Physical Theory of Semiconductor Surfaces

Abstract

The properties associated with the space-charge region and with surface states at a semiconductor surface are discussed. A theory of the space-charge region that takes into account charge-densities arising from immobile impurities and from both signs of mobile carrier is presented. The properties of the space-charge are discussed in terms of the surface potential and of the electrochemical potentials of holes and electrons, and related to the transport of added carriers in a homogeneous semiconductor. The change in surface conductivity arising from nonvanishing surface excesses of holes and electrons is treated. The space-charge systems at a free surface and at a p-n junction are compared, and the range of validity of the Mott-Schottky space-charge theory evaluated. The arrangement of surface states is discussed with reference to the Brattain-Bardeen model. Theories for the surface photoeRect and field-effect experiments are given, with and without surface states: it is concluded that the existence of surface states is without gross effect on the former, while relevant quantitative evidence from the latter is not yet available. The question of the relation between surface potential and contact potential is discussed. The properties of "channels" are discussed in terms of the theory. The paper concludes with a short section on long-time effects.

Surface photovoltage phenomena: theory, experiment, and applications

“…This condition is quite easily satis®ed in many materials of reasonable quality. Second, the defect-related recombination current must not be`too large' nor the depletion of carriers`too extreme' [3]. The latter conditions assure that even if J n , J p are not zero, the variation in the quasi-Fermi levels, F n and F p , given by [see Eq.…”

“…In 1955, Garrett and Brattain have published a classic paper [3], where a ®rst serious attempt was made at a comprehensive theory of semiconductor surfaces, including surface photovoltaic effects. They suggested that under certain conditions, the quasi-Fermi levels may be approximated as positionindependent (i.e.,`¯at') throughout the surface SCR.…”

“…In the earliest studies [2,3] it was assumed that the surface states were in equilibrium with the semiconductor bands, i.e., that Fermi±Dirac statistics [Eq. (2.11)] adequately described the surface state population even under non-equilibrium conditions.…”

dc-electric-field-induced second-harmonic generation in Si(111)-SiO2-Cr metal-oxide-semiconductor structures

“…Since the experimental bias dependences were measured vs applied voltage, we should rescale the bias voltage units to the interface electric-field ones. To find the chromium electrode potential (ϪL d ) with respect to the Si bulk ͑the latter is supposed to be neutral͒, one should solve the Poisson equation with the appropriate boundary conditions 24 in the one-dimensional geometry presented in Fig. 3, in the range of ϪL d ϽzϽϩϱ.…”

Tunneling spectroscopy on semiconductors with a low surface state density

“…However, on semiconductors with a low surface state density, such as H-terminated Si, cleaved GaAs͑110͒ or the layered materials WSe 2 and WS 2 , the situation is far more complex, since the applied tunneling voltage and the work function difference between the tip and the sample lead to an additional bandbending at the semiconductor surface and nonequilibrium effects need to be considered. [5][6][7][8][9][10][11][12][13][14] In a one-dimensional model the bandbending in a metalinsulator-semiconductor ͑MIS͒ diode was first determined by Garret and Brattain 15 and Kingston and Neustadter 16 by integrating the Poisson equation, including accumulation, depletion and inversion at the semiconductor surface. For a known bandbending the tunneling current can then be calculated using a tunneling theory for a MIS diode.…”