Phosphorus Emitter and Metal-Grid Optimization for Homogeneous ( n + p ) and Double-Diffused ( n + + n + p ) Emitter Silicon Solar Cells

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 np structures, η ≈ 25.5%, is found for emitters with thicknesses between (0.5-3) μm and surface doping concentrations in the range 2 x 10 cm– 4 x 10 cm; while the nnp structure a maximum efficiency of η ≈ 26.0% was identified for an even wider range of emitter profiles.


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 parameters 3 and the updated intrinsic concentration, n i = 9.65 x 10 9 cm -3 [4] .
Despite a complete theoretical re-optimization for homogeneous emitters having already been made 5 , the previous DD (doublediffused) emitter optimizations were carried out using either obsolete parameters 6,7,8 , or without considering the light trapping effect and the metal-grid design optimization 9 .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.

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 10 20 cm -3 and W e = 2.0 µm (13 Ω/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 annealing 3 , values corroborated by M. Kerr et.al. 10 .While under metal-contacted regions a constant S p = 3 x 10 6 cm/s, was used.
In order to better show the emitter limitations, a 1 Ω.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:

Upgraded Program
In order to produce contour plots assuring accuracy even for thicker and highly doped emitters for the range N s = 1 x 10 18 cm -3 -1 x 10 20 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 work 9 , 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 10 20 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.

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 Ω.cm 2 [13] .The initial finger width was D = 6 µm and after being electroplated, D F = 30 µm, 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 cells 14 .
The shadowing factor, F s was extracted from the total shadowing power losses (fingers, p sf plus bus-bar, p sb ).However, the metalcontacted 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 10 19 cm -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 10 18 cm -3 < N s < 4 x 10 18 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.

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 10 19 cm -3 , 1 x 10 19 cm -3 , 4 x 10 18 cm -3 and 2 x 10 18 cm -3 require W e = (0.94, 1.73, 3.68 and 6.17) µm, respectively to provide the same η c = 98%.

Homogeneous emitter recombination (n + )
The emitter recombination current densities under both metalcontacted, 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 10 18 cm -3 < N s < 2 x 10 19 cm -3 with thickness in the range, 0.5 µm < W e < 3 µm have J oemet between ≈3.6 x 10 3 fA.cm - and ≈3.3 x 10 2 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.) W e ( m)

Double-diffused emitters recombination (n ++ n + )
Differently from the homogeneous emitters, the metalcontacted recombination component of the DD ones is always J oemet = 315 fA.cm -2 , since it was assumed a fixed N s = 1 x 10 20 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 - ) than the DD case (12 fA.cm -2 < J oe < 200 fA.cm - ), 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 10 18 cm -3 < N s < 7 x 10 18 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 - and 18 fA.cm - .
Another remarkable point in Figure 5 is that the total J oe of both emitter types are practically coincident for moderately doped (5 x 10 18 cm -3 < N s < 4 x 10 19 cm -3 ) emitters with thickness range (2 µm < W e < 10 µm) and also for highly doped (N s > 6 x 10 19 cm -3 ) emitters with (0.7 µm < W e < 10 µm), due to a non-significant contribution of the metal-contacted region.

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 10 18 cm -3 with 1.7 µm, while the DD optimum emitter is given by N s = 3 x 10 18 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 10 18 cm -3 for homogeneous and N s = 3 x 10 18 cm -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).

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 Table 1.Comparison between the homogeneous and DD emitter recombination current density for the optimum complete structures from Figure 8 and 11: the components multiplied by the weight factors, (F m ).J oemet and (1-F m ).J oepass , and the total, J oe .
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 10 19 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 10 20 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.
Comparing the results of Figure 8 to the ones obtained in a previous work 9 , 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 10 19 -5 x 10 18 ) 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 10 18 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.

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 10 18 cm -3 in a wide range of thickness, 0.25 µm < W e < 4.0 µm.
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 10 18 cm -3 -1 x 10 19 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 10 18 cm -3 , 5 x 10 18 cm -3 , 1 x 10 19 cm -3 , 5 x 10 19 cm -3 ).Meanwhile, the metalcontacted region surface recombination velocity was a bit lower, S p = 1 x 10 6 cm/s.The parameters under the metal-contacted region were N s = 5 x 10 19 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. Demesmaeker 7 , by fulfilling grid-optimization, but adopting R. King 3 parameters and a higher surface doping concentration under the metal-contact region N s = 1 x 10 21 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 10 18 cm -3 -1 x 10 19 cm -3 and thickness 1 µm < W e < 10 µm.

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 - ).The total recombination, J oe of lowly doped homogeneous emitters showed to be strongly dependent on the metalcontacted recombination component, J oemet and on the optimized metal-grid designs.

Figure 2 .
Figure 2. Optimum shadowing factors, F s (%) and spacing between fingers, S (mm) as functions of surface doped concentration, N s and thickness, W e for DD emitters.

Figure 4 .Figure 5 .
Figure 4. Passivated current density recombination, J oepass (fA.cm -2 ) as a function of surface doping concentration, N s and thickness, W e for both types: homogeneous and DD-emitters (S p = N s x 10 -16 cm/s).

Figure 6 .
Figure6.Short-circuit current density contour plots, J sc (mA/cm 2 ) as a function of surface doping concentration, N s and thickness, W e of n + p structure solar cell with base resistivity 1 Ω.cm.

Figure 7 .
Figure 7. Open-circuit voltage contour plots, V oc (mV) as a function of surface doping concentration, N s and thickness, W e of n + p structure solar cell with base resistivity 1 Ω.cm.

Figure 10 .Figure 11 .
Figure10.Open-circuit voltage contour plots, V oc (mV) as a function of surface doping concentration, N s and thickness, W e of n ++ n + p structure solar cell with base resistivity 1 Ω.cm.s.
Solar cell efficiency contour plots, η (%) as a function of surface doping concentration, N s and thickness, W e of n + p structure solar cell with base resistivity 1 Ω.cm.Figure9.Short-circuit current density contour plots, J sc (mA.cm -2 ) as a function of surface doping concentration, N s and thickness, W e of n ++ n + p structure solar cell with base resistivity 1 Ω.cm.