6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-1 Lecture 16 - The pn Junction Diode (II) Equivalent Circuit Model April 8, 2003 Contents: 1. I-V characteristics (cont.) 2. Small-signal equivalent circuit model 3. Carrier charge storage: diffusion capacitance Reading assignment: Howe and Sodini, Ch. 6, 6.4, 6.5, 6.9 Announcements: Quiz 2: 4/16, 7:30-9:30 PM, Walker (lectures #10-17) open book, must bring calculator
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-2 Key questions How does a pn diode look like from a small-signal point of view? What are the leading dependences of the small-signal elements? In addition to the junction capacitance, are there any other capacitive effects in a pn diode?
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-3 1. I-V characteristics (cont.) Diode current equation: Physics of forward bias: I = I o (exp qv kt 1) p F p F n n potential difference across SCR reduced by V minority carrier injection in QNR s minority carrier diffusion through QNR s minority carrier recombination at surface of QNR s large supply of carriers available for injection I e qv/kt
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-4 p F n F p n Physics of reverse bias: potential difference across SCR increased by V minority carrier extraction from QNR s minority carrier diffusion through QNR s minority carrier generation at surface of QNR s very small supply of carriers available for extraction I saturates to small value
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-5 I-V characteristics: I = I o (exp qv kt 1) I log I 0.43 q kt =60 mv/dec @ 300K I o 0 I o 0 V 0 linear scale semilogarithmic scale V
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-6 Source/drain-body pn diode of NMOSFET:
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-7 Key dependences of diode current: I = qan 2 i ( 1 D n + 1 D p )(exp qv N a W p x p N d W n x n kt 1) I n2 i qv (exp 1) excess minority carrier concentration at edges of N kt SCR in forward bias: I n2 i qv N exp kt : the more carrier are injected, the more current flows in reverse bias: I n2 i N : the minority carrier concentration drops to negligible values and the current saturates I D: faster diffusion more current I 1 W QNR : shorter region to diffuse through more current I A: bigger diode more current
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-8 2. Small-signal equivalent circuit model Examine effect of small signal overlapping bias: I + i = I o [exp q(v + v) kt 1] If v small enough, linearize exponential characteristics: I +i = I o (exp qv kt qv exp kt 1) I o[exp qv qv (1+ kt kt ) 1] = I o (exp qv kt 1) + I o(exp qv kt ) qv kt Then: i = q(i + I o) v kt From small signal point of view, diode behaves as conductance of value: g d = q(i + I o) kt
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-9 Small-signal equivalent circuit model, so far: gd g d depends on bias. In forward bias: g d qi kt g d is linear in diode current.
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-10 Must add capacitance associated with depletion region: g d C j Depletion or junction capacitance: C j = C jo 1 V φ B
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-11 3. Carrier charge storage: diffusion capacitance What happens to the majority carriers? Carrier picture so far: log p, n Na po no Nd n p ni 2 Na ni 2 Nd 0 x If in QNR minority carrier concentration but majority carrier concentration unchanged quasi-neutrality is violated.
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-12 Quasi-neutrality demands that at every point in QNR: excess minority carrier concentration = excess majority carrier concentration n n-qnr n(x n ) n(x) N d q Nn p p(x n ) p(x) n i 2 q Pn N d 0 x n W n x Mathematically: p (x) =p(x) p o n (x) =n(x) n o Define integrated carrier charge: q Pn = qa 1 2 p (x n )(w n x n )= = qa w n x n 2 n 2 i N d (exp qv kt 1) = q Nn
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-13 Now examine small increase in V : n n-qnr n(x n ) - q Nn =- q Pn n(x) N d p p(x n ) + q 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 Pn dv
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-14 Can write q Pn in terms of I p (portion of diode current due to holes in n-qnr): q Pn = (W n x n ) 2 qa n2 i D p (exp qv 2D p N d W n x n kt 1) = (W n x n ) 2 I p 2D p Define transit time of holes through n-qnr: τ Tp = (W n x n ) 2 2D p Transit time is average time for a hole to diffuse through n-qnr [will discuss in more detail in BJT] Then: and q Pn = τ Tp I p C dn q kt τ TpI p
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-15 Similarly for p-qnr: C dp q kt τ TnI n where τ Tn is transit time of electrons through p-qnr: τ Tn = (W p x p ) 2 2D n Both capacitors sit in parallel total diffusion capacitance: with: C d = C dn + C dp = q kt (τ TnI n + τ Tp I p )= q kt τ TI τ T = τ TnI n + τ Tp I p I
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-16 Complete small-signal equivalent circuit model for diode: g d C j C d
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-17 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/ φ B V ) C d dominates in strong forward bias ( e qv/kt )
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-18 Key conclusions Small-signal behavior of diode: conductance: associated with current-voltage characteristics g d I in forward bias, negligible in reverse bias junction capacitance: associated with charge modulation in depletion region C j 1/ φ B V diffusion capacitance: associated with charge storage in QNR s to keep quasi-neutrality C d e qv/kt