High thermoelectric figure of merit of porous Si nanowires from 300 to 700 K

Approximately half of global primary energy is wasted as heat, with a significant portion above 573 K possessing high Carnot potential for electricity conversion. Thermoelectric (TE) technologies offer a cost-effective solution for converting this waste heat, especially at high temperatures where they become competitive with other zero-carbon technologies. However, challenges in scalability, reliability, stability, and toxicity hinder widespread adoption. Silicon nanowires (SiNWs) present a promising material due to their cost-effectiveness and mature manufacturing infrastructure. While previous research demonstrated the potential of SiNWs for TE applications, achieving high figure of merit (ZT) values at high temperatures has remained a challenge. This study aims to address this limitation by synthesizing and characterizing high-performance porous SiNWs for enhanced waste heat conversion.

Historically, silicon's high thermal conductivity (κ) resulted in a low ZT, making it unsuitable for TE applications. However, the discovery that rough surfaces or thin SiNW arrays could significantly reduce κ led to ZT values of approximately 0.6 and 0.2 at 300 K, respectively. To improve TE module efficiency (η), both the hot-side temperature (TH) and ZT need to be increased. High TH is also crucial for cost reduction in heat exchangers. Previous attempts to measure high-ZT SiNWs at high temperatures (TH) were limited by challenges such as measurement errors due to radiation heat loss, instability of Pt heaters/thermometers, and difficulty in simultaneously measuring κ, σ, and S on the same sample. Furthermore, prior studies often lacked systematic optimization of synthesis parameters, such as doping levels and porosity, resulting in inconsistent results and limited understanding of the underlying mechanisms.

This research systematically optimized the synthesis and doping conditions of porous SiNWs to enhance their thermoelectric performance. Porous SiNWs were fabricated using a combination of nanoimprint lithography (NIL) and metal-assisted chemical etching (MACE), resulting in ultra-thin Si crystallites (3.8–4.7 nm). Boron concentration was precisely controlled and quantified using secondary ion mass spectrometry (SIMS). The porosity was varied from ~9% to 61% by adjusting doping concentration and etching conditions. Thermoelectric properties were measured using a custom-fabricated suspended microdevice platform. This platform incorporated multiple radiation shields and high-temperature annealing steps to minimize measurement errors and extend the measurable temperature range. The effective thermal conductivity (κeff), electrical conductivity (σeff), and Seebeck coefficient (S) were measured simultaneously on the same individual nanowire. The effective medium theory was used to account for porosity effects in κ and σ. A detailed explanation of the fabrication and measurement procedures are given in the supplementary information.

The study achieved an average ZT of 0.31 at 300 K and 0.71 at 700 K for single porous SiNWs. This represents an over 18-fold increase compared to bulk Si and more than twice the ZT of any previously reported nanostructured Si-based TE materials at 700 K. The high ZT was attributed to a significant reduction in κ (due to pore boundary scattering), a moderate reduction in σ, and the maintenance of a similar S to bulk Si. The temperature-dependent κeff, σeff, and S were measured for SiNWs with varying porosity, doping concentration, and diameter. Higher porosity generally led to lower κeff, while σeff was strongly influenced by both porosity and doping concentration. The Seebeck coefficient showed an inverse relationship to σeff regarding doping concentration. The SiNWs with a porosity of 46% and boron doping concentration of 2.2 × 10²⁰ cm⁻³ exhibited the highest ZT. The effective thermal conductivity (κeff) was found to be mainly affected by porosity, whereas effective electrical conductivity (σeff) was strongly influenced by both porosity and doping levels. The Seebeck coefficient showed an inverse relationship to effective electrical conductivity in terms of doping concentration. The highest ZT value of 0.71 at 700 K was observed for porous SiNWs with 46% porosity and a boron doping concentration of 2.2 × 10²⁰ cm⁻³.

The experimental findings were supported by theoretical modeling using the Callaway-Holland model for κ and the Boltzmann transport equation for σ, incorporating nanopore boundary scattering. The model accurately predicted the observed trends in κ and σ, showing that κ was primarily influenced by porosity, while σ was sensitive to both porosity and doping concentration. The model also suggested that a ZT of approximately 1 could be achieved at 1000 K, assuming the temperature independence of Z observed at high temperatures is maintained. This implies that the high ZT value in this work is due to the significantly smaller crystallite size (3.8–4.7 nm) of Si compared to other forms of Si, leading to a lower thermal conductivity.

This study demonstrated a significant advancement in high-temperature SiNW-based thermoelectrics. The high ZT values achieved experimentally, combined with theoretical modeling, suggest the potential for efficient waste heat recovery at high temperatures. Future work should focus on validating the predicted ZT of ~1 at 1000 K, requiring the development of new high-temperature materials for the measurement platform. The findings highlight the potential of using nanostructured Si for high-temperature waste heat conversion applications.

The current study was limited by the upper temperature range of the measurement platform using Pt/Cr as the heater and sensors, which become unstable at temperatures above 1000K. The theoretical model, while showing good agreement with experimental data, relied on certain assumptions, such as the relationship between boundary scattering length and V/S, which might not be universally applicable. Further investigation is needed to validate this assumption for other types of porous nanowires and structures.