Peculiarities of the Current–Voltage Characteristic of

Keywords: 
current–voltage characteristics, double injection, solid solution, heterostructure.
DOI: 
10.1134/S1063785020110279
This work was aimed at studying the mechanism of
electric current transfer in 
n
-GaP–
p
-(InSb)
1 –
x
(Sn
2
)
x
(0 
≤
x
≤
0.05) heterostructures using the measurement
of their current–voltage (
I
–
V
) characteristics. The
heterostructures were prepared by epitaxial growth of
(InSb)
1 –
x
(Sn
2
)
x
solid solutions from liquid phase on
n
-GaP substrates [1]. The obtained films possessed 
p
-
type conductivity, had a thickness of about 
d
~ 14 
μ
m,
and exhibited a weakly variband character, whereby
bandgap width 
E
g
varied from 
E
g
(
d
) = 0.1 eV to 
E
g
(0) =
0.18 eV (Fig. 1).
Figure 2 shows the typical 
I
–
V
curve measured at
300 K. In the initial part with bias voltages 
V
varying
from 0.08 to 0.50 V, the curve is well approximated by
the exponential law reported by Stafeev [2]:
(1)
which is characteristic of so-called “long” 
p
–
n
diode
with rear ohmic contact, for which exponent 
c
can be
expressed as
(2)
where 
b
= 
μ
n
/
μ
p
is the ratio of 
n
-type (electron) and 
p
-
type (hole) mobilities. In particular, for a pure InSb
semiconductor compound, we have 
b
≈ 21 [3–5]. In
doped InSb, the carrier mobility decreases and char-
acteristic parameters of the base region of the struc-
ture under consideration can be estimated by formula
(2) with 
b
= 15. The exponential portion of the mea-
sured 
I
–
V
curve yields 
c
= 3.6, and the product of
1
=
0
exp(
/
),
I
I
qV ckT
+
+
=
+
2
( /
)
1
.
1
n
b
ch d L
c
b
mobility and lifetime of minority carriers is 
μ
n
τ
n
=
= 4.79 × 10
–6
cm
2
/V.
The exponential part of the measured 
I
–
V
curve is
followed by regions obeying the power law of the 
I
=
AV
m
type with various values of exponent 
m
and coef-
ficient 
A
dependent on the voltage: 
V
= 0.60–0.80V,
region 
I
= 
AV
3.1
with 
A
= 220 mA/V
3.1
; 
V
= 0.80–0.90V
region 
I
= 
AV
2.5
with 
A
= 195 mA/V
2.5
; 
V
= 0.90–1.40 V,
region 
I
= 
AV
2.1
with 
A
= 195 mA/V
2.1
; 
V
= 1.40–1.80V
region 
I
= 
AV
1.5
with 
A
= 232 mA/V
1.5
. At still higher
2
/(
)
n
qL
kT
Fig. 1. 
(a) Schematic diagram and (b) energy band struc-
ture of 
n
-GaP–
p
-(InSb)
1 –
x
(Sn
2
)
x
(0 
≤
x
≤
0.05) hetero-
structures.
n
p
+
0
d
0
d
R
:
E
C
E
V
(a)
(b)

---

TECHNICAL PHYSICS LETTERS 
Vol. 46 
No. 11 
2020
PECULIARITIES OF THE CURRENT–VOLTAGE CHARACTERISTIC
1125
voltages, from 2.10 to 2.48 V, the curve exhibits a sub-
linear behavior where the current weakly depends on
the voltage as can be well described in the framework
of the theory of “injection depletion effect” [6] by the
formula
(3)
where 
N
t
is the concentration of deep-level traps and 
J
is the current density. Based on experimental data for
the sublinear region, the 
μ
p
N
t
product was estimated at
4 × 10
16
cm
–1
V
–1
s
–1
. The sublinear region of 
I
–
V
curve is followed by the region described by the power
dependence 
I
= 207
V
1.38
.
Previously, we have reported results of an experi-
mental investigation of 
n
-(GaAs)–
p
-(InSb)
1 –
x
(Sn
2
)
x
(0 
≤
x
≤
0.05) heterostructures [7], in which no 
I
–
V
curve regions obeying the power law were observed.
This was probably related to the fact that the ratio of
base length 
d
to carrier diffusion length 
L
n
in the base
=
μ
0
exp(
/2
),
p
t
V
V
Jd
kT
N
was below 3 (
d
/
L
n
≈ 2.88), which implied that the base
was not sufficiently long for realization of the regimes
of ohmic and dielectric relaxation. In contrast, the 
n
-
GaP–
p
-(InSb)
1 –
x
(Sn
2
)
x
(0 
≤
x
≤
0.05) heterostruc-
tures studied in the present work have 
d
/
L
n
≈ 4. In
addition, there are differences between the values of
μ
n
τ
n
and 
μ
p
N
t
products for the 
p
-(InSb)
1 –
x
(Sn
2
)
x
films
grown on 
n
-(GaAs) and 
n
-GaP substrates. In the for-
mer case, we had 
μ
n
τ
n
= 6.76 × 10
–6
сm
2
/V and 
μ
p
N
t
=
9.57 × 10
16
сm
–1
V
–1
s
–1
, whereas, for 
n
-GaP sub-
strates, we have 
μ
n
τ
n
= 4.79 × 10
–6
сm
2
/V and 
μ
p
N
t
=
4 × 10
16
сm
–1
V
–1
s
–1
. A decrease in 
μ
n
τ
n
and 
μ
p
N
t
products in the present case is probably related to the
scattering of carriers on crystal lattice defects of the
(InSb)
1 –
x
(Sn
2
)
x
solid solution. Since the difference of
the sum of covalent radii of molecular components
InSb (
r
In
+ 
r
Sb
= 2.80 Å), Sn
2
(
r
Sn
+ 
r
Sn
= 2.80 Å), and
substrate GaAs (
r
Ga
+ 
r
As
= 2.44 Å) amounts to
∼
12.8%, while that in the case of GaP molecular sub-
strate (
r
Ga
+ 
r
P
= 2.36 Å) is 
∼
15.7%, the crystalline lat-
tice of (InSb)
1 –
x
(Sn
2
)
x
films grown on GaP substrates
is deformed to a greater extent as compared to the
films grown on GaAs.
At first glance, the observed sequence of 
I
–
V
curves might seem rather unclear because, in accor-
dance with the classical injection theory, (i) the
regimes with 
I
∝
V
3
and 
I
∝
V
2
must follow each other
in the reverse order and (ii) the appearance of relation
V
∝
exp(
Jd
/2
kT
μ
p
N
t
) requires counterdirected carrier
diffusion and drift f lows. Unlike this, the structure
under consideration is of the 
n
–
p
–
R
Ω
type (Fig. 1a),
so that the drift of carriers from the side of ohmic con-
tact is not expected. However, by virtue of the weakly
variband character of the obtained material (Fig. 1b),
any excitation leads to the appearance of counter f lows
of carriers from the region with lower 
E
g
toward the
region with higher 
E
g
.
Let us consider the sequence of 
I
–
V
characteristics
and explain the observed behavior. The main equation
for the problem of description of the distribution of
free carriers in 
p
-base under stationary conditions can
be written as follows [6]:
(4)
where the first term describes the diffusion of free car-
riers, the second term refers to their drift, and the third
term describes the electron–hole recombination
according to the Schockley–Read statistics. Ambipo-
lar drift velocity 
ϑ
a
for 
p
-type base can be expressed as
[6]
2
1
−
− ϑ
−
=
τ
2
2
0,
n
n
a
n
n
n
d n
dn
D
dx
dx