By Eberhard Schäfer
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The power of this technique is illustrated in the interpretation of the absorption edge exhibited in Fig. 19. In this figure we show the optical 2. THE OPTICAL ABSORPTION EDGE OF a-Si :H 35 E (ev) FIG. 19. Optical absorption coefficient determined by transmission for two phosphorusdoped a-Si : H, films (2%PH3 in SiH, at a substrate temperature of 250°C). absorption coefficient of n-type a-Si :H, that was prepared from a mixture of 2%PH, in SiH, at a substrate temperature of 250°C. The data were taken by optical transmission on two films.
Following Abe and Toyazawa, we start with Eq. ( 15), rewritten as where I ( E )= &2(E)= ( 2 ~ e Q ) ~ W ( 2E / II dEl dE2 ), (40) 2 6(Ec- E,)6(El- E2 - E)l(vlTlc)126(Ev- E2). The Tauc model simplifies Eq. (41) through the random phase approximation. Abe and Toyazawa restate Eq. Thus, Z(E) = where I dE, dE2 S ( E l ,E2)6(E,- E2- E ) , S(E1, E2) = 2 4 E c - E1)6(EV- &)I c,v (vl TIC) 12, (42) (43) and they define SW,, E2)= M E , ~2)Nc(EI)Nv(E2), II where from Eqs. (43) and (17), dE, dE2 S(El,E2)= NO.
The large value of M for a-Si :H, cautions us to avoid attaching much significance to the precise numerical magnitude of Eq. (23) for a-Si : H,. Indeed, this and other data to be presented suggest that, while theform of the fundamental equation of the Tauc model [Eq. (2 l)] is of general applicability, its magnitude can differ considerably from freeelectron estimates. We next give two examples which exhibit the usefulness of Eq. (2 1). The first is the analysis of the exponentialregime (region B of Fig.