Surface state density

Under Httle or no illumination,/ must be minimized for optimum performance. The factor B is 1.0 for pure diffusion current and approaches 2.0 as depletion and surface-mode currents become important. Generally, high crystal quality for long minority carrier lifetime and low surface-state density reduce the dark current density which is the sum of the diffusion, depletion, tunneling, and surface currents. The ZM product is typically measured at zero bias and is expressed as RM. The ideal photodiode noise current can be expressed as follows ... 

These authors provided further evidence in support of their conclusions by performing TCV experiments on n-GaAs samples that had been treated with (a) RuC13 and (b) ammonium sulphide. Ru is known to increase the surface state density and sulphur is known to remove surface states. 

In cases in which the surface state density is high Nc/i,Nm, Ny/i,Nm - 1), electron distribution in the siuface state conforms to the Fermi function (the state of degeneracy) and the Fermi level is pinned at the surface state level. This is what is called the Fermi level pinning at the surface state. 

The potential i sc of the space charge layer can also be derived as a fixnction of the surface state charge Ou (the surface state density multiplied by the Fermi function). The relationship between of a. and M>sc thus derived can be compared with the relationship between and R (Eqn. 5-67) to obtain, to a first approximation, Eqn. 5-68 for the distribution of the electrode potential in the space charge layer and in the compact layer [Myamlin-Pleskov, 1967 Sato, 1993] ... 

Simple calculation gives a comparable distribution of the electrode potential in the two layers, (64< >h/64( sc) = 1 at the surface state density of about 10cm" that is about one percent of the smface atoms of semiconductors. Figure 5—40 shows the distribution of the electrode potential in the two layers as a function of the surface state density. At a surface state density greater than one percent of the surface atom density, almost all the change of electrode potential occurs in the compact layer, (6A /5d )>l, in the same way as occurs with metal electrodes. Such a state of the semiconductor electrode is called the quasi-metallic state or quasi-metallization of the interface of semiconductor electrodes, which is described in Sec. 5.9 as Fermi level pinning at the surface state of semiconductor electrodes. 

Fig. 5-57. Surface states in the band gap of semiconductors Z> = surface state density.

Electron-hole recombination velocities at semiconductor interfaces vary from 102 cm/sec for Ge3 to 106 cm/sec for GaAs.4 Our first purpose is to explain this variation in chemical terms. In physical terms, the velocities are determined by the surface (or grain boundary) density of trapped electrons and holes and by the cross section of their recombination reaction. The surface density of the carriers depends on the density of surface donor and acceptor states and the (potential dependent) population of these. If the states are outside the band gap of the semiconductor, or are not populated because of their location or because they are inaccessible by either thermal or tunneling processes, they do not contribute to the recombination process. Thus, chemical processes that substantially reduce the number of states within the band gap, or shift these, so that they are less populated or make these inaccessible, reduce recombination velocities. Processes which increase the surface state density or their population or make these states accessible, increase the recombination velocity. 

As an example, let us consider a typical value of the excess surface state density ns = 1012 electrons cm 2 and the bulk density b = 1017 electrons cm 3. This means that for 100 jttm thick film, the sensitivity AGS/Gb = 10-3. However, for d = lOnm the sensitivity is 10 and for thin films (<100nm) the space charge region extends throughout the whole film thickness. 

Other intrinsic characteristic parameters of LAPS have been investigated by different research groups such as the chemical response time, the surface-state densities and zeta potential (for Si3N4), and the minority carrier diffusion length for resolution estimations. For a more detailed description of these experimental set-ups, see, e.g., Refs. [57-61],... 

The relative changes in VH and Vsc as a function of surface state density are shown in Fig. 10.20. At low surface state density (<1012), the potential drop across the Helmholtz layer is small and remains almost constant with a change in electrode potential. However, at high surface state densities (>1013), the potential drop in the Helmholtz region increases and exceeds the potential drop in the space charge region for surface state densities greater than 5 x 1013 cm 2. 

Fig. 10.20. Relative potential drop in the space charge region and in the Helmholtz region as a function of surface state density. (Reprinted from K. Chandresakaran, R. C. Kainthla, and J. O M. Bockris, Elec-trochim. Acta 33 334, Fig. 12, copyright 1988, with permission from Elsevier Science.)...

Calculate the potential difference in the Helmholtz layer in the solution for a semiconductor in which the surface state density is 1014 cm-2 (assume the effective dielectric constant is 6 and the thickness of the double layer 5 A). As an approximation, neglect the contribution due to oriented dipoles of adsorbed water. (Bockris)... 

The activation energy for the 7a Si at room temperature is 0.41 eV. This suggests that the shallow surface states have been largely eliminated by hydrogenating the c-Si surface. The log 7a Si versus 1 IT curve becomes linear at T a 150°C here 7sa = 1.05 eV, which is close to the band-gap value of c-Si. For 7ox, however, no such linearity is reached up to 200°C, beyond which a = 0.95 eV. This is another indication that the 7 and 7t components are much larger in 7ox than in 7a si. Therefore one can conclude that the a-Si H passivation has reduced both die deep surface state and the shallow surface state densities. 

Fig. 8.14. Theoretical plots showing competition between recombination and current doubling. Calculated for a surface state density of 5 x 10,2cm "2. The surface state is located 0.3eV below the bulk Fermi level. Donor density 1.5 x I0,ftcm. Arinj 5 x 104s" rccn = 2 x 10 7 s. Band bending values (a) 0.40 eV, (b) 0.35 eV, (c) 0.30 eV, (d) 0.2 eV. Note the transition in the IMPS response from current from current doubling control at 0.4 eV to...

The surface states are detected by ESR, PDS and photoemission experiments. In the first two cases, the surface state density is deduced from the thickness dependence of the defect density (Jackson, Biegelson, Nemanich and Knights 1983). When there are cm surface states and Njj cm bulk states, then the total number of defects in a film of thickness d, is... 

Table 7.1 Effective work functions and surface-state densities of polymers.

Polymer Work function, Wi(eV) Surface-state density, Ds (eV-1m-2xlO-16)... 

Fig. 7.18 Energy level diagrams for two different insulators, before and after contact in the two limiting cases (a) low surface state densities and (b) high surface state densities.

Quantitative calculations of the number of surface states that are needed to achieve Fermi level pinning will not be described here. However, such calculations show that even surface state densities as low as 10% of a monolayer (10 states cm ) can provide sufficient charge to induce complete... 

Lower surface state densities will, of course, produce less of a Fermi level pinning effect. This will result in an increased sensitivity of Vbi to changes in A quantitative measure of the degree of ideality of a junction can be obtained by plotting changes in Vpi (or [Pg.4351]

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