(a) Show that the general expression for the base transport factor of a p+-np BJT with an arbitrary base impurity doping profile can be expressed by
Note that the above equation will reduce to (14.33) if the base doping profile is uniform.
(b) Using the expression for the base transport factor defined by (a), find values of the base transport factor for the base impurity dopant profiles given by (a) and (b) of Problem 14.7.
The Gummel number can be calculated from the denominator of (14.27) if the impurity profile in the base region is known. Calculate the Gummel number of a silicon p-n-p transistor with
(a) Uniformly doped base with ND = 5 Ã— 1016 cmâˆ’3 and a base width of 1 Âµm.
(b) Nd(x) = N0eâˆ’x/w, where N0 = 1018 cmâˆ’3 with a 1 Âµm base width.