“…This contradiction, which is sometimes termed as "the current paradox" in the literature 18 and which traces back to some fundamental problems of Quantum Mechanics, 19,20 was already given several elaborated solutions for particular cases. 16,[21][22][23][24] In the present article, we will take a different simpler approach: as it is clear that Eqs. ͑7͒…”
The article presents a quantum mechanical model for the electron field emission from semiconductor surfaces covered by dielectric layers. By systematically connecting electronic wave functions at various interfaces, the model obtains in a unified manner the field emission current density from both clean and dielectric-covered semiconductor substrates. No energy quantization is imposed for the interface layer and thermodynamic nonequilibrium is allowed between the conduction electrons from the interface (accumulation) layer and those of the bulk. The model is applied to study the electron field emission from Si tips covered by ultrathin oxide layers and also to explain the resonance effects observed in field emission from Si covered by thicker dielectric layers.
“…This contradiction, which is sometimes termed as "the current paradox" in the literature 18 and which traces back to some fundamental problems of Quantum Mechanics, 19,20 was already given several elaborated solutions for particular cases. 16,[21][22][23][24] In the present article, we will take a different simpler approach: as it is clear that Eqs. ͑7͒…”
The article presents a quantum mechanical model for the electron field emission from semiconductor surfaces covered by dielectric layers. By systematically connecting electronic wave functions at various interfaces, the model obtains in a unified manner the field emission current density from both clean and dielectric-covered semiconductor substrates. No energy quantization is imposed for the interface layer and thermodynamic nonequilibrium is allowed between the conduction electrons from the interface (accumulation) layer and those of the bulk. The model is applied to study the electron field emission from Si tips covered by ultrathin oxide layers and also to explain the resonance effects observed in field emission from Si covered by thicker dielectric layers.
“…In principle, proper determination of the electronic structure requires large calculations for self-consistently solving the Poisson-Schrödinger equations [10,11]. Recently, King et al adopted the modified ThomasFermi approximation (MTFA) proposed by Übensee et al [12] (see Appendix B) to reduce the computational time and to reproduce their angle-resolved photoelectron spectroscopy (ARPES) results [13].…”
“…This is formulated as a 1D self-consistent PoissonSchrödinger problem. The problem has been solved iteratively [21][22][23][24] and also using the modified Thomas-Fermi approximation (MTFA) [25][26][27][28]. These two strategies have been found equivalent [26,29].…”
Two-dimensional electron gases (2DEGs) at surfaces and interfaces of semiconductors are described straightforwardly with a one-dimensional (1D) self-consistent Poisson-Schrödinger scheme. However, their band energies have not been modeled correctly in this way. Using angle-resolved photoelectron spectroscopy we study the band structures of 2DEGs formed at sulfur-passivated surfaces of InAs(001) as a model system. Electronic properties of these surfaces are tuned by changing the S coverage, while keeping a high-quality interface, free of defects and with a constant doping density. In contrast to earlier studies we show that the Poisson-Schrödinger scheme predicts the 2DEG band energies correctly but it is indispensable to take into account the existence of the physical surface. The surface substantially influences the band energies beyond simple electrostatics, by setting nontrivial boundary conditions for 2DEG wave functions.
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