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Effect of the Local Mechanical Stress on Properties of Silicon Solar Cell

Authors:
  • Andijan state university
  • Andijan state university

Abstract

It is important to study the nature of the flexo-photovoltaic effect of silicon-based solar cells under the influence of local mechanical stresses. This is because it can change the properties of the solar cells and increase the efficiency of solar cell. In this paper, the effect of local mechanical stress on a monocrystalline silicon-based solar cell has been studied. A short-circuit current was found to increase 1.3 times when a monocrystalline silicon-based solar cell was stressed with the 6 N mechanical stress. The direct proportionality of the short-circuit current of the solar cell to the root of the mechanical stress was determined, and by the statistical analysis of the experimental results it has been calculated the proportionality coefficient a = 0.8114 A/N 0.5. In addition, the effect of local mechanical stress on a silicon-based solar cell has been modeled using the Comsol Multiphysics program. It has been found that the distribution of the effect of mechanical stress, which is applied on the surface of a solar cell, along the thickness of the solar cell is exponential.
Journal of Mechanical Engineering Research and Developments
ISSN: 1024-1752
CODEN: JERDFO
Vol. 44, No. 9, pp. 125-133
Published Year 2021
125
Effect of the Local Mechanical Stress on Properties of
Silicon Solar Cell
Jasurbek Gulomov*, Rayimjon Aliev, Bobur Rashidov
Renewable energy source laboratory, Andijan state university, 170100, Uzbekistan
*Correspondence author email: jasurbekgulomov@yahoo.com
ABSTRACT
It is important to study the nature of the flexo-photovoltaic effect of silicon-based solar cells under the
influence of local mechanical stresses. This is because it can change the properties of the solar cells and
increase the efficiency of solar cell. In this paper, the effect of local mechanical stress on a monocrystalline
silicon-based solar cell has been studied. A short-circuit current was found to increase 1.3 times when a
monocrystalline silicon-based solar cell was stressed with the 6 N mechanical stress. The direct proportionality
of the short-circuit current of the solar cell to the root of the mechanical stress was determined, and by the
statistical analysis of the experimental results it has been calculated the proportionality coefficient a = 0.8114
A/N0.5. In addition, the effect of local mechanical stress on a silicon-based solar cell has been modeled using
the Comsol Multiphysics program. It has been found that the distribution of the effect of mechanical stress,
which is applied on the surface of a solar cell, along the thickness of the solar cell is exponential.
KEYWORDS
Local mechanical stress; solar cell; short circuit current; silicon; p-n junction
INTRODUCTION
In the period of exacerbation of global environmental problems, more attention of specialists in renewable
energy is paid to the wider introduction of solar cells (SC) of energy. Despite the varieties used as the base
material for the SC, it remains the main one - semiconductor silicon. For modern silicon SCs, the maximum
energy conversion efficiency exists a theoretical limit determined by the Shockley Queisser theory and is
about 29% for single-layer SCs with one p-n-junction [1]. In order to experimentally overcome this limit,
experts have proposed various innovative methods. In [2], a method was proposed for using the effect of
generation of hot charge carriers that appear in a semiconductor upon absorption of light with an energy
exceeding the band gap. In [2,3], a method was proposed for using the capabilities of quantum-size effects to
increase the efficiency of phase transitions from organic materials and silicon phase transitions. This opened a
new stage in the development of semiconductor photovoltaics - the use of the effect of nanoplasmonics to
increase the efficiency of photoconductivity [4,5]. Materials scientists of semiconductor photovoltaics have
proposed the discovered new properties of silicon for the creation of a cheap technology for creating a SC [6].
The authors of [7] discovered a new photovoltaic effect due to local pressure on a semiconductor crystal that
does not have a center of symmetry, when they are illuminated with light with a wavelength of 520 nm. The
application of local pressure to a crystal leads to the appearance of a mechanical stress gradient in it, and a new
flexo-photovoltaic (SCV) effect is observed, the physical mechanism of which has not yet been disclosed.
However, based on the crystallographic representation of semiconductor materials, it can be assumed that such
an effect can be observed in other semiconductors, including silicon. On the other hand, we know from the
physics of semiconductor structures that if a p-n junction is formed, the sensitivity of the structure is much
increased compared to a structure without a p-n junction. Moreover, if the front of the p-n junction is
deliberately oriented in accordance with the direction (direct or transverse) of mechanical stress, then one can
expect its certain positive (additional) contribution to the traditional photovoltaic effect. Therefore, it seems
Effect of the Local Mechanical Stress on Properties of Silicon Solar Cell
126
relevant - a purposeful study of the effect of local mechanical stress on the process of photoelectric conversion
in silicon structures with a p-n-junction, to which this research work is devoted.
MATERIALS AND METHODS
Research methodology
For the study, theoretical and experimental methods were used, as well as a digital system of instrumental and
technological modeling. In particular, on the basis of the theory of the structure of a semiconductor with a
diamond-like crystal lattice (Fig. 1a) and a covalent interatomic bond, as well as the mechanism of directed
charge transfer through the p-n junction, the relationship between the deforming external force and the short-
circuit photocurrent is revealed. For the experimental study, a simplified scheme (Fig. 1c) of the formation of
local mechanical stress on the front surface of a silicon SC 1 with a p-n-structure 2, with a face 3 and a back
electrode 4 was chosen. the force of gravity 6, supplied to the free end of the flexible rod 7, which is fixed with
the other end to the rack 8. When illuminating the SC, on the front surface of which mechanical pressure is
exerted, the value of the short-circuit photocurrent is measured. (Fig. 1 c). When carrying out statistical
processing of the results of the experimental study, the method of the smallest crystals was used. The
COMSOL Multiphysics environment was used as a digital system for instrumental and technological
modeling. This environment includes numerous physics models and simulation programs. Unlike other
common programs, the selected system allows you to explore a variety of physical processes in [8]. It is
possible to simulate an entire system consisting of many processes that differ in physical nature. The developed
models can be generated in the form of “Java” program codes, which opens up wide possibilities for using the
basic data of 14 libraries of the “COMSOL Multiphysics” environment.
Theory
It is known that the electric current in a semiconductor is expressed by the equation [9]:
  
(1)
where I is the current, q is the charge of the carrier, n is the concentration of charge carriers, v is the directional
velocity of the charge carriers, S is the cross-sectional area.
You can choose an n-type semiconductor and the electron velocity can be expressed through the mobility (µe)
in the form:
  
(2)
where E is the electric field strength [13]:
  (3)
For simplicity, we assume that the current flows in one direction
 
(4)
and putting (2), (3) and (4) in (1) you can get (L-physical length of the semiconductor):
  
(5)
For an electric current flowing through a diode, the following equations are known [10]:
  
  (6)

(7)
  

  (8)
Effect of the Local Mechanical Stress on Properties of Silicon Solar Cell
127
where Io is the saturation current, U is the voltage, ni is the carrier concentration in the intrinsic semiconductor,
Dp and Dn are the diffusion coefficient of holes and electrons, Lp and Ln are the diffusion length of holes and
electrons, and Nd and Na are the concentrations of donors and acceptors.
By comparing equations (5) and (8), you can write:
 
(9)
Equation (9) can be used both for a diode and for a SC with a p-n junction. For a diode, the following condition
holds:
     (10)
and for SC:
     (11)
The crystal lattice of silicon - diamond is similar (Fig. 1a) and between neighboring atoms there is a covalent
bond with the force of action [11]:
  
(12)
where F is the Coulomb force, A is a constant, k is the proportionality coefficient, e is the electron charge, r is
the crystal lattice constant.
a b
Figure 1. Diamond-like crystal lattice of silicon (a) and a simplified scheme of the formation of local
mechanical stress on the front surface of a silicon SC with a p-n-structure (c)
Under the action of an external local gravity force, the crystal lattice can be deformed, that is, when the external
force changes, the interaction forces between atoms change, therefore the crystal lattice constant changes.
Therefore, for simplicity, we accept the condition that determines the relationship between the crystal lattice
constant and the carriers free path:
r ~ Lр,п , r = γ Lр,п,, dr = γ dLр,п, (13)
where γ is the coefficient of proportionality. where γ is the coefficient of proportionality.
If we assume that under the influence of an external force, the Coulomb force changes and, therefore, the
interatomic distance changes. Then we have:
    
 (14)
where ΔF is the increase in the force of interaction of atoms and Δr is the change in the interatomic distance.
Effect of the Local Mechanical Stress on Properties of Silicon Solar Cell
128
From here you can get the following equation:   



  
 (15)
Now consider the case where a small change in the force of interaction between atoms can cause a change in
the interatomic distance.

  


  
 
  
  
 (16)
Taking into account conditions (13) for dL, we obtain:
  
 (17)
Thus, the obtained equation (17) makes it possible to physically reflect the influence of the instantaneous
external force exerted on the crystal lattice on the instantaneous change in the diffusion length of charge carriers
in a semiconductor. It is the change in the diffusion length of charge carriers that is one of the most significant
parameters that determine the nature of charge transfer in a material or structure.
RESULTS AND DISCUSSIONS
Based on the theoretically obtained equation (17), it is possible to determine the nature of the effect of
mechanical stress on the photoelectric parameters created on such a semiconductor p-n junction. To do this, one
can first determine the changes in the current depending on the diffusion length of the NS by differentiating
equation (9):
  
 (18)
   
 (19)
  
 (20)
 

 (21)
Taking into account condition (11) for a change in the short-circuit current of the SC, we obtain:
 

 (22)
To obtain a specific value of the short-circuit current of the SC, we integrate (22):  



   
  (23)
   (24)
   
 (25)
Here Fk is an external force, Fо is the initial force of interaction between atoms. It is known that the force of
interaction between atoms is in the order of 10-9 N, that is, it can be assumed that [12]:
  (26)
Effect of the Local Mechanical Stress on Properties of Silicon Solar Cell
129
Then equation (25) can be rewritten:    

   (27)
where α is the proportionality coefficient: 
  .
Thus, the force applied to the surface leading to deformation (stress) of the silicon crystal can lead to a change in
the short-circuit current of the SC, which can be expressed in the form (27). The resulting equation (27)
qualitatively reflects the theoretical ideas about the effect of deformation on the photoelectric current of a
semiconductor structure with a p-n junction. The correctness of this equation can be verified experimentally. As
a result of the experimental study carried out using a simplified scheme (Fig. 1c), the dependence of the short
circuit current was determined. on the magnitude of the force of gravity and the measurement results are
presented in Fig. 2 (curve 1).
Figure 2. Dependence of the short circuit current of a silicon SC with a p-n-junction on the magnitude of the
force of gravity acting on a local point of the frontal surface
Using equation (27), we can express the dependence of the short circuit current in the form of curve 2 (Fig. 2).
Statistical processing by the least squares method of the experimental results (curve 1) allows one to obtain the
following empirical equation:
   (28)
with a coefficient of proportionality. This confirms the correctness of the theoretical equation (27).
When creating a new digital model, the following sequential steps were performed: - “creating a geometric
model of the system” in one of the 1D, 2D or 3D formats, - “choosing materials and their parameters”, -
“forming the physical properties of the system”, - “dividing the system into large-scale grids “, - “selection of a
calculation method and obtaining results” [8]. To solve the problem posed in this work, a 2D format model was
created, silicon was selected as the main investigated material, and a metal needle for providing vertical local
pressure on the silicon surface was copper and geometric shapes of the mesh modeling object (a) and for digital
calculation (c and c) are shown in Fig. 3.
The calculation is performed in a stationary mode, since the elastic process in a solid is considered, Hooke's law
holds
   (29)
where S - mechanical stress, Fv - volumetric force.
    (30)
3
3.2
3.4
3.6
3.8
4
4.2
4.4
4.6
4.8
02468
Isc (mA)
F (N)
1 2
Effect of the Local Mechanical Stress on Properties of Silicon Solar Cell
130
     (31)
where Sext is the additional mechanical stress, C is the four-dimensional structural tensor, εel is the two-
dimensional elastic stress tensor, ε is the total stress, and εinel is the inelastic stress.
The four-dimensional constructive tensor (C) and Poisson's ratio (v) are expressed in terms of Young's modulus
(E) in the following form:
   (32)
а
b
c
Figure 3. Geometric shapes of the mesh modeling object (a) and for digital calculation (b and c)
The calculation results obtained by the digital simulation method are shown in Fig. 4,a in the form of a graph of
the dependence of mechanical stress on the depth of silicon and in Fig. 4,b in the form of a graph of the
Effect of the Local Mechanical Stress on Properties of Silicon Solar Cell
131
dependence of the mechanical stress on the transverse distance on the silicon surface (curve 1) and at a depth of
1 μm from the surface (curve 2). According to Fig. 3,a, it can be noted that when an external force ΔF = 350
N/m2 is applied to a local point of the silicon surface, the magnitude of the mechanical stress decreases with
depth. Moreover, two areas of exponential decrease in mechanical stress with depth are characteristic: the first
decreases by almost 8% in the range d1≤20µm and the second decreases by almost 73% in the range 20µm
d2≤150µm. If we pay attention to the geometric structure of traditional semiconductor phase transitions, it turns
out that the first section covers both the depth of the p-n junction and the width of the space charge region
(SCR). In other words, significant mechanical stress (the first and second sections of the graph in Fig. 4,a
corresponds to almost the entire thickness of active absorption of light and generation-recombination of carriers.
One can expect a direct effect of mechanical stress on both the generation-recombination processes of carriers
and the external quantum efficiency of the photoelectric conversion of the SC.
a
b
Figure 4. Dependences of mechanical stress on the silicon depth (a) and on the transverse distance (b) on the
silicon surface (curve 1) and at a depth of 1 μm from the surface (curve 2).
50
100
150
200
250
300
350
0 0.05 0.1 0.15 0.2
ΔF, N/m2
d, mm
0
500
1000
1500
2000
2500
4.94 4.96 4.98 5 5.02 5.04 5.06
ΔF, N/m2
d, mm
1
2
Effect of the Local Mechanical Stress on Properties of Silicon Solar Cell
132
The graph data in Fig. 4,b indicate that the distribution of the external force in the transverse direction is also
complex. Analyzing the dependence of the mechanical stress on the transverse distance on the silicon surface
(curve 1) and at a depth of 1 μm from the surface (curve 2), it can be seen that there is a relatively large stress
gradient at both triple tip of copper/silicon/air” boundaries. As the needle approaches the center of the cross-
section, the mechanical stress is balanced. At a depth of 1 μm, the value of mechanical stress decreases, which
corresponds to the data in Fig. 4,a. But at the same time, the mechanical stress outside under the needle is
significantly higher than on the surface, although it also decreases with distance from the needle. Naturally, the
local action on the surface of the force causes a higher mechanical stress in the depth of the plate.
CONCLUSION
Thus, in the work, firstly, the effect of deformation of a silicon crystal under the action of mechanical pressure is
theoretically analyzed and a new equation is obtained that describes the dependence of the short circuit current
on the magnitude of the acting force. Second, an experimental study of the dependence of the short circuit
current of a silicon SC with a diffusion p-n junction on the magnitude of the locally acting force was carried out,
and a new empirical equation was obtained. Third, it was established by digital modeling that a relatively high
mechanical stress caused by a local external force on the surface of a silicon crystal corresponds to almost the
entire thickness of active absorption of light and generation-recombination of carriers, which is very important in
the design of device structures. The results obtained are of practical interest for the development of technical
solutions aimed at realizing the effect of increasing the photoelectric parameters (photocurrent and efficiency) of
semiconductor SCs by applying mechanical stress to the crystal. It is also promising to search for technological
ways of obtaining a semiconductor material with a deformed lattice in order to create more efficient phase
transitions on its basis.
ACKNOWLEDGMENTS
The authors want to thank the staff of the Renewable Energy Sources Laboratory at Andijan State University for
their close assistance in writing this article.
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  • U Rau
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