Revealing the hopping mechanism of conduction in heavily doped silicon diodes
Measurements of temperature dependences of excess tunnel current in heavily doped silicon p-n junction diodes at fixed values of the forward bias are carried out in liquid helium temperature region. In some voltage interval, these dependences are described well by the Mott law for variable range hop...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2005
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| Zitieren: | Revealing the hopping mechanism of conduction in heavily doped silicon diodes / V. L. Borblik, Yu. M. Shwarts, M. M. Shwarts // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2005. — Т. 8, № 1. — С. 41-44. — Бібліогр.: 8 назв. — англ. |
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irk-123456789-1206522017-06-13T03:02:46Z Revealing the hopping mechanism of conduction in heavily doped silicon diodes Borblik, V. L. Shwarts, Yu. M. Shwarts, M. M. Measurements of temperature dependences of excess tunnel current in heavily doped silicon p-n junction diodes at fixed values of the forward bias are carried out in liquid helium temperature region. In some voltage interval, these dependences are described well by the Mott law for variable range hopping conductivity. The interpretation of these results considers a p-n junction from a nontraditional point of view, namely, as heavily doped and highly compensated semiconductor. 2005 Article Revealing the hopping mechanism of conduction in heavily doped silicon diodes / V. L. Borblik, Yu. M. Shwarts, M. M. Shwarts // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2005. — Т. 8, № 1. — С. 41-44. — Бібліогр.: 8 назв. — англ. 1560-8034 PACS: 07.07.Df, 72.20.Ee, 73.40.-c http://dspace.nbuv.gov.ua/handle/123456789/120652 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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Measurements of temperature dependences of excess tunnel current in heavily doped silicon p-n junction diodes at fixed values of the forward bias are carried out in liquid helium temperature region. In some voltage interval, these dependences are described well by the Mott law for variable range hopping conductivity. The interpretation of these results considers a p-n junction from a nontraditional point of view, namely, as heavily doped and highly compensated semiconductor. |
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Borblik, V. L. Shwarts, Yu. M. Shwarts, M. M. |
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Borblik, V. L. Shwarts, Yu. M. Shwarts, M. M. Revealing the hopping mechanism of conduction in heavily doped silicon diodes Semiconductor Physics Quantum Electronics & Optoelectronics |
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Borblik, V. L. Shwarts, Yu. M. Shwarts, M. M. |
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Borblik, V. L. |
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Revealing the hopping mechanism of conduction in heavily doped silicon diodes |
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Revealing the hopping mechanism of conduction in heavily doped silicon diodes |
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Revealing the hopping mechanism of conduction in heavily doped silicon diodes |
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Revealing the hopping mechanism of conduction in heavily doped silicon diodes |
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Revealing the hopping mechanism of conduction in heavily doped silicon diodes |
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revealing the hopping mechanism of conduction in heavily doped silicon diodes |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2005 |
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Revealing the hopping mechanism of conduction in heavily doped silicon diodes / V. L. Borblik, Yu. M. Shwarts, M. M. Shwarts // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2005. — Т. 8, № 1. — С. 41-44. — Бібліогр.: 8 назв. — англ. |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
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2025-07-08T18:17:04Z |
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 2. P. 41-44.
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
41
PACS: 07.07.Df, 72.20.Ee, 73.40.-c
Revealing the hopping mechanism of conduction
in heavily doped silicon diodes
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/Fax: +38 (044) 525 7463
*Phone: +38 (044) 525 6292, e-mail: borblik@lab2.semicond.kiev.ua
Abstract. Measurements of temperature dependences of excess tunnel current in heavily
doped silicon p-n junction diodes at fixed values of the forward bias are carried out in
liquid helium temperature region. In some voltage interval, these dependences are
described well by the Mott law for variable range hopping conductivity. The
interpretation of these results considers a p-n junction from a nontraditional point of
view, namely, as heavily doped and highly compensated semiconductor.
Keywords: junction diode, temperature sensor, silicon, heavy doping, high
compensation, hopping conductivity.
Manuscript received 18.04.05; accepted for publication 18.05.05.
1. Introduction
Silicon p-n junction diodes used as the temperature
sensors have usually a sharp kink in their response
curves in the temperature range where freezing-out of
the current carriers occurs. In order to avoid this kink,
we have developed and investigated silicon diodes
where both sides of their p-n junctions were doped up to
the impurity concentrations providing metallic
conductivity. In this case, the response curve holds
quasi-linear character down to the liquid helium
temperature [1]. In the region of such low temperatures,
a current through the diode proves to be tunnel.
Herewith, direct band-to-band tunneling is impossible,
therefore we are talking here about the so-called excess
tunnel current that is connected with presence of
localized states in the forbidden semiconductor band.
This current is characterized by the dependence
)/exp(0 TUUII = (1)
where U is the bias voltage, and TU is the temperature-
independent constant. The above dependence is believed
to be connected with narrowing (under forward bias) the
space charge region of the p-n junction (see Ref. [2] and
references therein). In the frame of such the approach,
the factor 0I is proportional to )/exp( Tbi UqV− , where
q is an electron charge, biV is a built-in potential of the
p-n junction. Its weak temperature dependence just
determines the diode response curve in the range where
tunnel current dominates. Under the degeneracy
conditions FpFngbi TEqV εε ++= )( where )(TEg is
the temperature-dependent energy gap of semiconductor,
and FpFn εε , are degeneracy degrees of electrons and
holes, respectively. Therefore, temperature dependence
of biV is determined, mainly, by )(TEg . Because
)()0()( 2 TbaTETE gg +−= where a and b are the
constants [3], at not low temperatures
cTETE gg −≈ )0()( and )exp(0 ATI ∝ . Such depen-
dence was observed in the experiments so far [4]. We
have studied the excess tunnel current at so low
temperatures when const)0()( =≈ gg ETE and found as a
result weak temperature dependence of 0I satisfying the
Mott law [5]. The obtained data have been interpreted by
us on the basis of the electron theory of heavily doped
semiconductors.
2. Measurement results
Measured current-voltage characteristics (CVC) of the
heavily doped silicon n++-p+ structure both sides of which
possess metallic conductivity are represented in Fig. 1 (for
the cryogenic temperature region). As was shown in
Ref. [1], a visual criterion for domination of tunnel diode
current in some range of temperatures and bias voltages is
the quasi-parallel character of the CVCs (plotted in semi-
logarithmic scale) corresponding to different tempe-
ratures. In Fig. 1, this region extends from 1.0 to 1.08 V
within the temperature range of 4.2 – 13.5 K.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 2. P. 41-44.
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
42
1.00 1.02 1.04 1.06 1.08 1.10
10-8
10-7
10-6
10-5
4.22 K
5.35 K
6.55 K
8.25 K
11.0 K
13.5 K
I,
A
U, V
Fig. 1. Current-voltage characteristics of the silicon
n++-p+-type diode in the cryogenic temperature region.
Shown in Fig. 2 are the temperature dependences of
the diode current for a number of fixed values of the
forward bias from the abovementioned interval. They are
by no means described by )exp(AT . These dependences
plotted against reciprocal temperature (Fig. 3) give an
evidence for variable activation energy of conductivity
that is characteristic for variable range hopping
conduction [5, 6]. The same temperature dependences of
the forward current (at the fixed bias voltages) plotted in
the form which anticipates the Mott law [5] for
conductivity
( )[ ]4/1
0exp TTI −∝ (2)
fall on straight lines satisfactorily in semi-logarithmic
scale (Fig. 4). For greater persuasiveness, for one of the
bias voltages (U = 1.02 V), three temperature
dependences of the diode current are integrated in Fig. 5:
the first one is plotted as a function of reciprocal
temperature, the second one – versus (1/T)1/2 (such
dependences are also observed often under hopping
conduction conditions), and the third one – against
(1/T)1/4. Their comparison says persuasively in favor just
of Mott’s character of the temperature dependence for
the diode current.
In our opinion, this fact firstly appears to be the first
observation of Mott's conductivity in semiconductor
structures with p-n junctions, and, secondly, sheds
additional light on the nature of the excess tunnel current
in heavily doped junction diodes.
3. Interpretation of the measurement results
With a metallic character of the conductivity both in the
emitter and in the base, the diode current is determined
completely by resistance of the p-n junction. The latter
may be considered as heavily doped and highly
compensated semiconductor. From this point of view,
self-consistent spatial fluctuations of the electrostatic
potential have to arise in the p-n junction region which
will bend both the bottom of the conduction band and
the top of the valence one. As is known [6], the limiting
scale of such fluctuations is available as to both
magnitude and spatial extent.
From above their amplitude is limited by the
bandgap value gE and their extent – by sizes of the order
of 4
22
qN
E
R
t
g
g
ε
≅ where ADt NNN += is total con-
centration of donors and acceptors in the region of
complete compensation, i.e. at metallurgical boundary of
the p-n junction, and ε is dielectric constant of
semiconductor. Let us compare this characteristic scale
(i.e. gR ) with the width w of the junction space charge
region as it is was defined in a traditional theory of p-n
junctions [3]. Omitting the numerical coefficients (as
well as it was made in the expression for gR ) we have
4 6 8 10 12
10-8
10-7
1.05 V
1.04 V
1.03 V
1.02 VI,
A
T, K
1.01 V
Fig. 2. Temperature dependences of the diode current at a
number of bias voltages.
0.10 0.15 0.20 0.25
10-8
10-7
1.05 V
1.04 V
1.03 V
1.01 V
I,
A
1/T, K-1
1.02 V
Fig. 3. Forward diode current versus reciprocal temperature at
a number of voltage U values.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 2. P. 41-44.
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
43
2qN
E
w
t
gε
≈ . The ratio 33
6
2
2
εg
t
g E
qN
R
w
≈ is proved to be of
the order of unity if we take for estimations Nt ∼1018 cm–3,
Eg ∼ 1 eV, ε /ε0 ∼ 10 (ε0 is permittivity of vacuum). It is
not surprising because both characteristic lengths are
screening radii.
Thus, the so-called built-in potential of the p-n
junction may be considered as the most-large-scale
electrostatic potential fluctuation. With deviation from
the metallurgical boundary of the p-n junction, the com-
pensation degree will decrease, therefore the amplitude γ
of the large-scale potential fluctuations will reduce in
accordance with the formula [7] =− )( AD NNγ
3/1
3/22
AD
maj
NN
Nq
−
=
ε
where Nmaj is concentration of the
majority impurity. The characteristic scale cR of the
large-scale fluctuations also reduces: =− )( ADc NNR
3/2
3/1
AD
maj
NN
N
−
= .
Naturally, small-scale potential fluctuations will be
superimposed in this large-scale picture according to the
theory [6, 7]. These small-scale fluctuations are limited
from below by the size ( ) 9/13
Bmaj
B
q
aN
aR = where Ba is
the Bohr radius of the bonded state of electron (or hole)
at the single impurity center. Herewith, gBq RaR <<<
because in the case under consideration 13 >>BmajaN .
Free current carriers come together in the wells of these
minimal potential fluctuations forming “metallic drops”.
The obtained band picture is shown schematically in
Fig. 6.
Under forward bias, the mechanism by means of
which the current carriers overcome the main potential
barrier remains the same as it was believed so far [2, 3] ,
i.e., tunneling through the intermediate localized states
in the gap with subsequent recombination (paths A, B or
C). But further, carriers have to pass through the “drops”
systems at both sides of the p-n junction. At low
temperatures, such conduction will be hopping with the
distinction that the hopes will be here not between
localized states of carriers at the impurity centers (as
usually) but between the “metallic drops” [7]. We
believe that just this type of conduction is responsible
for the Mott temperature dependence of the diode
current observed by us, because under our conditions all
current carriers have to be localized in the wells isolated
one from another.
0.55 0.60 0.65 0.70
10-8
10-7
1.05 V
1.04 V
1.03 V
1.02 V
I,
A
(1/T)1/4, K-1/4
1.01 V
Fig. 4. Forward diode current at fixed voltage values as a
function of ( ) 4/11 T .
0.30 0.35 0.40 0.45
0.55 0.60 0.65 0.70
0.10 0.15 0.20
I,
A
(1/T) , T –1/1/ 22
versus 1/T
I,A
(1/T)1/4, T-1/4
versus (1/T)1/2
versus (1/T)1/4
1/T, K–1
3E-8 3E-8
4E-8 4E-8
5E-8 5E-8
Fig. 5. Comparison of temperature dependences of the diode
current (at V02.1=U ) plotted as a function of reciprocal
temperature, and also versus ( ) 211 T and against ( ) 4/11 T .
Fig. 6. Band scheme of a heavily doped p-n junction in the bias
absence (a) and under forward bias (b) with account of
potential fluctuations (the filled states are shaded).
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 2. P. 41-44.
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
44
It should be noted that it was the strong
compensation ( 99.0≈
D
A
N
N ) that had allowed to
observe the variable range hopping conductivity in
silicon for the first time [8]
Variable magnitude of the conductivity activation
energy may be defined here as a derivative 1)(
)(ln
−−
kTd
Id .
Corresponding analysis of the curves in Fig. 3 gives
continuous series of this energy magnitudes decreasing
from 0.55 to 0.27 meV (for any bias voltage of
considered interval). And a value of the parameter 0T in
(2) determined by analysis of the curves in Fig. 4 varies
slightly with the voltage near the value of 0T = 300 K.
In accordance with the theory of variable range
hopping conduction [6], the average hopping length R
is associated with a localization radius of current carriers
by the dependence
41
0 ⎟
⎠
⎞
⎜
⎝
⎛≈
T
TaR (3)
which describes lengthening of the hop with temperature
lowering. In the temperature range where we observe
Mott’s conductivity, the ratio T
T0 varies from
approximately 25 to 80, and, consequently, the ratio a
R
varies from 2.3 to 3. Taking into consideration the
evaluative character of the formula (3), one should
believe that, in our case, average hopping length coin-
cides, on the order of magnitude, with the localization
radius for current carriers in anticipated drops.
4. Conclusions
So, the way of “linearization“ of the thermodiode
response curve by means of heavy doping the diode base
undertaken by us in Ref. [1] gave really rise to desirable
aim, but with some loss of sensitivity in the range of
lowest temperatures. This fact is connected with
domination in the diode current (under these conditions)
of the tunnel current component lightly varying with
temperature. However, its detailed investigation has
allowed to us to reveal some fundamental properties of
heavily doped diode structures. In particular, variable
range hopping conductivity predicted for heavily doped
and highly compensated (macroscopically homo-
geneous) semiconductors is found to be realized in
heavily doped silicon p-n junction diodes.
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