## Materials Research

##
*Print version* ISSN 1516-1439*On-line version* ISSN 1980-5373

### Mat. Res. vol.5 no.4 São Carlos Oct./ Dec. 2002

#### http://dx.doi.org/10.1590/S1516-14392002000400006

**Homogeneous Gaussian Profile P ^{+}-Type Emitters: Updated Parameters and Metal-Grid Optimization**

* M. Cid, N. Stem**

*Laboratório de Microeletrônica - Depto. de Engenharia de Sistemas Eletrônicos Escola Politécnica da Universidade de São Paulo C.P. 61548, 05424-970 São Paulo - SP, Brazil*

*e-mail: nstem@lme.usp.br

Received: May 4, 2001; Revised: April 16, 2002

P^{+}-type emitters were optimized keeping the base parameters constant. Updated internal parameters were considered. The surface recombination velocity was considered variable with the surface doping level. Passivated homogeneous emitters were found to have low emitter recombination density and high collection efficiency. A complete structure p^{+}nn^{+} was analyzed, taking into account optimized shadowing and metal-contacted factors for laboratory cells as function of the surface doping level and the emitter thickness. The base parameters were kept constant to make the emitter characteristics evident. The most efficient P^{+}-type passivated homogeneous emitters, provide efficiencies around 21% for a wide range of emitter sheet resistivity (50 ¾ 500 W/) with the surface doping levels N_{s}=1×10^{19} cm^{-3} and 5×10^{19} cm^{-3}. The output electrical parameters were evaluated considering the recently proposed value n_{i}=9.65×10^{9} (cm^{-3}). A non-significant increase of 0.1% in the efficiency was obtained, validating all the conclusions obtained in this work, considering n_{i}=1×10^{10} cm^{-3}.

**Keywords:** *theoretical optimization, homogeneous passivated emitters, p ^{+}-type, Gaussian profile, metal-grid*

**1. Introduction**

It is well-known that some effects such as band gap narrowing, Fermi level degeneracy and changes on behavior of minority carrier lifetime and mobility occur when a region is highly doped, as for solar cell emitters. Many theoretical optimizations have been made taking these effects into account^{1,2}. According to these theoretical predictions the best p^{+}-type passivated homogeneous emitters were found to have surface doping level N_{s}=1×10^{19} cm^{-3} and thickness W_{e} =4 mm, for conventional cells with finger width of 100 mm.

Traditionally, the passivated emitter surface recombination velocity has been considered constant S_{p}=1640 cm/s. Recently, A. Cuevas *et al.*^{3} showed the dependence of the surface recombination velocity on the surface doping level, making new optimizations imperative.

In this work, theoretical models with analytical solutions have been used to study p^{+} emitter regions. The recombination and collection efficiency are written as function of series of multiple integrals and in order to assure good accuracy, a fifth order approximation was considered. A simulator code was developed to optimize each particular region of the solar cell (emitter, base and n^{+} region) and the complete structure p^{+}nn^{+}. In this code a Gaussian profile was chosen and the passivated homogeneous emitters were optimized. Emitters had the recombination current density and efficiency collection calculated as function of the surface doping level and sheet resistivity, considering passivated region surface recombination velocity variable^{3}. The surface recombination velocity was kept constant for metal contacted region, S_{n}=3×10^{6} cm/s.

To calculate theoretical solar cell efficiency, a complete p^{+}nn^{+} structure was considered. The base region was assumed to have 300 mm thickness and resistivity of 2.3 W.cm. The lifetime was assumed to be 1.5 ms^{4}. In order to make the emitter influence evident, the rear surface recombination velocity and the base recombination current density were assumed to be null. Neither light trapping effects and nor surface reflection have been taken into account. The short-circuit current density was obtained adopting the standard spectrum AM1.5G (ASTM892-87) and updated optical absorption coefficients^{5}.

The metal-grid optimization was carried out using the traditional expressions to calculate the power loss^{6} and considering typical laboratory solar cells with Ti-Pd-Ag contacts with finger width of 5mm and 30mm before and after electroplating, respectively.

The shadowing factor, F_{s}, and the metal grid factor, F_{m}, were optimized as function of the emitter sheet resistivity and the correspondent metal-semiconductor contact resistivity. The metal-semiconductor contact resistivity dependence on surface doping level was extracted from Swirhun curves^{7}. An interactive process was adopted and the optimum shadowing factor for each surface doping level was obtained when the normalized total loss power (grid loss power, contact metal-semiconductor loss power and loss power due to the lateral current flow in the emitter) became equal to the shadowing loss, assuring an accuracy of 0.1%. The metal sheet resistivity (Ag) was assumed to be constant, r_{c} »2mW^{8}. In order to make evident the emitter characteristics, the base loss power was assumed to be null.

Thus, the optimum metal-contacted factor, F_{m}, was calculated taking into account the optimum shadowing factor, F_{s}, for each surface doping level according to Eq. 1.

The output parameters (short-circuit current density, J_{sc}, open-circuit voltage, V_{oc} and efficiency, h) and the intrinsic fill factor, FF_{O} were calculated using well-known relationships^{6}. The final fill factor, FF presented in Eq. 2 takes into account the optimum normalized grid loss power, P_{t} and the intrinsic fill factor, FF_{O}.

**2. Updated Internal Parameters and Expressions**

Table 1 shows the expressions and the internal parameters that were adopted in this work. It can be observed that the intrinsic concentration was assumed to be 1×10^{10} cm^{-3} and an updated surface recombination velocity was considered dependent on surface doping level for passivated region^{3}.

All the calculations in this work were made adopting n_{i}=1×10^{10} cm^{-3}, despite the recent change^{9} to n_{i}=9.65×10^{9}cm^{-3 9} , since the former is still the most accepted in the scientific community.

Although initially developed for the outdated value of n_{i}=1.45×10^{10} cm^{-3}, the minority carrier mobility and band gap narrowing expressions^{2} presented in Table 1 keep on being the best fitting to the experimental results. These empirical expressions were obtained with the PCD technique, by the measurement of the reason J_{o}/n_{i}^{2}. Therefore, a change of n_{i} only interferes in the obtained J_{o} and not in the reason J_{o}/n_{i}^{2}. Thus, the minority carrier mobility and the band gap narrowing expressions are independent on n_{i}. This conclusion is quite important, because it validates the expressions presented in Table 1 for both n_{i}=1×10^{10} cm^{-3} and the recently proposed n_{i}=9.65×10^{9} cm^{-3} (for 300 K).

**3. Emitter Optimization**

*3.1. Recombination*

Figure 1 shows current densities for two kinds of regions (metal-contacted and passivated) as function of emitter sheet resistivity, R_{} and doping level, N_{s}, considering their respective surface recombination velocities, S_{p}=3×10^{6} cm/s and S_{p}=500 (Na/10^{16})^{1/3} cm/s.

It can be observed that for metal-contacted regions the recombination current density decreases as the surface doping level and the emitter sheet resistivity increase (corresponding to shallower emitters). Therefore, the best recombination current densities are found for thick and highly doped emitters.

However, for the passivated region the lowest recombination current densities were found for low surface doping levels (N_{s}=5×10^{18} cm^{-3} and 1×10^{19} cm^{-3}), being practically constant as emitter sheet resistivity increases. It can be observed that highly doped emitters present lower recombination than passivated emitters when a low emitter sheet resistivity is considered.

Thus, in order to evaluate the contributions of the metal-contacted and passivated regions to the total recombination (J_{oe}), the surface doping level N_{s}=1×10^{19} cm^{-3} was chosen, due to lower metal-semiconductor contact resistivity. To calculate the components, it was taken into account the occupation area of both kinds of regions, metal-contacted and passivated, multiplying the components by the weight factors, F_{m} and (1-F_{m}), respectively, as it can be seen in equation (3).

Figure 2 shows the total emitter recombination current density, J_{oe}, and its components, the passivated, J_{pass}, and the metal-contacted, J_{met}, region recombination current densities versus emitter thickness, W_{e}, considering N_{s}=1×10^{19} cm^{-3} .

In this figure, it can be observed that the passivated component presents a larger contributition than the metal-contacted one, due the difference found in the weight factors of both in Eq. 3.

To make a more detailed evaluation of the total recombination current density behavior, each emitter region recombination current density (metal-contacted, J_{met}, and passivated, J_{pass}) was divided into two components: volume recombination, J_{vol} and surface recombination, J_{s}, as it can be seen in Figs. 3 and 4.

According to Figs. 3 and 4 the surface recombination current density, J_{s}, is the major contributor to the recombination of both regions (metal-contacted, J_{met}, and passivated, J_{pass}) about 99.6% and 94.6%, respectively.

However, in Fig. 3, it can be seen in the metal-contacted region that the volume recombination, J_{vol}, is practically constant as the emitter thickness increases, while if it is compared to Fig. 4, for passivated region, a more significant contribution of this component is found. In the latter figure the volume recombination increases the contribution about 10 times as the emitter thickness increases from 0.2 to 3.4 mm.

*3.2. Emitter collection efficiency*

Figure 5 shows a comparison between the emitter collection efficiency as function of emitter sheet resistivity and surface doping level, considering homogeneous passivated emitters.

According to this figure, the highly doped emitter collection effciencies are higher than the moderately doped ones since the same value of emitter sheet resistivity is considered. However, when optimized emitters are focused, the moderately doped emitters present slightly higher efficiencies. Thus, analyzing the optimum short-circuit current densities in Fig. 6 for each surface doping level case, it can be found that the moderately doped emitters present the highest optimum emitter sheet resitivities (the thickest optimized emitters). For instance, chosing the optimum sheet resistivies from Fig. 6 curves, it can be seen in Fig. 5 that the optimized collection efficencies for N_{s}=5×10^{18} cm^{-3} and N_{s}=1x10^{20} cm^{-3} cases are quite close h_{c } = (98.4 97.9)% with their correspondent sheet resistivities (255-106) W/.

One point to be stressed is that such close values are not found when the respective short-circuit current densities are calculated as it can be seen in Fig. 6. In these curves, the maximum short-circuit current densities are quite different when compared moderately and highly doped emitters, N_{s } = 5×10^{18} cm^{-3} and N_{s } = 1×10^{20} cm^{-3}, respectively. This difference is attributed to the metal-grid shadowing factor (1-F_{s}) influence.

**4. A Complete Structure: P ^{+}NN^{+} Solar Cells**

In order to compare the emitter effects on the complete structure P^{+}nn^{+}, the base and n^{+} regions have been considered constant. The recombination current density of base region and the rear surface recombination velocity were assumed to be null, as mentioned before. Thus, the outuput electrical parameters (short-circuit current density, J_{sc}, open circuit voltage, V_{oc}, and efficiency, h) as function of the emitter sheet resistivity and the surface doping level are shown in Figs. 6-8, respectively.

The short circuit densities, J_{sc}, were obtained taking into account the photogenerated current densities in emitter and base regions, considering the weight factor (1-F_{s}) correspondent to the illuminated area.

According to this figure, the highest short-circuit densities (approximately J_{sc}»38.2 mA/cm^{2}) are reached for N_{s}=5×10^{19} cm^{-3} and N_{s}=1×10^{20} cm^{-3,}, corresponding to a wide emitter sheet resistivity range R_{}=(185-93) W/ and R_{}=(211-71) W/ respectively, despite the highest emitter collection efficiency had been obtained for N_{s}=5×10^{18} cm^{-3} , as it was shown in Fig. 5. This fact, as mentioned before, is due to the high shadowing factor, F_{s}, provided by the moderately doped emitters, correlated to the increase of the metal-semiconductor contact resistivity.

In Fig. 7 it can be observed that the highest open circuit voltage are reached for the sheet resistivity ranges (10-100) W/ and (25-200) W/ corresponding to relatively deep, and moderately doped emitters, (N_{s}= 5 × 10^{18} cm^{-3} ¾ 1 × 10^{19} cm^{-3}), respectively, since they provide the lowest recombination, as it can be seen in Fig. 1.

Thus, as both parameters (short-circuit current density and open-circuit voltage) are competitive, the best surface doping levels are going to be determined by the solar cell efficiencies.

According to Fig. 8, there is a wide range of emitter sheet resistivity (50 ¾ 500 W/) that provides efficiencies around 21%, when the surface doping levels N_{s}=1×10^{19} cm^{-3} and 5×10^{19} cm^{-3} are considered; the most efficient P^{+}-type passivated homogeneous emitters correspond to h=21.2% with the thickness range (1.6 ¾ 0.4) mm.

**5. Updating Output Electrical Parameters**

In order to evaluate the influence of the recently proposed n_{i}=9.65×10^{9} cm^{-3}, the optimized output electrical parameters (short-circuit current density, open-circuit voltage, fill factor and efficiency) were compared for both values of n_{i}, as follows in Table 2.

It can be observed that, if the recently proposed n_{i} is considered, no modification is obtained in the short-circuit current densities, J_{sc}, but there is a slight increase in the V_{oc}, consequently providing a slight increase (»0.1%) in the efficiency, h. These results validate the present conclusions even if small corrections are made in the currently carrier intrinsic concentration n_{i}=1×10^{10} cm^{-3} (T=300 K).

**6. Conclusion**

Passivated homogeneous p^{+}-type emitters have low emitter recombination (J_{oe} = 1.2×10^{-13} A/cm^{2} for N_{s}=1×10^{19} cm^{-3} and R_{}=145 W/) and are dominated by the surface recombination component, behaving as transparent emitters for thicknesses up to 3.0 mm.

Gaussian profile p^{+}-type emitters also presented high emitter collection efficiencies, even if they are highly doped and shallow. It was found that only if the optimized emitter sheet resistivities for each surface doping level is considered, the collection efficiency of the moderated doped emitters are slightly higher than the highly doped ones.

As long as the high quality of p^{+}-type homogeneous emitters was made evident, p^{+}nn^{+} solar cells optimization was carried out, taking into account the contribution of the optimum metal-grid and shadowing factors to the output electrical parameters (short-circuit current density, open-circuit voltage and efficiency).

It was found that the metal-semiconductor contact resistivity dependence on surface doping level increased the optimum shadowing factor for moderately doped emitters, N_{s}=1×10^{19} cm^{-3} and 5×10^{18} cm^{-3}; and therefore, decreasing their short-circuit current densities. On the other hand, the moderately doped emitters also presented the highest open-circuit voltages due to their excellent recombination current densities.

Thus, there is a trade-off between both parameters (short-circuit current density and open-circuit voltage), the maximum efficiencies, h»21.2% were found for the surface doping levels (1×10^{19} - 5×10^{19}) cm^{-3}, emitter thicknesses range (1.6 and 0.4) mm and sheet resistivities (145 -185) W/, respectively. Another point to stress is that these surface doping levels can provide efficiencies around 21% for a wide range of emitter sheet resistivity (50-500 W/).

Although in this work all theoretical optimizations were made considering n_{i } = 1 × 10^{10} cm^{-3}, a brief evaluation of the recently proposed value influence (n_{i}=9.65×10^{9} cm^{-3}) on the optimized results showed a non-significant change, validating all present conclusions.

**Aknowledgments**

This work was supported by FAPESP under contract n^{o}95/09435-0.

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