Space charge surface potential

Perhaps the two most frequently measured electrical properties in surface science are the surface space charge potential Pdipoie the related work function . 

A more realistic model will take full account of the atomic nature of the surface and yield charge densities and electronic potentials similar to those obtained by the jellium model. In this circumstance, however, the charge density on the solid side of the surface exhibits fluctuations that are often called Friedel oscillations and which are due to the screening by the free electrons (Figure 5.1). The amplitude of this oscillation is a sensitive function of the electron density, as are the height and extent of the surface space-charge potential. 

Gas adsorption on insulator or semiconductor surfaces can cause very large changes in the height of the surface space-charge potential and its Debye length. As... 

If, on the other hand, the field forces the mobile holes away from the surface, a space charge region consisting of the ionized acceptor atoms, which are fixed in the lattice, forms over an appreciable distance into the semiconductor. The thickness of the surface space charge region is a function of the strength of the field at the surface and the semiconductor doping profile, as is the difference between the surface potential and the bulk potential of the semiconductor. If the surface potential deviates sufficiently far from the bulk potential, the surface will invert that is, it will contain an excess of mobile electrons. In this case, an -type conductive channel... 

Figure 25. Grain boundary capacitance of a Fe-doped StTiOj polycrystal (rriFe = 6.5 x 10,9cm"3), normalized to the electrode surface and measured at various oxygen partial pressures as a function of reciprocal temperature.100 Typical space charge potentials vary between 300 and 800 mV. (Reprinted from I. Denk, J. Claus and J. Maier, Electrochemical Investigations of SrTiOj Boundaries. J. Electrochem. Soc. 144, 3526-3536. (Copyright 1997 with permission from The Electrochemical Society, Inc.)...

Figure 5.36 Model of a solid plate of photocatalyst of thickness 2d irradiated uniformly from both sides (1). The graph also defines the surface potential U, and the width of the near-surface space charge region 6. Reprinted with permission from Emeline et al. (2003). Copyright (2003) American Chemical Society.

The electrode potential where the space charge potential becomes zero is called the flat band potential, E. The space charge is positive at electrode potentials more positive (i.e., more anodic) than Efo, and it is negative at electrode potentials less positive (i.e., more cathodic) than E. In fact, the space charge potential, ASC, is defined by the difference between the band edge level in the semiconductor interior and that at the semiconductor surface. Since the Fermi level is not allowed to move out of the band gap, the space charge potential always amounts to less than the band gap of the semiconductor. 

Since cGe4+ is one fourth the surface hole concentration, Chs, due to the electrical charge balance (cGe4+ = 4chs), the surface ion concentration, cGl,4, is described as a function of both the space charge potential, Acj>sc, and the hole concentration, cj[, in the bulk of the semiconductor ... 

The magnitude of the space-charge potential is closely dependent on the local structure of the surface, as will be discussed in relation to work function measurements. In the... 

When two different metal surfaces are brought into contact, the surface space charges that were present at their interfaces with a vacuum will be modified. The electrons from the metal of lower work function will flow into the other metal until an interface potential develops that opposes further electron flow. This is called the contact potential and is related to the work-function difference of the two metals. The contact potential depends not only on the materials that make up the solid-solid interface but also on the temperature. This temperature dependence is used in thermocouple applications, where the reference junction is held at one temperature while the other Junction is in contact with the sample. The temperature difference induces a potential (called the Seebeck effect), because of electron flow from the hot to the cold Junction, that can be calibrated to measure the temperature. Conversely, the application of an external potential between the two Junctions can give rise to a temperature difference (Peltier effect) that can be used for heat removal (refrigeration). 

Poeppel, R. B. and Blakely, J. M., Origin of equilibrium space charge potentials in ionic crystals. Surface Sci., 15, 507-23, 1969. 

Figure 17.2 Ratio of depletion length to Debye length versus space charge potential at a depleted surface or interface. Note, zj= 1 and T=300K.

The space charge potential at the silver chloride-aqueous solution interface can be derived from thermodynamic arguments following the concept of Grimley and Mott with the assumptions that the phase boundary potential X remains constant and that there are no adsorbed surface charges. For the silver chloride-aqueous solution system the silver ion is the most mobile one in the solid and is therefore the potential-determining ion. Let and be the electrochemical potentials of the silver ion in the solution and in the crystal, respectively. Assuming ideal solutions. 

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