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An advantage for some wide bandgap materials, that is often overlooked, is that the thermal coefficient of expansion (CTE) is better matched to the ceramics in use for packaging technology. It is shown that the optimal choice for uni-polar devices is clearly GaN. It is further shown that the future optimal choice for bipolar devices is C (diamond) owing to the large bandgap, high thermal conductivity, and large electron and hole mobilities. A new expression relating the critical electric field for breakdown in abrupt junctions to the material bandgap energy is derived and is further used to derive new expressions for specific on-resistance in power semiconductor devices. These new expressions are compared to the previous literature and the efficacy of specific power devices, such as heterojunction MOSFETs, using GaN are discussed.