Optical Path Length Factor at Near-Bandgap Wavelengths in Si Solar Cells

By using the Rand and Basore (R&B) physical model for light trapping, a particular analytical expression for near-bandgap optical path length factor <formula formulatype="inline"><tex>$Z_{0}$</tex></formula> is derived for the case where back surface reflectivity <formula formulatype="inline"><tex>$R_{\rm BACK}$</tex></formula> is equal to unity <formula formulatype="inline"><tex>$(R_{\rm BACK} = \hbox{1})$</tex></formula>. This expression shows that according to the R&B physical model, at <formula formulatype="inline"><tex>$R_{\rm BACK} = \hbox{1}$</tex></formula>, <formula formulatype="inline"><tex>$Z_{0}$</tex></formula> has a finite value. At <formula formulatype="inline"><tex>$R_{\rm BACK} = \hbox{1}$</tex></formula>, the R&B expression for <formula formulatype="inline"><tex>$Z_{0}$</tex></formula> is shown to diverge. By using the original R&B derivation procedure, a new expression for <formula formulatype="inline"><tex>$Z_{0}$</tex></formula> is obtained, which at <formula formulatype="inline"><tex>$R_{\rm BACK} = \hbox{1}$</tex></formula>, reduces to the aforementioned particular expression for ideal back surface reflectance. The new expression is immune from the physical incongruity and tendency to overestimate <formula formulatype="inline"><tex>$Z_{0}$</tex></formula> that affect the R&B expression. By using the new expression, a relationship between <formula formulatype="inline"><tex>$Z_{0}$</tex></formula> and the Yablonovitch and Cody (Y&C) absorption-enhancement factor is derived for devices where parasitic absorption predominantly occurs at backside reflector. This relationship is shown to be in agreement with the literature. In the derivation, a connection between the approaches to light trapping of R&B and Y&C is exploited. This connection allows obtaining a new method to evaluate <formula formulatype="inline"><tex>$R_{\rm BACK}$</tex></formula> at near-bandgap wavelengths in most Si solar cells. The new method is checked on two real Si solar cells and found to provide plausible results. Compared to the method used by R&B, the method presented in this paper is shown to be more reliable.