Lecture 16 The pn Junction iode (III) Outline I V Characteristics (Review) Small signal equivalent circuit model Carrier charge storage iffusion capacitance Reading Assignment: Howe and Sodini; Chapter 6, Sections 6.4 6.5 1
1. I V Characteristics (Review) iode Current Equation: I = I e V th 1 o ( V ) 2
Physics of forward bias: iode Current equation: I = I o exp qv 1 Junction potential φ J (potential drop across SCR) reduced by V minority carrier injection into QNRs Minority carrier diffusion through QNRs Minority carrier recombination at contacts to the QNRs (and surfaces) Large supply of carriers injected into the QNRs I exp qv 3
Physics of reverse bias: I = I o exp qv 1 Junction potential φ J (potential drop across SCR) increased by V minority carrier extraction from QNRs Minority carrier diffusion through QNRs Minority carrier generation at surfaces & contacts of QNRs Very small supply of carriers available for extraction I saturates to small value I Io 4
2. Small signal equivalent circuit model Examine effect of small signal overlapping bias: i ( V v ) q + d = I+ id = Io exp 1 If v d small enough, linearize exponential characteristics: qv qv d I + i d = I o exp exp 1 qv qv d = I o exp 1 + 1 Then: i qv qv = I o exp 1 + I o exp d = q ( I + I ) o v d qv d From a small signal point of view. iode behaves as conductance of value: g d ( + ) q I I qi = o 5
Small signal equivalent circuit model gd g d depends on bias. In forward bias: g d = qi g d is linear in diode current. 6
Capacitance associated with depletion region: ρ(x) +qn d (a) p-side x n-side p v x n = V x qn a Q J = qn a x p ρ(x) (b) p-side x p x p +qn d x n x n n-side x v = V + v d > V --> x p < x p, q J < Q J q J = qn a x p qn a q j = qn a Δx p Δρ(x) = ρ(x) ρ(x) + qn d (c) p-side x p x p X d x n x n n-side x q j = q j Q j > 0 = qn a x p ( qn a x p ) = qn a (x p x p ) = qn a Δx p qn a q j = qn d Δx n epletion or junction capacitance: C j = C j (V ) = dq J dv V C j = A qε s N a N d 2 ( N a + N d )( φ B V ) 7
Small signal equivalent circuit model g d C j can rewrite as: C j = A qε s N a N d 2 ( N a + N d )φ B φ B ( ) φ B V or, C j = C jo 1 V φ B Under Forward Bias assume C j = 2C jo V φ B 2 C jo zero-voltage junction capacitance 8
3. Charge Carrier Storage: diffusion capacitance What happens to majority carriers? Carrier picture thus far: ln p, n Na po no Nd p ni 2 Na n ni 2 Nd 0 x If QNR minority carrier concentration but majority carrier concentration unchanged? quasi neutrality is violated. 9
excess minoriv carrier concentplation =excess rnajoriw carrier concentration A carrier concentrations In n-type Si, at every x: In p-type Si, at every x:
Quasi neutrality demands that at every point in QNR: excess minority carrier concentration = excess majority carrier concentration Mathematically: p ( x) = p ( x) p n ( x) = n ( x) n n n no efine integrated carrier charge: q Pn = qa 1 2 n p (x n ) ( W n x n ) = qa W n x n 2 n i 2 n no exp qv N d 1 = q Nn 11
Now examine small increase in V : n n-qnr n(x n ) - Δq Nn =-Δq Pn n(x) N d p p(x n ) + Δq Pn n i 2 p(x) N d 0 x n W n x Small increase in V small increase in q Pn small increase in q Nn Behaves as capacitor of capacitance: C dn = dq dv Pn v 2 W n xn ni q qv = qa exp 2 N = d V 12
Can write in terms of I p (portion of diode current due to holes in n QNR): 2 2 q (W x ) n n n i p qv C dn = qa exp 2 p N d W n x n 2 q (W n x n ) I p 2 p efine transit time of holes through n QNR: (W n x n ) 2 τ Tp = 2 p Transit time is the average time for a hole to diffuse through n QNR [will discuss in more detail in BJT] Then: C q τ I dn Tp p 13
Similarly for p QNR: C dp q τtn I n where τ Tn is transit time of electrons through p QNR: ( τ Tn = W p x p ) 2 2 n Both capacitors sit in parallel total diffusion capacitance: C d = C dn + C dp = q ( τ I + τ I ) Complete small signal equivalent circuit model for diode: Tn n Tp p g d C j C d 14
Bias dependence of C j and C d : C C Cd Cj 0 0 V C j dominates in reverse bias and small forward bias 1 φb V C d dominates in strong forward bias qv exp 15
What did we learn today? Summary of Key Concepts Large and Small signal behavior of diode: iode Current: qv I I o e = 1 Conductance: associated with current voltage characteristics g d I in forward bias, g d negligible in reverse bias Junction capacitance: associated with charge modulation in depletion region C j B 1 φ V iffusion capacitance: associated with charge storage in QNRs to maintain quasi neutrality. C d e qv 16
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