# Analysis of the Thermal Stress for Combined Electrode of Soldered Crystalline Silicon Solar Cells under Temperature Field

Authors: He Wang; Ao Wang; Hong Yang; Dengyuan Song
Journal: International Journal of Photoenergy
 (2016)

---

## Abstract

Based on the theory of material mechanics and thermal stress analysis, the stress distribution of combined electrode for crystalline silicon solar module was studied for the first time. The shear stress and normal stress distribution of soldered structure for crystalline silicon solar cells under the thermal field were discussed. And the results show that the stress distribution is not simply linear relationship as some results found. But there is a stress concentration at the edge, which was considered as the true reason that caused microcracks at the edge of soldered solar cells. The conclusions we got in this paper provide a theoretical basis for deceasing the breakage rates of soldered crystalline silicon solar cells and improving the reliability of crystalline silicon solar modules.


---

## Body

## 1. Introduction

Crystalline silicon solar cells have become the main force of the photovoltaic industry. Crystalline silicon solar module is the critical component of photovoltaic (PV) generation system. Effective controlling of power degradation and increasing the conversion efficiency have the same importance for the investment income and reliability of PV power plant [1–3]. Manufacturers usually guarantee that the lifetime of the solar cell module is expected to be 25 years with 20% reduction in its power output over this period. Installed and operated in hot and humid climate, the PV modules’ typical operating temperature will change in the range −30~+100°C. In the process of crystalline silicon solar modules production, the cells of PV modules are electrically connected in series by interlacing tin-coated copper ribbon. Due to the large difference of the coefficient of thermal expansion (CTE) between metal and silicon, thermal stress of such combined electrode will appear and accumulate in the metallization interconnection system when the PV module is suffering from a temperature cycle. The cyclic thermal stress will cause microcracks and voids, which will increase the contact resistance of the electrode and reduce PV modules’ lifetime. Although many researches on module reliability have been done [4–7], there was no quantitative research for the thermal stress distribution of combined electrode inside the crystalline silicon solar module.In this paper, a model of the thermal stress distribution of combined electrode for crystalline silicon solar module is established for the first time. The shear stress and normal stress distribution of soldered structure for crystalline silicon solar cell under the thermal field were discussed. And the results show that the stress distribution is not simply linear relationship as some results found [8]. But there is a stress concentration at the edge, which was considered as the true reason that caused microcracks at the edge of the soldered solar cell.


## 2. Structure Model of Combined Electrode for Crystalline Silicon Solar Cells

### 2.1. Theoretical Model

When the PV module is working outdoors and suffering from a temperature cycle, thermal stress will be caused in different materials which have different coefficients of thermal expansion (CTE). Because of the adhesion and restriction between each structure material, a kind of stress cycle will appear in the interface and gradually lead to various reliability problems like crack, low power, or even failure [9].As we know, glass layer is the main binder phase at Ag paste/Si contact interface, and the peeling off of cell electrodes always occurred in Ag paste layer. The coefficients of thermal expansion of metal materials are quite different from Si substrate, while the glass frit is between metal and Si. As shown in Figure1, a simplified structure model with only three layers was established (Cu ribbon, Ag paste layer, and Si substrate). The assumption that each layer satisfies the homogeneous, isotropic, and linear conditions is made to simplify the model.Figure 1
Mechanical analysis of the metallization interconnection system.The thickness, width, and Young’s modulus of each layer aret
m, b
m, and E
m for ribbon, t
s, b
s, and E
s for Si substrate layer, and t
c, b
c, and E
c for thin glass layer, respectively. L is the bond length. Considering the element shown in Figure 1, the equations of equilibrium for metal layer and Si substrate layer can be written as(1)
d
F
m
d
x
+
τ
c
=
0
,
d
F
s
d
x
-
τ
c
=
0
.F
m and F
s represent the forces caused by thermal stresses for metal layer and Si substrate layer. τ
c is shear stress in the middle layer.


### 2.2. Thermal Stress Model of Combined Electrode for Crystalline Silicon Solar Cells

As shown in Figure2, this paper takes the expansive behavior of solar cell under a high temperature as an example to analyze shear stress distribution. Figure 3 shows the structure deformation of an element in the location x. As the thickness of the middle thin glass layer is too thin, the shear stress in the glass layer can be considered as the same value τ
c along thickness, and the shear stress in metal layer and Si substrate layer changes linearly along thickness.Figure 2
Simplification of cell structure. (a) Coordinate system with the origin at the center of the metallization. (b) Thermal expansion of the simplified structure.
(a)
(b)Figure 3
The shear stress and strain analysis of the simplified structure.The shear stresses in the middle layer, metal layer, and Si substrate layer can be written as follows:(2)
τ
c
=
γ
c
G
c
=
Δ
x
Δ
y
G
c
=
u
c
m
x
-
u
c
s
x
t
c
·
G
c
,
(3)
τ
m
=
τ
c
-
τ
c
-
τ
m
′
t
m
y
,
τ
s
=
τ
c
+
τ
c
-
τ
s
′
t
s
y
.τ
c, τ
m, and τ
s are the shear stresses in the middle layer, metal layer, and Si substrate layer, respectively. τ
m
′ and τ
s
′ are the shear stresses of the upper surface and lower surface. u
c
m
x and u
c
s
x are the coordinates of the two interfaces of the element in the location x. u
m
′ and u
s
′ are the coordinates of the upper surface and lower surface. G and γ are the shear modulus and shear strain, respectively.According to the stress-strain relationship, the coordinate functions in metal layer and Si substrate layer can be expressed as(4)
U
m
x
,
y
=
u
c
m
x
+
∫
0
y
γ
m
y
d
y
=
∫
0
y
τ
m
y
G
m
d
y
=
u
c
m
+
τ
c
G
m
y
-
τ
c
-
τ
m
′
2
t
m
G
m
y
2
+
C
1
,
U
s
x
,
y
=
u
c
s
x
+
∫
0
y
γ
s
y
d
y
=
∫
0
y
τ
s
y
G
s
d
y
=
u
c
s
+
τ
c
G
s
y
+
τ
c
-
τ
s
′
2
t
s
G
s
y
2
+
C
2
.The displacement functions w
(
x
,
y
) can be expressed as follows:(5)
w
x
,
y
=
U
x
,
y
-
x
.Substituting (4) into (5), the displacement functions in metal layer and Si substrate layer can be expressed as differential equations: (6)
d
w
m
d
x
=
d
u
c
m
d
x
-
1
+
y
G
m
d
τ
c
d
x
-
y
2
2
t
m
G
m
d
τ
c
-
d
τ
m
′
d
x
,
d
w
s
d
x
=
d
u
c
s
d
x
-
1
+
y
G
s
d
τ
c
d
x
+
y
2
2
t
s
G
s
d
τ
c
-
d
τ
s
′
d
x
.The normal stresses of elementd
x for the metal layer and Si substrate layer under temperature field are expressed as (7)
σ
m
=
E
m
α
m
Δ
T
d
x
-
d
w
m
d
x
=
E
m
α
m
Δ
T
-
d
w
m
d
x
,
σ
s
=
E
s
α
s
Δ
T
d
x
-
d
w
s
d
x
=
E
s
α
s
Δ
T
-
d
w
s
d
x
,in which α is the coefficient of thermal expansion (CTE).Compared to the thickness of the metal layer and Si layer, the middle layer is so thin that it can be reasonably ignored. The forces in metal layer and Si layer can be expressed as(8)
F
m
=
∫
0
t
m
σ
m
d
y
=
E
m
α
m
Δ
T
·
t
m
-
E
m
d
u
c
m
d
x
t
m
-
t
m
+
t
m
2
3
G
m
d
τ
c
d
x
-
t
m
2
6
G
m
d
τ
m
′
d
x
,
F
s
=
∫
0
-
t
s
σ
s
d
y
=
-
E
s
α
s
Δ
T
·
t
s
+
E
s
d
u
c
s
d
x
t
s
-
t
s
-
t
s
2
3
G
s
d
τ
c
d
x
-
t
s
2
6
G
s
d
τ
s
′
d
x
.They can also be written in the form of differential equation. Substituting (1) gives(9)
d
2
u
c
m
d
x
2
=
τ
c
E
m
t
m
-
t
m
3
G
m
d
2
τ
c
d
x
2
+
t
m
6
G
m
d
2
τ
m
′
d
x
2
,
d
2
u
c
s
d
x
2
=
τ
c
E
s
t
s
+
t
s
3
G
s
d
2
τ
c
d
x
2
+
t
s
6
G
s
d
2
τ
s
′
d
x
2
.Equation (2) can be written in the form of the following differential equation:(10)
d
2
τ
c
d
x
2
=
G
c
t
c
d
2
u
c
m
d
x
2
-
d
2
u
c
s
d
x
2
.Substituting (9) into (10) gives(11)
d
τ
c
2
d
x
2
-
β
2
τ
c
+
C
=
0
,where(12)
β
=
1
/
E
m
t
m
-
1
/
E
s
t
s
t
s
/
3
G
s
+
t
m
/
3
G
m
+
t
c
/
G
c
1
/
2
;
C
=
t
s
6
G
s
d
τ
s
′
d
x
-
t
m
6
G
m
d
τ
m
′
d
x
.As shown in Figure3, the shear stresses of the upper surface and lower surface were very small and as well assumed to be 0. That is to say, coefficient C is 0. Hence,(13)
d
τ
c
2
d
x
2
-
β
2
τ
c
=
0
.By solving differential equation (13), we can get the shear stress of the middle layer in the following form:(14)
τ
c
=
A
sinh
⁡
β
x
+
B
cosh
⁡
β
x
.The unknown constantsA and B can be obtained by substituting the boundary conditions.


### 2.3. Boundary Conditions

Figure4 gives out the analysis of the normal stress and strain. According to the thermal stress caused by expansion and contraction of materials under temperature Δ
T, the shear stress of location L (x
=
L) can be calculated.Figure 4
The normal stress and strain analysis.In the interface of metal layer and middle layer, two thin layers are analyzed. An assumption that the two thin layers are a rigid body and have the same cross section (S) is made to simplify the problem. After the expansion behavior, the final length of this interface layer is l
c
m.The final length of this interface can be expressed as(15)
l
c
m
=
L
+
Δ
l
m
+
ε
m
L
=
L
+
α
m
Δ
T
L
+
ε
m
L
=
L
+
α
c
Δ
T
L
+
ε
c
L
.For the two thin layers, (16)
σ
m
S
=
-
σ
c
S
.According to the normal stress definition, there are(17)
σ
m
=
-
σ
c
=
-
k
1
α
m
E
m
Δ
T
,
(18)
l
c
m
=
L
+
α
m
Δ
T
L
1
-
k
1
.Similarly, by analyzing the interface of the middle layer and Si substrate layer, we got(19)
σ
c
′
=
-
σ
s
=
-
k
2
α
c
E
c
Δ
Tin which(20)
k
1
=
1
-
α
c
/
α
m
1
+
E
m
/
E
c
;
k
2
=
1
-
α
s
/
α
c
1
+
E
c
/
E
s
.The final length of this interface can be expressed as(21)
l
c
s
=
L
+
α
c
Δ
T
L
1
-
k
2
.Therefore,(22)
τ
c
=
γ
c
G
c
=
l
c
m
-
l
c
s
t
c
·
G
c
=
α
m
Δ
T
L
1
-
k
1
-
α
c
Δ
T
L
1
-
k
2
t
c
·
G
c
.With the boundary conditions x
=
0,  τ
c
=
0,(23)
x
=
L
,
τ
c
=
α
m
Δ
T
L
1
-
k
1
-
α
c
Δ
T
L
1
-
k
2
t
c
·
G
c
.The unknown constants in (14) can be obtained by substituting the boundary conditions(24)
B
=
0
,
A
=
1
sinh
⁡
β
L
∗
k
α
1
E
1
T
.


## 2.1. Theoretical Model

When the PV module is working outdoors and suffering from a temperature cycle, thermal stress will be caused in different materials which have different coefficients of thermal expansion (CTE). Because of the adhesion and restriction between each structure material, a kind of stress cycle will appear in the interface and gradually lead to various reliability problems like crack, low power, or even failure [9].As we know, glass layer is the main binder phase at Ag paste/Si contact interface, and the peeling off of cell electrodes always occurred in Ag paste layer. The coefficients of thermal expansion of metal materials are quite different from Si substrate, while the glass frit is between metal and Si. As shown in Figure1, a simplified structure model with only three layers was established (Cu ribbon, Ag paste layer, and Si substrate). The assumption that each layer satisfies the homogeneous, isotropic, and linear conditions is made to simplify the model.Figure 1
Mechanical analysis of the metallization interconnection system.The thickness, width, and Young’s modulus of each layer aret
m, b
m, and E
m for ribbon, t
s, b
s, and E
s for Si substrate layer, and t
c, b
c, and E
c for thin glass layer, respectively. L is the bond length. Considering the element shown in Figure 1, the equations of equilibrium for metal layer and Si substrate layer can be written as(1)
d
F
m
d
x
+
τ
c
=
0
,
d
F
s
d
x
-
τ
c
=
0
.F
m and F
s represent the forces caused by thermal stresses for metal layer and Si substrate layer. τ
c is shear stress in the middle layer.


## 2.2. Thermal Stress Model of Combined Electrode for Crystalline Silicon Solar Cells

As shown in Figure2, this paper takes the expansive behavior of solar cell under a high temperature as an example to analyze shear stress distribution. Figure 3 shows the structure deformation of an element in the location x. As the thickness of the middle thin glass layer is too thin, the shear stress in the glass layer can be considered as the same value τ
c along thickness, and the shear stress in metal layer and Si substrate layer changes linearly along thickness.Figure 2
Simplification of cell structure. (a) Coordinate system with the origin at the center of the metallization. (b) Thermal expansion of the simplified structure.
(a)
(b)Figure 3
The shear stress and strain analysis of the simplified structure.The shear stresses in the middle layer, metal layer, and Si substrate layer can be written as follows:(2)
τ
c
=
γ
c
G
c
=
Δ
x
Δ
y
G
c
=
u
c
m
x
-
u
c
s
x
t
c
·
G
c
,
(3)
τ
m
=
τ
c
-
τ
c
-
τ
m
′
t
m
y
,
τ
s
=
τ
c
+
τ
c
-
τ
s
′
t
s
y
.τ
c, τ
m, and τ
s are the shear stresses in the middle layer, metal layer, and Si substrate layer, respectively. τ
m
′ and τ
s
′ are the shear stresses of the upper surface and lower surface. u
c
m
x and u
c
s
x are the coordinates of the two interfaces of the element in the location x. u
m
′ and u
s
′ are the coordinates of the upper surface and lower surface. G and γ are the shear modulus and shear strain, respectively.According to the stress-strain relationship, the coordinate functions in metal layer and Si substrate layer can be expressed as(4)
U
m
x
,
y
=
u
c
m
x
+
∫
0
y
γ
m
y
d
y
=
∫
0
y
τ
m
y
G
m
d
y
=
u
c
m
+
τ
c
G
m
y
-
τ
c
-
τ
m
′
2
t
m
G
m
y
2
+
C
1
,
U
s
x
,
y
=
u
c
s
x
+
∫
0
y
γ
s
y
d
y
=
∫
0
y
τ
s
y
G
s
d
y
=
u
c
s
+
τ
c
G
s
y
+
τ
c
-
τ
s
′
2
t
s
G
s
y
2
+
C
2
.The displacement functions w
(
x
,
y
) can be expressed as follows:(5)
w
x
,
y
=
U
x
,
y
-
x
.Substituting (4) into (5), the displacement functions in metal layer and Si substrate layer can be expressed as differential equations: (6)
d
w
m
d
x
=
d
u
c
m
d
x
-
1
+
y
G
m
d
τ
c
d
x
-
y
2
2
t
m
G
m
d
τ
c
-
d
τ
m
′
d
x
,
d
w
s
d
x
=
d
u
c
s
d
x
-
1
+
y
G
s
d
τ
c
d
x
+
y
2
2
t
s
G
s
d
τ
c
-
d
τ
s
′
d
x
.The normal stresses of elementd
x for the metal layer and Si substrate layer under temperature field are expressed as (7)
σ
m
=
E
m
α
m
Δ
T
d
x
-
d
w
m
d
x
=
E
m
α
m
Δ
T
-
d
w
m
d
x
,
σ
s
=
E
s
α
s
Δ
T
d
x
-
d
w
s
d
x
=
E
s
α
s
Δ
T
-
d
w
s
d
x
,in which α is the coefficient of thermal expansion (CTE).Compared to the thickness of the metal layer and Si layer, the middle layer is so thin that it can be reasonably ignored. The forces in metal layer and Si layer can be expressed as(8)
F
m
=
∫
0
t
m
σ
m
d
y
=
E
m
α
m
Δ
T
·
t
m
-
E
m
d
u
c
m
d
x
t
m
-
t
m
+
t
m
2
3
G
m
d
τ
c
d
x
-
t
m
2
6
G
m
d
τ
m
′
d
x
,
F
s
=
∫
0
-
t
s
σ
s
d
y
=
-
E
s
α
s
Δ
T
·
t
s
+
E
s
d
u
c
s
d
x
t
s
-
t
s
-
t
s
2
3
G
s
d
τ
c
d
x
-
t
s
2
6
G
s
d
τ
s
′
d
x
.They can also be written in the form of differential equation. Substituting (1) gives(9)
d
2
u
c
m
d
x
2
=
τ
c
E
m
t
m
-
t
m
3
G
m
d
2
τ
c
d
x
2
+
t
m
6
G
m
d
2
τ
m
′
d
x
2
,
d
2
u
c
s
d
x
2
=
τ
c
E
s
t
s
+
t
s
3
G
s
d
2
τ
c
d
x
2
+
t
s
6
G
s
d
2
τ
s
′
d
x
2
.Equation (2) can be written in the form of the following differential equation:(10)
d
2
τ
c
d
x
2
=
G
c
t
c
d
2
u
c
m
d
x
2
-
d
2
u
c
s
d
x
2
.Substituting (9) into (10) gives(11)
d
τ
c
2
d
x
2
-
β
2
τ
c
+
C
=
0
,where(12)
β
=
1
/
E
m
t
m
-
1
/
E
s
t
s
t
s
/
3
G
s
+
t
m
/
3
G
m
+
t
c
/
G
c
1
/
2
;
C
=
t
s
6
G
s
d
τ
s
′
d
x
-
t
m
6
G
m
d
τ
m
′
d
x
.As shown in Figure3, the shear stresses of the upper surface and lower surface were very small and as well assumed to be 0. That is to say, coefficient C is 0. Hence,(13)
d
τ
c
2
d
x
2
-
β
2
τ
c
=
0
.By solving differential equation (13), we can get the shear stress of the middle layer in the following form:(14)
τ
c
=
A
sinh
⁡
β
x
+
B
cosh
⁡
β
x
.The unknown constantsA and B can be obtained by substituting the boundary conditions.


## 2.3. Boundary Conditions

Figure4 gives out the analysis of the normal stress and strain. According to the thermal stress caused by expansion and contraction of materials under temperature Δ
T, the shear stress of location L (x
=
L) can be calculated.Figure 4
The normal stress and strain analysis.In the interface of metal layer and middle layer, two thin layers are analyzed. An assumption that the two thin layers are a rigid body and have the same cross section (S) is made to simplify the problem. After the expansion behavior, the final length of this interface layer is l
c
m.The final length of this interface can be expressed as(15)
l
c
m
=
L
+
Δ
l
m
+
ε
m
L
=
L
+
α
m
Δ
T
L
+
ε
m
L
=
L
+
α
c
Δ
T
L
+
ε
c
L
.For the two thin layers, (16)
σ
m
S
=
-
σ
c
S
.According to the normal stress definition, there are(17)
σ
m
=
-
σ
c
=
-
k
1
α
m
E
m
Δ
T
,
(18)
l
c
m
=
L
+
α
m
Δ
T
L
1
-
k
1
.Similarly, by analyzing the interface of the middle layer and Si substrate layer, we got(19)
σ
c
′
=
-
σ
s
=
-
k
2
α
c
E
c
Δ
Tin which(20)
k
1
=
1
-
α
c
/
α
m
1
+
E
m
/
E
c
;
k
2
=
1
-
α
s
/
α
c
1
+
E
c
/
E
s
.The final length of this interface can be expressed as(21)
l
c
s
=
L
+
α
c
Δ
T
L
1
-
k
2
.Therefore,(22)
τ
c
=
γ
c
G
c
=
l
c
m
-
l
c
s
t
c
·
G
c
=
α
m
Δ
T
L
1
-
k
1
-
α
c
Δ
T
L
1
-
k
2
t
c
·
G
c
.With the boundary conditions x
=
0,  τ
c
=
0,(23)
x
=
L
,
τ
c
=
α
m
Δ
T
L
1
-
k
1
-
α
c
Δ
T
L
1
-
k
2
t
c
·
G
c
.The unknown constants in (14) can be obtained by substituting the boundary conditions(24)
B
=
0
,
A
=
1
sinh
⁡
β
L
∗
k
α
1
E
1
T
.


## 3. Solution and Analysis

The following results can be obtained by substituting the values ofA and B into (14):(25)
τ
c
=
s
i
n
h
β
x
s
i
n
h
β
L
·
α
m
Δ
T
L
1
-
k
1
-
α
c
Δ
T
L
1
-
k
2
t
c
·
G
c
.Substituting the material parameters (shown in Table1) into (25), curves of the shear stress in the middle layer were obtained by MATLAB. Figure 5 shows the shear stress distribution in the middle layer when the temperature is 55°C. Figure 6 shows the shear stress in the middle layer under different temperature fields (−35°C, −20°C, −5°C, 10°C, 25°C, 40°C, 55°C, 70°C, 85°C, and 100°C).Table 1
Structural parameters of different material layers.
Parameters
E/Pa
G/Pa
α/°C−1
t/m
L
0/m
Cu ribbon layer
110
e
9
30
e
9
16.9
e
-
6
210
e
-
6
78
e
-
3
Middle layer
55
e
9
1.96
e
9
3.3
e
-
6
3
e
-
6
Si substrate layer
130
e
9
58
e
9
2.6
e
-
6
180
e
-
6Figure 5
The shear stress distribution of the middle layer.Figure 6
The shear stress distribution of the middle layer under temperature field from −35°C to 100°C.The final coordinates of the middle adhesive layer inx can be obtained by (18) and (21) after the thermal stability: (26)
u
c
m
x
=
x
+
1
-
k
1
α
m
Δ
T
x
=
x
+
1
+
k
1
α
c
Δ
T
x
,
u
c
s
x
=
x
+
1
-
k
2
α
c
Δ
T
x
=
x
+
1
+
k
2
α
s
Δ
T
x
.Taking the derivatives of (26) with respect to x and substituting them into (6), the following relationships were obtained:(27)
σ
m
=
E
m
k
1
α
m
Δ
T
-
E
m
y
G
m
-
y
2
2
t
m
G
m
·
β
cosh
⁡
β
x
sinh
⁡
β
L
·
α
m
Δ
T
L
1
-
k
1
-
α
c
Δ
T
L
1
-
k
2
t
c
·
G
c
σ
s
=
-
E
s
k
2
α
s
Δ
T
-
E
s
y
G
s
+
y
2
2
t
s
G
s
·
β
cosh
⁡
β
x
sinh
⁡
β
L
·
α
m
Δ
T
L
1
-
k
1
-
α
c
Δ
T
L
1
-
k
2
t
c
·
G
c
.By (27), when x is a fixed value, the relationship of normal stress and y is a quadratic function. When the value of y is 0.03, the distribution of upper and lower normal stress can be simulated by MATLAB. The result of simulation is shown in Figure 7.Figure 7
The normal stress distribution in Si substrate (a) and ribbon (b).
(a)
(b)


## 4. Experimental Verification for the Thermal Stress Model of Combined Electrode for Soldered Crystalline Silicon Solar Cells

According to the above analysis, the stress of the soldered solar cells’ side increases with increasing solder temperature, so microcracks induced by high stress begin from the side of the soldered solar cells. Figure8 gives out the electroluminescence images of crystalline silicon solar module with microcracks at the edge of the soldered solar cell induced by thermal stress.Figure 8
The electroluminescence images of solar modules with microcracks at the edge of soldered solar cell induced by thermal stress.From Figure8, the microcracks always emerge on the side of the combined electrode for crystalline silicon solar cells. This proved the validity of the thermal stress model for soldered crystalline silicon solar cells. From the results, the way to decrease the breakage rates of soldered crystalline silicon solar cells is to reduce the thermal stress of combined electrode during the production of crystalline silicon solar modules.


## 5. Conclusions

In this paper, the stress distribution of combined electrode for crystalline silicon solar module was studied for the first time. The shear stress and normal stress distribution of soldered crystalline silicon solar cell under the thermal field were discussed. Studies have shown that the value of shear stress at the midpoint is the smallest and the shear stress along the direction of welding strip increases by function of cosh. The concentrated stress of edges leads to microcracks of the soldered solar cells. The results laid a theoretical basis for reducing the breakage rates of soldered crystalline silicon solar cells and improving the reliability of crystalline silicon solar modules during the production of solar modules.



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*Source: 5306925-2016-09-26.xml*