Abstract
This work describes, through the semi-classical Boltzmann transport theory and simulation, a novel nanostructured material design that can lead to unprecedentedly high thermoelectric power factors, with improvements of more than an order of magnitude compared to optimal bulk material power factors. The design is based on a specific grain/grain-boundary (potential well/barrier) engineering such that: i) carrier energy filtering is achieved using potential barriers, combined with ii) higher than usual doping operating conditions such that high carrier velocities and mean-free-paths are utilized, iii) minimal carrier energy relaxation is achieved after passing over the barriers to propagate the high Seebeck coefficient of the barriers into the potential wells, and, importantly, iv) an intermediate dopant-free (depleted) region is formed. Thus, the design consists of a ‘three-region geometry’, in which the high doping resides in the center/core of the potential well, with a dopant-depleted region separating the doped region from the potential barriers. It is shown that the filtering barriers are optimal when they mitigate the reduction in conductivity they introduce, and this can be done primarily when they are ‘clean’ from dopants during the process of filtering. The potential wells, on the other hand, are optimal when they mitigate the reduced Seebeck coefficient they introduce by: i) not allowing carrier energy relaxation, and ii) mitigating the reduction in mobility that the high concentration of dopant impurities causes. It is shown that dopant segregation, with ‘clean’ dopant-depletion regions around the potential barriers, serves this key purpose of improved mobility toward the phonon-limited mobility levels in the wells. Using quantum transport simulations based on the non-equilibrium Green's function method as well as semi-classical Monte Carlo simulations, we also verify the important ingredients and validate this ‘clean-filtering’ design.
Highlights
Thermoelectric (TE) materials have made dramatic progress over the last several years
To model TE transport in the structure we examine, we start with the Boltzmann transport equation (BTE) formalism and calibrate our model to match the mobility of p-type bulk Si, so that we remain within realistic exploration boundaries
The question we essentially want to answer here is: how high can we dope the middle region, or how high will the EF be if a certain mobile carrier density needs to be achieved in the entire material region, given that it will only be supplied from the central/core region? as shown in Fig. 3c and d, the built-in barriers are formed in the undoped region, which is largely extended because the depletion region is preferentially placed in the intrinsic region of the nþþ/i junction
Summary
Thermoelectric (TE) materials have made dramatic progress over the last several years. Current research efforts in improving the PF have diverted in many other directions, including: i) taking advantage of the density of states in lowdimensional materials through quantum confinement [31], or in bulk materials that include low-dimensional ‘like’ features [32,33], ii) band structure engineering and band-convergence strategies [32e36], iii) modulation doping and gating [37e45], iv) introducing resonances in the density of states [46], and even more recently v) concepts that take advantage of the Soret effect in hybrid porous/ electrolyte materials [47] These approaches target improvements either in the Seebeck coefficient or in the electrical conductivity, with the hope that the other quantity will not be degraded significantly, and sometimes they report moderate PF improvements. No significant developments that lead to meaningful improvements, wider applicability, or generalization to many materials have been achieved by these methods either
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