Degradation of the ZT thermoelectric figure of merit in silicon when nanostructuring: From bulk to nanowires

Since the landmark paper by Hicks and Dresselhaus [Phys. Rev. B 47, 16631(R) (1993)], there has been a general consensus that one-dimensional nanoscale conductors, i.e. nanowires, provide the long sought paradigm to implement the so-called phonon-glass electron-crystal material, which results in large improvements in the thermoelectric figure of merit ZT. Despite some encouraging—though isolated—experimental results, this idea has never been subjected to a rigorous scrutiny and the effect of the coupled dynamics of electrons and phonons has usually been oversimplified. To bypass these limitations, we have calculated the effective thermoelectric parameters for silicon nanowires (SiNWs) by iteratively solving the coupled electron-phonon Boltzmann transport equation (EPBTE) supplied with first-principles data. This allows for an unprecedented precision in determining the correct dependence of the thermoelectric parameters with system size; including, but not limited to, the figure of merit and its enhancement or degradation due to nanostructuring. Indeed, we demonstrate that the commonly used relaxation time approximation (RTA), or the uncoupled beyond the RTA (iterative) solution fail to describe the correct effect of nanostructuring on the thermoelectric properties and efficiency in SiNWs due to the strong contribution of phonon drag to the Seebeck coefficient, so that the use of fully coupled solution of the EPBTE is essential to obtain the correct effect of nanostructuring. Most importantly, we show that, contrarily to what commonly argued, resorting to NWs is not necessarily beneficial for ZT. Indeed, in a wide range of diameters nanostructuring diminishes the Seebeck coefficient faster than the decrease in thermal conductivity, due to the suppression of very long wavelength phonons responsible for the largest contribution to the phonon drag component of the Seebeck coefficient. This penalty to ZT can be mitigated if the NWs have a very rough surface, providing additional reduction to the thermal conductivity. Additionally, we demonstrate that our methodology provides improved data sets for an accurate determination of doping concentration in NWs through electrical-based inference and excellent agreement with the available experimental data.