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YANGI O'ZBEKISTON ILMIY
TADQIQOTLAR JURNALI
www.in-academy.uz
2-JILD, 5-SON 2-QISM, (YOʻITJ)
MODELING THE EFFECT OF TEMPERATURE ON SILICON-
BASED SEMICONDUCTOR DEVICES
1.Sh.M. Urinbaev , 2.G.E. Nurmetova, 3.A. Farhodov
1.assistant of NRU of TIIAME,
2. assistant of Tashkent Medical Academy
3. student of NRU of TIIAME
sharofiddinurinbaev@gmail.com
+998990899697
https://doi.org/10.5281/zenodo.15533394
ARTICLE INFO
ABSTRACT
Qabul qilindi:16-may 2025 yil
Ma’qullandi:18-may 2025 yil
Nashr qilindi: 28-may 2025 yil
The behavior of silicon-based semiconductor
devices is significantly influenced by temperature.
Temperature variations affect key parameters such as
carrier mobility, bandgap energy, and recombination
rates, thereby altering the current-voltage (I-V)
characteristics. This study aims to model these effects
and provide insights into the performance of silicon-
based devices under varying thermal conditions. By
incorporating temperature-dependent equations and
numerical simulations, the study highlights the critical
parameters that engineers must consider in device
design and optimization.
KEY WORDS
Temperature
effect,
silicon
semiconductors, current-voltage
characteristics, mobility, bandgap
energy, recombination rates.
Introduction
Silicon-based semiconductors are pivotal in modern electronics, valued for their
consistent performance, affordability, and widespread material availability. Nevertheless,
their functionality is susceptible to environmental influences, particularly temperature.
Comprehending the thermal properties of semiconductors is vital for applications spanning
microelectronics to high-power devices, especially in environments with extreme
temperature conditions.
This study delves into the core effects of temperature on silicon semiconductors, with a
primary focus on its impact on current-voltage (I-V) characteristics. It examines temperature-
driven changes in intrinsic carrier concentration, bandgap energy, and charge carrier mobility,
which together govern the electrical performance of silicon devices. [1] [2].
Theoretical Part
The performance of silicon-based semiconductors at different temperatures is
determined by several fundamental physical principles, such as intrinsic carrier concentration,
charge carrier mobility, bandgap energy, and the processes of carrier generation and
recombination. A thorough understanding of these factors is essential for evaluating the
temperature-dependent current-voltage (I-V) characteristics and for enhancing the efficiency
of semiconductor devices across various thermal conditions. [3] [4].
1. Intrinsic Carrier Concentration
The intrinsic carrier concentration, n
i
, increases exponentially with rising
temperature, governed by its dependence on bandgap energy and thermal energy [5]
exp
.
g
i
c v
E
n
N N
kT
=
-
(1)
In this:
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YANGI O'ZBEKISTON ILMIY
TADQIQOTLAR JURNALI
www.in-academy.uz
2-JILD, 5-SON 2-QISM, (YOʻITJ)
n
i
:
Intrinsic carrier concentration
(cm
-3
) Describes the quantity of free electrons
or holes in an undoped semiconductor at thermal equilibrium, influenced by
temperature (�) and the energy bandgap (E
g
).
N
c
:
Effective density of states in the conduction band
(cm
-3
) Indicates the number
of available energy states in the conduction band for electrons. It depends on
temperature as
3 2
c
N
T
µ
N
v
:
Effective density of states in the valence band
(cm
-3
) Indicates the number of
available energy states in the valence band for holes. Similar to N
c
, it also depends on
temperature as
3 2
c
N
T
µ
E
g
:
Bandgap energy
(eV) Represents the energy difference between the conduction
band and the valence band. It is temperature-dependent, decreasing as T increases.
k:
Boltzmann constant
(8.617×10
−5
eV/K) Relates temperature to energy in physical
systems.
T:
Temperature
(K) The absolute temperature of the system, which strongly affects
n
i
.
At elevated temperatures, a greater number of electrons acquire the energy needed to
transition from the valence band to the conduction band, thereby augmenting the native
charge carrier density. This escalation in the quantity of charge carriers enhances the
semiconductor's conductivity, consequently amplifying the current flow.
2. Bandgap Energy Variation
2
0
( )
g
g
T
E T
E
T
a
b
=
-
+
(2)
The bandgap energy E
g
decreases with temperature, modeled as [6]:
This is where:
E
g
(T):
Bandgap energy at temperature T
(eV) The energy gap decreases with
temperature due to lattice vibrations and thermal expansion effects.
E
g0
:
Bandgap energy at 0 K
(eV) Represents the bandgap energy when the
temperature is at absolute zero (e.g., E
g
0 =1.17eV for silicon).
α:
Material-specific constant
(eV/K) Determines the rate at which the bandgap
decreases with temperature.
β:
Material-specific constant
(K) Accounts for higher-order temperature effects.
3. Current-Voltage Characteristics
The temperature dependence of the diode equation is given by:
1 ,
qV
kT
s
I I e
=
-
(3)
I:
Current through the diode
(A) Represents the total current flowing through the
diode, consisting of the forward current and the small reverse current.
I
s
:
Reverse saturation current
(A) The current that flows through the diode in
reverse bias due to minority carriers. It is highly sensitive to temperature.
q:
Elementary charge
(1.6×10
−19
C) Represents the charge of a single electron.
V:
Voltage across the diode
(V) The applied voltage across the p-n junction of the
diode.
Where I
s
(reverse saturation current) is highly sensitive to temperature:
2
exp
.
g
s
qE
I
AT
kT
=
-
(4)
I
s
:
Reverse saturation current
(A) Represents the current due to thermally generated
carriers in reverse bias. It increases exponentially with temperature.
134
YANGI O'ZBEKISTON ILMIY
TADQIQOTLAR JURNALI
www.in-academy.uz
2-JILD, 5-SON 2-QISM, (YOʻITJ)
A:
Material-dependent constant
(A/K
2
) Represents the pre-factor, which depends on the
material and structure of the semiconductor .
Results and Discussion
Numerical Modeling:
To model these temperature effects numerically, we can use Python to
simulate the impact of temperature on the I-V characteristics of a silicon diode. Below is a
simple code snippet to plot the temperature dependence of a silicon diode's current using the
Shockley equation.
Fig. 1 - Temperature dependence of intrinsic
carrier concentration.
Fig. 2 – Band Gap energy of Silicon diode
at different temperature
Simulation Insights:
Modeled current-voltage (I-V) characteristics demonstrate a pronounced shift in the
diode's turn-on voltage as temperatures rise.
Transistor efficiency exhibits diminished current amplification at higher temperatures,
aligning with the deterioration of charge carrier mobility.
Visual Aids:
Bandgap vs. Temperature:
The graph illustrates the temperature
Fig.3 - I-V characteristics of a silicon diode
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dependence of the energy bandgap E
g
(T) for silicon (Si) across a temperature range
from 0 K to 500 K, calculated at three specific temperatures: 100 K (black), 300 K (blue), and
500 K (red). The energy bandgap decreases smoothly as the temperature increases, which is
consistent with the behavior of semiconductors. At 100 K, E
g
is approximately 1.16 eV, at
300 K it decreases to around 1.12 eV, and at 500 K it further reduces to about 1.06 eV. This
trend reflects the physical phenomenon where thermal energy causes lattice vibrations,
reducing the bandgap by increasing electron-phonon interactions. The smooth, downward-
curving lines confirm the expected non-linear relationship described by the formula (2) ,
highlighting silicon's suitability for temperature-dependent electronic applications.
I-V Curves at Different Temperatures:
Overlayed graphs showing the effect of
temperature on a silicon diode's I-V response.
Conclusion
Temperature significantly influences the electrical characteristics of silicon-based
semiconductor devices. Elevated temperatures result in:
Increased native charge carrier density,
Decreased energy bandgap,
Reduced charge carrier mobility,
Modified current-voltage (I-V) profiles.
These observations highlight the critical need to account for thermal influences in the
modeling of semiconductor devices to ensure precise predictions and dependable
performance in practical applications.
odeling for accurate predictions and reliable performance in real-world applications.
References
:
[1] Sh.M. Urinbaev ,G.E. Nurmetova, R.F. Akimbaev, «The effect of temperature on the voltage-
ampere characteristics of silicon-based semiconductor materials,» т. 15, № 1, pp. 286-293,
29 11 2024.
[2] S. M. Sze, Physics of Semiconductor Devices, т. 3 rd edition, Wiley, 2007.
[3] R. F. Pierret, Semiconductor Device Fundamentals, Addison-Wesley, 1996.
[4] N. D. A., Semiconductor Physics and Devices, т. 4th edition, McGraw-Hill, 2012.
[5] G.E. Nurmetova Sh.M. O‘rinbayev, «Yarimo'tkazgichlarda potensial to‘siqning
temperaturaga bog‘liqligini phyton dasturida modellashtirish,»
International journal of
scientific researchers,
т. 8, № 1, pp. 843-847, 24 10 2024.
[6] Sh.M. O‘rinbayev, G.E. Nurmetova, R.A.Farxodovich, «Kirishmali yarimo‘tkazgichlarda
fermi sathini joylashishini phyton dasturiy ta’minotida modellashtirish,» Toshkent, 2024.
