196 Kuno: P-N Junction Diode switching Fig. k-Planar junction diode model current Ip to the minority carrier charge Q stored in the such that base region of the diode by the reverse and forward time constants Ta and Tp, respectively. The equations are ex- 60,0+9=gO. pressed in terms of measurable diode parameters, via Te, TR, and Ci, external circuit resistor R, and the forward Then we get to reverse current ratio IP/IR ag=0,0-Q ANALYsis oF SWITCHING OPFRATION Charge Equation Considering the junction capacitance C, as shown in Fig. 1, the total current i(t) Alowing into the terminal 1 In order to simplify the analysis, let us consider a is given by planar junction diode shown in Fig. 1. ( We do not lose generality by this simplification. )We shall also assume that the conductivity of the p-type material o, is much i(0=ir(,t+ at greater than that of the n-type material on, so that the hole current at the junction may be considered to be the i, (0, t)+C total current. The continuity equation in the n-type (base)region can be written in terms of the excess hole whe nsity as [8] P C (v)dvi where Thus we can relate the total current i(t) that flows into p(, t=P(, t-Po he terminal l to the charge Q()stored in the base region of the diode and the junction voltage V, by the following namely, the charge equation Q 十+C; 1) P(, t)=hole density Integrating this equation over the region <a <w Now let us consider the switching circuit shown in and defining the total charge stored in the base region Q Fig. 2. Initially, the switch S is in position 1, and the such that diode is forwardly biased and conducting current IF We shall assume that the switch s has been in position 1 Q(0=9, for a long time so that a steady state may be assumed the time t=0. Then the initial condition can be ob- we get tained by substituting steady-state condition do Q dt i, (0, t)-i,(w, t) Noting that the term Q/T, represents the recombination dQ rate in the base region where a w and that i,(w, t) represents the recombination rate at the boundary a =wo let us define the total recombination rate constant, tp to i, be subscript F is chosen since, for steady state, Q is related into(1) Authorized licensed use limited to: IEEE Xplore. Downloaded on December 15, 2008 at 03: 47 from IEEE Xplore. Restrictions apply1964. Kuno: P-N Junction Diode Switching 5 Fig. 1-Planar junction diode model. current IF to the minority carrier charge Q stored in the base region of the diode by the reverse and forward time constants rR and TF, respectively. The equations are ex￾pressed in terms of measurable diode parameters, vix., rP, T~, and Ci, external circuit resistor 8, and the forward to reverse current ratio IF,/IR. ANALYSIS OF SWITCHING OPERATION Charge Equation In order to simplify the analysis, let us consider a planar junction diode shown in Fig. 1. (We do not lose generality by this simplification.) We shall also assume that the conductivity of the ptype material a, is much greater than that of t,he n-type material o,, so that the hole current at the junction may be considered to be the total current. The continuity equation in the n-type (base) region can be written in terms of the excess hole density as [8] where = hole current P(x, t) = hole density P,(x) = hole density in thermal equilibrium. Integrating this equation over the region 0 _< x 5 w, and defining the total charge stored in the base region Q such that Q(t) = P \m P dx, -0 we get Noting that the term Q/T~ represents the recombination rate in the base region where 0 < x < w and that ip(w, t) represents the recombination rate at the boundary x = w, let us define the total recombination rate constant, TF,~ to IF by The subscript F is chosen since, for steady state, Q is related such that Then we get Considering the junction capacitance Cj as shown in Fig. 1, the total current i(t) flowing into the terminal 1 is given by where Vi = junction voltage Thus we can relate the total current i(t) tlhat flows into the terminal 1 to the charge Q(t) stored in the base region of the diode and the junction voltage Vi by the following, namely, the charge equation Initial Condition Now let us consider the switching circuit shown in Fig. 2. Initially, the switch X is in position 1, and the diode is forwardly biased and conducting current IF. (We shall assume that the switch S has been in position 1 for a long time so that a steady state may be assumed at the time t = 0-). Then the initial condition can be ob￾tained by substituting steady-state conditions i(O-) = IF into (1). Authorized licensed use limited to: IEEE Xplore. Downloaded on December 15, 2008 at 03:47 from IEEE Xplore. Restrictions apply