In Hyperabrupt junctions (m<0), how can we derive the equation (5.72)?
5.7 Nonuniformly Doped pn Junctions
x=0
31
n-type doping profiles
+1
Bxg
m=0
x=0
xo
Figure 5.28: Generalized doping profiles of a one-sided pn junction. From Sze[15].
The generalized n-type doping concentration for x > 0 is given by N = Bx^m (5.71). The case of m=0 corresponds to the uniformly doped junction, and m+1 corresponds to the linearly graded junction just discussed. The cases of m=+2 and m=+3 shown would approximate a fairly low-doped epitaxial n-type layer grown before. The equation for the hyperabrupt junction at x=0 when m is negative is given by e^(B(m+1)C+1)/(1+m+2Vbi+VR) (5.72).