On the relationship between the temperature coefficient of resistance and the thermal conductance of integrated metal resistors

The concepts of temperature coefficient of resistance (TCR) and thermal conductance (Gth) entail devices with uniform temperature. However, Joule heated integrated metal resistors usually feature a non-constant temperature profile. After defining an effective TCR and an effective Gth, this paper describes simple relationships able to correlate these two parameters with measured quantities. These relationships are applied to the case of the heating element of a micromachined gas sensor and are exploited to derive the effective TCR and Gth of the same element when a passivation layer is added on top of it. The information presented in this paper could also provide useful rules of thumb for the verification of finite element modeling simulations.