*3.29 A short-base diode is one where the widths of the p and n regions are much smaller than Ln and Lp, respectively. As a result, the excess minority-carrier distribution in each region is a straight line rather than the exponentials shown in Fig. 3.12. (a) For the short-base diode, sketch a figure corresponding to Fig. 3.12 and assume as in Fig. 3.12 that NA  ND. (b) Following a derivation similar to that given in Section 3.5.2, show that if the widths of the p and n regions are denoted W p and Wn then I = Aqni2Wn −Dxp nND + Wp −DnxpNA eV/VT −1 and Qp = 1 2 Wn −xn2 D p Ip 1 2 W 2 n D p Ip , for Wn  xn (c) Also, assuming Q Qp, I Ip, show that Cd = τ T VT I where τ T = 1 2 W 2 n D p (d) If a designer wishes to limit Cd to 8 pF at I = 1 mA, what should W n be? Assume Dp = 10 cm2/s.

3.22 A p+n junction is one in which the doping concentration in the p region is much greater than that in the n region. In such a junction, the forward current is mostly due to hole injection across the junction. Show that I I p = Aqni2 Dp Lp ND eV/VT −1 For the specific case in which ND = 1017/cm3, Dp = 10 cm2/s, Lp = 10 μm, and A = 104 μm2, find IS and the voltage V obtained when I = 1 mA. Assume operation at 300 K where n i = 1.5×1010/cm3.