solution

(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.

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 N_D = 5 × 10¹⁶ cm^−3 and a base width of 1 µm.

(b) Nd(x) = N0e^−x/w, where N₀ = 10¹⁸ cm^−3 with a 1 µm base width.