Record‐High Thermoelectric Performance in Al‐Doped ZnO via Anderson Localization of Band Edge States

Abstract Oxides are of interest for thermoelectrics due to their high thermal stability, chemical inertness, low cost, and eco‐friendly constituting elements. Here, adopting a unique synthesis route via chemical co‐precipitation at strongly alkaline conditions, one of the highest thermoelectric performances for ZnO ceramics (PFmax= 21.5 µW cm−1 K−2 and zTmax= 0.5 at 1100 K in Zn0.96Al0.04O) is achieved. These results are linked to a distinct modification of the electronic structure: charge carriers become trapped at the edge of the conduction band due to Anderson localization, evidenced by an anomalously low carrier mobility, and characteristic temperature and doping dependencies of charge transport. The bi‐dimensional optimization of doping and carrier localization enable a simultaneous improvement of the Seebeck coefficient and electrical conductivity, opening a novel pathway to advance ZnO thermoelectrics.

Rietveld refinement for powder X-ray diffraction patterns

Single parabolic band model calculations
The experimental transport data can be analyzed using a single parabolic band (SPB) model with the relaxation time approximation. 1 The following equations are applicable for a single scattering mechanism, where the energy dependence of the carrier relaxation time can be expressed by a simple power-law τ = τ 0 E λ , with λ being the scattering parameter. 2The Hall factor r H , given by: with the j-th order Fermi integrals, F j (η) defined by where ε is the reduced carrier energy, η is the reduced electrochemical potential related to Fermi energy via where E F is the Fermi level, E c is the conduction band edge, and k B is the Boltzmann constant.Reduced chemical potential can be calculated from Seebeck coefficient by the following equation: where e is the electron charge.Lorenz number can be calculated as follows Effective mass estimated by where m * d is the density-of-states effective mass, the chemical carrier concentration n = n H r H (with n H representing the Hall charge carrier concentration), h is the Planck's constant, and m e the electron mass.
Calculated parameters are presented in Table S3.  1 .
1 .S4.  ) T e m p e r a t u r e ( K )

Analysis of lattice thermal conductivity
The experimental data of κ L were fitted and analyzed by the Debye-Callaway 7 model modified by Glassbrenner and Slack 8 for high temperatures above the Debye temperature (T ≫ θ D ).In the model by Glassbrenner and Slack the lattice thermal conductivity is given by where υ a is the average velocity of sound determined as with υ t and υ l being the transverse and longitudinal sound velocities (2750 m s -1 and 5940 m s -1 , 9 respectively), θ D is the Debye temperature, x = ℏω/k B T , ω is the phonon frequency and τ c is the total phonon relaxation time.The overall relaxation rate τ −1 c can be determined by combining the various scattering processes based on Matthiessen's rule.For simplicity, we considered mainly phonon-phonon and point defect scattering, which are the most important contributions at high temperatures.
Thus, τ −1 c is expressed as where τ U and τ P D , are the relaxation times for Umklapp scattering and point defect scattering.Umklapp relaxation rate is defined as: where B U and B H are frequency and temperature independent coefficients, with B H being a higher order four-scattering parameter. 8Point defect term is expressed as: where V a is the average atomic volume, Γ is the disorder scattering parameter. 10According to Abeles and Slack the disorder scattering parameter Γ includes both, the strain field Γ S and the mass fluctuation scattering Γ M , and can be calculated by as Γ = Γ M + Γ S .
where n is the number of different crystallographic sublattice types in the lattice and c i is the relative degeneracy of the respective sites.In the pure ZnO, n = 2, c i = 2, M is the average atomic mass, f k i is the fractional occupation of the k-th atom on the i-th site, M k i and r k i are the atomic mass and radius of the k-th atom, ε i is a function of the Grüneisen parameter, γ, which characterizes the anharmonicity of the lattice. 11M i and r i are the average atomic mass and radius on the i-th site, respectively: For the strain field fluctuation, ε is directly estimated by: here ψ determined as where υ p is the Poison ratio:

e x p e r i m e n t a l s i m u l a t e d d i f f e r e n c e P 6 3 m c F d 3 mD i f f r a c t i o n a n g l e , 2 qD i f f r a c t i o n a n g l e , 2 q
Figure S1: Rietveld refinement for the Zn 1−x Al x O (x = 0, 0.02, 0.04, 0.06) samples.

Figure S2 :Figure
Figure S2: FE-SEM microphotographs of undoped ZnO polished surface in (a,c) backscattered electron mode, and (b,d) mixed backscattered and secondary electron mode.

Figure S4 :
Figure S4: Grain size area distributions calculated from EBSD analysis for Zn 0.96 Al 0.04 O.

Figure S5 :
Figure S5: Grain size diameter distributions calculated from EBSD analysis for Zn 0.96 Al 0.04 O.

Figure S6 :
Figure S6: The experimental temperature dependence of resistivity for (a) ZnO and (b) Zn 0.98 Al 0.02 O samples.

H ( c m 2 ⋅V - 1 ⋅s - 1
g l e Z n O c r y s t a l s : H u t s o n L o o k P o l y c r y s t a l s o f Z n O : H a n G u a n U n d o p e d Z n O ( t h i s w o r k ) : Z n O m

Table S2 :
Average grain size estimated from SEM images D SEM of the Zn 1−x Al

Table S3 :
Room-temperature Hall constant r H , calculated chemical potential η, Lorenz number L, and effective mass m * d for Zn 1−x Al x O samples (x = 0, 0.02, 0.04, 0.06)

Table S4 :
Temperature dependence of Hall carrier concentration n H , and Hall carrier mobility µ H . Nominal composition T (K) n H (10 18 cm −3 ) µ H (cm 2 V −1 s

Table S5 :
Thermal conductivity fitting parameters