REEVALUATION OF THE DERIVATIVES OF THE HALF ORDER FERMI INTEGRALS

The Fermi integrals of half orders are important in the simulation of semiconductor transport processes. Several of these integrals ( - 1/2, 1/2, 3/2, 5/2) have been recently retabulated since the 1938 study by McDougall and Stoner [Phil. Trans. Roy. Soc. A 237, 67 (1938)], but t he derivatives were not re-evaluated. The original integral values wer e calculated without the aid of high speed computers by using approxim ate series evaluation and tabulations of exponentials and zeta functio ns. In addition, a discrepancy was found in the literature since the o riginal study in 1938. The second derivative of F1/2 has been mistaken ly represented as being proportional to a Fermi integral of another or der. This article tabulates the half order Fermi integrals from -1/2 t o 5/2 over the reduced energy range -5 to 20 in 0.25 increments. The f irst two derivatives of F-1/2 are also calculated by numerical integra tion and tabulated to aid in interpolation. It is shown that the secon d derivative of F1/2 is not proportional to another Fermi integral. A suitable interpolation scheme is proposed to calculate the values of t he Fermi integrals of various order to high accuracy over the total re duced energy range.