A generalized analytical method to determine the density of energy states of electron emission source (EES) is devised by using a thermal excitation and emission model for an exoelectron in the MgO layer and the emission time constants of the exoelectron extracted from experimental stochastic distributions of discharge delay time. When applied to Si-doped MgO, the emission time constant of the exoelectron from the Si EES becomes shorter at high temperature and at short time intervals due to thermal excitation. The density of energy states of the Si EES DSi(E) shows the main peak at 736 meV, a satellite peak at 601 meV, and broad energy structures over the range of 586–896 meV. The effective number of Si EES is 5.5 times larger than that in purified MgO. The excitation energy in a Si-doped MgO cluster with a crystal structure is obtained to be 0.83 eV by using the symmetry-adapted-cluster configuration interaction method and the Si EES contributes to exoelectron emission. The thermal excitation is governed by the transition from the Si–O bound state and the Mg edge state to the antisymmetrical edge states and the extended surface state. The excitation energy in an MgO cluster with a Si-doped atom inside and a nearest oxygen vacancy taking account of structural relaxation is calculated to be 0.75 eV, which shows good agreement with the main peak in DSi(E). The excitation energies of 0.64, 0.73, and 0.78 eV are also obtained in an MgO cluster with a Si-doped atom at the surface and a nearest oxygen vacancy. The first excitation energy corresponds with the satellite peak. The broad energy structures of DSi(E) are caused by the dependence of excitation energy on the position of Si-doped atoms inside and at the surface of the MgO cluster, and on the interatomic distance of Si–O due to structural relaxation. The energy structures can be also attributed to the thermal excitation to the various symmetrical Mg edge states and the surface states. When the number of complex structures of the Si EES with adjacent oxygen vacancies increases, oxygen vacancies are generated from the complex structures and the increase in the electron traps degrades electron emission rate. Therefore, the number of complex structures has an optimum value that leads to the maximum effective number of Si EES.
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