Microscopic Insight into Enhanced Electron Heat Capacity in Silicon Nanoparticles

We report a strong size dependence in the electronic heat capacity of silicon nanoclusters, tracing its origin to the distinctive electronic structure of surface atoms. By combining ab initio calculations with machine-learned local density of states and exploiting the extensivity of heat capacity, we develop a computational framework that resolves individual atomic contributions to the electronic heat capacity of silicon nanoparticles ranging from 1 to 100 nm. Deviating significantly from bulk behavior, atomic heat capacity increases by up to an order of magnitude for the undercoordinated surface atoms. Our analysis reveals that a surface layer approximately 3-4 Å thick-independent of structural order and cluster size-exhibits a distinct electronic density of states and dominates the electronic heat capacity as the cluster size decreases. The nonlinear temperature dependence is mainly governed by this surface layer. This work bridges the atomic-scale electronic structure with nanoscale thermal phenomena, resolving the microscopic mechanism behind a key thermodynamic property in silicon nanostructures. The future extension to the vibrational contribution and to other materials and surface states remains an open challenge for a comprehensive description of atom-scale thermal properties in nanostructures.