A B S T R A C TFor several years, high resistivity solar cells have been modcled successfully at Stanford using an ambipolar Auger coefficient, C, = 1.66 x 10-30cm6/sec, and an ambipolar diffusion constant, D, = 18 cm2/sec. Recently these assumptions have been questioned, including the introduction of t,lie intriguing possibility of carrier-induced bandgap narrowing. When this was done, the dramatically different values of C, = 3.88 x 10-31cm6/sec and D, = 9 cm2/sec were used to fit the experimentally observed performance of point-contact solar cells.Wc have performed a number of experiments and determined that below n = 2 x 1017cm-3 that C, = 1.66 x 10-30cm6/sec and D, = 17 cm2/sec . Finally, we discuss the remaining discrepancies between our experimental cell data and our cell modeling.
I N T R O D U C T I O NHigh-resistivity silicon solar cells continue to have promise for concentrator and high efficiency applications and conscquently accurate knowledge of material parameters in high-injection is imperative. Recently there has been some uncertainty in the the value of the ambipolar diffusion constant,, D,, the ambipolar Auger coefficient, C,, and the intrixisic carrier density, n;.In the past the authors have used the transport models described in [l] with D , = 18 cm2/sec , the recombination parameters measured in [2] with C, = 1.66 x cm6/sec , ancl the conventional value of n; = 1.45 x 10" cm-3 at 300Ii [3] . Over the years good agreement has been obtained for a. wide va.riety of cell types and fabrication parameters when modeled with a quasi-analytic 3-dimensional code [41.
Two significant changes have recently been proposed [5]as a. consequence of 2-D numerical modeling performed on high-resistivity point-contact concentrator solar cells. First, a sinaller than expected open-circuit voltage at high concentra.tions has been attributed in part to carrier-induced bandgap narrowing (BGN) rather than to Auger recombination exclusively. This leads to a higher value of n, = 1.7 -1.9 x 10" cm-3 and a smaller value of C, = 3.88 x cm6/sec . Second, the sublinearity in short-circuit current has been fit by the use of an ambipolar diffusion constant, D,, of 9 cm2/sec .Finally, a recent study by Green [6] points to a lower vdue for n, of 1.08 x lo1' ~m -~. This paper describes the results of our investigation into these issues.
E X P E R I M E N T AmbiDolar DiffusionThe classic expression (1) 2kT tLnPLlo D --___ a -Q tLn+CLp yields D, = 18 cm2/sec using the asymptotic low doped mobilities where only phonon scattering is present. In [5] , the drop off of short-circuit responsivity with concentration for high-resistivity cells was fit by changing D, from 18cm2/sec to 9 cm2/sec . This reduction was assigned to p P .To test this we performed two experiments. First we took 500 R-cm float zone wafers with high bulk lifetime and low surface recombination velocities, and placed regularly spaced, 150pm deep sawcuts on the surface of the wafer at distances varying between 1 mm and 1 cm. (Fig. 1). The wafer was illuminated with a...