Charge state entropy and heat capacity of quantised states in a dopant atom quantum dot single-electron transistor

The dependence of the entropy and heat capacity on applied drain and source bias and temperature in a few-nanometre-scale dopant atom quantum dot (QD) single- electron transistor (SET) has been investigated theoretically. In this system, the quantisation energy is comparable to the Coulomb charging energy. To make this study relevant, we choose energy scales matching experimental work on dopant atom QD SETs capable of room-temperature operation. The entropy of both a single QD, and double QDs, is investigated, where the latter provides additional information for a simple multiple QD system. Energy state diagrams are used to explain resonant tunnelling features in the Coulomb diamond plot and the Gibbs entropy S. For well-defined states within Coulomb diamonds, if spin is neglected, S tends to 0 at low temperature. In contrast, at finite drain bias, electron transport via higher energy quantised states increases their occupation probability, significantly perturbing S. Within regions of constant average current, the entropy reaches a maximum Smax = kB ln⁡M, for M ‘effective’ states. The single-electron heat capacity is extracted, using S vs. temperature plots. A Schottky anomalous heat capacity-like peak occurs, linking single-particle dynamics to macroscopic, many-particle behaviour.