Carrier mobility versus carrier density in ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}/\mathrm{G}\mathrm{a}\mathrm{N}$ quantum wells

Experimental measurements show that, in ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}/\mathrm{G}\mathrm{a}\mathrm{N}$ triangular quantum wells, the free-carrier mobility experiences a strong decrease with increasing carrier density. A theoretical analysis of the various scattering mechanisms that can explain such a behavior is presented. It shows that, even though phonon and carrier-carrier scattering mechanisms naturally lead to a mobility decrease versus carrier density, they are by themselves not able to justify the whole set of experimental data. Instead, we propose to attribute an extrinsic origin to the scattering associated with the progressive appearance of strain relaxation defects and give explicit expressions for the collision time associated with interface roughness and interface charge spatial fluctuations (“electrical” roughness) which may result from the existence of cracks in ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N},$ thickness inhomogeneity, misfit dislocations, and alloy disorder.