Classical and quantum conductivity in β-Ga(2)O(3)

The conductivity σ, quantum-based magnetoconductivity Δσ = σ(B) − σ(0), and Hall coefficient R(H) (= µ(H)/σ) of degenerate, homoepitaxial, (010) Si-doped β-Ga(2)O(3), have been measured over a temperature range T = 9–320 K and magnetic field range B = 0–10 kG. With ten atoms in the unit cell, the normal-mode phonon structure of β-Ga(2)O(3) is very complex, with optical-phonon energies ranging from kT(po) ~ 20–100 meV. For heavily doped samples, the phonon spectrum is further modified by doping disorder. We explore the possibility of developing a single function T(po)(T) that can be incorporated into both quantum and classical scattering theory such that Δσ vs B, Δσ vs T, and µ(H) vs T are all well fitted. Surprisingly, a relatively simple function, T(po)(T) = 1.6 × 10(3){1 − exp[−(T + 1)/170]} K, works well for β-Ga(2)O(3) without any additional fitting parameters. In contrast, Δσ vs T in degenerate ScN, which has only one optical phonon branch, is well fitted with a constant T(po) = 550 K. These results indicate that quantum conductivity enables an understanding of classical conductivity in disordered, multi-phonon semiconductors.