Unstable Inverse Heat Transfer Problems in Microelectronics

Inverse heat transfer problems are very important for the thermal testability of integrated circuits. Temperature sensors integrated on the same chip measure in real time the power dissipation in one or more critical heat sources of the circuit in order to prevent overheating. It will be demonstrated that these kinds of problems can give rise to mathematical unstabilities or the ill conditioning of the inverse problem. This statement will be proved with the help of several particular cases.