Electrostatics of the nanowire radial -- diode
In this paper, the electrostatic theory of the nanowire radial core-shell -- homojunction has been considered. The calculations carried out show that, in contrast to a planar -- diode, the built-in electric field of the nanowire radial -- diode proves to be inhomogeneous. This field reaches its maxi...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2019
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| Цитувати: | Electrostatics of the nanowire radial -- diode / V.L. Borblik // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2019. — Т. 22, № 2. — С. 201-205. — Бібліогр.: 16 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860479966855036928 |
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| author | Borblik, V.L. |
| author_facet | Borblik, V.L. |
| citation_txt | Electrostatics of the nanowire radial -- diode / V.L. Borblik // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2019. — Т. 22, № 2. — С. 201-205. — Бібліогр.: 16 назв. — англ. |
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| description | In this paper, the electrostatic theory of the nanowire radial core-shell -- homojunction has been considered. The calculations carried out show that, in contrast to a planar -- diode, the built-in electric field of the nanowire radial -- diode proves to be inhomogeneous. This field reaches its maximum in the region of the i-layer adjoining the core. When moving away the i-layer from the nanowire center, the degree of field inhomogeneity decays, and both edge values of the field in the i-layer eventually reach the magnitude, which takes place in an analogous planar -- diode. This magnitude can be both higher and lower than the maximal field in the nanowire -- diode (depending on doping conditions). Simultaneously, the capacitance of the nanowire p-i-n diode can both increase and decrease in its value, going, at the same time, to weak voltage dependence inherent to the planar -- diode.
|
| first_indexed | 2026-03-23T18:52:40Z |
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ISSN 1560-8034, 1605-6582 (On-line), SPQEO, 2019. V. 22, N 2. P. 201-205.
© 2019, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
201
Hetero- and low-dimensional structures
Electrostatics of the nanowire radial p-i-n diode
V.L. Borblik
V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine,
41, prospect Nauky, 03680 Kyiv, Ukraine
E-mail: borblik@isp.kiev.ua
Abstract. In this paper, the electrostatic theory of the nanowire radial core-shell p-i-n
homojunction has been considered. The carried out calculations show that, in contrast to
planar p-i-n diode, the built-in electric field of the nanowire radial p-i-n diode proves to be
inhomogeneous. This field reaches its maximum in the region of the i-layer adjoining to the
core. When moving away the i-layer from the nanowire center, the degree of field
inhomogeneity decays, and both edge values of the field in the i-layer reach eventually the
magnitude, which takes place in analogous planar p-i-n diode. This magnitude can be both
higher and lower than the maximal field in the nanowire p-i-n diode (depending on doping
conditions). Simultaneously, the capacitance of the nanowire p-i-n diode can both increase
and decrease in its value, going, at the same time, to weak voltage dependence inherent to
the planar p-i-n diode.
Keywords: nanostructures, core-shells nanowire, radial p-i-n junction, capacitance.
https://doi.org/10.15407/spqeo22.02.201
PACS 61.46.Km, 62.23.St, 85.30.Kk
Manuscript received 06.03.19; revised version received 24.03.19; accepted for publication
19.06.19; published online 27.06.19.
1. Introduction
In the recent time, a great interest of the investigators is
attracted to semiconductor nanowires, especially to the
multilayer ones, whose layers are either doped in
different ways or form a heterostructure. On the base of
these objects, principally new constructions of the core-
shell devices are created, which use both transverse
(radial) transport of the current carriers (radial solar cells
[1], radial photodiodes [2], radial light emitting devices
[3]) and their longitudinal transport (field-effect
transistor [4], high electron mobility transistor [5]).
Cylindrical symmetry inherent to these
nanostructures introduces a number of peculiarities to
their electrophysical properties. In particular, depletion
widths of the radial p-n junction depend on its radius in a
rather nonstandard way: as radius of the p-n junction
decreases, depletion width of the core increases [6], but
that of the shell, on the contrary, decreases [7, 8]. As a
result, in the devices where the heterostructure p-n
junction is used, this fact results in changing the relative
contribution to the device performance characteristics
from different constituent materials. Namely, the lesser
radius of the heterostructure p-n junction, the larger is
contribution from the core material.
In the radial p-n junction, the dependence 1/C
2
versus U (C is the barrier capacitance, U – applied
voltage) proves to be nonlinear [6, 8]. Furthermore,
strong asymmetry in injection from the core to shell and
from the shell to core appears [9].
These studies concern nanowire p-n junction
structures. At the same time, radial nanowire structures
use often not p-n but p-i-n junctions [10-14]. In
particular, this makes it possible to broaden the region of
strong electric field in the junction, which is additional
advantageous in materials with short minority carrier
diffusion lengths [15]. Electrostatics of these structures
was not studied so far. In this paper, electrostatics of the
radial p-i-n homojunction has been investigated
theoretically.
2. Theory
Schematic view of the structure under consideration is
presented in Fig. 1. Here rp is the depletion region
boundary in the core, rn – depletion region boundary in
the shell, and i-layer is located between r1 and r2.
In the depletion approximation, we have Poisson’s
equations
S
AqN
rE
dr
d
r
1
, 1rrrp , (1a)
0
1
rE
dr
d
r
, 21 rrr , (1b)
mailto:borblik@isp.kiev.ua
SPQEO, 2019. V. 22, N 2. P. 201-205.
Borblik V.L. Electrostatics of the nanowire radial p-i-n diode
202
0 rn
p
n
rp r1
r2
i
Fig. 1. Schematic view of the nanowire structure under
consideration.
S
DqN
rE
dr
d
r
1
, nrrr 2 , (1c)
where q is the electron charge, εS – dielectric constant of
the semiconductor, NA and ND are the concentrations of
acceptors and donors, respectively. Solution of these
equations gives the electric field distribution in the
structure
r
rrqN
E
p
S
A
22
2
, 1rrrp , (2a)
r
A
E , 21 rrr , (2b)
r
rrqN
E n
S
D
22
2
, nrrr 2 , (2c)
where A is the integration constant.
Matching the electric fields at r1 and r2, we obtain
22
2
22
1
22
n
S
D
p
S
A rr
qN
rr
qN
A
, (3)
whence it follows
2
2
222
1 rrNrrN nDpA
. (4)
The second integration of Eq. (2) gives the
potentials
r
r
r
rrqN
rV
p
p
p
S
A ln
22
2
22
, 1rrrp , (5a)
constln rArV , 21 rrr , (5b)
bi
n
n
n
S
D V
r
r
r
rrqN
rV
ln
22
)( 2
22
, nrrr 2 ,
(5c)
where the following boundary conditions are used
0prV , bin VrV , (6)
Vbi is the built-in potential of the junction. Matching of
the potentials at r = r1 and r = r2 allows us to exclude
const and obtain equation
bi
n
n
S
Dp
p
S
A V
r
r
A
r
r
r
qN
r
r
r
qN
1
2
2
2
1
2 lnln
2
ln
2
. (7)
Equations (4) and (7) have to be solved jointly in order to
obtain rp and rn. All the rest quantities are expressed
through them.
The barrier capacitance
dU
dQ
C
p
, where Qp is the
electric charge concentrated in the depleted p-region of
the junction. This charge is given by
LrrqNQ pAp
22
1 (8)
where rp is voltage-dependent and L is length of the
nanowire. Inasmuch as
pnpA
Sp
rrrqNdU
dr
ln
1
, (9)
the capacitance per unit area of the p-i-n junction is
pn
S
rrr
C
ln
1
1
. (10)
3. Numerical results
For numerical solution of Eqs. (4) and (7), the parameters
of silicon at room temperature have been chosen. Three
doping situations have been considered: NA = ND,
NA >> ND, and NA << ND. The calculation results for the
electric field distribution in the structure are presented in
Fig. 2. The characteristic feature of these distributions is
inhomogeneity of the field in the i-layer, which sharply
differs from the case of planar p-i-n diode, where electric
field in the i-layer is homogeneous [16]. The field
inhomogeneity is especially strong when NA = ND or
NA >> ND and diminishes with thickening of the i-layer.
In any case, the electric field is maximal near the
nanowire core.
SPQEO, 2019. V. 22, N 2. P. 201-205.
Borblik V.L. Electrostatics of the nanowire radial p-i-n diode
203
10 20 30 40 50 60 70
0.0
2.0x10
5
4.0x10
5
6.0x10
5
8.0x10
5
30,40 nm
r, nm
E
,
V
/c
m
30,50 nm
N
A
= N
D
= 5x10
18
cm
-3
30,60 nm
a 30,30 nm
20 30 40 50 60 70 80
1x10
5
2x10
5
3x10
5
4x10
5
5x10
5
30,30 nm
N
A
= 5x10
18
cm
-3, N
D
= 5x10
17
cm
-3
30,60 nm
30,50 nm
E
,
V
/c
m
r, nm
30,40 nm
b
10 20 30 40 50 60 70 80 90 100
0
1x10
5
2x10
5
3x10
5
N
A
= 5x10
17
cm
-3, N
D
= 5x10
18
cm
-3
80,95 nm
80,85 nm
80,90 nm
r, nm
E
,
V
/c
m
c 80,80 nm
Fig. 2. Electric field distribution in the nanowire p-i-n diode at
NA = ND (a), NA >> ND (b), and NA << ND (c); numbers near the
curves are radial coordinates of the i-layer showing its extent,
dashed lines corresponds to the i-layer of zero extent (p-n
diode).
20 40 60 80 100 120
0
1x10
5
2x10
5
3x10
5
4x10
5
5x10
5
6x10
5
N
A
= N
D
= 5x10
18
cm
-3
E
,
V
/c
m
807060
r
1
= 20 nm
30
40
r, nm
50
r
2
- r
1
= 20 nma
inf
0 20 40 60 80 100 120 140
0
1x10
5
2x10
5
3x10
5
4x10
5
5x10
5
N
A
= 5x10
18
cm
-3, N
D
= 5x10
17
cm
-3
60
r, nm
E
,
V
/c
m
r
2
- r
1
= 20 nm
80
70
50
40
r
1
= 20 nm
30
b
inf
20 40 60 80 100 120 140 160
0.0
5.0x10
4
1.0x10
5
1.5x10
5
2.0x10
5
2.5x10
5
N
A
= 5x10
17
cm
-3, N
D
= 5x10
18
cm
-3
r, nm
E
,
V
/c
m
r
2
- r
1
= 20 nm
120110
r
1
= 60 nm 70
80 90 100
c inf
Fig. 3. Electric field distribution in the nanowire p-i-n diode
depending on radial position of the i-layer at NA = ND (a),
NA >> ND (b), and NA << ND (c); dashed lines shows to what
magnitude both edge values of the field in the i-layer go, when
the nanowire p-i-n diode becomes the planar one.
SPQEO, 2019. V. 22, N 2. P. 201-205.
Borblik V.L. Electrostatics of the nanowire radial p-i-n diode
204
-0.4 -0.2 0.0 0.2 0.4 0.6
2.5x10
5
3.0x10
5
3.5x10
5
4.0x10
5
4.5x10
5
5.0x10
5
5.5x10
5
r
1
= 20 nm
r
2
- r
1
= 20 nm
N
A
= N
D
= 5x10
18
cm
-3
C
,
p
F
/c
m
2
U, V
70
30
40
50
100
200
500
a
-0.4 -0.2 0.0 0.2 0.4 0.6
1.5x10
5
2.0x10
5
2.5x10
5
3.0x10
5
3.5x10
5
4.0x10
5
4.5x10
5
r
2
- r
1
= 20 nm
N
A
= 5x10
18
cm
-3, N
D
= 5x10
17
cm
-3
U, V
C
,
p
F
/c
m
2
r
1
= 20 nm
30
40
50
60
80
120
200
300
500
b
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
5.0x10
4
1.0x10
5
1.5x10
5
2.0x10
5
2.5x10
5
r
2
- r
1
= 20 nm
N
A
= 5x10
17
cm
-3, N
D
= 5x10
18
cm
-3
C
,
p
F
/c
m
2
500
300
200
150
120
U, V
r
1
= 60 nm
70
80
90
100
c
Fig. 4. Voltage dependences of the nanowire p-i-n diode
capacitance at NA = ND (a), NA >> ND (b), and NA << ND
(c) as a function of the distance between the i-layer and
the nanowire center.
It is of interest to study dependence of the electric
field distributions on radial position of the i-layer in this
nanowire. Fig. 3 represents such dependences for three
doping situations at the same thickness of the i-layer
equal to 20 nm. It is seen that, as the i-layer moves away
from a center of the nanowire, inhomogeneity of the
electric field distribution becomes more and more weak,
i.e., the field goes to homogeneous one inherent to planar
p-i-n diodes.
The dash lines in these figures demonstrate
asymptotical confluence of both edge values of the field
in the i-layer, when r1 goes to infinity, i.e., the nanowire
curvature becomes ignorable. It is seen also that the
maximum electric field in the i-layer of nanowire proves
to be higher than that in an analogous planar diode at
NA = ND and NA >> ND and, on the contrary, is lower at
NA << ND.
Fig. 4 represents the voltage dependences of the
nanowire p-i-n diode capacitance given by the formula
(10) for three doping combinations as a function of the
distance between the i-layer and center of the nanowire at
the same value of the i-layer thickness equal to 20 nm.
As it follows from these figures, the capacitance of
the nanowire p-i-n diode decreases with moving away the
i-layer from the nanowire center at NA = ND and
NA >> ND and, on the contrary, increases at NA << ND. In
any case, the voltage dependence of the capacitance
diminishes as it has to be in planar p-i-n diode [16].
4. Conclusions
Being used as solar cells or photodiodes, the nanowire
radial p-i-n diodes have certain advantages as compared
with the planar analogs. In particular, at Ncore = Nshell or
Ncore >> Nshell, the maximal built-in electric field in the i-
layer proves to be higher than that in planar p-i-n diode
under other equal conditions. But one has to keep in
mind that the highest electric field is localized in the
region of the i-layer adjoining to the core. It should be
also noted that the capacitance of the nanowire p-i-n
diode can be both larger and smaller than that of its
planar analog at the same parameter values.
Acknowledgement
This work was supported by the National Academy of
Sciences of Ukraine [project 2.2.6.34].
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Authors and CV
Dr. Vitalii L. Borblik graduated from
Kiev State University in 1968. He
received his PhD in physics and
mathematics from the Institute of
Semiconductors in Kiev (National
Academy of Sciences of Ukraine) in
1978. At present, he is senior scien-
tific researcher in the Department
of Electric and Galvanomagnetic Pro-
perties of Semiconductors at the V. Lashkaryov Institute
of Semiconductor Physics. His researches include electron
transport in semiconductor heterostructures, dynamical
concentration lattices in bipolar semiconductor plasma,
injection and exclusion phenomena in semiconductor
devices and physics of the diode temperature sensors.
Recent scientific interests of V.L. Borblik are electric and
optic properties of nanostructured materials.
ORSiD 0000-0002-8224-9170
https://doi.org/10.1038/nature04796
https://doi.org/10.1063/1.3125435
https://doi.org/10.1063/1.4794541
https://doi.org/10.1016/j.egypro.2013.07.055
|
| id | nasplib_isofts_kiev_ua-123456789-215464 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2026-03-23T18:52:40Z |
| publishDate | 2019 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Borblik, V.L. 2026-03-18T11:39:09Z 2019 Electrostatics of the nanowire radial -- diode / V.L. Borblik // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2019. — Т. 22, № 2. — С. 201-205. — Бібліогр.: 16 назв. — англ. 1560-8034 PACS: 61.46.Km, 62.23.St, 85.30.Kk https://nasplib.isofts.kiev.ua/handle/123456789/215464 https://doi.org/10.15407/spqeo22.02.201 In this paper, the electrostatic theory of the nanowire radial core-shell -- homojunction has been considered. The calculations carried out show that, in contrast to a planar -- diode, the built-in electric field of the nanowire radial -- diode proves to be inhomogeneous. This field reaches its maximum in the region of the i-layer adjoining the core. When moving away the i-layer from the nanowire center, the degree of field inhomogeneity decays, and both edge values of the field in the i-layer eventually reach the magnitude, which takes place in an analogous planar -- diode. This magnitude can be both higher and lower than the maximal field in the nanowire -- diode (depending on doping conditions). Simultaneously, the capacitance of the nanowire p-i-n diode can both increase and decrease in its value, going, at the same time, to weak voltage dependence inherent to the planar -- diode. This work was supported by the National Academy of Sciences of Ukraine [project 2.2.6.34]. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Hetero- and Low-Dimensional Structures Electrostatics of the nanowire radial -- diode Article published earlier |
| spellingShingle | Electrostatics of the nanowire radial -- diode Borblik, V.L. Hetero- and Low-Dimensional Structures |
| title | Electrostatics of the nanowire radial -- diode |
| title_full | Electrostatics of the nanowire radial -- diode |
| title_fullStr | Electrostatics of the nanowire radial -- diode |
| title_full_unstemmed | Electrostatics of the nanowire radial -- diode |
| title_short | Electrostatics of the nanowire radial -- diode |
| title_sort | electrostatics of the nanowire radial -- diode |
| topic | Hetero- and Low-Dimensional Structures |
| topic_facet | Hetero- and Low-Dimensional Structures |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/215464 |
| work_keys_str_mv | AT borblikvl electrostaticsofthenanowireradialdiode |