Nonlinear effects in transistors caused by thermal power feedback: simulation and modeling in SPICE

Restabilizing mechanisms after the onset of thermal instability in bipolar transistors

“…6, the region around the current-bifurcation point is plotted for different values of ∆r E = r E1 − r E2 . The critical-point condition given by (22) defines the current bifurcation for the case in which there is an infinitely small difference between the fingers, i.e., ∆r E → 0. As the difference in device parameters grows, the abruptness of the transition from stable to unstable case is less sharp, and the critical point must be defined in another way, for example, as the point at which the lower current has reached its maximum, i.e., where δI C1 = 0 [8].…”

“…Fig. 9 illustrates the solution loci of (22) in the (V CEX , I C ) plane for I E -controlled two-finger BJTs with equal R TH and different R M values. The curves represent the borders between stable (left) and unstable (right) operation regimes.…”

“…When a constant ϕ TOT is assumed and both external resistors and high-current effects are excluded, (22) reduces to…”

“…The method usually adopted to enable electrothermal simulations in SPICE is the structural macromodeling technique by which the built-in device model is expanded with supplementary passive and active standard components in order to describe specific transistor phenomena such as the thermal interactions [22], [23]. An effective alternative is the analog behavioral macromodeling (ABM), which makes use of a powerful facility introduced in latest SPICE versions [24].…”

“…2(b), the measured collector-current distribution is shown for several two-finger devices with different (R TH , R M ) values. The measurements are performed in an I E -controlled setup for V CBX = 0 V. The critical points are calculated by the model (22) and reported in the inset of the figure. As can be seen, the model gives a good prediction of both the critical point 1 and the critical point 2.…”