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Semiconductor Device Physics Lecture 8 PN Junction Diodes: I-V Characteristics Dr. Gaurav Trivedi, EEE Department, IIT Guwahati

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Empirical Observations of V BR Dominant breakdown mechanism is tunneling V BR : breakdown voltage V BR decreases with increasing N, V BR decreases with decreasing E G.

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Breakdown Voltage, V BR

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Breakdown Mechanism: Avalanching

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Breakdown Mechanism: Zener Process

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Effect of R–G in Depletion Region

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Effect of Series Resistance

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Effect of High-Level Injection

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High-Level Injection Effect

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Summary

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Minority-Carrier Charge Storage

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Charge Control Approach

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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

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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,

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Charge Control Approach In steady state Moreover, in a p + n junction:

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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.

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Narrow-Base Diode I–V We have the following boundary conditions: Then, the solution is of the form: Applying the boundary conditions, we have:

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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

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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

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Narrow-Base Diode I–V Because, then Then, for a p + n junction:

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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

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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 ),

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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 ),

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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.

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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.

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Relation Between C J and V A N B : bulk semiconductor doping, N A or N D as appropriate. For asymmetrical step junction, Therefore,

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Ideal Diode Equation. Important Points of This Lecture There are several different techniques that can be used to determine the diode voltage and current.

Ideal Diode Equation. Important Points of This Lecture There are several different techniques that can be used to determine the diode voltage and current.

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