Mid Term Exam
July 19, 2002
Assume J_{n} = 00 = q n u_{n} (-dV/dx) + q D_{n} (dn/dx)
D_{n} = V_{t} u_{n}
u_{n} n dV = u_{n} V_{t} dn
dV/V_{t} = dn/n
Integrate
[V(w_{n}) - V(0)]/V_{t} = ln [n(w_{n})/n(0)]
V_{an} = V(0) - V(w_{n}) = V_{t} ln [ N_{D} + P_{n}(0)/N_{D}]
True, since the electron concentration at the contact, n(w_{n}), is N_{D} and,
at the edge of the depletion region, n(0) = N_{D} + p_{n}(0)n(0) = N_{D} + p_{n}(0) is a statment of charge neutrality. Negative charge, n(0), equals the positive charge, N_{D} + p_{n}(0).
If p_{n}(0) equals N_{D}, V_{an} is significant since, V_{an} = V_{t} ln(2) = 18mV. 18mV of the applied voltage appears across the neutral region rather than across the junction. The resulting current is 1/2 what it would be if this fraction of the applied voltage had appeared across the junction.