Characteristics of diode temperature sensors which exhibit Mott conduction in low temperature region
Heavily doped silicon diodes of n⁺⁺-p⁺ type which exhibit the Mott temperature dependence of the forward current in a certain range of bias voltages and low temperatures have studied from the point of their use as temperature sensors. In the region of hopping conduction, the operating signal of d...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2007
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| Цитувати: | Characteristics of diode temperature sensors which exhibit Mott conduction in low temperature region / V.L. Borblik, Yu.M. Shwarts, M.M. Shwarts // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2007. — Т. 10, № 3. — С. 44-47. — Бібліогр.: 11 назв. — англ. |
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irk-123456789-1181202017-05-29T03:05:27Z Characteristics of diode temperature sensors which exhibit Mott conduction in low temperature region Borblik, V.L. Shwarts, Yu.M. Shwarts, M.M. Heavily doped silicon diodes of n⁺⁺-p⁺ type which exhibit the Mott temperature dependence of the forward current in a certain range of bias voltages and low temperatures have studied from the point of their use as temperature sensors. In the region of hopping conduction, the operating signal of diodes U (T) (U is a voltage drop across the diode during the passage of a constant current, T is the temperature) reproduces the Mott law (with opposite sign in the exponent), and the temperature sensitivity of such sensors after passing through a minimum (as the temperature is lowered) increases again up to the values typical of room temperature 2007 Article Characteristics of diode temperature sensors which exhibit Mott conduction in low temperature region / V.L. Borblik, Yu.M. Shwarts, M.M. Shwarts // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2007. — Т. 10, № 3. — С. 44-47. — Бібліогр.: 11 назв. — англ. 1560-8034 PACS 07.07.Df, 61.72.Tt, 72.20.-I, 85.30.Kk http://dspace.nbuv.gov.ua/handle/123456789/118120 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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English |
| description |
Heavily doped silicon diodes of n⁺⁺-p⁺ type which exhibit the Mott
temperature dependence of the forward current in a certain range of bias voltages and
low temperatures have studied from the point of their use as temperature sensors. In the
region of hopping conduction, the operating signal of diodes U (T) (U is a voltage drop
across the diode during the passage of a constant current, T is the temperature)
reproduces the Mott law (with opposite sign in the exponent), and the temperature
sensitivity of such sensors after passing through a minimum (as the temperature is
lowered) increases again up to the values typical of room temperature |
| format |
Article |
| author |
Borblik, V.L. Shwarts, Yu.M. Shwarts, M.M. |
| spellingShingle |
Borblik, V.L. Shwarts, Yu.M. Shwarts, M.M. Characteristics of diode temperature sensors which exhibit Mott conduction in low temperature region Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Borblik, V.L. Shwarts, Yu.M. Shwarts, M.M. |
| author_sort |
Borblik, V.L. |
| title |
Characteristics of diode temperature sensors which exhibit Mott conduction in low temperature region |
| title_short |
Characteristics of diode temperature sensors which exhibit Mott conduction in low temperature region |
| title_full |
Characteristics of diode temperature sensors which exhibit Mott conduction in low temperature region |
| title_fullStr |
Characteristics of diode temperature sensors which exhibit Mott conduction in low temperature region |
| title_full_unstemmed |
Characteristics of diode temperature sensors which exhibit Mott conduction in low temperature region |
| title_sort |
characteristics of diode temperature sensors which exhibit mott conduction in low temperature region |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/118120 |
| citation_txt |
Characteristics of diode temperature sensors which exhibit Mott conduction in low temperature region / V.L. Borblik, Yu.M. Shwarts, M.M. Shwarts // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2007. — Т. 10, № 3. — С. 44-47. — Бібліогр.: 11 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
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| first_indexed |
2025-07-08T13:23:56Z |
| last_indexed |
2025-07-08T13:23:56Z |
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| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 3. P. 44-47.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
44
PACS 07.07.Df, 61.72.Tt, 72.20.-I, 85.30.Kk
Characteristics of diode temperature sensors
which exhibit Mott conduction in low-temperature region
V.L. Borblik, Yu.M. Shwarts, M.M. Shwarts
V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine
41, prospect Nauky, 03028 Kyiv, Ukraine
Phone: +38(044)525-62-92, fax: +38(044)525-74-63
Abstract. Heavily doped silicon diodes of n++-p+ type which exhibit the Mott
temperature dependence of the forward current in a certain range of bias voltages and
low temperatures have studied from the point of their use as temperature sensors. In the
region of hopping conduction, the operating signal of diodes U (T) (U is a voltage drop
across the diode during the passage of a constant current, T is the temperature)
reproduces the Mott law (with opposite sign in the exponent), and the temperature
sensitivity of such sensors after passing through a minimum (as the temperature is
lowered) increases again up to the values typical of room temperature.
Keywords: junction diode, temperature sensor, silicon, hopping conductivity, heavy
doping, strong compensation.
Manuscript received 29.05.07; accepted for publication 27.09.07; published online 31.10.07.
1. Introduction
In [1], we have shown that, by means of the heavy
doping of the base of a silicon thermodiode, one can get
rid of a sharp kink in its response curve at temperatures
near 40 K connected with the freezing-out of free current
carriers into impurities. Under conditions of high-level
doping, the base conductivity becomes metallic and
current carriers do not freeze-out at any temperatures.
Herewith in [1], we observed a continuous decrease in
the temperature sensitivity of such a sensor with
temperature lowering connected with the domination of
the tunnel component in the diode current under such
conditions (heavy doping, low temperatures) (we are
talking here about the so-called excess tunnel current [2]
rather than the direct interband tunneling).
Continuing our investigations of the influence of a
high-level doping of the diode base on its characteristics,
we have manufactured the silicon diodes which exhibit
(in a certain range of temperatures and forward bias
voltages) the Mott temperature dependence of the diode
current at a constant voltage drop across the diode [3].
This dependence has been interpreted previously as a
manifestation of hopping conduction through the
electron “drops” which have to arise (in correspondence
with the theory [4]) in the central, strongly compensated,
region of the p-n junction that may be likened to heavily
doped and strongly compensated semiconductor.
In this paper, we represent the results of
comparative analysis of the characteristics for two of
such type diodes (which are distinguished lightly by
doping level) including also their response curves as
temperature sensors. The Mott temperature dependence
of the forward current observed in both diodes is shown
to be consistent with the published data on the
temperature dependence of the conductivity of heavily
doped and strongly compensated bulk silicon. The
diodes with such properties being used as temperature
sensors demonstrate (unlike the diodes studied in [1]) the
presence of a minimum in their temperature sensitivity
(when the temperature lowers), after which its subse-
quent sufficient increase is observed again. Herewith,
the value of sensitivity reaches (at the liquid helium
temperature) the magnitudes typical of silicon diode
sensors at room temperature, i.e. of the order of 2 mV/K.
2. Results of measurements and their analysis
2.1. Current-voltage characteristics
In Fig. 1, we present the temperature families of the
forward current-voltage characteristics (CVCs) of two
silicon planar diodes of n++-p+ type, whose bases as well
as the emitters were doped up to metallic conductivity
(samples N 6-6 and N 6-7). The p-n junctions were
formed by opposite diffusion of boron and phosphorus at
slightly different concentrations of the dopants. The
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 3. P. 44-47.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
45
1.00 1.02 1.04 1.06 1.08 1.10
1E-8
1E-7
1E-6
1E-5
N6-6
N6-7
I,
A
U, V
4.22 K
5.35 K
6.55 K
8.25 K
11.0 K
13.5 K
4.2 K
5.5 K
7 K
9 K
10.8 K
Fig. 1. Current-voltage characteristics of two silicon n++-p+
diodes N6-6 and N6-7 in cryogenic temperature region.
CVC families are shown for the range of voltages and
temperatures where the diode current is the tunnel one
completely. The visual indication of this fact (as was
shown by us in [1]) consists in the quasiparallel
character of the CVCs at different temperatures plotted
on the semilogarithmic scale; in Fig. 1, it is the range
between 1 and 1.08 V. In this region, the CVCs are
described by the expression [2]
=
tU
U
TITUI exp)(),( 0 , (1)
where U is the applied voltage, T is the temperature,
DA
DA
t
NN
NN
mU
+
χ=− *1 4
is a temperature-independent
constant, is the Planck constant (divided by 2π), *m is
the effective mass of tunneling carriers, χ is the
dielectric constant of the semiconductor, and DN and
AN are the concentrations of donors and acceptors,
respectively. Herewith [2]
[ ]tbi UTqVTITI )(exp)()( 000 −= , (2)
where q is the electron charge, )(TVbi is the built-in
potential of a p-n junction. Under the degeneration
conditions, pngbi TETqV FF)()( εε ++= [5], where
)(TEg is the temperature-dependent semiconductor
gap, nFε and pFε are the degeneracy degrees for the
conduction and valence bands, respectively. So, the
temperature dependence of biV is determined, mainly,
by the temperature dependence of the gap. Because
)()0()( 2 TbaTETE gg +−= [5] where a and b are
constants, then const)0()( =≈ gg ETE at low
temperatures, and one can expect to observe the
temperature dependence of the excess tunnel current not
obscured by the temperature dependence of the p-n
junction barrier.
From Fig. 1, we obtain the ratio of CVCs’ slopes
for two diodes 91.0
88
80
1
1
66
1
76
1
==
−
−
−
−
−
−
B
B
U
U
t
t . This is in
agreement with the value of 0.93 following from the
expression for 1−
tU with substitution of the
corresponding doping levels.
2.2. Temperature dependence of the forward current at
fixed bias voltages
In Fig. 2 a, b, we display the temperature dependences of
both diode currents at a number of fixed values for the
bias voltage. To clarify the mechanism of the current
flow, Fig. 3a, b shows the same temperature
dependences at a bias voltage of 1.02 V (at the rest
voltages, the picture is similar) in three different forms:
versus 1/T, ( ) 2/11 T , and ( ) 4/11 T . Herewith, because
the current interval where hopping conduction is
anticipated is rather small, Fig. 3 depicts the product of I
and T as a function of ( ) 4/11 T and the product of I
and T as a function of ( ) 2/11 T ; these procedures take
the pre-exponential factors in the Mott [6] and Efros-
Shklovskii [7] formulas, respectively, into account.
In the region of lowest temperatures (region I), the
current as a function of temperature is described well
just by the Mott law
4 6 8 10 12 14 16 18
1E-8
1E-7
I 1.02 V
1.03 V
1.04 V
1.05 V
1.06 V
N6-6
I,
A
T, K
a
4 6 8 10 12 14 16 18 20
1E-8
1E-7
1E-6 I
N6-7
I,
A
T, K
1.01V
1.02V
1.03V
1.04V
1.05V
b
Fig. 2. Temperature dependences of the forward current for the
diodes N6-6 (a) and N6-7 (b) at a number of bias voltages U .
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 3. P. 44-47.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
46
0.05 0.10 0.15 0.20 0.25
5.6028E-9
1.523E-8
0.25 0.30 0.35 0.40 0.45 0.50
0.50 0.55 0.60 0.65 0.70
5.6028E-9
1.523E-8
4.13994E-8
vs 1/T
N6-6 U=1.02 V
(1/T)1/2, K-1/2
(1/T), K-1
I,
A
(1/T)1/4, K-1/4
I*T
vs (1/T)1/2
I*(
T)
1/
2
I
vs (1/T)1/4
a
0.05 0.10 0.15 0.20 0.25
4.13994E-8
0.25 0.30 0.35 0.40 0.45 0.50
0.50 0.55 0.60 0.65 0.70
4.13994E-8
1.12535E-7
3.05902E-7
vs (1/T)
N6-7 U=1.02 V
1/T, K-1
(1/T)1/2, K-1/2
I,
A
(1/T)1/4, K-1/4
I*T
vs (1/T)1/2 I*T
1/
2
I vs (1/T)1/4
b
Fig. 3. Presentation of the temperature dependences of the
forward current for the diodes N6-6 (a) and N6-7 (b) in three
different forms: versus T1 , ( ) 2/11 T , and ( ) 4/11 T .
( ) TTTTI
− 4
1
0exp~)( . (3)
So, conductivity has here hopping character, and
the hopping length increases with decrease in
temperature; simultaneously, the conductivity activation
energy decreases. Defining the varying activation energy
by the derivative
1)(
ln
−
−
kTd
Id (k is the Boltzmann
constant), we obtain its values from 0.56 to 0.27 meV
(the same for both diodes).
But the characteristic temperatures, T0, for two
diodes are different. For diode N 6-7 with lower doping
level in the n-region, the averaged value of T0 is 2700 K;
but, for diode N 6-6, T0 ≈ 2200 K. Therefore, their ratio
is equal to 1.2. Because
3
0F
0
)(
const
aEgk
T = [6], where
)( FEg is the density of states near the Fermi level, 0a
is the localization radius of the states through which the
electron hops take place, then the ratio of characteristic
temperatures may be equated to the reciprocal ratio of
the densities of states if the localization radii are
believed to be the same. Then the ratio of the densities of
states reduces to the ratio of the doping levels that gives
approximately the same value:
4 5 6 7 8 9 10 11 12
5.00E-016
1.00E-015
1.50E-015
2.00E-015
I
N6-6 U=1.04 V
N6-7 U=1.02 V
I2 , A
2
T, K
Fig. 4. Temperature dependences of the current squared for
both diodes in the Mott law region.
3.1
/6.1
/1.2
660
760 ≈
◊Ω
◊Ω
=
−
−
T
T
.
So, the results of comparative analysis of the diode
characteristics do not contradict the idea of the hopping
nature of their conductivity at low temperatures.
The fact of the existence of Mott conductivity in a
heavily doped diode is consistent completely with the
long ago noticed analogy between heavily doped,
strongly compensated crystalline semiconductors and
amorphous materials [8]. There are large differences,
however, between magnitudes of the parameter T0.
According to [9, 10], T0 ≈ 107 K in amorphous Ge and
Si. But, in our case, T0 ≈ (2−3)103 K. This fact gives
evidence, in our opinion, of a larger density of localized
states in a heavily doped p-n junction in comparison
with amorphous materials. It indicates also that hopping
conductivity is connected here with current carriers
localized in electron drops rather than at impurities or
defect states.
It is worth to note also that, in the region of Mott
law action, the temperature dependence of the diode
current squared is very close to a linear one (see Fig. 4,
where different bias voltages are taken for different
diodes in order to get comparable current magnitudes).
Therefore, if no special carefulness is required, one can
estimate approximately the dependence I (T) as that
proportional to T . This is made, apparently, in [11]
while studying the low-temperature conductivity of
heavily doped and strongly compensated bulk silicon.
2.3. The response curves of the diodes
The response curve of a diode, U (T), is the variation of
the voltage drop across the diode with temperature when
a fixed operation current, operI , is passed through it.
According to Fig. 2, the conductivity of diodes decreases
as the temperature decreases. Therefore, for keeping the
operation current as constant (in the temperature
measurement regime), the voltage drop across the diode
has to increase. Just such a behavior is demonstrated by
the measurement results for both diodes (at an operating
current of 1 µA) presented in Fig. 5.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 3. P. 44-47.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
47
0 20 40 60 80 100 120 140
0.90
0.95
1.00
1.05
1.10
0,3 0,4 0,5 0,6 0,7
1
I
N6-7
N6-6
U,
V
(1/T)1/4, K-1/4
I
N6-7
N6-6
U
, V
T, K
Fig. 5. Temperature response curves for both diodes; the
insert – the same versus ( ) 4/11T .
It is interesting that, in the region where
conductivity varies with temperature by the Mott law
(2), the voltage drops across the diodes vary by the
opposite law (the plus sign in the exponent) and with
another values of characteristic temperatures:
( )
4
1
*
0exp~)( TTTU (4)
(see the insert in Fig. 5). Let us note also that we are
faced here with that rare case where the response curve
in the low-temperature region can be expressed
analytically. This circumstance facilitates the task of
obtaining the thermodiode calibration characteristic in
this temperature range.
Temperature sensitivity,
operII
dTdU
=
, of the
diodes studied is presented in Fig. 6. It is characterized by
the presence of a minimum near T = 20 K, after which the
sensitivity increases again with decrease in temperature
down to the values of the order of 1-1.5 mV/K and
continues to increase farther (as shown by the previous
measurements at somewhat lower temperatures).
0 20 40 60 80 100 120 140
0.0000
0.0005
0.0010
0.0015
0.0020
I
T, K
ab
s(
dU
/d
T)
, V
/K
N6-6
N6-7
Fig. 6. Temperature sensitivity of both diodes as temperature
sensors in cryogenic temperature region.
3. Conclusion
Thus, the idea of the utterly weak temperature
dependence of a tunnel current proves to be valid not
always. In heavily doped silicon diodes manufactured by
opposite diffusion, a potential pattern resulting in the
Mott hopping conduction can be produced. In such a
case, one can obtain such temperature sensitivity of the
diode sensors in the low-temperature region which is not
worse than that at room temperature under conditions of
dominating diffusion current.
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