Thermionic refrigeration in low-dimensional structures

The Richardson equation for thermionic emission is generalised to ND systems. An equation for thermionic emission heat current and an analytical expression for the coefficient of performance of ND thermionic refrigerators are also provided. It is found that when heat backflow is very small, lower-dimensional thermionic refrigerators outperform higher-dimensional systems. Conversely, when heat current backflow is significant, higher-dimensional thermionic refrigerators achieve higher COPs.