New evidence of the hopping nature of the excess tunnel current in heavily doped silicon - diodes at cryogenic temperatures
The new experimental data concerning the effect of a magnetic field on the electric properties of silicon diodes with high doping levels both in the emitter and base (conduction of which at low temperatures is determined by the excess tunnel current) have been analyzed. In addition to previous inves...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2017
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| Zitieren: | New evidence of the hopping nature of the excess tunnel current in heavily doped silicon - diodes at cryogenic temperatures / V. L. Borblik, Yu. M. Shwarts, M. M. Shwarts, A. B. Aleinikov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2017. — Т. 20, № 2. — С. 195-198. — Бібліогр.: 11 назв. — англ. |
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| author | Borblik, V. L. Shwarts, Yu. M. Shwarts, M. M. Aleinikov, A. B. |
| author_facet | Borblik, V. L. Shwarts, Yu. M. Shwarts, M. M. Aleinikov, A. B. |
| citation_txt | New evidence of the hopping nature of the excess tunnel current in heavily doped silicon - diodes at cryogenic temperatures / V. L. Borblik, Yu. M. Shwarts, M. M. Shwarts, A. B. Aleinikov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2017. — Т. 20, № 2. — С. 195-198. — Бібліогр.: 11 назв. — англ. |
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| container_title | Semiconductor Physics Quantum Electronics & Optoelectronics |
| description | The new experimental data concerning the effect of a magnetic field on the electric properties of silicon diodes with high doping levels both in the emitter and base (conduction of which at low temperatures is determined by the excess tunnel current) have been analyzed. In addition to previous investigations of the influence of magnetic fields up to 9.4 T on this tunnel current at 4.2 K, now the measurements have been carried out up to 14 T at temperatures lower than the liquid helium temperature. Under these conditions, the transfer to saturation of the diode magnetoresistance was observed, which agrees with the results predicted theoretically for the hopping conduction via impurity centers in high magnetic fields.
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| first_indexed | 2026-03-21T13:44:55Z |
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 2. P. 195-198.
doi: https://doi.org/10.15407/spqeo20.02.195
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
195
PACS 72.20.Ee, 72.20.My, 85.30.Kk
New evidence of the hopping nature of the excess tunnel current
in heavily doped silicon p-n diodes at cryogenic temperatures
V. L. Borblik 1, ∗, Yu. M. Shwarts1, 2, M. M. Shwarts1, A. B. Aleinikov1, 2
1V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine,
41, prospect Nauky, 03680 Kyiv, Ukraine
2International Laboratory of High Magnetic Fields and Low Temperatures,
Wroclaw, 53-421, Poland
∗Corresponding author e-mail: borblik@isp.kiev.ua
Abstract. The new experimental data concerning the effect of magnetic field on electric
properties of silicon diodes with high doping levels both in the emitter and base
(conduction of which at low temperatures is determined by the excess tunnel current) has
been analyzed. In addition to previous investigations of the influence of magnetic fields
up to 9.4 T on this tunnel current at 4.2 K, now the measurements have been carried out
up to 14 T at temperatures lower than the liquid helium temperature. Under these
conditions, the transfer to saturation of the diode magnetoresistance was observed, which
agrees with the results predicted theoretically for the hopping conduction via impurity
centers in high magnetic fields.
Keywords: p-n diode, silicon, heavy doping, excess tunnel current, hopping conduction,
magnetoresistance.
Manuscript received 23.12.16; revised version received 13.03.16; accepted for
publication 14.06.17; published online 18.07.17.
1. Introduction
Traditional silicon p-n diodes, at low temperatures,
suffer from the effect of freezing-out free carriers into
the impurities in the diode base and, as consequence,
from current instabilities related to their impact
ionization in the electric field [1].
When the doping level of the diode base is high
enough (i.e., the impurity concentration exceeds the
critical value for dielectric-metal transition), one can
avoid this problem, as it has been shown by us in a
number of papers [2-5]. In this case, any instability does
not appear, the diode resistance is completely
determined by resistance of the p-n junction, and the
current voltage characteristics demonstrate predomi-
nance of the excess tunnel current (via certain localized
states in the forbidden band of semiconductor, as it has
been accepted to believe [6, 7]).
It has been found [3-5] that the temperature
dependence of this excess tunnel current (at the constant
voltage drop across the diode) is well described by the
Mott’s law for hopping conduction
( )[ ]41
0exp)( TTTI −∝ , that suggests the hopping
character of the excess tunnel current at low
temperatures. It has been supposed in [3] that in this case
the electron hops take place via system of electron and
hole “lakes” which could be formed (in accordance with
the theory [8]) in heavily doped and highly compensated
region of the p-n junction at the expense of large-scale
potential. The lengthy compensation region could appear
because of opposing diffusion of boron and phosphorus
in the diode investigated.
Studying the influence of magnetic field on the
characteristics of these diodes at 4.2 K [9], we have
established that, in the region of low magnetic fields,
negative magnetoresistance takes place, that is typical
for the systems where conduction proceeds by carrier
hopping via localized states.
With growth of the magnetic field, the negative mag-
netoresistance turned into positive one with the quadratic
dependence on the field, which (in the fields not excee-
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 2. P. 195-198.
doi: https://doi.org/10.15407/spqeo20.02.195
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
196
ding 9.4 T) came close to a linear dependence. In this pa-
per, we show that with further increase in the magnetic
field, the above mentioned linear dependence of the diode
magnetoresistance ( ) )0()0()()0( RRBRRR −≡Δ passes
to the saturation demonstrating transition to dependence
3/1const)0( BRR ∝Δ (B is induction of the magnetic
field) predicted theoretically for the variable range
hopping conduction of Mott’s type in high magnetic
fields [10]. Thereby, it has been proved that the excess
tunnel current in heavy doped silicon diodes is
determined by electron hops via local impurity centers,
though this does not contradict (as it will be shown
below) to the previous point of view.
2. Results of measurements
In the experiment, a voltage drop U across the diode was
measured under the passing given current I through it
(the current-controlled regime). In this regime, variation
of U reflects variation of the diode resistance R. Results
of the measurements are presented in Fig. 1 for a number
of low temperatures as a function of magnetic field in-
duction for two orientations of the magnetic field re-
lative to the diode plane – in parallel and normal to it.
As it follows from Fig. 1, in the range of low
magnetic fields (for both field orientations), sections of
small negative magnetoresistance take place. These
sections demonstrate slight dependence of their extent in
magnetic field on temperature (marked by vertical dotted
lines).
The diode magnetoresistance is determined here as
a ratio of the voltage change at magnetic field B to the
voltage in the absence of the field:
)0(
)0()(
)0()0( U
UBU
U
U
R
R −
≡
Δ
=
Δ
. The corresponding data
are shown in Fig. 2.
As seen from Fig. 2, in the positive range, the diode
magnetoresistance depends on magnetic field at first
quadratically; then the dependence comes close to the
linear one and further exhibits a tendency to saturation in
high magnetic fields. With decrease in temperature, this
picture becomes more and more distinct.
0 2 4 6 8 10 12 14
1.080
1.085
1.090
1.095 b
n++- p+ diode
I = 1 μA
(perpendicular)
2.25 K
2.71 K
U
, V
B, T
3.42 K
4.22 K
Fig. 1. Dependences of the voltage drop across the diode on the magnetic field at parallel (a) and perpendicular (b) orientations of
the field relative to the diode plane at a number of temperatures.
0 2 4 6 8 10 12 14
0.000
0.002
0.004
0.006
a
n++- p+ diode
I = 1 μA
(parallel)
4.22 K
3.48 K
2.78 K
2.25 K
ΔU
/U
(0
)=
Δ
R
/R
(0
)
B, T
0 2 4 6 8 10 12 14
0.000
0.002
0.004
0.006
b
n++- p+ diode
I = 1 μA
(perpendicular)
4.22 K
3.42 K
2.71 K
Δ
U
/U
(0
)=
Δ
R
/R
(0
)
B, T
2.25 K
Fig. 2. Magnetic field dependences of the diode magnetoresistance at parallel (a) and perpendicular (b) orientations of the field at
different temperatures.
0 2 4 6 8 10 12 14
1.080
1.085
1.090
1.095 a
U
, V
B, T
4.22 K
3.48 K
2.78 K
2.25 Kn++- p+ diode
I = 1 μA
(parallel)
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 2. P. 195-198.
doi: https://doi.org/10.15407/spqeo20.02.195
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
197
3. Analysis and discussion of results
The theory of the variable range hopping conduction of
Mott’s type via impurity centers predicts, in the high
field limit, a magnetic field dependence of the resistance
in the form [10]
( )( )3/1
0 exp),( TBRBTR χ= , (1)
where ( )[ ] 3/1
FB1.2 aEgkce h≈χ , e is the electron
charge, c – light velocity, h – the Plank’s constant,
kB – Boltzmann constant, g(EF) – density of states at the
Fermi level, a – Bohr radius of the impurities (the
localization radius). In Fig. 3, the high-field sections of
the measurement results (for parallel field orientation)
are presented in semilogarithmic scale as a function of
( ) 3/1TB and indeed demonstrate going into linear
dependencies at high fields. At T = 4.22 K this going
takes place just after B = 9.4 T, where the measurements
in the paper [9] were finished. The lower temperature,
the lower is the magnetic field in which this going to the
linear dependencies occurs. The slope of the straight
lines (χ value) exhibits a slight temperature dependence.
Completely analogous results take place under
perpendicular field orientation including values of the
slope.
The obtained results imply that the mechanism of
excess tunnel current in the investigated diode is
hopping conduction via local impurity centers. However,
this fact by no means excludes the picture based on the
system of electron and hole “lakes” assumed in Ref. 3
(see Fig. 4). Indeed, the tunnel transitions through the
potential barriers from one “lake” to another one occur
via the same local impurity states within the barriers.
This statement is obviously true also for the case of low-
temperature conduction via the system of electron
“lakes” in macroscopically homogeneous heavily doped
and strongly compensated semiconductors (as in
Ref. 11).
1.2 1.3 1.4 1.5 1.6 1.7 1.8
1.080
1.085
1.090
n++- p+ diode
I = 1 μA
(parallel)
2.25 K
χ=0.010 (K/T)1/3
2.78 K
χ=0.011 (K/T)1/3
3.48 K
χ=0.010 (K/T)1/3
9.4 T
9.4 T
9.4 TU
, V
(B/T)1/3 , (T/K)1/3
9.4 T 4.22 K
χ=0.009 (K/T)1/3
Fig. 3. High-field sections of the measurement results (in semilo-
garithmic scale) as a function of ( ) 3/1TB at parallel field orien-
tation; the fields equal to 9.4 T are marked by dotted lines.
Fig. 4. The presumable picture for excess tunnel current in
heavily doped p-n diode with the lengthy compensated region
at low temperature. Here, the sinuous lines are bottom of the
conductivity band and top of the valence band with taking into
account the large-scale potential, the horizontal dashes indicate
empty donor states, the black points imply occupied acceptor
states, the dash-dotted lines show the Fermi levels, occupied
states in the bands are shaded, Jn and Jp are flows of electrons
and holes, respectively, and the vertical arrows mean electron-
hole recombination.
4. Conclusions
Thus, all taken together, namely –
1) the Mott law for the low-temperature
dependence of the diode conductivity,
2) availability of the negative magnetoresistance
in small magnetic fields,
3) transition (with increase in magnetic field) to
the positive magnetoresistance with quadratic
dependence on the field and then to its cube-root
dependence, as well as
4) practical independence of the diode
magnetoresistance on mutual orientation magnetic field
and the diode plane –
allows us to state that the excess tunnel current in
silicon heavily doped p-n diodes is determined by the
electron hops via the impurities centers irrespective of
whether the system of electron and hole “lakes” are
generated in the compensation region of the p-n junction
or not.
References
1. Aleinikov A.B., Berezovets V.A., Borblik V.L.,
Shwarts M.M., and Shwarts Yu.M. Effect of
magnetic field on hysteretic characteristics of
silicon diodes under conditions of low-temperature
impurity breakdown. Semiconductor Physics,
Quantum Electronics & Optoelectronics. 2012. 15,
No. 3. P. 288–293.
2. Shwarts Yu.M., Borblik V.L., Kulish N.R.,
Sokolov V.N., Shwarts M.M., and Venger E.F.
Silicon diode temperature sensor without a kink of
the response curve in cryogenic temperature region.
Sensors and Actuators. 1999. 76, No. 1-3. P. 107–
111.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 2. P. 195-198.
doi: https://doi.org/10.15407/spqeo20.02.195
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
198
3. Borblik V.L., Shwarts Yu.M., and Shwarts M.M.
Revealing the hopping mechanism of conduction in
heavily doped silicon diodes. Semiconductor
Physics, Quantum Electronics & Optoelectronics.
2005. 8, No.2. P. 41–44.
4. Borblik V.L., Shwarts Yu.M., and Shwarts M.M.
Manifestation of disorder effects in excess tunnel
current of heavily doped silicon diodes. Bull.
Russian Acad. Sci.: Physics. 2007. 71, No. 8.
P. 1073–1075.
5. Borblik V.L., Shwarts Yu.M., and Shwarts M.M.
Characteristics of diode temperature sensors which
exhibit Mott conduction in low-temperature region.
Semiconductor Physics, Quantum Electronics &
Optoelectronics. 2007. 10, No. 3. P. 44–47.
6. Sze S.M. Physics of Semiconductor Devices. 2nd
ed., John Wiley & Sons, New York, 1981.
7. Del Alamo J.A. and Swanson R.M. Forward-bias
tunneling: a limitation to bipolar device scaling.
IEEE Electron. Device Lett. 1986. EDL-7(11).
P. 629–631.
8. Shklovskii B.I. Hopping conduction of heavily
doped semiconductors. Sov. Phys.-Semicond. 1973.
7, No. 1. P. 77–83 (in Russian).
9. Borblik V.L., Rudnev I.A., Shwarts Yu.M., and
Shwarts M.M. Negative magnetoresistance of
heavily doped silicon p-n junction. Semiconductor
Physics, Quantum Electronics & Optoelectronics.
2010. 14, No. 1. P. 88–90.
10. Shkovskii B.I. and Efros A.L. Electronic
Properties of Doped Semiconductors. Berlin,
Springer, 1984.
11. Ionov A.N., Rentzsch R., and Shlimak I. Role of
electron “lakes” in the effect of negative
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203.
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| id | nasplib_isofts_kiev_ua-123456789-214933 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2026-03-21T13:44:55Z |
| publishDate | 2017 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Borblik, V. L. Shwarts, Yu. M. Shwarts, M. M. Aleinikov, A. B. 2026-03-04T12:53:05Z 2017 New evidence of the hopping nature of the excess tunnel current in heavily doped silicon - diodes at cryogenic temperatures / V. L. Borblik, Yu. M. Shwarts, M. M. Shwarts, A. B. Aleinikov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2017. — Т. 20, № 2. — С. 195-198. — Бібліогр.: 11 назв. — англ. 1560-8034 PACS: 72.20.Ee, 72.20.My, 85.30.Kk https://nasplib.isofts.kiev.ua/handle/123456789/214933 https://doi.org/10.15407/spqeo20.02.195 The new experimental data concerning the effect of a magnetic field on the electric properties of silicon diodes with high doping levels both in the emitter and base (conduction of which at low temperatures is determined by the excess tunnel current) have been analyzed. In addition to previous investigations of the influence of magnetic fields up to 9.4 T on this tunnel current at 4.2 K, now the measurements have been carried out up to 14 T at temperatures lower than the liquid helium temperature. Under these conditions, the transfer to saturation of the diode magnetoresistance was observed, which agrees with the results predicted theoretically for the hopping conduction via impurity centers in high magnetic fields. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics New evidence of the hopping nature of the excess tunnel current in heavily doped silicon - diodes at cryogenic temperatures Article published earlier |
| spellingShingle | New evidence of the hopping nature of the excess tunnel current in heavily doped silicon - diodes at cryogenic temperatures Borblik, V. L. Shwarts, Yu. M. Shwarts, M. M. Aleinikov, A. B. |
| title | New evidence of the hopping nature of the excess tunnel current in heavily doped silicon - diodes at cryogenic temperatures |
| title_full | New evidence of the hopping nature of the excess tunnel current in heavily doped silicon - diodes at cryogenic temperatures |
| title_fullStr | New evidence of the hopping nature of the excess tunnel current in heavily doped silicon - diodes at cryogenic temperatures |
| title_full_unstemmed | New evidence of the hopping nature of the excess tunnel current in heavily doped silicon - diodes at cryogenic temperatures |
| title_short | New evidence of the hopping nature of the excess tunnel current in heavily doped silicon - diodes at cryogenic temperatures |
| title_sort | new evidence of the hopping nature of the excess tunnel current in heavily doped silicon - diodes at cryogenic temperatures |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214933 |
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