An Analysis of Fill Factor Loss Depending on the Temperature for the Industrial Silicon Solar Cells

Abstract

Since the temperature of a photovoltaic (PV) module is not consistent as it was estimated at a standard test condition, the thermal stability of the solar cell parameters determines the temperature dependence of the PV module. Fill factor loss analysis of crystalline silicon solar cell is one of the most efficient methods to diagnose the dominant problem, accurately. In this study, the fill factor analysis method and the double-diode model of a solar cell was applied to analyze the effect of J₀₁, J₀₂, R_s, and R_sh on the fill factor in details. The temperature dependence of the parameters was compared through the passivated emitter rear cell (PERC) of the industrial scale solar cells. As a result of analysis, PERC cells showed different temperature dependence for the fill factor loss of the J₀₁ and J₀₂ as temperatures rose. In addition, we confirmed that fill factor loss from the J₀₁ and J₀₂ at elevated temperature depends on the initial state of the solar cells. The verification of the fill factor loss analysis was conducted by comparing to the fitting results of the injection dependent-carrier lifetime.

1. Introduction

The fill factor (FF), open circuit voltage (V_oc) and short circuit current (J_sc) of a solar cell are important parameters because they determine the maximum power that a solar cell can generate. It is well known that the fill factor of silicon solar cells is influenced by the recombination current and parasitic resistance. In order to clarify the effect of these factors on a fill factor, the double-diode model is generally used as a theoretical concept. In the double-diode model, the photo-generated current density reduces due to the saturation current densities (J₀₁, J₀₂), and parasitic resistance (R_s, R_sh) as the equation shows below.

$$J=J_{ph}-J_{01}\left[\exp \left\{\frac{q\left(V+J{R}_s\right)}{n_{1}kT}\right\}-1\right]-J_{02}\left[\exp \left\{\frac{q\left(V+J{R}_s\right)}{n_{2}kT}\right\}-1\right]-\frac{\left(V+J{R}_s\right)}{R_{sh}},$$

(1)

where J is the diode circuit current density, J_ph is the photo-generated current density, J₀₁ is the recombination current density in quasi-neutral region, V is the diode voltage, q is the elementary charge, k is Boltzmann’s constant, n₁ is the ideality factor for the diode 1, n₂ is the ideality factor for the diode 2, and T is the absolute temperature. The J₀₁ in the equation is the information of the recombination current from the base material (quasi-neutral region) and both side surface of the solar cell. J₀₂ generally describes the Shockley-Read-Hall (SRH) recombination at the p-n junction (space charge region), but there are also other recombination sources such as edge recombination [1] and localized high defect region [2,3].

Analyzing the recombination and resistive loss of a solar cell from the perspective of fill factor is a very efficient method because it directly shows the gain of the conversion efficiency from the loss factor. Hence, there were some effort to extract fill factor loss at the space charge region (J₀₂) by determining fill factor loss from J₀₁ (FF_J01) and subtracting the pseudo fill factor (pFF) that is not influenced by the series resistance [4,5]. Afterward, A. Khanna proposed a method to quantify the fill factor loss of silicon solar cells due to parasitic resistance as well as J₀₂, because there was a limitation that the shunt resistance must be extremely high to extract an exact fill factor loss due to J₀₂ in this method. In addition, since this approach does not need to assume n₂ value during the fitting procedure, it showed that a more accurate analysis is possible. The theoretical derivation is well described in [6].

This fill factor loss analysis was used in this experiment to investigate the source of fill factor loss depending on the elevated temperature, because the module efficiency assessed at the standard test condition (STC, 25 °C) reduces at the actual operating temperature [7]. Figure 1 shows the measured PV module temperature change according to the seasonal temperature in Daejeon and Seoul of South Korea. The PV module temperature rises to 60 °C which will highly degrade the module power when it is operating. The V_oc reduction is well known for the main source of efficiency loss. V_oc is a function of the saturation current (I₀) which is strongly dependent on the temperature as it can be seen in Equations (2) and (3) [8]. Where q is the elementary charge, A is the area, D is the diffusion constant, n_i is the intrinsic carrier concentration, L is the diffusion length, N_D is the doping concentration, and T is kelvin temperature. By extracting the fill factor loss of each parameter (J₀₁, J₀₂, R_s, and R_sh), it will be able to provide an accurate diagnosis and appropriate solution to reduce the temperature dependence of the PV module.

For the analysis of fill factor loss, industrial passivated emitter and rear cell (PERC), which is leading product in PV industries, was used [9]. Many researches for optimization of both side surface passivation [10,11,12,13,14,15,16] and laser ablation on rear aluminum oxide (AlO_x) layer [17,18] for the local back surface field formation (LBSF) [19] have improved efficiency of the PERC and reached 22.8% [20]. In this paper, temperature dependence of two industrial type PERC samples were compared to inspect dominant factor of fill factor loss.

$$I_0=qA\frac{D{n}_i^2}{L{N}_D},$$

(2)

$$n_i\left(T\right)=9.15\times {10}^9{\left(\frac{T+273.15}{300}\right)}^2\exp \left(\frac{-6880}{T+273.15}\right).$$

(3)

2. Experimental

2.1. Analysis Process of Fill Factor Loss

Figure 2 briefly summarizes the steps of the fill factor loss analysis. The analysis of the fill factor loss starts with the calculation of FF_J01. The FF_J01 can be determined when the effect of J₀₂, R_s and R_sh is absent. With this assumption, Equation (1) changes to Equation (4).

$$J=J_{ph}-J_{01}\left[\exp \left\{\frac{qV}{nkT}\right\}-1\right].$$

(4)

By imposing the boundary condition J = 0 at V = V_oc and J = J_sc at V = 0, relationship between J and V can be expressed in Equation (5), which FF_J01 is allowed to be obtained.

$$J=J_{sc}-\frac{J_{sc}}{\exp \left(\frac{q{V}_{oc}}{nkT}\right)-1}\left[\exp \left\{\frac{qV}{nkT}\right\}-1\right].$$

(5)

Afterwards, resistance free fill factor (FF₀), which does not have loss from the parasitic resistance, is derived as in Equation (6) by considering the double-diode model at maximum power point (MPP). Where, J_mpp and V_mpp is the current density and voltage at power maximum point, respectively. Equation (6) is composed of three terms: real fill factor, fill factor loss from R_s (FF_Rs), and fill factor loss from R_sh (FF_Rsh), respectively from the left term.

$$F{F}_0=FF+\frac{J_{mpp}^2{R}_s}{V_{oc}{J}_{sc}}+\frac{{\left(V_{mpp}+J_{mpp}{R}_s\right)}^2}{R_{\mathrm{sh}}{V}_{oc}{J}_{sc}}.$$

(6)

As a last step, the fill factor loss from J₀₂ can be readily determined from the difference of FF_J01 and FF₀ Equation (7), because the difference comes from the absence of the J₀₂ effect.

$$F{F}_{J02}=F{F}_{J01}-F{F}_0.$$

(7)

2.2. Sample Measurements with Elevated Temperature

Two industrial solar cells with PERC structure (Figure 3) were prepared as samples (PERC A and B). The PERC A and B were fabricated on different production lines, but the front contact pattern was unified to exclude optical loss due to the front contact. In case of the PERC A, silver paste for the front contact contains higher glass frit contents compared to the PERC B. The characteristics of illuminated J-V were measured by using an in-house solar simulator, which can control the temperature of substrate. Even though this fill factor analysis method assumed that J₀₁ follows an n factor of 1, there were changes in the n factor depending on the temperature. Therefore, n factor at 1-sun, extracted from the Suns-V_oc measurement, was used for analysis. The temperature of cells during the Suns-V_oc measurement was controlled by using a box that has an ambient heater. The conditions of the experimental temperature were set to 25 °C, 45 °C, and 65 °C.

3. Results and Discussion

3.1. Temperature Dependence

The two PERC solar cell samples were named by the PERC A and B. As a result of the illuminated J-V measurements (

Table 1. Results of illuminated J-V measurement and n factor (from Suns-V_oc) of PERC A and B according to temperature dependence.

Parameters	PERC A			PERC B
Temperature [°C]	25	45	65	25	45	65
Voc [mV]	654	616	578	671	635	596
Jsc [mA/cm2]	38.49	38.74	39.05	39.79	40.08	40.21
Vmpp [mV]	564	517	478	580	526	494
Jmpp [mA/cm2]	35.84	35.92	36.18	37.85	38.07	38.20
FF [%]	80.28	77.70	76.60	82.21	80.53	78.62
Rs [Ω·cm2]	1.58	1.77	1.631	1.49	1.42	1.60
Rsh [Ω·cm2]	10252	2796	2982	9553	26562	5126
η [%]	20.21	18.57	17.28	21.96	20.49	18.87
n factor (Suns-Voc)	1.07	1.14	1.17	1.05	1.12	1.19

), V_oc and fill factor of PERC B were 17 mV and 1.93 % higher at 25 °C, respectively. J_sc difference was not significant (~1.3 mA/cm²) and it comes from the different fraction of front metal contact. Graphs in Figure 4 show the drop of V_oc and fill factor (depending on temperature), and also presents the average temperature coefficient as well. The average drop of V_oc and fill factor with the PERC A cell were slightly higher than the PERC B cell. Especially, the larger fill factor drops occurred at 45 °C for the PERC A and 65 °C for the PERC B. Illuminated J-V measurements alone do not have enough evidence to accurately diagnose what the main problem is.

3.2. Results of Fill Factor Loss Analysis

Table 2. Results of fill factor loss analysis of PERC A and PERC B according to temperature (the values are absolute).

FF Loss Analysis	PERC A			PERC B
Temperature [°C]	25	45	65	25	45	65
Ideal FF [%]	83.78	82.89	82.36	84.08	83.43	82.67
Total FF loss [%]	3.50	5.19	5.78	1.88	2.91	4.06
FFJ01 [%]	0.82	1.70	2.10	0.58	1.42	2.30
FFJ02 [%]	1.86	2.47	2.69	0.48	0.70	0.75
FFRs [%]	0.81	0.97	0.94	0.80	0.78	0.98
FFRsh [%]	0.01	0.05	0.05	0.02	0.01	0.03
FF0 [%]	81.00	78.72	77.57	83.02	81.31	79.62
Real FF (LIV) [%]	80.28	77.70	76.60	82.21	80.53	78.62

organizes the values of each fill factor loss according to the parameters from double-diode model. From this data, Figure 5 and Figure 6 shows the effect of each parameter on the total fill factor loss. At initial temperature, percentage of FF_J01 was higher than FF_J02 for the PERC B cell. On the other hand, FF_J02 had a higher percentage of total fill factor loss than FF_J01 for the PERC A cell. As the temperature rose, FF_J01 ratio of both PERC A and B increased while FF_J02 ratio decreased. This can be explained by the temperature dependence of J₀₁ and J₀₂ in Equations (8) and (9).

$$J_{01}\left(T\right)=J_{01}\left(25 {}^{°}\mathrm{C}\right)\times {\left(\frac{n_i\left(T\right)}{n_i\left(25 {}^{°}\mathrm{C}\right)}\right)}^2,$$

(8)

$$J_{02}\left(T\right)=J_{02}\left(25 {}^{°}\mathrm{C}\right)\times \left(\frac{n_i\left(T\right)}{n_i\left(25 {}^{°}\mathrm{C}\right)}\right).$$

(9)

J₀₁ is proportional to square of n_i(T), which increases sensitively according to the temperature, while J₀₂ is directly proportional to n_i(T). Due to the difference of the temperature dependence, the effect of J₀₁ becomes dominate as temperature goes up. However, the FF_J02 ratio and the absolute value are still higher than FF_J01 at 65 °C for the PERC A cell. A possible explanation is that the initial value of FF_J02 (1.86%) was twice higher than that of FF_J01 (0.82%) and helped increase at a high temperature.

In addition, the temperature dependence of FF_J02 for the PERC B cell (Figure 6b) reveals that the FF_J02 will not increase significantly at elevated temperature if the initial ratio to the total fill factor loss is relatively small. On the other hand, the difference of FF_J01 between 25 °C and 65 °C increased up to 20%, even though the initial difference was only 7%. This means that the effect of J₀₁ on fill factor will be accelerated if the initial loss is relatively high.

In case of the PERC B cell, one can diagnose that the recombination of emitter, quasi-neutral region, or surface passivation have to be improved. Reduction of FF_Rs ratio for the PERC B cell will further reduce the temperature dependence, even though there were small variation at the elevated temperature. The ratio and temperature dependence of FF_Rsh were negligible for both PERC A and B cells.

3.3. Verification Through Injection Dependent-Carrier Lifetime

In order to verify the results of the fill factor loss analysis, the lifetime was measured through Sinton instrument’s Suns-V_oc equipment at 25 °C. The recombination current density of the samples was evaluated by using a lifetime fitting method. Through the specific resistance and thickness of the wafer, the Auger recombination and the radiative recombination are represented as lifetime according to the excess carrier concentration as graphs in Figure 7 show.

The expressions for the intrinsic carrier lifetime and bulk lifetime can be expressed as follows.

$$\tau =\frac{\Delta n}{R}$$

(10)

$$\frac{1}{{\tau }_{intrinsic+bulk}}=\frac{1}{{\tau }_{rad}}+\frac{1}{{\tau }_{Auger}}+\frac{1}{{\tau }_{SRH}}$$

(11)

Here, intrinsic recombination can be expressed as an Equation (12) [21].

$$R_{Intrinsic}=R_{Auger}+R_{Radiative}=np\left(1.8\times {10}^{-24}{n}_0{}^{0.65}+6\times {10}^{-25}{p}_0{}^{0.65}+3\times {10}^{-27}\Delta n^{0.8}+9.5\times {10}^{-15}\right)$$

(12)

Where n and p are the free electron and hole concentrations, n₀ and p₀ are the electron and hole concentration in thermal equilibrium, and △n is the excess carrier densities. The bulk lifetime of a wafer can be measured with quasi-steady-state photoconductance (QSSPC) equipment. To measure the bulk lifetime of the wafer, the doped layer was removed from the wafer using KOH solution after POCl₃ diffusion, and then the Al₂O₃/SiN_x stack passivation layer was deposited on both sides. Bulk lifetime can be calculated by the following two formulas [22,23].

$$J_o=\frac{S_{eff}}{q{n}_i^2}\times \left(N_A+\Delta n\right),$$

(13)

$$\frac{1}{{\tau }_{bulk}}=\frac{1}{{\tau }_{eff}}-\frac{2S_{eff}}{W},$$

(14)

Where W is the sample thickness, S_eff is the surface recombination velocity. The S_eff values were calculated as 9.8 cm/s at the 10¹⁵ cm⁻³ injection level which is commonly used [22]. As a result of our calculation, the bulk lifetime was 343 µs for our wafer. The graphs in Figure 7 shows these three lifetimes of radiative, Auger and bulk recombination. If the parameter of J₀₁ is added to this formula, lifetime graph at high injection can be fit by using the formula below:

$$\frac{1}{{\tau }_{eff}}-\frac{1}{{\tau }_{intrinsic}}=\frac{1}{{\tau }_{bulk}}+\frac{J_{01}\left(N_A+\Delta n\right)}{q{n}_i{}^{2}w}.$$

(15)

By fitting the lifetime graph through the J₀₁ value, the J₀₁ value was calculated as 350 fA/cm² for the PERC A cell and 180 fA/cm² for the PERC B cell. Similar to the results of the fill factor loss analysis, the J₀₁ value was significantly higher for the PERC A cell.

Furthermore, we could draw the theoretical graph of FF₀ as function of J₀₂ (25 °C) by applying the J₀₁ value from Figure 7 to the J-V equation of double diode model without resistance Equation (16). The J₀₂ (25 °C) of the PERC A cell was extracted by finding the point that the FF₀ from the fill factor loss analysis equal to the graph (black line in Figure 8). In this way, the J₀₂ (25 °C) of the PERC A and B cells were assessed as 27 nA/cm² and 7.35 nA/cm², respectively. The difference of the J₀₂ value was also expected from the graph in Figure 7. The graphs generally showed poor fitting results at low-level injection region. This means that the PERC A cell has poor properties of J₀₂ or shunt resistance because these are well known as main reasons for low lifetime of solar cells in the low-level injection region [24].

$$J=J_{ph}-J_{01}\left[\exp \left\{\frac{qV}{n_{1}kT}\right\}-1\right]-J_{02}\left[\exp \left\{\frac{qV}{n_{2}kT}\right\}-1\right].$$

(16)

In case of the temperature above 25 °C, J₀₁ and J₀₂ values were calculated by using Equations (8) and (9). Through these J₀₁ and J₀₂ values, temperature conditions of the J₀₂ (25 °C)-FF₀ graph were extended from 30 to 70 °C. We confirmed that the FF₀ from Table 2 matched quite well with the theoretical graph. Consequently, we confirmed that the fill factor loss analysis was conducted precisely by checking the theoretically extracted J₀₁ and J₀₂ values.

4. Conclusions

We conducted fill factor loss analysis to investigate the temperature dependence of industrial PERC cells based on the double diode model. While analyzing the loss of fill factor for the industrial PERC A and B cells, it was confirmed that both samples showed temperature dependence of fill factor (~0.092%/ °C). However, the main parameter that dominantly contribute to temperature dependence were different depending on the initial state of the samples.

For PERC A, J₀₂ was the main parameter of fill factor loss in initial state (25 °C). However, the contribution of the J₀₁ to the fill factor loss increased as the temperature rose. It could be estimated that the PERC A cell has potential to improve fill factor by optimizing J₀₂ or shunt resistance. On the other hand, PERC B has a higher FF_Rs ratio at initial state (25 °C) than other parameters, but the ratio of FF_Rs reduced due to the rapid increase in the FF_J01. Therefore, we believe that the J₀₁ has to be reduced for the PERC B cell by optimizing the doping process, passivation quality, and metal contacts.

In addition, we verified the accuracy of the fill factor loss analysis by comparing it to the fitting results of the injection dependent-carrier lifetime. The J₀₁ and J₀₂ values at 25 °C were extracted, and it was confirmed that the values of FF₀ obtained from the fill factor loss analysis were in good agreement with the theoretically calculated values. In conclusion, it seems very important to reduce initial fill factor loss from the J₀₁, because it has a high temperature dependence. In case of the J₀₂ and R_s, they seem less detrimental for the reduction of fill factor at an elevated temperature. Also, we confirmed that the fill factor loss analysis used in this experiment is very efficient to diagnose the temperature dependence of the solar cells, as well as their initial state.