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

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
t
is much smaller than the minority carrier lifetime in the emitter τ
p
,
\tau_{t} \ll \tau_{p}
. 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
OC
of n
⁺
-p junction silicon solar cells made on low-resistivity substrates. The calculated V
OC
agrees with experimental values for high
S_{P}( \geq5 \× 10^{4}
cm/s) provided the effects of bandgap narrowing (modified by Fermi-Dirac statistics) are included in the transparent-emitter model.