COMSOL Modeling of GNR Quantum Heat Engine
Quantum heat engines (QHEs) perform a thermodynamic cycle by exchanging heat between a hot and a cold reservoir employing quantum systems as the working medium. Such thermoelectric generators could theoretically reach Curzon-Ahlborn efficiency due to the excellent properties of the quantum dots (QDs) as energy filters [1]. To allow the heat engine to operate up to higher temperatures, the addition energies of QDs must be large. Graphene nanoribbons (GNRs) could be suitable for such an operation allowing the engineering of the band gap by chemical design.
The experimental realization of efficient QHEs necessitates precise control over the device's thermal and electrostatic environment. For a GNR based QHE, the design challenge is to engineer and quantify two critical aspects: firstly, the generation of a temperature gradient (ΔT) between the hot and cold reservoirs, and secondly, the ability to electrostatically tune the energy levels of the GNR quantum dot (QD). The COMSOL Multiphysics® software was utilized to address coupled electro-thermal and electrostatic physics. The model setup consists of a 3D geometry of the quantum heat engine. The Electric Currents (ec) module was applied to simulate current flow through the micro-heater from an applied AC current. This choice mimics the experimental procedure, where the thermoelectric current between source and drain electrodes is extracted by demodulating the electrical signal at the second harmonic (2ω) of the heating frequency (ω) using a lock-in amplifier [2]. This was directly coupled with the Heat Transfer in Solids (ht) module via the built-in Joule Heating multiphysics node. Boundary conditions were established to define the external faces of the substrate as thermal sinks at room temperature. For the electrostatic analysis, the AC/DC Module's Electric Currents (ec) was used to model the gate electrostatic effect on the device. By applying a voltage to the gate terminal, the resulting potential landscape through the gate-oxide layer and for different materials was simulated.
The electro-thermal model yields a detailed temperature map of the device under operation (Fig. 1), allowing for the extraction of the achievable ΔT as a function of the amplitude and the frequency of the applied AC current up to the point at which the frequency is too high for the device to thermalize, due to self-heating effects. The electrostatic simulation provides the potential profile in the vicinity of the nanogap between the needle-shaped electrodes (Fig. 2) and allows for the extraction of the gate coupling parameter. This simulation work establishes a robust and validated workflow for designing the core components of a GNR QHE. This framework informs the device fabrication strategy, mitigates challenges in the experimental phase, and provides the necessary inputs for quantum transport models that predict the thermoelectric performance and efficiency of the heat engine.
