Bandgap narrowing effects on the open circuit voltage in Si, GaAs and InP solar cells

S&f-Sfule Hecrronics Vol. 38, No. 1,pp. 139-I42, 1995 Copyright 0 1995 Elscvier Science Ltd

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BANDGAP NARROWING EFFECTS ON THE OPEN CIRCUIT VOLTAGE IN Si, GaAs AND InP SOLAR CELLS P. NUBILE Instituto de Pesquisas Espaciais, Laboratbrio Associado de Materiais e Sensores, Caixa Postal 515, CEP 12201 fGo Jose dos Campos, Brazil (Received 18 October 1993; in revised form 22 December 1993) Abstract-Bandgap narrowing affects semiconductor device operation. Solar cells are pn junction devices for which the energy bandgap is a very important parameter. The aim of this paper is to investigate how bandgap narrowing can influence the open circuit voltage of silicon, gallium arsenide and indium phosphide solar cells. The increase in the base doping concentration for improving device operation is limited by bandgap narrowing effects. A quantitative study of the open circuit variation with base doping concentration and ideality factor is presented and the critical values for these parameters are determined for these materials.

I. INTRODU~ION

Open circuit voltage in solar cells is an important parameter to be optimized in order to achieve better conversion efficiencies[ 11.Bandgap narrowing (BGN) induced by heavily doped layers tends to decrease open circuit voltage values, although other parameters can be improved by it[2]. This paper studies the open circuit voltage behaviour with doping concentration in silicon, gallium arsenide and indium phosphide solar cells. Solar cells are pn junction structures. Silicon solar cells are formed by an n-type heavily doped emitter and a less doped p-type base. Emitter doping concentration can vary from lo’* to 10” cmm3 and base doping levels vary from 10” to 10” cme3. Gallium arsenide cells are p-AlGaAs/p-GaAs/n-GaAs structures with doping concentrations lying from 10” to 10” cmm3. Indium phosphide cells are homojunction n +/p cells with emitter doping concentration over 10’8cm-3 and base doping level lying from 10” to 10’8cm-3[l,3]. 2. ANALYSIS

Open circuit voltage for an homojunction is given by: Vw=AEln 4

,

:+l (

0

solar cell

carrier concentration. A small variation in the short circuit current is also expected with BGN effects because of the spectra1 response shifting to the ultraviolet region when the doping concentration increases. The saturation current variation with bandgap energy is given by: Jo = J,exp

2

(2)

where Jao is the saturation current without BGN and AEg is the bandgap narrowing energy value. With its exponential behaviour with BGN, the saturation current variation greatly exceeds any effect caused by the variation on the short circuit current. In the following calculations, only BGN effects over the saturation current are considered. Combining eqns (1) and (2), the open circuit voltage is given by: VW=!

.

KTln>-A&

4

00

I

There are four main contributions to the BGN: the shift in the majority and minority carriers band edge due to exchange and carrier-impurity interactions. Adding these contributions, the BGN is calculated by[4

51: AEg = aN ‘I’ - bN ‘14+ cN ‘I*.

(1)

>

where A is the ideality factor, J, is the short-circuit current, Jo is the saturation current, K is the Boltzman constant, T is the temperature and q is the electron charge. Energy gap variations induce variations in the intrinsic carrier concentration. The parameter most influenced by the BGN is the saturation current, because of its exponential variation with intrinsic

(4)

The open circuit voltage variation is calculated for silicon, gallium arsenide and indium phosphide homojunction solar cells using eqns (3) and (4). Figure 1 shows the percentage of open circuit voltage variation as a function of the base doping level (less doped side) for A = 1. Curves are plotted for the three materials. Silicon is the least affected material by BGN effects. Gallium arsenide and indium phosphide are expected to have 15 and 19% of open 139

P. NUBILE

140

Si -

GaAs

20 -

-

15 PZ!

1.

_

5-

100

10

0.1

0.01

fvd( 1&n-3) Fig.

1. Open circuit voltage variation as a function of base doping level for silicon, gallium arsenide and indium phosphide solar cells with A = 1.

circuit voltage reduction respectively for a doping concentration of 10zocme3. The same calculations for A = 2 shows open circuit voltage greater than that observed for A = I. The amount of open circuit voltage reduction rises to 39% for indium phosphide, 25% for gallium arsenide and 19% for silicon solar cells for a doping level of 10zocm-‘. The ideality factor is determined by the junction characteristics and by the dominant transport mechanism. For higher injection levels the injection current is dominant and the ideality factor tends to increase. The effect of higher values in this parameter is to round out the knee in the current vs voltage curve[l]. The effect of the ideality factor on the open circuit voltage can be seen in Fig. 2. For the three is calculated curves, the doping concentration 10” cm-3. This figure shows that bandgap narrowing

1000 I

I

I

....

950

becomes much more important factor increases.

when the ideality

3. DISCUSSION AND CONCLUSIONS

This work shows that the BGN limits this kind of optimization for the open circuit voltage. Figure 3 shows the curves for the open circuit voltage as a function of doping concentration in the base for the three materials. The open circuit voltage for low base doping concentration are 616 mV for silicon, 960 mV for gallium arsenide and 823 mV for indium phosphide solar cells[6]. The open circuit voltage enhancement due to the increasing in the doping level saturates for a given concentration and above this level the BGN effect becomes dominant. In silicon, this concentration level corresponds to a base resistivity of 0.001 0 cm. Otherwise, for an ideality factor

I

I

. . . . . . . .._

I

I

I

Si .GaAs :::,-._ InP -

. . . . . . . ..,.__

900

I

850 17

800

1

1.5

2

2.5

;

3.5

4

4.5

5

Fig. 2. Open circuit voltage variation as a function of the ideality factor for silicon, gallium arsenide and indium phosphide solar cells.

Bandgap narrowing effects in solar cells

1200

1

I

n-

I

1100 ,,..”

141

,,..”

_,,.....‘.

1000 -

Fig. 3. Open circuit voltage as a function of base doping level for silicon, gallium arsenide and indium phosphide solar cells with A = 1.

of 2, the saturation point is reached for a doping concentration of 10’9cm-3, which corresponds to a base resistivity of 0.01 R cm. Figure 4 shows the curves for the open circuit voltage as a function of base doping concentration for A = 1 and A = 2 for a silicon solar cell. The utilization of a Back Surface. Field to increase the open circuit voltage seems to be more convenient, since the base resistivity can be kept at a low level, avoiding BGN effects and lifetime killing present in heavily doped materials. Indium phosphide and gallium arsenide cells have their open circuit voltage more affected by BGN and this can represent a real problem, since the doping levels for these cells are near the saturation regions shown in Fig. 3. It is clear, after these calculations, that open circuit voltage can not be optimized without taking into account BGN effects. The open circuit voltage enhancement due to the increase in the base doping level is compensated by BGN effects. There is a trade off

1000

I

between these two effects. Furthermore, other parameters have to be considered for the determination of the best doping base concentration, as the series and parallel cell resistance. BGN effects on Back Surface Field layers can impoverish the solar cell operation, although BSF are not specially designed to improve the open circuit voltage. The ideality factor is another important parameter to be optimized. BGN effects are largely dependent on this factor. As the ideality factor depends on junction phenomena, like minority carrier recombination, carriers tunneling and junction abruptness, when using heavily doped base, BGN effects has to be minimized by keeping the ideality factor near unity. Emitter doping concentration is not so important in this case as the doping profile and the quality of the wafer’s crystalline structure. Recombination phenomena in the junction depend on these parameters and, in consequence, the ideality factor value is determined by them.

I

f

I

A=l--

950 -

A=2

900 -

. .._

850 800 -

550 500 0.01

I

I

I 10

0.1

100

ivd( l0L-3) Fig. 4. Open circuit voltage as a function of base doping level for a silicon solar cell for A = 1 and A = 2.

142

P.

NUBILE

REFERENCES

I. H.J.HoveI,SolarCells.AcademicPress,NewYork(I975). 2. S. M. Sze, Physics of Semiconductor Devices. Wiley, New York (1981).

3. M. Lundstrom, Solar Cells 24, 91 (1988). 4. S. C. Jain and D. J. Roulston, Solid-St. Electron. 34, 453 (1991). 5. S. C. Jain et al., J. appl. Phys. 68, 3747 (1990). 6. I. Weinberg, Solar Cells 31, 331.