In steady state QPQP QPQP Integrating over the n quasineutral region (after all terms multiplied by Adx), Furthermore, in a p + n junction, So: 0
Charge Control Approach In steady state, we can calculate pn junction current in two ways: From slopes of Δn p (–x p ) and Δp n (x n ) From steady-state charges Q N and Q P stored in each “excess minority charge distribution” Therefore, Similarly,
Charge Control Approach In steady state Moreover, in a p + n junction:
Narrow-Base Diode n-side contact Narrow-base diode: a diode where the width of the quasineutral region on the lightly doped side of the junction is on the order of or less than one diffusion length.
Narrow-Base Diode I–V We have the following boundary conditions: Then, the solution is of the form: Applying the boundary conditions, we have:
Narrow-Base Diode I–V Solving for A 1 and A 2, and substituting back: Note that The solution can be written more compactly as
Narrow-Base Diode I–V With decrease base width, x c ’ 0: Δp n is a linear function of x due to negligible thermal R–G in region much shorter than one diffusion length J P is constant This approximation can be derived using Taylor series approximation
Narrow-Base Diode I–V Because, then Then, for a p + n junction:
Narrow-Base Diode I–V If x c ’ << L P, Resulting Increase of reverse bias means Increase of reverse current Increase of depletion width Decrease of quasineutral region x c ’ x c –x n
Wide-Base Diode Back to ideal diode solution Rewriting the general solution for carrier excess, For the case of wide-base diode (x c ’ >> L P ),
Wide-Base Diode Back to ideal diode solution Rewriting the general solution for diffusion current, For the case of wide-base diode (x c ’ >> L P ),
Small-Signal Diode Biasing V 0 << V A R S : serial resistance C: capacitance G: conductance Y : admittance When reversed-biased, a pn junction diode becomes functionally equivalent to a capacitor, whose capacitance decreases as the reverse bias increases. Biasing additional a.c. signal v a can be viewed as a small oscillation of the depletion width about the steady state value.
Total pn Junction Capacitance Junction / depletion capacitance, due to variation of depletion charges Diffusion capacitance, due to variation of stored minority charges in the quasineutral regions Minority carrier lifetime C J dominates at low forward biases, reverse biases. C D dominates at moderate to high forward biases.
Relation Between C J and V A N B : bulk semiconductor doping, N A or N D as appropriate. For asymmetrical step junction, Therefore,