Kinetics of photoinduced defect creation in amorphous semiconductors: Analogy to a logistic equation in a biological system

Abstract

We have found that a novel kinetic equation, similar to the logistic function in biological systems, replicates well the experimentally observed light-induced defect creation in amorphous semiconductors. It is proposed that a created defect, itself, has a triggering e ect for successive defect creation, which leads to new insight into understanding photodegradation in amorphous semiconductors.Photodegradation occurs in both hydrogenated amorphous silicon (a-Si : H) and amorphous chalcogenides (a-Ch), when illuminated by bandgap light (Shimakawa et al. 1995). The number of defects increases owing to bandgap irradiation. In a-Si : H, the creation of light-induced metastable defects (LIMDs) is now termed the Staebler± Wronski (SW) (1977) e ect.Although a great number of studies have been made to understand the origin of LIMD creation, how LIMDs are created is still not understood well (Shimakawa et al. 1995). Principally, several types of microscopic model for the SW e ect have been proposed. The most popular is based on the idea of breaking of weak Si± Si bonds induced by non-radiative recombination of band-tail electrons and holes (non-radiative recombination (NRR) model (Stutzmann et al. 1985, Morigaki 1988. The second class is the charge-transfer model in which electrons and holes are trapped at charged defects (Adler 1981). The other classes, for example, are an impurityrelated model (Red® eld and Bube 1990) and a self-trapped exciton (STE) model (Shimakawa et al. 1995) which requires a strong carrier± lattice interaction and is equivalent to bond breaking. In the NRR model (Stutzmann et al. 1985), the rate equation for inducing the defects is given bywhere N is the number of inducing defects, and n and p are the concentrations of band-tail electrons and holes respectively. Note that n and p are expected to vary inversely with N (self-limiting) and hence N is given as

A compressed logistic equation on bacteria growth: inferring time-dependent growth rate

“…Both of which show excellent fit to the actual population growth. The origin of the SLE (α < 1.0) may be attributed to a dispersive nature (broad distribution of parameters) in the kinetic processes, although details are not clearly understood [31]. In the present bacteria growth, we found CLE (α > 1.0).…”

“…Interestingly, the present logistic function N(X) (or P(X)) replicates well with the Gaussian distribution erf G(X) (or G(X)), although the functional forms differ. Finally, it should be mentioned that the stretched logistic equation (SLE), in which α-value is smaller than unity, has been found for the number increase of microscopic defects (photoinduced defect creation) in amorphous semiconductors (inorganic material in solid state physics) [31] and for the infection evolution of the COVID 19 [32]. Both of which show excellent fit to the actual population growth.…”

Kinetics of self-bleaching in some photodarkened Ge–As–S amorphous thin films

“…The exact origin of photodarkening remains to be unclear, however, it is widely accepted that the photodarkened state is metastable and can be converted back (bleached) to or close to a ground state by (i) aging, (ii) annealing and (iii) illumination with photons which energy is lower than the optical gap energy. Various aspects of kinetics of photodarkening were examined in the number of papers for instance [6][7][8][9][10].…”

Aspectos relacionados à utilização da equação logística quadrática em processos eletroquímicos

“…Considerando que características como não-linearidade, dissipação e retro-alimentação (feedback) em sistemas dinâmicos estão contidas na ELQ, sua utilização vem sendo recentemente descrita para a modelagem de processos físico-químicos como resposta de células a combustível com eletrólito polimérico 5,6 , transporte de cargas em filmes orgânicos -e inorgânicos 8 finos. Outro exemplo bastante ilustrativo da utilização da ELQ por analogia com sistemas biológicos trata da criação sucessiva de defeitos, como o processo de fotodegradação em semicondutores amorfos 10 . Particularmente considerando as aplicações de filmes eletroativos em, por exemplo, baterias secundárias, dispositivos eletrocrômicos e sensores [11][12][13][14][15][16] se fazem necessárias investigações a respeito dos mecanismos de transporte nesses filmes.…”