Analytic fill factor expression for double junction tandem solar cells

Abstract

We present closed form analytic formulae for the fill factor of single and double junction tandem solar cells. We start with the observation that the difference between maximum power voltage and open circuit voltage is small compared to their values. Then an explicit relation relating the maximum power voltage to the open circuit voltage is derived for the single junction (SJ) cell. Consequently, fill factor (FF) is expressed solely as a function of the open circuit voltage. Our expressions are examined against those given in literature for the SJ cell and show very good agreement. Comparing the results of our calculations against data points given in literature, the ideality factor is varied as a parameter and cumulative error is calculated. Satisfactory agreement is observed for Silicon cells with n = 1.1 and III-V compound cells with n = 1.7. The SJ derivation validates our approach which is also applied to the double junction (DJ) cells. Clearly, the complexity is increased for the DJs. Additional factors such as the photo current ratio of the sub cells enters the equations. Nevertheless, closed form expression is obtained for the FF in terms of the open circuit voltage. The prediction of our double junction formula is compared with the data points quoted in literature with ideality factor as a parameter and good agreement is obtained with n = 1.8 assuming sub-cell photo current ratio of 2:1. Having established the above parameters, our calculations are within 10% of the results quoted in literature. In fact, the agreement is better than 5% for near 90% of the cases considered.