Analysis of simple scattering models on the thermoelectric performance of analytical electron dispersions

Abstract

Recent first-principles calculations have shown that a simple DOS scattering model, wherein the electronic scattering rates are assumed to be proportional to the density-of-states, better approximates the true scattering properties than the commonly used constant relaxation-time and constant mean-free-path approximations. This work investigates how the thermoelectric properties predicted with the DOS model compare to the other two scattering models, using three analytical electron dispersions (parabolic band in 3D/2D/1D, Kane band in 3D/2D/1D, and ring-shaped quartic band in 2D). Our findings show that the scattering models can lead to significant differences, and can disagree about whether certain band structures can provide benefits. A constant relaxation-time is found to always be optimistic compared to a constant mean-free-path, while the DOS scattering model shows no such clear trend. Notably, the 1D parabolic band and 2D quartic band exhibit the highest power factors with the DOS model, resulting from a rapid decrease in density-of-states, and thus scattering -suggesting a possible strategy for improved thermoelectrics based on engineering band structures with sharp/discontinuous drops in density-of-states. This work highlights the importance of simple and accurate scattering models when rigorous ab-initio scattering calculations are not feasible. arXiv:1911.06414v1 [cond-mat.mtrl-sci]

Material Descriptors for the Discovery of Efficient Thermoelectrics

“…Under the CRT approximation, a descriptor that offers satisfactory Pearson coefficients for both carrier types is DOS The situation is less straightforward when we consider energy-dependent electron-phonon scattering, because in addition to having more conducting states, a higher DOS results in a stronger scattering rate, 23,60 and the two effects could cancel each other out. 23,27,60 We first examine the adequacy of existing descriptors already proposed in the literature, in DOS that gives a total DOS same as the sum of the DOS of the individual valleys. 34 The unsatisfactory performance of this descriptor with respect to our calculations (re = 0.12 and rh = 0.06) resides in two reasons.…”

“…We deliberately avoid using parameters related to the DOS due to the reason that under energy dependent scattering the DOS cancels out with the inverse DOS dependence of the relaxation times, and at first order drops out of the transport coefficients. 23,60 Thus, when looking for effective mass parameters, we chose the conductivity effective mass, which does not cancel out in the evaluation of the TDF in equation (2). Since the deformation potential and conductivity effective mass are two parameters related to the mobility, Figure 6c plots the peak PF values versus the computed lattice mobility (low field and low carrier density), a measurable quantity related to electron-phonon scattering processes.…”

Thermoelectric properties of semiconducting materials with parabolic and pudding-mold band structures

“…Now we can calculate the thermoelectric properties of the model material using Eqs. ( 24)- (26), where the integrals G (c,v),i are calculated numerically using the SciPy package in Python [29]. We start with 3D systems in Secs.…”

“…To proceed with our calculation, we need to determine the dependence of τ on . Some common approaches for the calculation of relaxation time include treating the relaxation time as a constant or considering it to be inversely proportional to DOS [25,26]. Previous studies show that the constant relaxation time approximation (CRTA) can adequately explain experimental results [27,28], including the case of pudding-mold band structures [9].…”

Heat, particle, and chiral currents in a boundary driven bosonic ladder in the presence of a gauge field

“…Here we investigate how tuning the system parameters to tailor the energy bands can be used to significantly alter its thermopower conversion performance [29][30][31][32][33][34][35]. More in detail, we investigate the interplay between the boundary driving baths and the system parameters in tuning the heat-to-work conversion.…”