An elementary empirical model for the distribution of electronic states of an amorphous semiconductor is presented. Using this model, we determine the functional form of the optical absorption spectrum, focusing our analysis on the joint density of states function, which dominates the absorption spectrum over the range of photon energies we consider. Applying our optical absorption results, we then determine how the empirical measures commonly used to characterize the absorption edge of an amorphous semiconductor, such as the Tauc gap and the absorption tail breadth, are related to the parameters that characterize the underlying distribution of electronic states. We, thus, provide the experimentalist with a quantitative means of interpreting the physical significance of their optical absorption data.

The relationship between the distribution of electronic states and the optical absorption spectrum of an amorphous semiconductor: An empirical analysis

This Perspective reviews recent developments in experimental techniques and conceptual methods applied to the electrochemical properties of metal-oxide semiconductor nanostructures and organic conductors, such as those used in dye-sensitized solar cells, high-energy batteries, sensors, and electrochromic devices. The aim is to provide a broad view of the interpretation of electrochemical and optoelectrical measurements for semiconductor nanostructures (sintered colloidal particles, nanorods, arrays of quantum dots, etc.) deposited or grown on a conducting substrate. The Fermi level displacement by potentiostatic control causes a broad change of physical properties such as the hopping conductivity, that can be investigated over a very large variation of electron density. In contrast to traditional electrochemistry, we emphasize that in nanostructured devices we must deal with systems that depart heavily from the ideal, Maxwell–Boltzmann statistics, due to broad distributions of states (energy disorder) and interactions of charge carriers, therefore the electrochemical analysis must be aided by thermodynamics and statistical mechanics. We discuss in detail the most characteristic densities of states, the chemical capacitance, and the transport properties, specially the chemical diffusion coefficient, mobility, and generalized Einstein relation.

/pdf/physical-electrochemistry-of-nanostructured-devices-2io7v9d1y2.pdf

Physical electrochemistry of nanostructured devices

A mobility edge is defined as the energy separating localised and non-localised states in the conduction or valence bands of a non-crystalline material, or the impurity band of a doped semiconductor. This review is limited to three-dimensional systems, since in one or two dimensions a mobility edge in this sense does not exist, because all states are localised. The author distinguishes between the properties of electrons in the conduction bands of non-crystalline semiconductors, notably hydrogenated amorphous silicon (a-Si-H), and those in a degenerate electron gas, such as that in amorphous Si-Nb alloys or impurity bands in doped crystalline semiconductors. In the former the use of a one-electron model is legitimate, but a consideration of the interaction with phonons is essential; even at the absolute zero of temperature this leads to a broadening of the mobility edge. The main purpose here is to review recent work on the effects of this interaction on the pre-exponential factor sigma 0 in the conductivity expressed as sigma = sigma 0exp(-(Ec-EF)/kBT) and the pre-exponential factor in the drift mobility. In the final section he also gives a brief review of some of the recent work on the effects of the electron-electron interaction in metallic systems and also spin-orbit scattering.

https://iopscience.iop.org/article/10.1088/0022-3719/20/21/008/pdf

The mobility edge since 1967

The increasing use of amorphous semiconducting films in various commercial applications has stimulated considerable interest in the electronic transport properties of such materials. In this review, the authors describe the above phenomenon of 'anomalous dispersion'. Having initially outlined the present view of band structure and carrier transport mechanisms in non-crystalline materials, they continue with a description of the experimental techniques used in the investigation of the drift velocity of excess charge carriers. Details are then provided of the various characteristics associated with both 'conventional' and 'anomalous' dispersion. Models, in which the anomalous behaviour has been associated with both hopping and trap-limited band transport, are reviewed and assessed. Although anomalous dispersion was initially investigated as a phenomenon of interest in its own right, attention has increasingly turned towards the possibility that a detailed examination of the transient behaviour may be of use in determining details of the energy distribution of localised states in disordered films. The authors outline the various techniques which have been suggested and examine their successes and limitations, concluding with an indication of likely future developments and directions of investigations.

https://iopscience.iop.org/article/10.1088/0034-4885/46/10/002/pdf

Carrier diffusion in amorphous semiconductors

The role of disorder on charge transport in molecularly doped polymers and related materials

Monte Carlo simulation techniques have been employed in the examination of anomalously-dispersive transport characteristics of specimens with various energy distributions of localized states. For each of the four distributions studied, the ‘initial slope’ dispersion parameter, α1, varies similarly with temperature, and exhibits an approximately linear variation in the low-temperature regime. This demonstrates that such behaviour does not constitute evidence for the presence of a particular (e.g. exponential) energy distribution of traps. The ‘final slope’ dispersion parameter, α2 is found to be appreciably more sensitive than α1 to changes in the energy distribution of localized states. A comparison of experimental behaviour with the simulation data suggests that various non-crystalline semiconductors possess a comparatively structured distribution of trapping centres, rather than the featureless tail of localized states which has been inferred from some recent studies.

Influence of various distributions of localized states upon transit pulse dispersion in amorphous semiconductors

Homogeneous Gas Phase Nucleation of Silane in Low Pressure Chemical Vapor Deposition (LPCVD)

The differing interpretations of drift-mobility data for electrons in a-Si:H have been examined. On the one hand, there are the analyses which involve the ``thermalization approximation'' (TA). One such analysis, based on the density-of-states profile deduced by Spear from field-effect data, leads to the unexpectedly high value of the extended-state mobility ${\ensuremath{\mu}}_{\mathrm{ext}=500}$ ${\mathrm{cm}}^{2}$ ${\mathrm{V}}^{\mathrm{\ensuremath{-}}1}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$. Another analysis, which assumes an exponential distribution of tail states, results in the more commonly accepted value ${\ensuremath{\mu}}_{\mathrm{ext}=13}$ ${\mathrm{cm}}^{2}$ ${\mathrm{V}}^{\mathrm{\ensuremath{-}}1}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$. In this work, we show that both models are inconsistent with experimental data when a more thorough examination is made of the field dependence and the activation energy of the drift mobility ${\ensuremath{\mu}}_{d}$ as predicted by those models. On the other hand, we examined Spear's analysis, which does not involve the TA. We show that a thorough analysis of multiple-trapping transport in a tail-state distribution as proposed by Spear leads to more dispersion than he experimentally observed. Our examination is based on a newly developed computational procedure, which analyzes multiple-trapping transport by discretizing the continuous distribution of localized states. Apart from the relevance with respect to electron transport in a-Si:H, this work shows how a relatively simple but accurate analysis of drift mobility and transient photocurrents can be performed with a much wider applicability than the analyses based on the TA.

Extended-state mobility and its relation to the tail-state distribution in a-Si:H.

It is shown that most features of anomalously dispersive multiple-trapping transport in amorphous semiconductors can be calculated easily and accurately when the density of localized states is represented by a set of discrete levels. Calculation of the transient current, the occupation of the conduction band and the trapping levels, when the trap parameters are known, reduces to a set of simple matrix operations. The same holds for the solution of the inverse 'spectroscopic' problem; that is, given the transient photocurrent, for obtaining the distribution of localized states. For the last problem, it is shown very clearly that a given transient photocurrent cannot be interpreted unambiguously by a definite density-of-states distribution, thus the limitations of 'transient photocurrent spectroscopy' are neatly illustrated. The use of discrete levels also allows one to obtain an approximation to the transit time in a time-of-flight experiment, as shown earlier by Schmidlin (1977).

Analysis of dispersive transport in amorphous semiconductors by discretization of a continuous distribution of localized states

A general relation is deduced between the density of localized states N(E) and the transient photocurrent I(t) for an amorphous semiconductor exhibiting trapcontrolled electronic transport. It is demonstrated that the waiting-time distribution functionψ(t) is related to I(t) through a Volterra integral equation, which may be solved numerically. The relative density of states N(E) may be deduced in a straightforward manner from ψ(t), using an approximation which should not introduce more than a small degree of distortion. The computational method is applied to the case of an exponential tail of localized states, and to a system with three discrete sets of trapping centres. Finally, the consequences of an incomplete knowledge of some of the system parameters are considered.

H. Michiel

Papers

Influence of various distributions of localized states upon transit pulse dispersion in amorphous semiconductors

Homogeneous Gas Phase Nucleation of Silane in Low Pressure Chemical Vapor Deposition (LPCVD)

Extended-state mobility and its relation to the tail-state distribution in a-Si:H.

Analysis of dispersive transport in amorphous semiconductors by discretization of a continuous distribution of localized states

Determination of localized state distributions from anomalously-dispersive transport data