Peculiarities of the Current–Voltage Characteristic of

Fig. 2. 
(a) Typical dark current–voltage (
I
–
V
) characteris-
tic of 
n
-GaP–
p
-(InSb)
1 –
x
(Sn
2
)
x
(0 
≤
x
≤
0.05) hetero-
structure and (b) its forward branch plotted on the semi-
logarithmic scale for 
T
= 300 K.
0.1
1
10
(b)
3
2
1
0
1
2
3
0.5
0.4
0.3
0.2
0.1
200
0
200
400
600
800
1000
V
, V
V
, V
I
, mA
I
, mA
(a)

---

1126
TECHNICAL PHYSICS LETTERS 
Vol. 46 
No. 11 
2020
SAIDOV et al.
(5)
where 
γ
= 
N
t
/
n
1
t
is the factor of electron trapping, 
n
1
t
=
N
c
exp(–(
E
c
– 
E
t
)/
kT
) is the Schockley–Read statistics
factor for the 
E
t
trap level, 
is the concentration of
charged trap centers, 
N
a
is the concentration of shal-
low acceptors determining the conductivity type, 
E
∗
=
ε
E
/(4
π
q
), 
ε
is the dielectric constant, and 
E
=
J
/(
q
μ
n
(
bn
+ 
p
)) is the electric field (with neglect of the
Dember field).
Equation (4) describes all the known regimes of
double injection, but it cannot be analytically solved in
the general form. However, there are well-known
solutions for various partial regimes.
1.
When the carrier drift is much weaker than diffu-
sion, the second term in Eq. (4) can be ignored. This
approximation corresponds to the so-called “diffu-
sion” regime of double injection, for which the main
I
–
V
curve of a “long” diode (
d
/
L
n
> 1) obeys the
exponential law of Eq. (1) reported by Stafeev [2].
2.
If the field increases with the level of injection
and the drift of carriers can no longer be ignored, the
condition
(6)
Corresponds to realization of the ohmic relaxation
of space-charge limited current as described by the
well-known Lampert law
(7)
3.
As the level of injection grows further and the
field-dependent terms exceed the concentration of
doping acceptors, so that inequality (6) changes to
opposite, the regime changes to dielectric relaxation
and the 
I
–
V
curve shape changes to
(8)
In the particular case under consideration, the cur-
rent obeys the law of 
I
∝
V
3.1
(rather than 
I
∝
V
3
), but
the regime certainly refers to the dielectric relaxation.
As is well known, the exact 
I
∝
V
3
law is almost never
observed, because its realization would require a very
large ratio of 
d
/
L
≈ 100 (since it has been derived with
neglect of diffusion processes at the 
n
–
p
and 
n
–
n
+
junctions). At the same time, the “stronger” depen-
dence of 
I
∝
V
3.1
type was repeatedly reported by
numerous researchers.
We then observed weaker dependences of the 
I
∝
V
2.5
, 
I
∝
V
2.1
, and eventually 
I
∝
V
1.5
types, which at
−
−
μ



ϑ =
−
−



γ + +





+
−





2
2
*
*
(
1)
.
p
a
a
t
t
j
dE
d E
N
p
p
b
b
n
dx
dp
dN
N
n
E
dn
−
t
N
<
−
2
2
a
dE
d E
N
n
dx
dx
=
μ μ τ
2
3
9
.
8
p
n n
a
V
J
q
N
d
≈
μ μ τ
3
5
125
.
18
p
n n
V
J
d
first glance might seem paradoxical, because the dop-
ing impurity (
N
a
) accounts for the ohmic relaxation
and the onset of dielectric relaxation can only take
place when inequality (6) reverses. However, the
observed behavior can be reasonably explained by
assuming that the concentration of doping acceptors
(representing tin) can vary with increasing excitation
of the semiconductor. Apparently, uncontrolled
impurities of different nature are unavoidably present
during synthesis of the given variband solid solution
and some of these are capable of interacting with
acceptors to form complexes of the donor–acceptor
type. During the growth of injection excitation, these
complexes decay to yield new free acceptors. When
their concentration becomes sufficiently large,
inequality (6) reverses and the regime of dielectric
relaxation weakens because both terms in square
brackets for 
ϑ
a
in Eq. (5) become significant so that
the regime of ohmic relaxation would replace the
dielectric relaxation. This is followed by the 
I
∝
V
1.5
type dependence that is characteristic of a drift regime
under conditions of bipolar recombination, which is
quite possible with increasing level of injection
In the following, the behavior described by
Eq. (3) has been observed, which is inherent in the
phenomenon of injection depletion. This type
of
I
–
V
characteristics was previously reported for
p
–
n
structures based on various solid solutions, in