72 CHAPTER 2. ELECTRONIC LEVELS IN SEMICONDUCTORS
Figure 2.29: Measured electrical characteristics as a function of temperature for three different
GaN samples. The sample with the lowest sheet charge is doped with Si (a shallow donor in
GaN) to generate mobile electrons. In the sample with the highest sheet charge, carriers are
generated by grading AlGaN from 0% Al to 30% Al, resulting in a 3-dimensional electron dis-
tribution (as in figure 2.28b and c). In the third sample, a 2DEG is generated in an AlGaN/GaN
heterostructure (as in figure 2.28a). While the charge in the Si-doped sample decreases as tem-
perature is decrease (carrier freeze-out), the charge in the other two samples remains constant.
Figures courtesy of D. Jena, University of Notre Dame.
This corresponds to a density of 6. 06 × 1012 cm−^2 electronic charges.
In addition to the piezoelectric charge the spontaneous polarization charge is
Psp=0.3(0.089) + 0.7(0.029)− 0 .029 = 0.018 C/m^2which corresponds to a density of 1. 125 × 1013 cm−^2 charges. The total charge (fixed) arising at the
interface is the sum of the two charges.