Diffusion-limited Recombination Research Articles

Photovoltages in Polycrystalline Mosaic Solar Cells.

In some thin-film solar cells the light-absorbing layer is a mosaic of crystalline grains whose boundaries run from the back to the front of the cell. We used the semiconductor modeling software Sesame to do numerical calculations of the optoelectronic properties of such cells assuming that recombination of minority photocarriers occurs primarily at the grain boundaries. The work complements analytical results for diffusion-limited recombination at grain boundaries and dislocations. We chose idealized n-CdS/p-CdTe solar cells for illustration. We find that the open-circuit voltage, VOC, under illumination declines logarithmically with increasing ratio D/θ2, where D is the ambipolar diffusion constant governing minority-carrier transport and θ is the grain size (from 1 to 10 μm). While a decline in VOC as mobility increases is counterintuitive, this finding is consistent with related analytical results and confirms their utility. However, open-circuit voltages are about 0.04–0.10 V lower than the corresponding analytical estimates. We show that the deficit is mostly a consequence of a recombination shortcut. At open circuit, minority photocarrier currents at points closer to the n-CdS interface than to a grain boundary are directed through the conducting front layers and terminate near the “hot spot” at the intersection with the grain boundary. The shortcut lowers open-circuit voltages by about 0.05 V below the analytical estimates.

Temperature-Dependent Transient Absorption Spectroscopy Elucidates Trapped-Hole Dynamics in CdS and CdSe Nanorods.

Charge-carrier traps play a central role in the excited-state dynamics of semiconductor nanocrystals, but their influence is often difficult to measure directly. In CdS and CdSe nanorods of nonuniform width, spatially separated electrons and trapped holes display relaxation dynamics that follow a power-law function in time that is consistent with a recombination process limited by trapped-hole diffusion. However, power-law relaxation can originate from mechanisms other than diffusion. Here we report transient absorption spectroscopy measurements on CdS and CdSe nanorods recorded at temperatures ranging from 160 to 294 K. We find that the exponent of the power law is temperature-independent, which rules out several models based on stochastic activated processes and provides insights into the mechanism of diffusion-limited recombination in these structures. The data point to weak electronic coupling between trap states and suggest that surface-localized trapped holes couple strongly to phonons, leading to slow diffusion. Trap-to-trap hole hopping behaves classically near room temperature, while quantum aspects of phonon-assisted tunneling become observable at low temperatures.

Simulation-Based, Systematic Approach to Understanding the Long-Time Dynamics of Stoichiometrically-Mismatched, Self-Assembled Protein Hydrogel Networks

We present mesoscale simulation results and analytical derivations for the long-time equilibrium dynamics of model peptide networks assembled from mixing stoichiometrically mismatched amounts of “junction” and “linker” components. The analysis evaluates how the migration of defects controls the rate of relaxation of shear stress, and how this rate is related to junction multiplicity, defect concentration, linker stiffness, single vs. multiple junction pairings, and linker looping ability. The shear-relaxation time and viscosity are predicted to fall away sharply when junction and linker concentrations are mismatched by even 1%. The mean stress relaxation per defect migration event obtained through simulations of low valent networks with single junction pairings is from two to three times greater than assumed by standard simple theories. The rates of defect migration in networks with multiple junction pairings and/or loops are accelerated and result in lower shear relaxation times. Discounting the looped linkers from the density of active chains and treating linkers involved in multiple junction pairings as parallel springs leads to a static shear modulus (G) quadratic in the number of effective elastic chains (Nelastic) on a single master curve. Furthermore, the time-dependence of viscosity during gel “aging” is modeled as an approach to equilibrium through diffusion-limited recombination of complementary defects.

Effects of defects on the shear stress relaxation in self-assembled protein networks

The long-time reorganization of peptide networks formed by mixing “junction” and “linker” components, where the junctions contain multiple high-affinity, high-specificity binding sites for divalent “linkers”, is investigated using a mesoscale simulation model. An interesting feature of this type of system is that the concentration of defects can be controlled experimentally by varying the ratio of junction and linker concentrations in the system. In this study we use a simple simulation model to evaluate how the migration of defects controls the rate of relaxation of shear stress, and how this rate is related to junction multiplicity, defect concentration, and linker stiffness. The mean stress relaxation per defect migration event obtained through simulation was two to three times greater than assumed by standard simple theories. The results are used to develop a phenomenological theory to predict the dependence of shear viscosity on the equilibrium constant and rate constants associated with linker-junction binding, stoichiometric mismatch, and network topology. The shear stress relaxation time and viscosity are predicted to fall away sharply when junction and linker concentrations are mismatched by even 1%. Furthermore, the time-dependence of viscosity during gel “aging” is modeled as an approach to equilibrium through diffusion-limited recombination of complementary defects.

Comparative Studies of Carrier Dynamics in 3C-SiC Layers Grown on Si and 4H-SiC Substrates

Time-resolved nonlinear optical techniques were applied to determine the electronic parameters of cubic silicon carbide layers. Carrier lifetime, τ, and mobility, μ, were measured in a free-standing wafer grown on undulant Si and an epitaxial layer grown by hot-wall chemical vapor deposition (CVD) on a nominally on-axis 4H-SiC substrate. Nonequilibrium carrier dynamics was monitored in the 80 K to 800 K range by using a picosecond free carrier grating and free carrier absorption techniques. Correlation of τ(T) and μ a(T) dependencies was explained by the strong contribution of diffusion-limited recombination on extended defects in the layers. A lower defect density in the epitaxial layer on 4H-SiC was confirmed by a carrier lifetime of 100 ns, being ~4 times longer than that in free-standing 3C.

Different electric-field dependences of geminate and nongeminate recombination in photoluminescence of a-Si:H

In this paper, we present the results of the wideband quadrature frequency-resolved spectroscopy (QFRS) of the electric-field (F) effects on photoluminescence (PL) in a-Si:H: the recombination of geminate electron-hole pairs including excitons is quenched by an electric field, whereas that of nongeminate or distant pairs (DP) is enhanced. The quenching of the geminate recombination at intermediate temperatures is interpreted in terms of the classical Onsager theory. On the other hand, the enhancement of the DP recombination is explained using the effective temperature in diffusion-limited recombination.

Diffusion-limited recombination in polymer-fullerene blends and its influence on photocurrent collection

We propose a model of charge recombination in interpenetrating two-phase systems, and apply it to blends of poly [2-methoxy-5-${(3}^{\ensuremath{'}}{,7}^{\ensuremath{'}}$-dimethyloctyloxy)-1-4-phenylene vinylene], (MDMO-PPV) and 1-(3-methoxycarbonyl)-propyl-1-phenyl-$(6,6){\mathrm{C}}_{61}$ (PCBM). The main features of the model are that charge recombination is rate limited by the diffusion of positive polarons towards PCBM anions; that the density of polaron states contains a tail of deep traps which serve to delay recombination; and that polarons move between localized states largely by means of thermally activated hopping. The model is implemented using Monte Carlo simulations and is applied to reproduce the observed dependence of charge recombination kinetics on laser intensity, temperature, and background illumination, detected by transient optical spectroscopy. Modeling the experimental data yields a density of deep localized states in MDMO-PPV of order ${10}^{17}{\mathrm{cm}}^{\ensuremath{-}3},$ and a charge carrier lifetime of order 10 \ensuremath{\mu}s under solar illumination. An alternative model based on direct tunneling is ruled out by comparison with the observed temperature dependence. The recombination model is incorporated into a one-dimensional calculation of short-circuit photocurrent in a solar cell as a function of temperature and light intensity. We conclude that charge recombination is sufficiently slow not to limit photocurrent collection under solar intensities at short circuit, and propose that space charge effects may be responsible for the observed sensitivity of photocurrent to temperature.

Ultrafast Charge Carrier Recombination in a-Si:H and μc-Si:H

The ultrafast nonradiative bimolecular recombination of charge carriers was investigated in amorphous and microcrystalline silicon. The photoelectric method based on measurement of extraction time of the charge carrier reservoir in the space-charge-limited photocurrent mode was used. A series of models (Auger, diffusion-controlled, charge-carrier-fluctuation dominated) were experimentally tested but were not able to explain all features of bimolecular recombination in a-Si:H. The model of diffusion limited recombination taking into account the intrinsic random potential seems most suitable for a description of the observed suppressed bimolecular recombination.

Migration and interaction properties of ion beam generated point defects in c-Si

We have analyzed the room temperature migration properties of ion beam generated self-interstitials and vacancies in crystalline Si using deep level transient spectroscopy and in situ leakage current measurements. Silicon p +-n junctions, formed by B diffusion in n-type epitaxial Si wafers, were implanted at room temperature with 2.5 MeV He ions to fluences in the range 1×10 9–1×10 12 cm −2 . Diodes were reverse biased and leakage current was measured both during and immediately after ion implantation. At the beam turn-off, leakage current decreases by about a factor of 2 in times as long as few days. Ex situ deep level transient spectroscopy measurements show that the main contribution to leakage current is given by vacancy-type defects, i.e. phosphorous-vacancy and divacancy complexes. Hence, the leakage reduction at the beam turn off has been associated to the recombination of vacancy clusters by residual free interstitials. Assuming a diffusion limited recombination process, a value of 1.5×10 −15 cm 2/s has been determined for the interstitial diffusivity. When the dose rate of the beam is increased, a faster transient, lasting up to 1000 s, is revealed by the in situ measurements and it has been tentatively associated with the annihilation of residual free vacancies by migration to interstitial sinks or by trapping at impurity atoms (O, C).

Direct observation of the intersystem crossing in poly(3-octylthiophene)

Using subpicosecond photoinduced absorption, we monitor the evolution of singlet excitons in solutions of regiorandom poly(3-octylthiophene) (P3OT), regioregular poly(3-hexylthiophene) (P3HT), and a well-defined α-oligothiophene with 12 repeat units (T12). We find a luminescence lifetime of 500 ps, and we observe the intersystem crossing from the singlet manifold to the triplet manifold, with a rate constant of k−1ISC=1.2 ns. By measuring the quantum efficiency of luminescence, we estimate an intrinsic lifetime of 2 ns for the singlet excitons, and a nonradiative decay rate of k−1nr=1.5 ns. We find no difference in the intersystem crossing time for the different thiophene derivatives, implying the intersystem crossing rate is determined primarily by the relatively large spin–orbit interaction due to the sulfur heteroatom and not by chain defects, chain ends, or effects due to the side groups. In addition, we find that for t<50 ps a fraction of the photoexcitations undergo one-dimensional diffusion limited recombination.

Pairing correlations in diffusion-limited recombination: coupled-cluster study in Fock space

The purpose of the paper is to illustrate how the cluster method, introduced originally in classical statistical mechanics and later on generalized to describe correlation effects in quantum systems, can be extended for treating collective behaviour in diffusion limited recombination A+B to 0: This involves exploring a many-body state vector in second quantization form with pairing correlations between particles only. An algebraic approach for deriving kinetics equations for pair correlation functions glambda lambda ', (r, t) is proposed, where lambda , lambda '=a, b. solution of those equations is presented. In two-body approximation, gab(r,t) and the corresponding time-dependent rate constant reproduce the Smoluchowski results. Many-body effects are analysed both for a monomolecular regime (cb>>ca(t)) (MR) and a bimolecular regime (cb(t)=ca(t)) (BR). For MR at Cb to 0, gab(r, t) is shown to have exponential screening on the characteristic length inversely proportional to square root cb, and the rate constant acquires additional correction, proportional to square root cb, to the Smoluchowski value. For BR at the later stage of recombination, the pair correlation function is predominantly determined by the initial condition, i.e. gab(r, 0), and the average concentration ca is found to exhibit time dependence approximately=t-3/4 at the pre-asymptotic stage. However, at the true asymptotic, t to infinity , the model gives ca approximately=t-1. We confront these results with the previous analytical results and find a qualitative consistency in the MR case and some discrepancy for the BR case. The proposed description is rather simple and can be applied for exploring collective and correlation effects in other non-equilibrium classical systems.

Adiabatic Liouvillean in the theory of diffusion-limited recombination. I

A regular method of deriving the governing adiabatic Liouvillean on a lattice for a many-body system of locally and instantaneously recombining particles in reaction A+B to 0 is described. When the rate U of the recombination tends to infinity, U to infinity , the local reaction Liouvillean is shown to be replaced with a non-local operator involving renormalized matrix elements which are proportional to (slow) diffusive jump rates. Properties of the new Liouvillean are described. Quantum field formalism is employed.

Adiabatic kinetics in the theory of diffusion-limited recombination. II

For pt.I see ibid., vol.25, p.5283-95, (1992). Deterministic evolution that corresponds to the adiabatic Liouvillean for recombination A+B to 0 derived in the preceding paper I, is found. It is expressed by a set of linear kinetics equations for occupation numbers, nsigma i(t), sigma =a,b and describes flows of particles inside domains to time-independent interfaces between A and B phases, where the particles annihilate. The interface locations are defined by a static 'potential'. Averaging of nsigma i(t) has been carried out both over random distribution of locations of interfaces and a Gaussian distribution of initial density profile. For an arbitrary fraction of initial species and comparable diffusion coefficients, the expectation value of density decays as t-d/2, while standard variance, (( delta csigma i)2)1/2, decreases more slowly at t to infinity , i.e. a t-d/4 for the d-dimensional case, pointing to the importance of initial fluctuations for the deterministic kinetics.

Picosecond and c.w. optical probes of polydiacetylene at high pressure

We have employed the femtosecond photoinduced absorption (PA) technique at pressures up to 80 kbar in films of polydiacetylene 4BCMU. Pressure dramatically slows the singlet exciton recovery, suggesting that large-amplitude 3-D distortions of the chain are important to the picosecond recovery. At high pressure the slow PA decay can be modeled by diffusion-limited recombination of excitions. On the other hand, the initial 100 fs relaxation is not affected by pressure, and is identified as a 1-D process. We also present pressure studies of resonant Raman scattering (RRS) in 4BCMU. Amplitude-mode analysis of the RRS data shows that the 1-D properties of the excitons change very little with pressure. Changes in the RRS include: (1) hardening of the bare phonons; (2) softening of the distribution of the dressed phonons in parallel with the red shift of the absorption bands under pressure. These observations are consistent with an increase in the average conjugation length with pressure.

Models for the decay of radiation-induced conduction

The diffusion-limited recombination and tunneling-controlled recombination theories that account for the decay of insulator conductivity following irradiation are described. The diffusion-controlled recombination with a Coulomb or other long-ranged interaction shows a time-dependent reaction rate, but does not agree with experimental results. The tunneling model with first-order kinetics does agree with experimental results. A comparison of the two models and the experimental data obtained for the radiation-induced conductivity of a polyethylene sheet are presented. >

Diffusion on two-dimensional percolation clusters with multifractal jump probabilities

By means of Monte Carlo simulations we studied the properties of diffusion limited recombination reactions (DLRR's) and random walks on two dimensional incipient percolation clusters with multifractal jump probabilities. We claim that, for these kind of geometric and energetic heterogeneous substrata, the long time behavior of the particle density in a DLRR is determined by a random walk exponent. It is also suggested that the exploration of a random walk is compact. It is considered a general case of intersection ind euclidean dimension of a random fractal of dimension DF and a multifractal distribution of probabilities of dimensionsD q (q real), where the two dimensional incipient percolation clusters with multifractal jump probabilities are particular examples. We argue that the object formed by this intersection is a multifractal of dimensionsD' q =D q +D F -d, for a finite interval ofq.

Adsorption isotherms on fractal substrata.

By means of Monte Carlo simulations, diffusion-limited recombination reactions, followed by desorption and the desorption of single particles from fractal and multifractal substrata, are studied. From all these results, we conjecture that for both processes (a) the dissociative adsorption and associative desorption of diatomic molecules and (b) the nondissociative adsorption and desorption of single particles, the relationship between the particle coverage \ensuremath{\Theta} and the applied pressure p at the steady state (i.e., the adsorption isotherm) may be written, in the limit \ensuremath{\Theta}\ensuremath{\rightarrow}0 as ${\mathrm{\ensuremath{\Theta}}}^{1/2+1/2\mathrm{f}}$(1-\ensuremath{\Theta}${)}^{\mathrm{\ensuremath{-}}1}$\ensuremath{\propto}${\mathrm{p}}^{1/2}$ for (a) and \ensuremath{\Theta}(-ln\ensuremath{\Theta}${)}^{1\mathrm{\ensuremath{-}}1/\mathrm{f}}$(1-\ensuremath{\Theta}${)}^{\mathrm{\ensuremath{-}}1}$\ensuremath{\propto}${\mathit{p}}^{1/2}$ for (b), where f is the site-visitation random-walk exponent of the substratum. Classical isotherms are recovered for homogeneous surfaces with f=1.

Hydrogen adsorption on alkali modified aluminum

Coadsorption experiments of alkali metals and hydrogen on Al(100) are reported. The probability for H-H (D-D) dissociation and subsequent atomic adsorption is less than 1:10 4 at all alkali coverages. As a consequence, each overlayer had to be prepared by exposing the sodium or potassium modified surface to a beam of hydrogen (deuterium) atoms. We observed an attractive alkali-hydrogen interaction at all coverages. This interaction is best described as the formation of an alkali hydride in the presence of excess alkali atoms. The formation of the hydride shifts the recombination and desorption temperature of hydrogen adatoms on Al(100) from around 350 to around 500 K. While no isotope effect was detected on the clean aluminum surface (diffusion limited recombination), a significant 10–15 K shift was observed for both alkali hydrides (bond breaking). Furthermore, both alkali hydrides observed intense vibrational losses, thus revealing the ionic character of the metal-hydrogen bond. Electron energy loss spectra of an annealed monolayer of sodium hydride (deuteride) showed metal-hydrogen stretching bands at 1850 (1350) cm −1 and 1715 (1250) cm −1, a deformation band at 800 (600) cm −1, and a metal-metal band at 200 (200) cm −1. Corresponding peak positions for potassium hydride (deutride) were 1650 (1200) cm −1, 1500 (1100) cm −1, and 775 (585) cm −1. The metal-metal vibration could not be separated from the elastic peak because of the larger mass of potassium compared to sodium.

The role of activation energy distributions in diffusion related annealing in SiO2

Models for annealing processes in damaged, amorphous SiO2 are discussed. Using a series expansion approach, theories developed for diffusion-limited recombination are adapted to allow for a Gaussian distribution of activation energies. It is found that the effect of a distribution having deviation ΔE, and center EA can be accounted for by using an effective diffusion coefficient, D̃, such that in the series expansion any power (n) is defined by (D̃)n=Dn0 exp 1/2 (nΔE/kT)2 exp(−nEA/kT). This form is more complicated than that found previously for ‘‘pure’’ diffusion studies. The importance of the form of the distribution function for the activation energies is discussed in the context of the full diffusion-limited theory for annealing. It is argued that processes occurring at temperatures in excess of 500 °C are not due to diffusional recombination.

Amorphous Silicon Photoconductive Sensor

Photoconductive sensitivity and transient properties of non-doped and doped a-Si: H films were investigated. The non-exponential decays of photoconductivity were discussed using a dispersive diffusion limited recombination model. Doping effects on sensitivity and transient behaviors were also investigated. Phosphorus and boron dopings drastically reduced the pulsed light responsitivity. A photoconductive sensor array was fabricated and the performance was compared with that of CdS photosensors.