TEEE TRANSACTIONS ON ELECTRON DEVICES Fig.sTeady state hole density distributions in the base region Fig. 2-Diode switching circuit. The initial hole density distribution can be found by At this time, the total charge in the base region is given by solving the diffusion equation. Typical steady-state dis- tributions are shown in Fig 3 Q(t,=9 P(a, t,)dx at t=t, Normal Switching Operation Noting that Q(t )is related to IR, let us define TR,re In normal switching operation, switching transient con- lating the minimum amount of charge remaining in the sists of constant current phase(storage phase) and de- base region which is required to support the reverse cur- caying current phase as shown in Fig. 4. Now suppose rent, such that that att=0 the switch S is quickly thrown from position 1 to position 2. Then the current starts to fow in the Q()= IRTR opposite direction. The maximum reverse current is Although it is not immediately obvious why the mini- limited, by the external resistor R, to mum amount of charge required to support the reverse V,-V V current is linearly related to the reverse current, the (3) justification is made empirically as shown in a later Then the stored charge Q starts to decay in a manner Substituting (8)into(4), and solving for the storage For0<t<t,,(see Fig. 4), the constant reverse cur time t,w rent Ie flows and the junction voltage does not change (Strictly speaking, it changes slightly as shown in Fig 4 m(+分-m(+2)] but the term C,dv/dt)is negligible compared with other terms in (1)during the constant current phase. If we plot t, vs In (1+ Ir/Ie), we will get a straight Then(1) reduces to line with a slope Tr and offset by In (1+ TR/Tp),as 妲Q旦 wn in Fig. 6. dt (4) For t> t,, the hole density decays further, and current tarts to decay he stored charg With the initial condition given by(2), we can solve for gradient at z=0 necessary to support I g. Let us assume Q(0)and get that the reverse current ig(o is related to the charge Q(0), as we have defined TR, by the relationship Q(0=(I,+IxTp exp t)-IRTP Q(0= TRin(O (10 During the constant current phase, i.e., 0< t<t the where reverse current I n is given by t> t Ia=9 uEP-D, for 0<t<t,.(6) Considering the circuit shown in Fig. 2, the junction oltage V, is related to in by Att= t,, the hole density at the junction(r=0)becomes zero, and(6)become a Le Can et al, [51, and Moll et al. thus obtaining t,=T In (l+IriG (7) t correct, sinc orted by the hole density gradient at the junction as given by (7) Authorized licensed use limited to: IEEE Xplore. Downloaded on December 15, 2008 at 03: 47 from IEEE Xplore. Restrictions apply.10 S IEEE TRANXAGTIONS ON ELECTRON DEVICES January h 0 W 0 W - I- I-x c-x - Fig. 3-Steady state hole density distributions in the base region Fig. 2-Diode switching circuit. of various types of diodes. The initial hole density distribution can be found by solving the diffusion equation. Typical steady-state dis￾tributions are shown in Fig. 3. Normal Switching Operation In normal switching operation, switching transient con￾sists of constant current phase (storage phase) and de￾caying current phase as shown in Fig. 4. Now suppose that at t = 0' the switch S is quickly thrown from position 1 to position 2. Then the current starts to flow in the opposite direction. The maximum reverse current is limited, by the external resistor R, to Then the stored charge Q starts to decay in a manner shown in Fig. 5. For 0 < t < t,, (see Fig. 4), the constant reverse cur￾rent I, flows and the junction voltage does not change. (Strictly speaking, it changes slightly as shown in Fig. 4, but the term Ci(dVi/dt) is negligible compared with other terms in (1) during the constant current phase.) Then (1) reduces to (4) With the initial condition given by (2), we can solve for &(t) and get Q(t) = (I, 3- I,)T~ exp (-"> - IRTF. (5) During the constant current phase, Le., 0 < t < t,, the reverse current I, is given by 7F At 2 = t,, the hole density at the junction (x = 0) becomes zero, and (6) becomes At this time, the totaI charge in the base region is given by2 Q(t8) = q 1 P(x, t.) dx at t = t,. Noting that &(&) is related to I,, let us define 7x7 re￾lating the minimum amount of charge remaining in the base region which is required to support the reverse cur￾rent, such that W 0 Q(tJ = IRTR. (8) Although it is not immediately obvious why the mini￾mum amount of charge required to support the reverse current is linearly related to the reverse current, the justification is made empiricalIy as shown in a later section. Substituting (8) into (4), and solving for the storage time t,, we get If we plot t, vs In (1 + IF/'IE), we will get a straight line with a slope rF and off set by In (I 3- ~R/TF), as shown in Fig. 6. For t > t,, the hole density decays further, and current starts to decay, since the stored charge cannot keep the gradient at x = 0 necessary to support I,. Let us assume that the reverse current iR(t) is related to the charge &(t), as we have defined rR, by the relationship Ut) = TRiR(t) (10) where t > t,. Considering the circuit shown in Fig. 2, the junction voltage Vi is related to iR by thus obtaining t, = T~ In (1 + IF/IR), but their assumptions are LeCan et al., [5], and Moll et al., [6], assume that Q(t.) = 0, not correot, since the current.1, at t = t, is supported by the hole density gradient at the junctlon as given by (7). Authorized licensed use limited to: IEEE Xplore. Downloaded on December 15, 2008 at 03:47 from IEEE Xplore. Restrictions apply