Analytic study of electrical, thermal and thermoelectric properties of ultra-thin $$ \mathrm{In}_{{ x}}\mathrm{Ga}_{{ 1-x}}\mathrm{N} $$ In x Ga 1 - x N nanowires

The doping density, temperature, wire thickness, indium content, and surface roughness effects on electronic, thermal, and thermoelectric transport coefficients of ultra-thin InGaN/GaN nanowires are investigated by applying the analytic procedure to polar semiconductors where piezoelectric effect and polar optical phonon scatterings also play significant roles. We calculate the low-field electron mobility, electronic Seebeck coefficient, and lattice thermal conductivity based on relaxation time approximation within linear response theory and Boltzmann transport equation. The dispersion of longitudinal acoustic phonons and the corresponding group velocities in $$ \mathrm{In}_{x}\mathrm{Ga}_{1-x}\mathrm{N} $$ In x Ga 1 - x N nanowires are determined by applying the xyz-algorithm. The highest room temperature $$ \mathrm{ZT} = 0.25 $$ ZT = 0.25 is achieved for 4-nm-thick nanowire that is an order of magnitude larger than the bulk ZT value of 0.02 and the ZT value of the same $$ \mathrm{In}_{0.1}\mathrm{Ga}_{0.9}\mathrm{N} $$ In 0.1 Ga 0.9 N nanowire at $$T = 800 \, \mathrm{K} $$ T = 800 K reaches a magnitude of 0.55. The effect of nanostructuring is found to be more pronounced than alloying. Graphical abstract