The Surface Space Charge

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

1 The Surface Space Charge at the Solid-Vacuum Interface 

This distance is called the Debye length. It measures the penetration depth of the electrostatic surface effects. 

Thus the higher the free-carrier concentration in the material, the smaller the penetration depth of the applied field into the medium. For electron concentrations of 10 cm (10 m ) or larger, the space charge is restricted to distances on the order of one atomic layer or less, because the large free-carrier density screens the solid from the penetration of the electrostatic field caused by the charge imbalance. For most metals, almost every atom contributes one free valence electron. Because the atomic density for most solids is on the order of 10 cm (10 m ), the free-carrier concentration in metals is in the range of 10 -10 cm (10 -10 m ). Thus Fv and d are small. For semiconductors or insulators, however, typical free-carrier concentrations at room temperatures are in the range of cm lO - 

10 m ). Therefore, at the surfaces of these materials, there is a space-charge barrier of appreciable height and penetration depth that could extend over thousands of atomic layers into the bulk. This is the reason for the sensitivity of semiconductor devices to ambient changes that affect the space-charge barrier height. 

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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... 

In the discussion of the surface space-charge region, the idea of electrons spilling out or tunneling out of the solid into vacuum was presented. While the phenomenon has been understood within the solid state physics community for many years, it has recently received a much broader exposure in the context of scanning tunneling microscopy (STM). In STM, a very sharp tip is brought within close proximity (a... 

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. 

So far we have only considered the properties of the surface space charge at the solid-vacuum interface. Let us now immerse the solid into a liquid. The molecules in the liquid adsorb onto the solid surface and become polarized as they respond to the electrical field at the interface to produce an electrochemical double layer. They may also line up in preferential bonding directions if they possess a permanent dipole... 

The opposite situation from weak interaction of inert gases with the surface space charge is surface ionization, when the adsorbate is ionized by the substrate. This typically occurs in alkali-metal adsorption on transition-metal surfaces. In the more usual situation with chemisorbed molecules, only partial charge transfer occurs to or from the substrate to the molecule. If the negative pole of the molecule points toward the vacuum, the induced electric fields cause an increase in the work function. Table 5.4 lists the work-function changes obtained by the chemisorption of several molecules on rhodium. 

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... 

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). 

Since the SPV method has been intensively used for diffusion length measurement in undoped a-Si H, we shall discuss the theory of the method in some detail. The approach is to contrast and compare the theory to that already given for conventional semiconductors. The differences arise from two basic facts (1) Undoped a-Si H is a photoconductive semi-insulator rather than an extrinsic semiconductor (2) The thickness of the surface space-charge region (the surface barrier) may be comparable to the diffusion length, whereas in the SPV theory for conventional semiconductors it is assumed that W c Lp. 

The second difference, the incompatibility of the surface space-charge width and, is resolved by changing the model (Moore, 1983). We assume the sample to be one-dimensional and semi-infinite, divided into the space-charge region 0[Pg.245]

If W/L and a IF are both much less than one, then Eq. (8) reverts to Eq. (6) (except for the definition of Lq). These are just the conditions that make the surface space-charge region negligible with respect to the diffusion length. 

Wei, C. C. Ma, T. R. 1984. Reduction of apparent dopant concentration in the surface space charge layer of oxidized silicon by ionizing radiation. Applied Physics Letters, 45(8) 900 1.95407(1-3). 

As shown in Fig. 2.7, the upward band bending in the case of p-type MOXs determines the formation of an accumulation layer for holes. Accordingly, the conductivity in the surface space charge layer increases in comparison with the bulk, and conduction takes place differently compared with that described by the depletion layer. The current will now flow through the accumulation parallel to the surface and also through the bulk this situation can be described by two resistors in parallel. The latter contribution from the... 

Now, the integral in Equation [2.8] can be calculated by changing the variables and by using Equation [2.10]. For the average concentration of holes in the surface space charge layer, one obtains ... 

The experimental conductance and capacitance Cm as a function of at a frequency of 50 cps and for a silver chloride crystal 0.01 cm thick are shown in Figs. 9 and 10. Above 1000 cps the conductance and capacitance are dependent on frequency, but are constant with within experimental accuracy, the value at 1592 cps being 3.1 Xl0 ohm" and 5.5 X 10" F, respectively. The two space charge regions and the bulk region in the silver chloride crystal can be represented by an equivalent electrical circuit shown in Fig. 11, where Rg and Cs represent the surface space charge region and R and Cg the bulk crystal. We assume that the electrode-solution interface, the solution, and the crystal-solution interface do not contribute to the measured Rm and Cj. ... 

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