Derive and sketch the electrical field E of doping concentrations And(x) are given by,

(a) Nd (x) = ax, where a is a constant;
(b) Nd (x) = Noe-ax ;
(c) Nd (x) = 1016 – 1019x (cm-1), where x is distance from the slab surface and end at x = L
(d) In part (c), calculate Emax at x = 0 and the thickness L of the semiconductor lab if Nd reduce to 50% of the surface value.