Thermal Resistance

by Dr. Patrick Hopkins

Thermal Resistance Explored

Where thermal conductivity is an intrinsic material property, it is often more convenient to conceptualize heat flow through materials as thermal resistance networks. Thermal resistance is a basic thermal property that relates the steady-state temperature differential between two surfaces for a given level of power dissipation. It is typically expressed in terms of K/W, or, more generally for any given area of a component, m2 K/W. It can be formally defined as:

R = ΔT/Q

where ΔT is the temperature difference and Q is the power flux dissipated by the heated component. Thermal resistance is the reciprocal of thermal conductance and can be directly related to thermal conductivity via Fourier’s Law.

In a parallel to electrical resistance, thermal resistances of different materials of different thicknesses can then be compared to determine temperature changes and aid in material selection. Similarly, the concept of thermal resistance also allows us to compare heat transfer efficacy of different materials by considering the total resistance to heat flow for specific material thicknesses. The thermal resistance of some thickness of material, d, is given by:

Rth = d/k

The Results

Thus, the thicker a material, the more thermal resistance that layer of material has. Thermal resistance is commonly analogized to electrical circuits with temperature compared to voltage, thermal resistance to electrical resistance, and power dissipated to electrical current. In a semiconductor device, heat flows through a series of different materials and across a variety of interfaces, traveling from transistors and integrated circuits, to package, to heatsink (if present), to the ambient surroundings, and across every interfacial region along the way. Each of these points exhibits its own level of thermal resistance that contributes to the maximum temperature at a hot spot. These resistances sum to a total thermal resistance from chip to ambient. With this concept of thermal resistance, and knowing thicknesses of these layers, we can then start to understand where the largest temperature rises are in devices. For example, a 5 nm gate dielectric with a thermal conductivity of ~1 W/m/K can have 5X higher thermal resistance than the active region of a device that is is in contact with (assuming a device active layer thickness of 10 nm and a thermal conductivity of ~10 W/m/K).