Rare Transition Events in Nonequilibrium Systems with State-Dependent Noise: Application to Stochastic Current Switching in Semiconductor Superlattices

Using recent mathematical advances, a geometric approach to rare noise-driven transition events in nonequilibrium systems is given, and an algorithm for computing the maximum likelihood transition curve is generalized to the case of state-dependent noise. It is applied to a model of electronic transport in semiconductor superlattices to investigate transitions between metastable electric field distributions. When the applied voltage $V$ is varied near a saddle-node bifurcation at $V_th$, the mean life time $$ of the initial metastable state is shown to scale like $log \propto |V_th - V|^{3/2}$ as $V\to V_th$

Asymptotics of the trap-dominated Gunn effect in p-type Ge

We present an asymptotic analysis of the Gunn effect in a drift-diffusion model---including electric-field-dependent generation-recombination processes---for long samples of strongly compensated p-type Ge at low temperature and under dc voltage bias. During each Gunn oscillation, there are different stages corresponding to the generation, motion and annihilation of solitary waves. Each stage may be described by one evolution equation for only one degree of freedom (the current density), except for the generation of each new wave. The wave generation is a faster process that may be described by solving a semiinfinite canonical problem. As a result of our study we have found that (depending on the boundary condition) one or several solitary waves may be shed during each period of the oscillation. Examples of numerical simulations validating our analysis are included.Comment: Revtex, 25 pag., 5 fig., to appear Physica

Scaling properties of noise-induced switching in a bistable tunnel diode circuit

Noise-induced switching between coexisting metastable states occurs in a wide range of far-from-equilibrium systems including micro-mechanical oscillators, epidemiological and climate change models, and nonlinear electronic transport in tunneling structures such as semiconductor superlattices and tunnel diodes. In the case of tunnel diode circuits, noise-induced switching behavior is associated with negative differential resistance in the static current-voltage characteristics and bistability, i.e., the existence of two macroscopic current states for a given applied voltage. Noise effects are particularly strong near the onset and offset of bistable current behavior, corresponding to bifurcation points in the associated dynamical system. In this paper, we show that the tunnel diode system provides an excellent experimental platform for the precision measurement of scaling properties of mean switching times versus applied voltage near bifurcation points. More specifically, experimental data confirm that the mean switching time scales logarithmically as the 3/2 power of voltage difference over an exceptionally wide range of time scales and noise intensities.Comment: 9 pages, 9 figures, accepted manuscript for publication in the European Physical Journal B, Topical Issue: Non-Linear and Complex Dynamics in Semiconductors and Related Material

DESIGN AND REALIZATION OF A SILICON NANOWIRE PARTICULATE PHOTOCATALYST FOR SOLAR WATER SPLITTING

Particle suspension reactors (PSRs) offer a cost-effective architecture for solar fuelsproduction via photoelectrochemical water-splitting. However, most previously reportedphotocatalysts only absorb ultraviolet (UV) or blue light, limiting their possible solar-to-hydrogenenergy conversion efficiencies. Silicon absorbs well across the visible and nearinfrared (IR) spectrum, making it a top choice for photovoltaic modules, but its narrow bandgapdoes not produce the voltage necessary to split water. Therefore, a multijunction (MJ) particle isrequired.Here, we develop the synthesis of high-performance Si nanowire (SiNW) photodiodesand tunnel diodes, allowing for single MJ SiNW solar cells with tunable photovoltages up to atleast 10 V under 1-sun illumination. The photovoltage generated by the MJ SiNWs is sufficientto drive the photodeposition of catalytic metals and metal oxides from solutions of metal ions.The axial asymmetry of the potential in the SiNW allows for a spatioselective photodeposition ofwater-splitting co-catalysts (Pt and CoOx) and creation of the first Si-based particulatephotocatalysts. From prototype PSRs, we find that the spectral dependence of hydrogengeneration efficiency is closely related to the photonic characteristics of the sub-wavelengthdiameter SiNWs. Unlike wider bandgap oxide and chalcogenide materials previously studied for PSRs, MJ SiNWs bring the advantages of Si to the PSR design, providing a new approach forwater-splitting reactors.Doctor of Philosoph

Experimental metrics for detection of detailed balance violation

We report on the measurement of detailed balance violation in a coupled, noise-driven linear electronic circuit consisting of two nominally identical RC elements that are coupled via a variable capacitance. The state variables are the time-dependent voltages across each of the two primary capacitors, and the system is driven by independent noise sources in series with each of the resistances. From the recorded time histories of these two voltages, we quantify violations of detailed balance by three methods: 1) explicit construction of the probability current density, 2) by constructing the time-dependent stochastic area, and 3) by constructing statistical fluctuation loops. In comparing the three methods, we find that the stochastic area is relatively simple to implement, computationally inexpensive, and provides a highly sensitive means for detecting violations of detailed balance.Comment: 12 pages, 6 figures, this version contains additional material relative to the previous on

Asymmetric double barrier resonant tunneling structures with improved characteristics

We present a self-consistent calculation, based on the global coherent tunnelling model, and show that structural asymmetry of double barrier resonant tunnelling structures significantly modifies the current-voltage characteristics compared to the symmetric structures. In particular, a suitably designed asymmetric structure can produce much larger peak current and absolute value of the negative differential conductivity than its commonly used symmetric counterpart.Comment: 1 paper, 3 figure