2.1

For a high-low P ⁺P junction in equilibrium, N _A = for x < 0 and N _A = for x ? 0. (a) Prove that the internal potential barrier is and the potential drop in the region is . Plot the curve and determine the limits of variation of . (b) For = 10 ¹⁷ cm ^-3 and = 10 ¹⁵ cm- ³, plot the majority carrier profile.

2.2

For an MOS capacitor, assume p ₀ = N _A and n ₀ = / N _A . (a) Show that ; (b) Determine the analytical expression of the low-frequency semiconductor capacitance ; (c) Plot ( V _GB) assuming V _FB = 0, t _ox=100 , ? _ox / ? _o = 4, ? _s / ? _o = 12 ( ? _o is the permittivity of free space), for three different values of substrate doping, N _A =10 ¹⁶, 10 ¹⁷, 10 ¹⁸ cm ^-3. (Hint: ; ).

2.3

Consider the UCCM given by

Regional models for weak (WI) inversion or strong (SI) inversion can be derived from UCCM by dropping either the linear term or the ln term in the charge density, respectively. (a) Calculate the value of the inversion charge density, normalized to , for which the value of the...