Solid-State Ekcfronics Vol. 22, pp. 849-852 0 Pergamon Press Ltd.. 1979. Printed in Great Brun

W38-I 101/79/10014%49/$02 00/O

TEMPERATURE DEPENDENCE OF OPEN-CIRCUIT PHOTOVOLTAGE OF A BACK-SURFACE FIELD

SEMICONDUCTOR JUNCTION

AMUIITABHA SINHA and S. K. CHATTOPADHYAYA

Physics Department, Kurukshetra University, Kurukshetra 132119, India

(Received 21 October 1978; in revised form 6 March 1979)

Abstract-Temperature dependence of the open-circuit photovoltage of a back surface field, diffused silicon junction has been studied analytically, including the effect of bandgap narrowing in the heavily doped back surface region. Open circuit voltage of a BSF structure has been found to he slightly less dependent on temperature as compared with that of a conventional cell. Further, the hahaviour of a BSF cell is found to be relatively insensitive to base layer resistivity. These results support the experimental data published by some investigators on temperature dependence-of solar cells.

INTRODUCTION

It is well known that the presence of a high-low junction at the back of the normal n+p structure has been found to be responsible for the increased short circuit photo- current and unusually high open-circuit photo-voltage [ 11. Though large numbers of investigators have studied the performance of a back-surface field (BSF) silicon junc- tion for photovoltaic applications, not much information is available in the published literature on the perfor- mance of a BSF structure as a function of temperature. However, reference to this topic exists in the work of Mandelkorn and Lamneck[2] who reported some results of experimental investigation on the behaviour of con- ventional and BSF solar cells under different tem- peratures. Fossum and Burgess[3] have also reported some data on this topic, in their studies on silicon solar cells for concentrated sunlight and high temperature environment. In the present article, the authors make an attempt to study the temperature-dependence of a BSF silicon diffused junction (n+pp+), including the effect of bandgap narrowing in the heavily doped back p’-layer.

ANALYSIS

The analytical formulation of the subject presented here is based on the description of the BSF cells, by Fossum[4] who used in his analysis the classical Moll- Ross equation for minority carrier injection across the emitter-base junction of a bipolar transistor[S]. In the present paper, the analysis of Fossum for the calculation of open circuit voltage in a solar cell has been extended, to include the effect of bandgap narrowing in the heavily doped p+ region. For the purpose of analysis, the BSF structure considered, is shown in Fig. 1. Following the assumption that hole current J,. across the n’p junction, and recombination in the quasi neutral base are small, and considering electron injection Jnh across the n’p junction, into the base region as the dominant com- ponent, i.e. the emitter efficiency near unity[4], the illu- minated solar .cell current density can be written ap- proximately as

JI. = L - Jn,,. (1)

It may be pointed out here that these assumptions of negligible recombination made in the analysis, to apply the Mall and Ross technique, are the limitations of the present method. To get a more complete picture, the hole injection into the emitter region should also be con- sidered and the recombinations in these regions should be taken into account. The hole injection current Jpe into the emitter may particularly become important, when heavy doping effects in the front diffused region are taken into account. However, to calculate Jnb under the above-mentioned assumptions, one may refer to the method adopted by De Man [6], who calculated the emit- ter efficiency of a bipolar transistor, taking into account the effect of bandgap narrowing caused by heavy doping in the emitter. The same method will be used here to calculate the electron injection current into the base, Jnh. This gives an expression similar to that obtained by Moll and Ross[5], except that in this case, bandgap narrowing effect is also included. Assuming quasi-equilibrium con- dition throughout the cell, the expression for Jnb thus obtained may be written as

where ni, is the intrinsic carrier concentration at higher doping and nio is the intrinsic carrier concentration at low doping. D,,(X) is the electron diffusivity in the base region. VL is the photovoltage across the terminals sf the semiconductor junction. Equating eqn (1) to zero, we get an approximate expression for open circuit voltage fol- lowing the method given in Ref. [4]

(3)

This expression for V,,, is a general expression, taking into account bandgap reduction effect. Assuming that the base region of a conventional n+ - p cell has uniform doping and is not heavily doped, the expression of V,,

849

850 A. SINHA and S. K. CHAITOPADHYAYA

Light - -

Fig. 1. Diagram of a BSF solar cell structure.

for this structure assuming low injection level to be present, reduces to the form[4]

v oc I (4)

where .JsCl is the short circuit current of such cell and W,, is the width of p-region of a n+p cell. Na is the impurity concentration in the p type base. D,(NJ is the electron diffusivity at impurity concentration NA. Again from eqn (3) the open circuit voltage of a BSF cell can also be obtained as

+

where JsCz is the short circuit current of the BSF cell. The increase in open circuit voltage for the BSF cell, which may be attributed to the presence of pp+ junction, is given by the difference between the eqns (5) and (4).

At higher impurity concentrations, the effective in- trinsic concentration ni, is not only a function of tem- perature, but also a function of impurity concentration and has been calculated by Slotboom[7] as

&(N, T) = n:,,(T) exp( qA$+N)) (6)

where n:,(T) is the pn-product at low inputity concen- tration and is dependent on temperature, and A V,,(N) is the magnitude of decrease in the energy bandgap due to heavy doping. An empirical relation giving bandgap nar- rowing A V,,(N) as a function of impurity concentration (N), upto about 3 x 1019cmm’, has been derived by Slotboom[8], from a fit of experimental data on the measurement of bandgap narrowing in silicon bipolar transistors. It has also been shown by him[7] that this fit agrees well with the calculated value of bandgap nar- rowing. The same empirical relation has been used in the present work.

The heavily doped p+ back region is formed either by a special alloying technique or by dilfusion[l]. For the purpose of analytical simplicity it can be assumed that the doping concentration in this region is uniform[91. The expression of V,, given by eqn (5) for the BSF cell in

this case reduces to a very simplified form as

(7)

where NA’/exp(qAV,o(Na’)/kT) is the effective im- purity concentration in the p+ layer, and may be represented by N,‘(eff). Here D,(N,) is the diffusion constant at the impurity concentration NA in the p type base, Dn(NA+) is the diffusion constant at p+ layer impurity concentration Na+, and AV,,(Na’) is the bandgap narrowing at impurity concentration NA+. It is assumed that at impurity concentration N, in the p-type base region bandgap narrowing effect is negligible. On the right hand side of eqn (7) the integrals representing contribution of p and pt regions as given in eqn (5) have been replaced by the respective parameters of the regions assuming homogeneous doping.

The analysis given above is useful in the investigation of the temperature dependence of open circuit voltage of these cells. The effective intrinsic carrier concentration is a quantity which depends strongly on temperature. The temperature dependence of the intrinsic carrier concentration has therefore, to be taken into account in the calculations. The mobility (w) also depends on tem- perature to some extent and is known to be the result of two most important scattering mechanisms, e.g. the im- purity and lattice scattering, and, can be written as[lO],

where pLI is the impurity scattering term and p,_ is the lattice scatttering term. The values of impurity scattering mobility for silicon, has been taken from published literature [ 1 I]. The lattice scattering mobility ~~ for sili- con, has been found to follow a T-*.5 dependence[lO], which has been explained to some extent by some investigators [ 121 taking into account contributions of intra-valley and inter-valley scattering mechanisms. The values of pr. have therefore, been taken from the rela- tionship given in Ref. [13]. Thus, knowing CL, and pL, the values of cr. have been calculated as a function of tem- perature. Assuming that Einstein’s relation is applicable to semiconductors with impurity concentration Na’ s lOI cm-‘, the values of diffusion constant D,, as a func- tion of temperature may also be calculated from the mobility data. However, it has been found from the calculations, that, taking temperature dependence of 0, has only a small effect on the magnitude of calculated values of V,,, for the range of temperature considered in this paper. The other factor which will slightly depend on temperature, is the short circuit current of the cell. However, as available in published literature[3,14], it is known that the increase in J,, with temperature for one sun AM0 illumination is very small, and has been neglected in the present calculations.

Temperature dependence of backsurface field junctions 851

Table 1. Temperature coefficients of open circuit photovoltage

Temperature Coefficient, mV/“C

Base layer resistivity ohms-cm

10 loo

Cell Type

n+pp+ n’p Difference of n+pp+ and n’p cells

-2.14(-2.15+0.02)t -2.15( - 1.9+0.0l)t -2.38( - 2.3)t -2.55( - 2.6)t +0.24( + 0.14 + 0.002)t +0.41( t 0.65 -e 0.05)t

tExperimenta1 data obtained by Mandelkorn and Lamneck[Z] on similar structure are mentioned in the brackets. Exact correspondence is not expected as values of all the physical parameters are not available in Ref. [2].

RESULTS AND DISCUSSION

Figure 2 gives a plot of V,,, as calculated from eqns (4) to (7), as a function of temperature for both BSF and conventional cells, having nearly identical configurations. The device dimensions, doping levels and other parameters have been taken the same as that used by Fossum[4] in his computer simulations. The curves are drawn for the V,, of BSF cell, taking into account the effect of bandgap narrowing due to heavy doping in the pt region. For comparison, the V,, of such cell, without considering bandgap narrowing effect, have also been plotted. It is observed that taking bandgap narrowing effect into account, the magnitude of V,, obtained is lower than that when it has not been taken into account. This follows clearly from the fact that due to heavy doping in the p+ region, its effect on the potential barrier of pp+ high low junction may be taken into account by replacing the impurity concentration NA+ by an effective impurity concentration NA’(eff) as discussed earlier. This results in a reduction in the value of V,, of the BSF cells, which may be shown to be due to heavy doping effect on the magnitude of leakage velocity at the back surface determined by the high-low junction potential barrier. In fact, the authors have shown elsewhere[l5] that for a doping concentration greater than = lOI cmm3

Fig. 2. Temperature dependence of open circuit voltage of BSF and conventional structures. The dotted curves and the solid curves correspond respectively to the cases when bandgap nar- rowing effect has not been taken into account and when it has been taken into account. Here NA = 1.5 x 10’4cm-3, N,+ = lOI cm-‘, L = 150 Frn, W,+ = 0.5 pm. Curves numbered (1) and (2) are for BSF cell, numbered (3) is for n’p cell, and numbered (4) and (5) are the difference in V,, between n’pp+ and n’p

cells.

in the p+ layer, further improvement in the minority carrier reflecting properties of a high low junction may not be observed. It is also observed from Fig. 2 and Table 1 that the temperature coefficient of the BSF cells is less than that of the conventional cells. However, the curves are almost linear for both the cases. The difference in V,, between BSF and conventional cells, which is due to the presence of the back ppf junction, is also plotted in the same figure.

Figure 3 gives a plot of the open circuit voltage as a function of temperature for both BSF and conventional n’p solar cells, taking different values of resistivity in the p-type base region. It is observed from the figure that for BSF cells, V,, vs T curves almost coincide for both 10 and 100 R. cm resistivity base regions, whereas for nfp cells, there is a significant difference in the two curves plotted for 10 and 100 R. cm resistivity bases. This is easily explained from the expression of V,, for n’p conventional cell given in eqn (4) which shows that

Fig. 3. Temperature dependence of open circuit voltage at different base layer resistivities for BSF and n’p structures.

Here NA’ = 10’Pcm-3, L = I50 pm and w,+ = 0.5 pm.

Curve No.

1. 2. 3. 4.

5.

Cell. Base layer resistivity type (at 27°C)

n+pp+ both 10 and 100 R. cm

n+p IOn.cm

n+p lOOfl.cm difference between lOOfl.cm n+pp+ and n+p cells difference between lOR.cm n+pp+ and n’p cells

852 A. SINHA and S. K. CHATTOPADHYAYA

with increase in p-layer doping concentration NA, V,,

will slightly increase. For a BSF cell however, the open circuit voltage, which is given by eqns (5) and (7) is found to be relatively insensitive to the doping concen-

tration of p-layer, since the first integral representing the contribution of p-layer is negligibly small as com- pared with the contribution of the integral for the p+ region, owing to the fact that N, is much less than Na+ (eff). V,, of a BSF structure is therefore, relatively insensitive to the doping concentration of p-region as long as its value remains reasonably small as compared with that of p+ layer. Both these results agree reasonably well with the experimental data published by Mandelkorn and Lamneck[2]. The difference in photovoltage of the n+ p+ and n’p junctions, which is due to the presence of the pp+ junction, has also been plotted in Fig. 3 for both IO and 100 s2 . cm resistivity bases.

The assumption of uniform doping in the p+ layer considerably simplifies the analysis, as the expression for V,, can now be written as shown in eqn (7). If however, a gaussian profile is assumed in the p+ layer, then one has to take the help of numerical integration to get the values of V,, for such structures. Preliminary cal- culations performed by the authors assuming a Gaussian impurity profile at the back for p+ layer indicate that the values of V,, thus obtained, for a BSF cell are lower than that obtained for a BSF cell having uniform impurity in the p+ layer. This is expected because of the reduced value of potential barrier of a diffused high low junction as compared with that of an abrupt high low junction con-

sidered in this paper. Details of these results will be published separately.

Acknowledgement-Thanks are due to the Government of India, Department of Atomic Energy, for financial assistance to one of the authors (A. Sinha).

REFERENCES

1. J. Mandelkorn and J. H. Lamneck, Simplified fabrication of back surface electric field silicon cells and novel charac- teristics of such cells. NASA TM X 68060, NASA Lewis Research Centre, Cleveland. Ohio (1972).

2. J. Mandelkorn and J. H. Lamneck, I I th IEEE Photo. Spec. Conf. NASA TM X-71723 (1975).

3. J. G. Fossum and E. L. Burgess, 12th IEEE Photo. Spec. Conf. (1976).

4. J. G. Fossum, IEEE Trans. Electron. Dev. ED-28, 322 (1977). 5. J. L. Mall and I. M. Ross, Proc. IRE 44, 72 (1956). 6. H. J. J. De Man, IEEE Transactions on EIectron Dev. ED-II,

833 (1971). 7. J. W. Slotboom, So/id-St. Electron. 20, 279 (1977). 8. J. W. Slotboom and H. C. De Graaff, Solid-St. Ektron. 19,

857 (1976). 9. M. P. Goldlewski, C. R. Baraona and H. W. Brandhorst, 10th

IEEE Photo. Spec. Conf., p. 40 (1973). 10. A. S. Grove, Physics and Technology of Semiconductor

Devices, p. 109. Wiley, New York (1967). 11. E. M. Conwell, Proc. IRE 10, 1327 (1952). 12. L. Marton, Advances in Electronics and Electron Physics,

Vol. VII. Academic Press, New York (1955). 13. Helmut F. Wolf, Silicon Semiconductor Data, p. 76. Per-

gamon Press, Oxford (1%9). 14. H. J. Hovel, Semiconductors and semimetals; Solar Cells

Vol. 11, p. 169. Academic Press, New York (1975). 15. A. Sinha and S. K. Chattopadhyaya, IEEE Trans. Electron

Dew ED-25, 1412 (1978).