Thermal properties of very fast transistors

Recent predictions that thermal effects will limit future transistor speed improvement motivated an interest in predicting and measuring these effects. A mathematical model of the three-dimensional transient heat flow problem is presented which takes into account the physical structure of the device and the actual region of power dissipation. At any point within the device, the model predicts the time-dependent temperature response to a change in power dissipation. A new method of measuring the local time-dependent thermal behavior of small bipolar transistors is described and used to verify the model. It was found that the thermal spreading resistance becomes important in silicon transistors when the emitter stripe dimensions approach 1 µ. Furthermore, the thermal response is much slower than the electrical response. Also, it was confirmed that adjacent devices in integrated circuits are essentially thermally isolated as far as thermal spreading resistance is concerned.