advertisement

Lecture 13 OUTLINE • pn Junction Diodes (cont’d) – Charge control model – Small-signal model – Transient response: turn-off Reading: Pierret 6.3.1, 7, 8.1; Hu 4.4, 4.10-4.11 Minority-Carrier Charge Storage • Under forward bias (VA > 0), excess minority carriers are stored in the quasi-neutral regions of a pn junction: QN qA xp n p ( x)dx QP qA pn ( x)dx xn qApn ( xn ) LP qAn p ( x p ) LN EE130/230A Fall 2013 Lecture 13, Slide 2 Derivation of Charge Control Model Consider the n quasi-neutral region of a forward-biased pn junction: •The minority carrier diffusion equation is (assuming GL=0): pn 2 pn pn DP 2 t x p •Since the electric field is very small, •Therefore EE130/230A Fall 2013 J P qDP (qpn ) J P qpn t x p Lecture 13, Slide 3 p n x Derivation Assuming a Long Base • Integrating over the n quasi-neutral region: J P () 1 qA pn dx A dJ P qA pn dx t x n p xn J p ( xn ) • Note that A J P () dJ P AJ P () AJ P ( xn ) AJ P ( xn ) I P ( xn ) J p ( xn ) dQP QP I P ( xn ) • So dt p EE130/230A Fall 2013 Lecture 13, Slide 4 Charge Control Model We can calculate pn-junction current in 2 ways: 1. From slopes of np(-xp) and pn(xn) 2. From steady-state charges QN, QP stored in each excessminority-charge distribution: dQP QP I P ( xn ) 0 dt τp QP I P ( xn ) τp QN Similarly, I N ( x p ) τn EE130/230A Fall 2013 Lecture 13, Slide 5 Charge Control Model for Narrow Base • For a narrow-base diode, replace p and/or n by the minority-carrier transit time tr – time required for minority carrier to travel across the quasineutral region – For holes in narrow n-side: 1 QP qA pn ( x)dx qA pn ( xn )WN xn 2 dpn pn ( xn ) I P AJ P qADP qADP dx WN WN QP WN τ tr , p IP 2 DP 2 WP – Similarly, for electrons in narrow p-side: τ tr ,n 2 DN 2 EE130/230A Fall 2013 Lecture 13, Slide 6 Charge Control Model Summary • Under forward bias, minority-carrier charge is stored in the quasi-neutral regions of a pn diode. – Long base: ni2 qVA / kT QN qA e 1 LN NA ni2 qVA / kT QP qA e 1 LP ND – Narrow base: 1 ni2 qVA / kT QN qA e 1 WP 2 NA 1 ni2 qVA / kT QP qA e 1 WN 2 ND EE130/230A Fall 2013 Lecture 13, Slide 7 • The steady-state diode current can be viewed as the charge supply required to compensate for charge loss via recombination (for long base) or collection at the contacts (for narrow base). – Long base (both sides): I QN QP τn τp QN QP – Narrow base (both sides): I τtr ,n τtr , p where τ tr ,n 2 WP 2 DN and τ tr , p 2 WN 2 DP Note that EE130/230A Fall 2013 Lecture 13, Slide 8 LN DN L D and P P τn LN τ p LP Small-Signal Model of the Diode Under forward bias: i + va dva i C R dt v 1 dI DC d d qVA / kT I 0 (e 1) I 0 e qVA / kT R dVA dVA dVA Small-signal I DC 1 q qVA / kT conductance: G I 0e R EE130/230A Fall 2013 kT Lecture 13, Slide 9 kT / q Charge Storage in pn Junction Diode • Excess minority carriers in the quasi-neutral region: pn(x) np(x) -xp xn x • Majority carriers stored at the edges of the depletion regions: -xp r(x) xn EE130/230A Fall 2013 Lecture 13, Slide 10 x pn Junction Small-Signal Capacitance 2 types of capacitance associated with a pn junction: depletion capacitance CJ due to variation of depletion charge diffusion capacitance dQdep dVA dQ CD dVA –due to variation of stored minority charge in the quasi-neutral regions For a one-sided p+n junction Q = QP + QN QP so τ p I DC dQP dI CD τp τ pG dVA dVA kT / q EE130/230A Fall 2013 Lecture 13, Slide 11 Depletion Capacitance C. C. Hu, Modern Semiconductor Devices for ICs, Figure 4-8 CJ dQdep dVA A s W What are three ways to reduce CJ? EE130/230A Fall 2013 Lecture 13, Slide 12 Total pn-Junction Capacitance C = CD + CJ τI DC CD e qVA / kT 1 kT / q CJ A s W •CD dominates at moderate to high forward biases •CJ dominates at low forward biases, reverse biases EE130/230A Fall 2013 Lecture 13, Slide 13 Using C-V Data to Determine Doping 2(Vbi VA ) 1 W2 2 2 2 2 A q S N CJ A s EE130/230A Fall 2013 Lecture 13, Slide 14 Example If the slope of the (1/C)2 vs. VA characteristic is -2x1023 F-2 V-1, the intercept is 0.84V, and A is 1 mm2, find the dopant concentration Nl on the more lightly doped side and the dopant concentration Nh on the more heavily doped side. Solution: N l 2 /( slope q s A2 ) 2 /( 2 10 1.6 10 23 19 10 12 10 ) 8 2 6 1015 cm 3 2 qV 0.84 ni kTbi 10 20 0.026 kT N h Nl 18 3 Vbi ln N e e 1 . 8 10 cm h 2 q Nl 6 1015 ni EE130/230A Fall 2013 Lecture 13, Slide 15 Small-Signal Model Summary C C J CD I DC I 0 (e qVA / kT 1) A s Depletion capacitance C J W τI DC Diffusion capacitance CD kT / q EE130/230A Fall 2013 I DC Conductance G kT / q Lecture 13, Slide 16 R. F. Pierret, Semiconductor Device Fundamentals, p. 302 Transient Response of pn Diode • Suppose a pn-diode is forward biased, then suddenly turned off at time t = 0. Because of CD, the voltage across the pn junction depletion region cannot be changed instantaneously. The time delay in switching between the FORWARD-bias and REVERSE-bias states is due to the time required to change the amount of excess minority carriers stored in the quasi-neutral regions. EE130/230A Fall 2013 Lecture 13, Slide 17 R. F. Pierret, Semiconductor Device Fundamentals, Fig. 8.2 Turn-Off Transient • In order to turn the diode off, the excess minority carriers must be removed by net carrier flow out of the quasi-neutral regions and/or recombination – Carrier flow is limited by the switching circuitry EE130/230A Fall 2013 Lecture 13, Slide 18 R. F. Pierret, Semiconductor Device Fundamentals, p. 328 Decay of Stored Charge Consider a p+n diode (Qp >> Qn): pn(x) i(t) ts t vA(t) R. F. Pierret, Semiconductor Device Fundamentals, Fig. 8.3 For t > 0: dpn dx EE130/230A Fall 2013 x xn i 0 qAD p Lecture 13, Slide 19 ts t Storage Delay Time, ts • ts is the primary “figure of merit” used to characterize the transient response of pn junction diodes Qp i I R dt τp τ p dQ p Qp 0 t ts • By separation of variables and integration from t = 0+ to t = ts, noting that I F Q p (t 0) / τ p and making the approximation Q p (t t s ) 0 IF We conclude that t s τ p ln 1 IR EE130/230A Fall 2013 Lecture 13, Slide 20 Qualitative Examples Illustrate how the turn-off transient response would change: Increase IF Decrease p Increase IR i(t) i(t) ts EE130/230A Fall 2013 t i(t) ts Lecture 13, Slide 21 t ts t