Transport In Amorphous Semiconductors Research Articles

Isotropic gap formation, localization, and waveguiding in mesoscale Yukawa-potential amorphous structures

Amorphous photonic structures are mesoscopic optical structures described by electrical permittivity distributions with underlying spatial randomness. They offer a unique platform for studying a broad set of electromagnetic phenomena, including transverse Anderson localization, enhanced wave transport, and suppressed diffusion in random media. Despite this, at a more practical level, there is insufficient work on both understanding the nature of optical transport and the conditions conducive to vector-wave localization in these planar structures, as well as their potential applications to photonic nanodevices. In this study, we fill this gap by investigating experimentally and theoretically the characteristics of optical transport in a class of amorphous photonic structures and by demonstrating their use to some basic waveguiding nanostructures. We demonstrate that these 2-D structures have unique isotropic and asymmetric band gaps for in-plane propagation, controlled from first principles by varying the scattering strength and whose properties are elucidated by establishing an analogy between photon and carrier transport in amorphous semiconductors. We further observe Urbach band tails in these random structures and uncover their relation to frequency- and disorder-dependent Anderson-like localized modes through the modified Ioffe-Regel criterion and their mean free path - localization length character. Finally, we illustrate that our amorphous structures can serve as a versatile platform in which photonic devices such as disorder-localized waveguides can be readily implemented.

Visualization of Mesoscopic Conductivity Fluctuations in Amorphous Semiconductor Thin-Film Transistors.

Charge transport in amorphous semiconductors is considerably more complicated than the process in crystalline materials due to abundant localized states. In addition to device-scale characterization, spatially resolved measurements are important to unveiling electronic properties. Here, we report gigahertz conductivity mapping in amorphous indium gallium zinc oxide (a-IGZO) thin-film transistors by microwave impedance microscopy (MIM), which probes conductivity without Schottky barrier's influence. The difference between the dc and microwave conductivities reflects the efficacy of the injection barrier in an accumulation-mode transistor. The conductivity exhibits significant nanoscale inhomogeneity in the subthreshold regime, presumably due to trapping and release from localized states. The characteristic length scale of local fluctuations, as determined by the autocorrelation analysis, is about 200 nm. Using a random-barrier model, we can simulate the spatial variation of the potential landscape, which underlies the mesoscopic conductivity distribution. Our work provides an intuitive way to understand the charge transport mechanism in amorphous semiconductors at the microscopic level.

Hopping charge transport in hydrogenated amorphous silicon–germanium alloy thin films

Measurements of the dark conductivity and thermoelectric power in hydrogenated amorphous silicon–germanium alloys (a-Si1-xGex:H) reveal that charge transport is not well described by an Arrhenius expression. For alloys with concentrations of Ge below 20%, anomalous hopping conductivity is observed with a power-law exponent of 3/4, while the temperature dependence of the conductivity of alloys with higher Ge concentrations is best fit by a combination of anomalous hopping and a power-law temperature dependence. The latter has been attributed to charge transport via multi-phonon hopping. Corresponding measurements of the Seebeck coefficient reveal that the thermopower is n-type for the purely a-Si:H and a-Ge:H samples but that it exhibits a transition from negative to positive values as a function of the Ge content and temperature. These findings are interpreted in terms of conduction via hopping through either exponential band tail states or dangling bond defects, suggesting that the concept of a mobility edge, accepted for over five decades, may not be necessary to account for charge transport in amorphous semiconductors.

Charge transport in the spatially correlated exponential random energy landscape: effect of the nonpositive correlation function.

Charge transport in amorphous semiconductors having spatially correlated exponential density of states (DOS) has been considered for the arbitrary behavior of the correlation function of random energies. Average carrier velocity is exactly calculated for the quasi-equilibrium (nondispersive) transport regime. For the symmetric exponential DOS with exponential tails for low and high energies and nonpositive correlation function the temperature of the transition to the dispersive transport regime depends on correlation properties and becomes greater than the traditional estimation based on the DOS decay energy kT = U0. Another new feature of the transport in the landscape having nonpositive correlation function is the decrease of the mobility with the field in the low field region and development of the universal mobility field dependence for stronger fields.

Solutions of q-deformed multiple-trapping model (MTM) for charge carrier transport from time-of-flight transient (TOF) photo-current in amorphous semiconductors

This paper is devoted to investigating the description of the q-deformed multiple-trapping equation for charge carrier transport in amorphous semiconductors. For this, we at first modified the multi–trapping model (MTM) of charge carriers in amorphous semiconductors from time-of-flight (TOF) transient photo-current in the framework of the q-derivative formalism, and then, we have constructed, our simulated current by using a method based on the Laplace method. This method is implemented in a program proposed recently by [14] which allows us to construct a current using the Padé approximation expansion.

Local Discontinuous Galerkin Method for Nonlinear Time-Space Fractional Subdiffusion/Superdiffusion Equations

Fractional partial differential equations with time-space fractional derivatives describe some important physical phenomena. For example, the subdiffusion equation (time order 0<α<1) is more suitable to describe the phenomena of charge carrier transport in amorphous semiconductors, nuclear magnetic resonance (NMR) diffusometry in percolative, Rouse, or reptation dynamics in polymeric systems, the diffusion of a scalar tracer in an array of convection rolls, or the dynamics of a bead in a polymeric network, and so on. However, the superdiffusion case (1<α<2) is more accurate to depict the special domains of rotating flows, collective slip diffusion on solid surfaces, layered velocity fields, Richardson turbulent diffusion, bulk-surface exchange controlled dynamics in porous glasses, the transport in micelle systems and heterogeneous rocks, quantum optics, single molecule spectroscopy, the transport in turbulent plasma, bacterial motion, and even for the flight of an albatross (for more physical applications of fractional sub-super diffusion equations, one can see Metzler and Klafter in 2000). In this work, we establish two fully discrete numerical schemes for solving a class of nonlinear time-space fractional subdiffusion/superdiffusion equations by using backward Euler difference 1<α<2 or second-order central difference 1<α<2/local discontinuous Galerkin finite element mixed method. By introducing the mathematical induction method, we show the concrete analysis for the stability and the convergence rate under the L2 norm of the two LDG schemes. In the end, we adopt several numerical experiments to validate the proposed model and demonstrate the features of the two numerical schemes, such as the optimal convergence rate in space direction is close to Ohk+1. The convergence rate in time direction can arrive at Oτ2−α when the fractional derivative is 0<α<1. If the fractional derivative parameter is 1<α<2 and we choose the relationship as h=C′τ (h denotes the space step size, C′ is a constant, and τ is the time step size), then the time convergence rate can reach to Oτ3−α. The experiment results illustrate that the proposed method is effective in solving nonlinear time-space fractional subdiffusion/superdiffusion equations.

Photo-excited hot carrier dynamics in hydrogenated amorphous silicon imaged by 4D electron microscopy

Charge carrier dynamics in amorphous semiconductors has been a topic of intense research that has been propelled by modern applications in thin-film solar cells, transistors and optical sensors. Charge transport in these materials differs fundamentally from that in crystalline semiconductors owing to the lack of long-range order and high defect density. Despite the existence of well-established experimental techniques such as photoconductivity time-of-flight and ultrafast optical measurements, many aspects of the dynamics of photo-excited charge carriers in amorphous semiconductors remain poorly understood. Here, we demonstrate direct imaging of carrier dynamics in space and time after photo-excitation in hydrogenated amorphous silicon (a-Si:H) by scanning ultrafast electron microscopy (SUEM). We observe an unexpected regime of fast diffusion immediately after photoexcitation, together with spontaneous electron-hole separation and charge trapping induced by the atomic disorder. Our findings demonstrate the rich dynamics of hot carrier transport in amorphous semiconductors that can be revealed by direct imaging based on SUEM.

Hopping charge transport in amorphous semiconductors with the spatially correlated exponential density of states.

Hopping charge transport in amorphous semiconductors having spatially correlated exponential density of states has been considered. Average carrier velocity is exactly calculated for the quasi-equilibrium (nondispersive) transport regime. We suggest also a heuristic approach for the consideration of the carrier velocity for the non-equilibrium dispersive regime.

Finite-size scaling of charge carrier mobility in disordered organic semiconductors

Simulations of charge transport in amorphous semiconductors are often performed in microscopically sized systems. As a result, charge carrier mobilities become system-size dependent. We propose a simple method for extrapolating a macroscopic, nondispersive mobility from the system-size dependence of a microscopic one. The method is validated against a temperature-based extrapolation [Phys. Rev. B 82, 193202 (2010)]. In addition, we provide an analytic estimate of system sizes required to perform nondispersive charge transport simulations in systems with finite charge carrier density, derived from a truncated Gaussian distribution. This estimate is not limited to lattice models or specific rate expressions.

Non-Arrhenius anomalous hopping electronic transport in hydrogenated amorphous silicon and composite amorphous/nanocrystalline thin films

The temperature dependence of the dark conductivity of hydrogenated amorphous silicon (a-Si:H) thin films and a-Si:H films containing germanium or silicon nanocrystalline inclusions are examined. Analysis using the reduced activation energy provides clear evidence that conduction is non-Arrhenius, and is more accurately described by an anomalous hopping expression σ(T)=σ1 exp[−(T0/T)κ] where the exponent is κ ∼ 0.75 ± 0.05. This observed temperature dependence is discussed in terms of alternative models for electronic transport in amorphous semiconductors.

Time-dependent transport in amorphous semiconductors: Instability in the field-controlled regime

A time-dependent trap-limited conduction scheme is used to analyze the transient behavior of bistable homogeneous amorphous semiconductors when either the electric field or the current density is prescribed. Numerical outcomes confirm that, for a current-controlled system, the working point is unique and stable in any region of the current-voltage characteristic, while in a field-controlled system the negative differential-resistance region is unstable even in absence of circuit parasitics. The proposed theoretical approach represents a valid tool to grasp the relevant time-dependent features of the Ovonic switching in chalcogenide materials.

Measurement and modelling of transport in amorphous semiconductors

Experimental transient photoconductivity in a-Si:H and μc-Si:H is analysed by a Fourier Transform technique to reveal a relative density of states. It is often found that a deep-lying structure probably associated with defects, at around 0.5 – 0.6 eV depth exhibits an apparent shift against the background of band-tail states as the temperature is varied. We investigate by numerical modelling whether this shift arises from differential attempt-to-escape frequencies in a multi-trapping context, or from a temperature - dependent hopping transport energy.

Phonon driven transport in amorphous semiconductors: transition probabilities

Starting from Holstein’s work on small polaron hopping, the evolution equations for localized and extended states in the presence of atomic vibrations are systematically derived for an amorphous semiconductor. The transition probabilities are obtained for transitions between all combinations of localized and extended states. For any transition process involving a localized state, the activation energy is not simply the energy difference between the final and initial states; the reorganization energy of atomic configuration is also included as an important part of the activation energy (Marcus form). The activation energy for the transitions between localized states decreases with rising temperature and leads to the Meyer-Neldel rule. The predicted Meyer-Neldel temperatures are consistent with observations in several materials. The computed field-dependence of conductivity agrees with experimental data. The present work suggests that the upper temperature limit of variable range hopping is proportional to the frequency of the first peak of the phonon spectrum. We have also improved the description of the photocurrent decay at low temperatures. Analysis of the transition probability from an extended state to a localized state suggests that there exists a short-lifetime belt of extended states inside the conduction band or valence band.

Ultrafast Dynamics of Carrier Mobility in a Conjugated Polymer Probed at Molecular and Microscopic Length Scales

We used time-resolved electric-field-induced second-harmonic generation to probe the charge-carrier-mobility dynamics in amorphous organic materials on an ultrafast time scale. We were able to show that the mobility in poly-spiro-bifluorene-co-benzothiadiazol decreases from 0.1 cm 2/V s at 1 ps to 10-6 cm2/V s within 1 mus. We attribute this dramatic decrease to the relaxation of the charge carriers within the density of states, clearly demonstrating the impact of disorder on the nanoscale charge transport in amorphous semiconductors.

Percolation current in organic semiconductors

The charge transport in organic semiconductors has been investigated theoritically. A n analytical model describing the hopping current is developed. This model is based on VRH (variable range hopping) theory and percolation theory. The results of calculation are compared to the prediction of Mott’s formalism, which has been widely used to describe hopping transport in amorphous semiconductors. The model is also found to be in good agreement with recent experimental data.

Computer Modelling of Non-Equilibrium Multiple-Trapping and Hopping Transport in Amorphous Semiconductors

AbstractIn this paper we demonstrate a simple computational procedure for the simulation of transport in a disordered semiconductor in which both multi-trapping and hopping processes are occurring simultaneously. We base the simulation on earlier work on hopping transport, which used a Monte-Carlo method. Using the same model concepts, we now employ a stochastic matrix approach to speed computation, and include also multi-trapping transitions between localised and extended states. We use the simulation to study the relative contributions of extended state conduction (with multi-trapping) and hopping conduction (via localised states) to transient photocurrents, for various distributions of localised gap states, and as a function of temperature. The implications of our findings for the interpretation of transient photocurrents are examined.

Analysis, Synthesis, and Estimation of Fractal-Rate Stochastic Point Processes

Fractal and fractal-rate stochastic point processes (FSPPs and FRSPPs) provide useful models for describing a broad range of diverse phenomena, including electron transport in amorphous semiconductors, computer-network traffic, and sequences of neuronal action potentials. A particularly useful statistic of these processes is the fractal exponent α, which may be estimated for any FSPP or FRSPP by using a variety of statistical methods. Simulated FSPPs and FRSPPs consistently exhibit bias in this fractal exponent, however, rendering the study and analysis of these processes non-trivial. In this paper, we examine the synthesis and estimation of FRSPPs by carrying out a systematic series of simulations for several different types of FRSPP over a range of design values for α. The discrepancy between the desired and achieved values of α is shown to arise from finite data size and from the character of the point-process generation mechanism. In the context of point-process simulation, reduction of this discrepancy requires generating data sets with either a large number of points, or with low jitter in the generation of the points. In the context of fractal data analysis, the results presented here suggest caution when interpreting fractal exponents estimated from experimental data sets.

Invasion percolation and Eden growth: Geometry and universality.

The mapping of optimal paths in the strong disorder limit to the strands of invasion percolation clusters is shown to lead to a new universal property of these clusters. We suggest that the corresponding strands arising in the annealed Eden growth process are in the same universality class as directed polymers in weak quenched disorder with an upper critical dimension #6. (S0031-9007(96)00188-3) PACS numbers: 64.60.Ak We address several issues in this Letter. What are the geometries of the optimal polymer in a strongly disordered medium in higher dimensions? What is the upper critical dimensionality for this problem? Is the geometry of the polymer in a strongly disordered medium universal? Our study is carried out in the context of a growing invasion percolation cluster. In this procedure, the bonds of the lattice are assigned strengths in a quenched random manner, and a cluster grows by invading the weakest interfacial bond. We will show that both bond and site variants of percolation lead to the same universality class. We then go on to study an analogous model with annealed instead of quenched disorder. In this case all interfacial bonds have an equal probability of being invaded. We present arguments and numerical evidence that even though the randomness is annealed, the effects of quenched disorder are self-generated within the model leading to geometries that are self-affine and characterized by the roughness exponent aDP . Thus, within the same process, the interface of the Eden cluster is characterized by a dynamical exponent zKPZ, whereas the static wandering exponent of the strands of the cluster is given by 1yzKPZ (a strand is defined as the unique path that excludes dead ends from an arbitrary site to a central seed site). Our results have a wide range of applicability— the strong disorder limit is relevant up to a correlation length in a variety of situations (7) including transport in amorphous semiconductors at low temperatures, electrical conduction and fluid flow in porous rocks, and the magnetic properties of doped semiconductors. Further, there are novel forms of percolation that are equivalent to the problem of the optimal polymer in a strongly disordered environment (6). Our prediction of the self- generated quenched randomness ought to be observable in Eden growth and other random invasion processes. We begin with an alternative way to view the geometry of the polymer in a strongly disordered environment. We

Equilibrium and non-equilibrium transport in band tails

General theoretical concepts developed recently for equilibrium and non-equilibrium transport in amorphous semiconductors are discussed. Particular attention is given to the application of these concepts to the interpretation of experimental data. At low temperatures hopping of carriers through localized states in band tails dominates the transport properties. The concept of the so-called transport energy appears to be useful for the description of both equilibrium and non-equilibrium transport. This concept allows a natural extension to the case of nonlinear high-electric-field transport. Much experimental and theoretical work was devoted in the last few years to the investigation of this challenging regime. No consistent theoretical description has been suggested yet. The notion of the effective temperature seems to be the most fruitful so far. Monte-Carlo simulations can be used to verify and substantiate the concept of the effective temperature. At very low temperatures the conductivity is due to energy-loss of carriers through the localized tail states. The corresponding theory for intrinsic material is well developed, whereas experiments in doped materials show some surprising results, namely pronounced asymmetry in the contributions of electrons and holes to the photoconductivity. We show how these results can be accounted for in the energy-loss hopping approach. Finally, some open problems are discussed.

Fractal renewal processes as a model of charge transport in amorphous semiconductors.

We construct two relatively simple fractal renewal processes that provide a framework for understanding charge transport in amorphous semiconductors. These processes exhibit fractal behavior, with power spectral densities that vary as 1/${\mathit{f}}^{\mathit{D}}$, deriving from interevent-time probability density functions that themselves decay in a power-law fashion.