Random band-edge model description of thermoelectricity in high-mobility disordered semiconductors: Application to the amorphous oxide In-Ga-Zn-O

Unraveling the dominant charge transport mechanism in high-mobility amorphous oxide semiconductors is still a matter of controversy. In the present study we extended the random band-edge model suggested before for the charge transport and Hall-effect mobility in such disordered materials [Fishchuk et al., Phys. Rev. B 93, 195204 (2016)], and also describe the field-effect-modulated thermoelectricity in amorphous In-Ga-Zn-O ($a$-IGZO) films under the same premises. The model is based on the concept of charge transport through the extended states and assumes that the transport is limited by the spatial variation of the position of the band edge due to the disorder potential, rather than by localized states. The theoretical model is formulated using the effective medium approximation framework and describes well basic features of the Seebeck coefficient in disordered materials as a function of energy disorder, carrier concentration, and temperature. Carrier concentration dependencies of power factor and thermoelectric figure of merit have been also considered for such systems. Besides, our calculations reveal a remarkable turnover effect from a negative to a positive temperature dependence of Seebeck coefficient upon increasing carrier concentration. The suggested unified model provides a good quantitative description of available experimental data on the Seebeck coefficient and the charge mobilities measured in the same $a$-IGZO transistor as a function of the gate voltage and temperature by considering the same charge transport mechanisms. This promotes a deeper understanding and a more credible and accurate description of the transport process in $a$-IGZO films.

Figure 1

(a) Carrier concentration dependencies of Seebeck coefficient ${\alpha }_e$ calculated using Eqs. (17, 18, 19) for different disorder parameters $\delta$ at $T=300\mathrm{K}$ and $q=1$ (curves 2–5). Curve 1 is calculated by Eq. (21) at $\delta =0$ for an ordered (disorder-free) system. (b) Seebeck coefficient ${\alpha }_e$ vs $\delta$ calculated parametric in carrier concentrations $n$.

Figure 2

(a) Seebeck coefficient ${\alpha }_e$ vs carrier concentration $[{\alpha }_e\propto log\left(n\right)]$ calculated at different temperatures for an amorphous system using Eqs. (17, 18, 19) at $\delta =75$ meV and $q=1$ (solid lines) and for a crystalline system ($\delta =0$) using Eq. (21) (thin dashed lines). Temperature change from 200 to 350 K in 50-K steps is shown by arrows. The turnover of the calculated dependencies at $n_{cr}$ is marked by a vertical dashed line. Inset: the turnover point $n_{cr}$ vs $\delta$. (b) Electrical conductivity vs carrier concentration (in log-log representation) calculated for the same amorphous system using Eq. (17).

Figure 3

Dependence of the effective FET mobility ${\mu }_e$ on the gate voltage ($V_{\mathrm{G}}-V_{\mathrm{TH}}$) parametric in temperatures. Symbols: experimental data from [14]. Solid lines: calculated using the present model [Eq. (17)].

Figure 4

Comparison between calculations and experimental field-effect-modulated Seebeck coefficient vs ($V_{\mathrm{G}}-V_{\mathrm{TH}}$) measured in $a$-IGZO TFT at different temperatures. Symbols: experimental data from [14]. Solid curves are calculated using Eqs. (17, 18, 19) and parameter $q=0.78$. All fitting parameters were the same as in Fig. 3 for the charge mobility.

Figure 5

The normalized power factor (solid curves) calculated as a function of carrier concentration for different energy disorder (δ) at constant $T$ = 350 K (a), and for different temperatures at constant δ = 75 meV (b). δ change in 25-meV steps and temperature change from 200 to 350 K in 50-K steps are shown by arrows in (a) and (b), respectively. Dashed curve in (a) depicts the power factor for a crystalline system ($\delta =0$).

Figure 6

The effective thermoelectric figure of merit ${\left(zT\right)}_e$ calculated as a function of carrier concentrations in an amorphous system at $T$ = 300 K for different $B$ factors at $\delta =100$ meV. For simplicity, we assume $q=q_1=1$ in these calculations.