MODELING TUNNELING-ASSISTED GENERATION-RECOMBINATION RATE IN SPACE-CHARGE REGION OF PN A-SI:H JUNCTION

Abstract A theoretical model of generation-recombination mechanism of charge carriers in pn a-Si:H junctions with high internal built-in electric ﬁelds is developed in which the capture-emission transitions are treated in a similar way as in the SRH generation-recombination approach. In this way, the effects of the tunneling-assisted transitions between the transport edges and the trap s areexpressed by an enhanced capture cross-section which in turn increases the generation-recombination rate of charge carriers. Th etunneling and thermal capture and emission of carriers to and from localized states determine the occupancy function in themobility gap of a-Si:H. Generation-recombination dynamics are then expressed by virtue of occupancy function and the continu-ous distribution of states in the gap of a-Si:H. Keywords: amorphous silicon, tunneling, GR model 1. Introduction The thermal generation-recombination process is one of themost important mechanisms for the transport of chargecarriers in a semiconductor. The fundamental theory ofgeneration-recombination statistics describing the creationand annihilation of electrons and holes through traps in thegap of a semiconductor was developed a quarter century agoby Shockley and Read [1], and Hall [2]. This approach, knownas the SRH theory, has been successfully used forunderstanding fundamental semiconductor device physics andfor analysis of the electrical characteristics of semiconductordevices.Following the successful introduction of substitutional dopingin amorphous silicon, hydrogenated amorphous silicon (a-Si:H) and other amorphous semiconductors have becomehighly important materials for various devices such as thin-ﬁlm transistors [3] and solar cells [4]. In contrast to crystallinesemiconductors, the density of states in the gap of amorphoussemiconductors is much higher due to the inherent disorder ofatoms in the deposited amorphous layers. Considering thecontinuous density of states (DOS) distribution in the gap, anextended SRH approach has been successfully applied for themodeling of trapped carrier concentrations and of generation-recombination rates in a-Si:H [5, 6-8]. The purpose of this paper is to develop a mathematical modelfor formulating capture and emission mechanisms and trap-assisted carrier transport in space-charge regions of theforward biased pn a-Si:H junctions. In the case of highlydoped layers on both sides of the junction, there is a highbuilt-in electric ﬁeld inside the space-charge transition region,strongly affecting the tunneling transport between band statesand continuously distributed traps in the mobility gap of a-Si:H. The developed model should also account for loweringthe band energy barrier at an increased electric ﬁeld, thusincluding the Poole-Frenkel effect.Carrier generation from traps in the energy gap of a-Si:H isregarded as a thermally assisted tunneling process combinedby the Poole-Frenkel emission over the lowered barrier. In theinverse process of carrier capture, the incident carriers whichtake part in the tunneling transport are majority carriers in thelow ﬁeld regions at the edges of the transition region. Afraction of incident carriers either surmount the barrier ortunnel through a part of the barrier. Carriers, penetrating oroverpassing the barrier, are captured, thermalizing to theground level of the traps.Adding trap-assisted carrier transitions to the pure thermalcapture-emission process yields expressions for the non-equilibrium occupancy function in the presence of highelectric ﬁelds. Integrating over all states in the gap results inexpressions for the trapped electron and hole charge, and forgeneration recombination rates in the pn junction space-charge regions. The derived expressions for the generationrecombination rate in a-Si:H are similar in form to equationsfor c-Si [9] which, however, were developed in a different wayfor a single trap level and did not account for Poole-Frenkeleffect. Moreover, the effects of high electric ﬁelds on trappedcarrier concentrations in a-Si:H have not been examinedbefore. In concluding the paper, the developed generation-recombination model is applied to calculate current-voltagecharacteristics of a p