Using materials quality factor B_ΔΕ∗ for design of thermoelectric materials with multiple bands

The quality factor B involving carrier mobility, state density effective mass, and lattice thermal conductivity has always been regarded as the guidance for the thermoelectric materials design. However, the traditional quality factor considers a single band and neglects the influence of band gap and the sub-band, whose edge energy is 5 k_BT lower than valence band maximum for the p-type or higher than conduction band minimum for n-type semiconductor. In this work, we took into account the band gap and second band based on the three-parabolic-band model and derived an advanced quality factor B_ΔE^∗, which is better proportional to the peak ZT values of many compounds with multiple bands. A specific example is also validated based on this quality factor that a highest B_ΔE^∗ appears when x = 0.8 for (Yb_0.9Mg_0.1)Mg_xZn_2-xSb₂, leading to the highest ZT value at this composition.