Density of gap states

In the early 1970s, Spear and coworkers (Spear, 1974 Le Comber et al., 1974), although unaware of the presence of hydrogen, demonstrated a substantial reduction in the density of gap states (with a corresponding improvement in the electronic transport properties) in amorphous silicon films that were deposited from the decomposition of silane (SiH4) in an rf glow discharge. 

Lang, D. V. et al., Amorphouslike density of gap states in single-crystal pentacene, Phys. Rev. Lett., 93, 086802, 2004. 

Fig. 1. Depletion region under equilibrium conditions for a material with a continuous density of gap states. The charge density is related to an integral involving the amount of band bending at each point x as indicated. The definition of various symbols is given in the text.

Compared to field effect, the analysis of low frequency capacitance versus voltage measurements to yield a density of gap states in a-Si H is rather straightforward. Such stupes were first presented by Dohler and Hirose... 

Hopping near the Fermi level needs a high density of gap states, i.e., Affph is expected to be low the presence of an accumulation layer, on the other hand, generally indicates a low density of gap states, i.e., may attain rather high values. 

Thus P approximately equals unity if the Fermi level lies far below the centroid of the donor distribution. In a crystalline semiconductor with a low density of gap states, donor levels deliver their electrons directly into the conduction band. In an amorphous semiconductor, the situation usually is different (Spear and LeComber, 1975, 1976) Most of the electrons will condense into empty states near the Fermi level. Let Anb be the concentra-... 

The surface chemistries of a-Si and c-Si are very similar. A major difference arises from the presence of hydrogen in a-Si H, which saturates most dangling bonds, reduces the surface reactivity, and affects the oxidation process. The experimental determination of the surface-state density has been much more successful with c-Si than with a-Si H, however, because of the much lower density of gap states in c-Si. We shall compare results on crystalline and amorphous Si surfaces in the following. 

The analysis of the capacitance data thus is dependent on the gap-state densities and the barrier profiles. An analysis method described by Snell et al. (1979) used measured values of the density of gap states to determine the field profile in the depletion region. Other investigators have used the C-V results to derive the density of gap states in differently prepared a-Si H (Viktorovitchand Jousse, 1980 and Femandez-Canque eta/., 1983). These results are discussed in more detail in Chapter 2 by Cohen. 

The values of the best fit parameters are < o 1-0 e V and x = 300 A. This value for Xn corresponds to a bulk density of states of 7 X 10 cm eV" or, equivalently, to 10 cm" eV states per interface. This density of states is more than sufficient to pin the Fermi level in high-quality a-Si H, where the density of gap states in the upper half of the gap is < 10 cm eV. The fit, shown in Fig. 12, is excellent given the range of samples covered and the expected sensitivity of the band bending at the substrate interface to substrate preparation conditions. 

The new transfer doping mechanism produces conductive material with a lower density of gap states than phosphorus-doped material of comparable resistivity, where the substitutional dopant always introduces extra defect states. Evidence for the lower density of defects comes from the magnitude of the low energy shoulder in the photoconductivity response spectrum shown in Fig. 14, where the absorption of the layered material at photon energies below 1.4 eV is more than an order of magnitude lower than the phosphorus-doped material of comparable dark resistivity. Furthermore, the photoconductivity of the transfer-doped material is large (10 Q cm ) compared with the photoconductivity achievable in heavily P-doped material under similar illumination. 

X lO cm". There is considerable evidence that the density of gap states far exceeds this number. We therefore conclude that the position of Epis not determined by Eq. (5.22) but by the distribution and occupation of localized gap states. These localized gap states may very well be inherent to the NCS and thus one of the intrinsic properties. However, it is better to refer to Eq. (5.22) as the condition for intrinsic conduction because a NCS can exist in many structural states and there is no way to operationally define the distribution of localized states which is inherent to the material. 

The space charge regions in NCS are only a few hundred Angstrom units wide when they contain a large density of gap states near the Fermi level. This width, however, seems still too large to explain the frequent occurrence of low contact resistance and small rectification ratios in medium band gap amorphous semiconductors. 

Can we estimate the density of localized gap states Their presence is noticed in measurements for instance of drift mobility, photoconduction, (Arnoldussen, Bube, Fagen and Holmberg (1972a, b)Weiser(1972)), thermo-stimulated currents (Kolomiets and Mazets (1970)), recombination radiation (Kolomiets, Mamontova, and Babaev (1970)), and high field conduction. A density of gap states cannot be obtained from these experiments though, without having values for the appropriate trapping and recombination cross sections. 

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