Transistor Junction Temperature as a Function of Time

An analysis of the heat flow in transistors is presented which enables one to determine the variation of junction temperature with time for a given transistor excitation. A one-dimensional heat flow model is considered which is repsentative of grown-junction and some alloy transistors. The step and impulse temperature responses are obtained from the solution of the heat equation. A comparison made between the step response so obtained and the often assumed simple exponential response indicates that the assumed response can be low by a factor of two or more. Utilizing the impulse temperature response for the transistor, the junction temperature as a function of time is determined for periodic rectangular pulse excitation. Numerical calculations are made and curves presented for the maximum, average, and minimum junction temperatures in terms of the duty cycle, repetition rate, and fundamental thermal time constant. These curves indicate that the maximum junction temperature can be several times the average value at low duty cycles and low repetition rates. Measurements of junction temperatures are presented which essentially substantiate both the step response and the repetitive pulse response which were theoretically obtained. Finally, using simplified approximate expressions, the procedure for calculating the maximum, average, and minimum junction temperatures for repetitive pulse excitation is described. The use of these predicted junction temperatures with relation to the maximum junction temperature ratings, thermal stability, and electrical parameter changes is also discussed.