Heavily doped transparent-emitter regions in junction solar cells, diodes, and transistors

Abstract

An analytical treatment of heavily doped transparentemitter devices is presented that includes the effects of bandgap narrowing, Fermi-Dirac statistics, a doping concentration gradient, and a finite surface recombination velocity S at the emitter surface. Transparency of the emitter to minority carrier is defined by the condition that the transit time τ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</inf> is much smaller than the minority carrier lifetime in the emitter τ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</inf> , <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\tau_{t} \ll \tau_{p}</tex> . As part of the analytical treatment, a self-consistency test is formulated that checks the validity of the assumption of emitter transparency for any given device. The transparent-emitter model is applied to calculate the dependence of the open-circuit voltage V <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">OC</inf> of n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> -p junction silicon solar cells made on low-resistivity substrates. The calculated V <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">OC</inf> agrees with experimental values for high <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S_{P}( \geq5 \× 10^{4}</tex> cm/s) provided the effects of bandgap narrowing (modified by Fermi-Dirac statistics) are included in the transparent-emitter model.