We suggest an analytic theory based on the effective medium approximation (EMA) which is able to describe
charge-carrier transport in a disordered semiconductor with a significant degree of degeneration realized at high
carrier concentrations, especially relevant in some thin-film transistors (TFTs), when the Fermi level is very
close to the conduction-band edge. The EMA model is based on special averaging of the Fermi-Dirac carrier
distributions using a suitably normalized cumulative density-of-state distribution that includes both delocalized
states and the localized states. The principal advantage of the present model is its ability to describe universally
effective drift and Hall mobility in heterogeneous materials as a function of disorder, temperature, and carrier
concentration within the same theoretical formalism. It also bridges a gap between hopping and bandlike
transport in an energetically heterogeneous system. The key assumption of the model is that the charge carriers
move through delocalized states and that, in addition to the tail of the localized states, the disorder can give rise
to spatial energy variation of the transport-band edge being described by a Gaussian distribution. It can explain
a puzzling observation of activated and carrier-concentration-dependent Hall mobility in a disordered system
featuring an ideal Hall effect. The present model has been successfully applied to describe experimental results
on the charge transport measured in an amorphous oxide semiconductor, In-Ga-Zn-O (a-IGZO). In particular, the
model reproduces well both the conventional Meyer-Neldel (MN) compensation behavior for the charge-carrier
mobility and inverse-MN effect for the conductivity observed in the same a-IGZO TFT. The model was further
supported by ab initio calculations revealing that the amorphization of IGZO gives rise to variation of the
conduction-band edge rather than to the creation of localized states. The obtained changes agree with the one
we used to describe the charge transport. We found that the band-edge variation dominates the charge transport
in high-quality a-IGZO TFTs in the above-threshold voltage region, whereas the localized states need not to be
invoked to account for the experimental results in this material.