Efficiency of ideally filtered thermionic devices
It has long been known that thermionic devices may be used for power generation. Thermionic refrigeration was first suggested by Mahan using vacuum based devices, however, it was stated that such devices would not be useful for room temperature applications due to the low work functions required. It was then suggested that such small barrier heights may be achieved using semiconductor heterostructures and later, that highly-efficient devices could be constructed using multilayer structures. Successful thermionic cooling has been reported by Shakouri et al. using a single barrier InGaAsP based structure and by LaBounty et al. using a 25-barrier InGaAsP based multilayer system. The reported cooling in both instances was about one degree.
A thermionic device consists of two electron reservoirs separated by a barrier system, such as a single-barrier or multiple-barrier semiconductor nanostructure. Electrons may travel from one reservoir to the other due to thermal excitation. The system will behave as either a heat engine or refrigerator depending on the bias on the system. If the mean free path of an electron in the system is greater than the separation of the reservoirs then electron transit will be ballistic. For such ballistic travel a quantum-mechanical transmission probability function may be calculated which defines the probability of an electron with a particular energy traversing the system between the reservoirs. Thus, the system between the reservoirs forms an energy filter which may be designed so as to favourably engineer the energy spectrum of transmitted electrons. In a general semiconductor thermionic device, which is translationally invariant in the y and z directions, electron energies will be filtered in the direction of transport, x, only. We shall denote this as a 'kx filtered thermionic device'. We shall compare this to a theoretical one-dimensional thermionic device which has been previously investigated.
In this paper we shall examine the ‘electronic efficiency’, which is the efficiency due to electronic processes only. It has been shown for a one-dimensional system that the Carnot efficiency may be achieved with ideal filtering, that is, when electrons of only a single energy are transmitted between the reservoirs. Here it is shown that a three-dimensional kx filtered thermionic device does not achieve Carnot efficiency for arbitrary reservoir electrochemical potentials.