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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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