# Thermoshape effect for energy harvesting with nanostructures

## TL;DR

This paper introduces the thermoshape effect, a shape-dependent thermoelectric phenomenon in nanostructures, demonstrating its potential for energy harvesting and highlighting the significance of geometry in nanoscale thermoelectric devices.

## Contribution

It presents the first theoretical analysis of the thermoshape effect, showing how shape alone influences thermoelectric transport in nanostructures and proposing a potential device application.

## Key findings

- Thermoshape voltage is on the order of mV/K in non-degenerate regimes.
- Voltage oscillates around zero in weakly degenerate regimes.
- Geometry significantly impacts thermoelectric properties at the nanoscale.

## Abstract

We propose a mechanism for nanoscale energy conversion, an electric voltage induced by a temperature gradient in a junction composed of the same material having exactly the same geometric sizes, but distinct shapes. The proposed effect appears as a result of only temperature and shape difference, hence it is called thermoshape effect. For GaAs quantum confined semiconductor nanostructures, we first introduce the existence of quantum shape effects on thermoelectric transport coefficients at ballistic regime. We show that the shape alone enters as a control parameter on transport properties of confined nanostructures. The thermoshape voltage is then calculated by using the Landauer formalism. Our calculations show that the thermoshape voltage has a constant value in the order of mV/K for the variation of chemical potential in non-degenerate regime and it decreases rapidly after entering weakly degenerate regime where it oscillates around zero within plus/minus 10$\mu$V/K magnitude. A persistent voltage range may pave the way for easier experimental demonstration of the effect. Our work explicitly shows how important the effect of overall geometry is in nanoscale thermoelectric materials, and can be utilized even if all sizes are the same. A thermoshape junction not only represents a viable setup for the macroscopic manifestation of quantum shape effects, but also constitutes their first possible device application.