n
For x > 2L, they supposed that x is virtually constant in
the integral of equation (3a) and the induced current is
given by:
= −VA∆n (Neuman equation) (6b)
∂z
x = 0, ∆n = 0
(Dirichlet equation) (6c)
∂∆n
x
L
I(x) = kx2e−
.
(4)
x = w1, Dn
= V1∆n (Neuman equation) (6d)
∂x