Semiconductor total charge density

Fig. 17. Diagram in

Note that the energy of an electron is related to its potential by = —e(j) and that the potential in the bulk of the semiconductor is conveniently chosen as zero (see Fig. 2.12). Since the bulk is electrically neutral, its electron concentration, rib, niust be equal to the number of ionized donors. The latter are assumed to be fully ionized, so that Np = No = b Combining this with (2.31) and (2.32), the total charge density at point x can be written as... 

Fig. 15. Total valence electron charge density for the Si(111)-(lxl) surface. A (110) plane is shown with the top of the diagram representing the semiconductor surface. The cores are shown as shaded discs, and heavy lines represent bonds. Charge density contours are normalized to e/fi where is the bulk unit cell. (from Ref. 53) ... 

Figure Bl.22.4. Differential IR absorption spectra from a metal-oxide silicon field-effect transistor (MOSFET) as a fiinction of gate voltage (or inversion layer density, n, which is the parameter reported in the figure). Clear peaks are seen in these spectra for the 0-1, 0-2 and 0-3 inter-electric-field subband transitions that develop for charge carriers when confined to a narrow (<100 A) region near the oxide-semiconductor interface. The inset shows a schematic representation of the attenuated total reflection (ATR) arrangement used in these experiments. These data provide an example of the use of ATR IR spectroscopy for the probing of electronic states in semiconductor surfaces [44]-...

Let d be the thickness of a monolayer and n the total number of layers (that is, the thickness of the film divided by d). The layers are numbered starting from the insulator-semiconductor interface. To estimate the density n (per unit area) of charge-carriers in the ith layer we apply Gauss s law to a cylinder of unit cross section limited by the boundaries between the ith layer and each of its neighboring layers. For a long channel device, the electric field F is perpendicular to the film, and we have ... 

It is common to treat the semiconductor-electrolyte interface in terms of charge and current density boundary conditions. The total charge held within the electrolytic solution and the interfacial states, which balances the charge held in the semiconductor, is assumed to be constant. This provides a derivative boundary condition for the potential at the interface. The fluxes of electrons and holes are constrained by kinetic expressions at the interface. The assumption that the charge is constant in the space charge region is valid in the absence of kinetic and mass-transfer limitations to the electrochemical reactions. Treatment of the influence of kinetic or mass transfer limitations requires solution of the equations governing the coupled phenomena associated with the semiconductor, the electrolyte, and the semiconductor-electrolyte interface. 

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