Thermionic Generators with Linear and Non-linear Electron Dispersion Relations: Chances and Limits

Direct heat to electricity energy conversion by use of thermionic electron emission from hot elec-trodes is a long standing issue; however, it suffers from several shortcomings. In this work, a thermionic theory for general electron dispersion relations E(k), relating electron wave number k to its energy in the electrode-material and depending only on the magnitude of wave-vector k, will be presented. The theory does not require the construction of a model-Hamiltonian for the electrode's materials. Instead use is made of band-structure data, as e.g. the parabolic E(k) ap-proximation for the Richardson-Dushman equation and linear E(k) as used for Dirac semimetals. The new theory confirms previous findings on parabolic E(k), e.g. that the emission current is independent of effective electron mass in the material as long as it is larger than the electron mass m0. For effective mass lower than m0 , the emission is reduced and tends to zero for vanishing effective mass. It turns out that linear E(k) dispersion for the Dirac semimetals, does not have the potential to surpass Richardson emission. Also, a more rigorous electron emission theory is established by utilizing the real anisotropic band-structure data En(k) of a periodic crystal elec-trode-material. However, the theory is incomplete, for lack of a general theory relating the elec-tron's wave-numbers transverse to the 1D electric field in the vacuum to the wave-numbers in the material which are integrated over. In the special case of collimated electron emission normal to the surface, the transverse wave-numbers can be set to zero, i.e. the transverse derivatives of En(k) disappear or are very small. It is not known, whether such electrode-materials can exist. If so, a considerable increase of electron emission is possible compared to the Richardson- Dush-man theory, especially for small lattice constants perpendicular to emission direction. For realistic values, an increase of the emission current by a factor 100 or more can be achieved. The new findings may pave the way for optimized material design with respect to thermionic emission.