Phosphorus emitter and metal - grid optimization for homogeneous (n+p) and double-diffused (n++n+p) emitter silicon solar cells

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Phosphorus emitter and metal - grid optimization for homogeneous (n⁺p) and double-diffused (n⁺⁺n⁺p) emitter silicon solar cells

Manuel Cid Sánchez^*; Nair Stem

Departamento de Engenharia de Sistemas Eletrônicos, Escola Politécnica, Universidade de São Paulo - USP, Av. Prof. Luciano Gualberto, Travessa 3, 158, 05508-970 São Paulo - SP, Brazil

ABSTRACT

This work focuses on studying two types of structure: homogeneous and double-diffused emitter silicon solar cells. The emitter collection efficiencies and the recombination current densities were studied for a wide range of surface dopant concentrations and thicknesses. The frontal metal-grid was optimized for each emitter, considering the dependence on the metal-semiconductor contact resistivity and on the emitter sheet resistance. The best efficiency for n⁺p structures, η≈ 25.5%, is found for emitters with thicknesses between (0.5-3) µm and surface doping concentrations in the range 2 x 10¹⁹ cm^-3- 4 x 10¹⁸ cm^-3; while the n⁺⁺n⁺p structure a maximum efficiency of η≈ 26.0% was identified for an even wider range of emitter profiles.

Keywords: modelling, emitter optimization, efficiency limits

1. Introduction

Solar cell emitters can be divided into two different types: a) homogeneous and b) double-diffused (DD) or selective. The homogeneous emitters are characterized by having the same doping level under passivated and metal-contacted regions, while the DD ones present a higher doping level under the metal-contacted one. The passivated regions can be obtained experimentally by a light phosphorus diffusion. In case of DD emitters, this light diffusion is usually preceded by a heavy diffusion only under the metal-grid region.

The theoretical simulations are quite helpful in the development of fabrication processes of silicon solar cells, allowing defining the requirements for high quality emitters and high efficiency solar cells. In this work a re-optimization aiming to compare double-diffused (n⁺⁺n⁺) and homogeneous (n⁺) Gaussian profile phosphorus emitters was performed using a one-dimensional model with analytical solutions^1,2, the currently accepted internal parameters³ and the updated intrinsic concentration, n_i = 9.65 x 10⁹ cm^-3[4].

Despite a complete theoretical re-optimization for homogeneous emitters having already been made⁵, the previous DD (double-diffused) emitter optimizations were carried out using either obsolete parameters^6,7,8, or without considering the light trapping effect and the metal-grid design optimization⁹. Thus, a re-optimization for the double-diffused emitter solar cells (n⁺⁺n⁺p) is necessary. In order to establish a direct comparison between DD and homogeneous emitter structures, the latter will also be re-optimized here.

2. Theoretical Modelling Assumptions

The homogeneous emitters have the same N_s and W_e under the passivated and the metal-contacted regions; on the other hand the double-diffused (DD) emitters are characterized by having a higher N_s under the metal-contacted one, with N_s = 1 x 10²⁰ cm^-3 and W_e = 2.0 µm (13 W/square) used in this work. The adopted expression for the surface recombination velocity under passivated region, S_p = N_s x 10^-16 cm/s, is the one typically found in oxidized surfaces followed by FGA annealing³, values corroborated by M. Kerr et. al.¹⁰. While under metal-contacted regions a constant S_p = 3 x 10⁶ cm/s, was used.

In order to better show the emitter limitations, a 1 W.cm resistivity p-type base region with 300 µm thickness, a 1.5 ms minority carrier lifetime and a zero rear surface recombination velocity was assumed. In sequence, the electrical output parameters (J_sc, V_oc, FF and η ) of n⁺p and n⁺⁺n⁺p complete structures were studied. The short-circuit current density, J_sc was calculated taking into account the light trapping effect and the AM1.5G spectrum (ASTM G173-03). The open-circuit voltage, V_oc was determined as a function of total emitter recombination, J_oe, the base recombination and J_sc. The relation between the fill factor, FF and the device series resistance was expressed as function of the optimized total resistive power loss, p_tot and the intrinsic fill factor, FF_o^[11], as defined in the expression:

3. Upgraded Program

In order to produce contour plots assuring accuracy even for thicker and highly doped emitters for the range N_s = 1 x 10¹⁸ cm^-3 - 1 x 10²⁰ cm^-3 and W_e = (0.1 to 10) µm, the 10^th order approximation was adopted to fulfill the optimizations.

As a matter of fact, the 5^th order approximation, used to calculate with accuracy the emitters with thicknesses up to 5 µm at the previous work⁹, became unsatisfactory for higher values of thicknesses (required at this work).

Since the emitter can be divided into two different regions: passivated and metal-contact and the surface doping concentration was kept constant under the latter one, the accuracy on the recombination under the passivated region was chosen to be analyzed.

For instance, a 10 µm thickness emitter with N_s = 1 x 10²⁰ cm^-3 presented J_oepass = 158 fA.cm^-2 as the recombination current density under the passivated region (without the metal-contact factor, F_m) using the 10^th order approximation, being about 5% inferior than the solution obtained by the PC1D code. On the other hand, if a 3^rd and a 5^th order approximations were considered these errors would increase up to 39.2 and 26.5%, respectively.

4. Metal-Grid Optimization

In the present work, Ti-Pd-Ag metal-grid designs, typical of laboratory solar cell with 2 x 2 cm area, are optimized using classical models^5,11. This optimization is performed by an iterative method until the shadowing loss becomes equal to the total resistive power loss, p_tot (emitter layer, metal fingers and metal contacts) for each emitter. The metal (Ti) - semiconductor (Si) contact resistances were calculated taking into account their dependence on the emitter^5,12 and Ag contact resistance was considered to be ≈ 2 x 10^-6 W.cm^2[13]. The initial finger width was D = 6 mm and after being electroplated, D_F= 30 mm, with a 10 µm thickness. The bus-bar was supposed to be tapered and with a two-step Ag plating, typical of high efficiency solar cells¹⁴.

The shadowing factor, F_s was extracted from the total shadowing power losses (fingers, p_sf plus bus-bar, p_sb). However, the metal-contacted factor, F_m, due to the area increase caused by the electroplating, is a fraction of the p_sf (20%) and p_sb (50%), as presented in expression (2).

Figures 1 and 2 show the optimized shadowing factors, F_s and the spacing between fingers, S as functions of N_s and W_e for single and double emitters.

Comparing these figures, it can be observed that the higher the surface doping concentration (>2 x 10¹⁹cm^-3) of thick emitters (>3 µm), the higher the required spacing between fingers (>1.79 mm), and consequently, the lower F_s (about 2.4-2%) for both types of emitters. Nevertheless, for lowly doped emitters (1 x 10¹⁸ cm^-3 < N_s < 4 x 10¹⁸ cm^-3) a significantly different behavior can be observed. While the F_s and S contour plots of homogenous emitters present a plateau as the thickness increases, the DD plots decrease continuously. This difference in behavior is due to the higher metal-contact resistance of homogeneous emitters, making a higher F_s necessary; and therefore, a lower S.

5. Emitter Optimization

The emitters had their collection efficiency, η_c and their recombination current density components under metal-contacted, J_oemet, and passivated, J_oepass, regions calculated as function of N_s and W_e. The total emitter recombination current densities, J_oe result from the sum of the components J_oemet and J_oepass multiplied by their respective optimized weight factors, (F_m) and (1-F_m), as commented in the following.

According to the modelling results the Gaussian profile emitters can provide high collection efficiencies (η_c> 98%). Moreover, in order to maintain a high η_c as the thickness increases, a steady decrease in the surface doping concentration is imperative. Thus, emitters with N_s = 2 x 10¹⁹ cm^-3, 1 x 10¹⁹ cm^-3, 4 x 10¹⁸ cm^-3 and 2 x 10¹⁸ cm^-3 require W_e = (0.94, 1.73, 3.68 and 6.17) µm, respectively to provide the same η_c = 98%.

5.1. Homogeneous emitter recombination (n⁺)

The emitter recombination current densities under both metal-contacted, J_oemet and passivated, J_oepass regions are shown in Figure 3 and Figure 4, respectively. In Figure 3, it can be observed that the moderately doped emitters, 4 x 10¹⁸ cm^-3 < N_s < 2 x 10¹⁹ cm^-3 with thickness in the range, 0.5 µm < W_e < 3 µm have J_oemet between ≈ 3.6 x 10³ fA.cm^-2 and ≈ 3.3 x 10² fA.cm^-2. In contraposition, Figure 4 shows that the passivated recombination component in the same region, J_oepass is much lower, between ≈ 11 fA.cm^-2 and ≈ 88 fA.cm^-2. Despite this difference, sometimes the determining contributor to the total J_oe is the passivated region, J_oepass, since these components must be also multiplied by the corresponding area weight factors.

5.2. Double-diffused emitters recombination (n⁺⁺n⁺)

Differently from the homogeneous emitters, the metal-contacted recombination component of the DD ones is always J_oemet = 315 fA.cm^-2, since it was assumed a fixed N_s = 1 x 10²⁰ cm^-3 and W_e = 2 µm under this region for each studied case. Under the passivated region the component, J_oepass is the same shown in Figure 4.

A comparison between the total recombination, J_oe for both types of emitters is shown in Figure 5 as function of emitter N_s and W_e. It can be observed that the homogeneous total recombination, in the majority of cases, is higher (30 fA.cm^-2 < J_oe < 200 fA.cm^-2) than the DD case (12 fA.cm^-2 < J_oe < 200 fA.cm^-2), due to the lower recombination loss under the metal-contacted regions in the latter type of emitters. This difference becomes meaningful mainly for the lowly/moderately doped emitters (1 x 10¹⁸ cm^-3 < N_s < 7 x 10¹⁸ cm^-3) pratically in the whole thickness range (0.1 µm < W_e < 10 µm), where the DD J_oe can reach values between 12 fA.cm^-2 and 18 fA.cm^-2.

Another remarkable point in Figure 5 is that the total J_oe of both emitter types are practically coincident for moderately doped (5 x 10¹⁸ cm^-3 < N_s < 4 x 10¹⁹ cm^-3) emitters with thickness range (2 µm < W_e < 10 µm) and also for highly doped (N_s > 6 x 10¹⁹ cm^-3) emitters with (0.7 µm < W_e < 10 µm), due to a non-significant contribution of the metal-contacted region.

5.3. Emitter recombination for optimum homogeneous and DD structures

A comparison between the emitter recombination current density (including the component contributions and the total J_oe) of the optimum emitters from Figures 8 and ¹¹ is presented in Table 1. The optimum homogeneous emitter is N_s = 7.5 x 10¹⁸ cm^-3 with 1.7 µm, while the DD optimum emitter is given by N_s = 3 x 10¹⁸ cm^-3 and W_e = 1.4 µm.

Analyzing Table 1, it can be concluded that the passivated region of both types of emitters is the dominant component. The higher J_oepass presented by the homogeneous emitter is principally due to the difference between the respective surface doping concentrations, N_s = 7.5 x 10¹⁸ cm^-3 for homogeneous and N_s = 3 x 10¹⁸cm^-3 for DD, since their optimum metal-contacted factors are quite close, the former F_m≈ 0.88% (F_s = 3.21% in Figure 1) and the latter F_m≈ 0.93% (F_s = 3.49% in Figure 2).

6. Output Electrical Parameters of N⁺P Solar Cells

The output electrical parameters (short-circuit current density, J_sc; open-circuit voltage, V_oc and efficiencies, η ) of homogeneous emitter silicon solar cells are shown in the contour plots of Figures 6, 7 and 8, respectively.

According to Figure 6, the short-circuit current densities reach the maximum, J_sc = 43.0 mA.cm^-2 - 43.5 mA.cm^-2, for emitters with surface doping concentration 4 x 10¹⁸ cm^-3 < N_s < 2 x 10¹⁹ cm^-3 and thickness 0.4 µm < W_e< 4.0 µm. However, it can be noticed that high short-circuit current densities can be reached even for highly doped emitters (2 x 10¹⁹ cm^-3 - 1 x 10²⁰ cm^-3) since their thickness are about (0.4-0.6) µm.

In Figure 7, the V_oc were calculated as a function of the total J_oe, taking into account both components (J_oepass and J_oemet) and their respective weight factors from the metal-grid optimization, as shown by Figures 1 and 2, and Equation (2).

This figure shows that the maximum open-circuit voltages, V_oc are between 700 mV and 715 mV, for emitters with surface doping concentrations N_s < 2 x 10¹⁹ cm^-3 and thickness range 0.4 µm < W_e < 10.0 µm, similarly to the bottom right corner of Figure 4. On the other hand, there is a decrease of 30 mV for highly and thin doped emitter N_s = 1 x 10²⁰ cm^-3 and W_e = 0.2 µm, the upper left corner, resulting in efficiencies of about η = 24.3%, as it can be seen in Figure 8.

According to Figure 8, the maximum efficiencies, η = 25.5 25.3%, are obtained in the range N_s = 2 x 10¹⁹ cm^-3 - 4 x 10¹⁸ cm^-3. The surface doping concentration upper bound (≈ 2 x 10¹⁹ cm^-3) allows lower thicknesses (≈ 0.5 µm < W_e < ≈ 1 µm); while the lower bound (≈ 4 x 10¹⁸ cm^-3) requires thicker emitters, ≈ 1 µm < W_e < ≈ 3 µm. The output parameters of a solar cell with an intermediate N_s from the optimum range, N_s = 7.5 x 10¹⁸ cm^-3 and 1.7 µm (R_square≈ 87.5 W/square), are J_sc= 43.4 mA.cm^-2, V_oc = 710.3 mV, FF = 0.826 and η = 25.5% with an optimized metal-grid design given by F_s = 3.21%, F_m = 0.88% and S ≈ 1.24 mm. Thus, in order to mantain a high efficiency there must be a trade off between high short-circuit current density and open-circuit voltage (minimum recombination).

Comparing the results of Figure 8 to the ones obtained in a previous work⁹, it can be seen that the maximum efficiencies at that work, η = (21.6-21.7%), were reached for surface doping concentration and thickeness ranges, N_s = (1 x 10¹⁹ - 5 x 10¹⁸) cm^-3 and W_e = (1.2 - 2.0) µm respectively, also belonging to the optimum ranges of the η = 25.3% contour plot in Figure 8. Nevertheless, the difference between the absolute values of efficiencies is strictly related to the introduction of the light trapping effect in the semiconductor, generating an important increase of the short-circuit current density, changing from 38.6 mA.cm^-2 to 43.5 mA.cm^-2. The open-circuit voltages that were about 690 mV for emitters with surface doping level, N_s = 5 x 10¹⁸ cm^-3, reached the maximum value V_oc > 700 mV, as shown in Figure 7. The main cause for the differences between the maximum V_oc can be owed to the fact that the previous structures were made of three different regions n⁺pp⁺; and therefore, the recombination coming from a p⁺ region was inserted.

7. Output Electrical Parameters of N⁺⁺N⁺P Solar Cells

Similarly to the homogeneous emitter solar cells, the output electrical parameters (short-circuit current density, open-circuit voltage and efficiency) of the DD emitter solar cells were analyzed in contour plots, as presented in Figures 9, 10 and ¹¹.

Analyzing that the short-circuit current density, J_sc surrounded by the 43.4 mA.cm^-2 contour plot in Figure 9 present the J_sc between 43.4 mA.cm^-2 < J_sc< 43.6 mA.cm^-2. On the other hand, in Figure 10, it can be verified high open-circuit voltages V_oc = 725 mV for low doped emitters, with N_s < 2 x 10¹⁸ cm^-3 in a wide range of thickness, 0.25 µm < W_e < 4.0 µm.

Comparing Figures 7 to 10, it can be concluded that higher open-circuit voltages are reached in the double-diffused emitter silicon solar cells as it was predicted previously in Figure 5.

Meanwhile, the n⁺⁺n⁺p structures (see ^{Figure 11}) can provide higher efficiencies, η = 26.0-25.7% for a wider range of emitter regions, 1 x 10¹⁸ cm^-3 < N_s < 1 x 10¹⁹ cm^-3 with 0.5 µm < W_e < 10 µm, in agreement with previous results⁹. However, in that work the maximum efficiencies were lower, η = 21.9% (no light trapping) and provided by a narrower range of emitter profiles, N_s = 1 x 10¹⁹ cm^-3 - 5 x 10¹⁸ cm^-3 and W_e = (1.2-2.0) µm, due to fewer cases having been analyzed (0.1 µm < W_e < 5 µm and 5 x 10¹⁸ cm^-3 < N_s < 1 x 10²⁰ cm^-3).

For an optimized n⁺⁺n⁺p structure with N_s = 3.0 x 10¹⁸ cm^-3 and W_e = 1.4 µm (R_square = 172.4 W/square), the output parameters are J_sc = 43.5 mA.cm^-2, V_oc = 721.5 mV, FF = 0.829 and η = 26.0%. The corresponding optimized metal-grid is defined by F_s = 3.49%, F_m = 0.93% and S = 1.11 mm.

These results are slightly different from those ones found by A. Aberle et al.⁸, where the maximum efficiencies η ≈ 27% were provided also for lightly doped emitters N_s = 5 x 10¹⁸ cm^-3 - 1 x 10¹⁹ cm^-3, but for a lower thickness range W_e = (0.1-0.3) µm. As shown in ^{Figure 11}, despite shallow emitters could also provide high efficiencies, the maximum values, η = 26% were obtained for a shifted thickness range, 1 µm < W_e < 10 µm. This fact is due to the differences between the used input parameters. At that work, the frontal surface recombination velocity was not variable under passivated region as in this work: S_p = 500 cm/s was kept constant for the four studied surface doping concentrations (N_s = 1 x 10¹⁸ cm^-3, 5 x 10¹⁸ cm^-3, 1 x 10¹⁹ cm^-3, 5 x 10¹⁹ cm^-3). Meanwhile, the metal-contacted region surface recombination velocity was a bit lower, S_p = 1 x 10⁶ cm/s. The parameters under the metal-contacted region were N_s = 5 x 10¹⁹ cm^-3 and W_e = 2 µm. As it can be noticed, these results overestimated the efficiencies for shallow and moderately doped emitters, since the metal-contact factor F_m was underestimated by fixing it at 3%. On the other hand, E. Demesmaeker⁷, by fulfilling grid-optimization, but adopting R. King³ parameters and a higher surface doping concentration under the metal-contact region N_s = 1 x 10²¹ cm^-3, obtained more similar results to this work. Despite the lower optimum efficiencies η = 21%, the correspondent ranges of maximum efficiencies were N_s = 2 x 10¹⁸ cm^-3 - 1 x 10¹⁹ cm^-3 and thickness 1 µm < W_e < 10 µm.

8. Conclusions

Gaussian profile phosphorus emitters were optimized showing high quality, high collection efficiencies (>98%) and low recombination (minimum J_oe for homogeneous and DD are respectively 30 fA.cm^-2 and 12 fA.cm^-2). The total recombination, J_oe of lowly doped homogeneous emitters showed to be strongly dependent on the metal-contacted recombination component, J_oemet and on the optimized metal-grid designs.

The optimum homogeneous structure efficiencies (η = 25.5 25.3%) were found for surface doping in the range N_s = 2 x 10¹⁹ cm^-3 4 x 10¹⁸ cm^-3 together with a thickness of W_e≈ (0.5-3) µm. On the other hand, the best DD structures can provide higher efficiencies (η = 26.0-25.7%) for a wider range of emitter profiles, 1 x 10¹⁸ cm^-3 < N_s < 1 x 10¹⁹ cm^-3 and 0.5 µm < W_e < 10 µm.

Acknowledgements

Nair Stem was supported by CNPq scholarship under process nº 141460/20008.

Received: May 19, 2008

Revised: February 5, 2009

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Publication Dates

• Publication in this collection
  18 May 2009
• Date of issue
  Mar 2009

History

• Received
  19 May 2008
• Reviewed
  05 Feb 2009