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Energy gap and pre‐exponential factor in dark conduction by organic semiconductors

1967; Wiley; Volume: 17; Issue: 1 Linguagem: Inglês

10.1002/polc.5070170107

1935-3065

D. D. Eley,

Electrochemical Analysis and Applications

Abstract The values of Δε and σ 0 in the expression σ = σ 0 exp {−Δε/ 2kT } for the dark conductivity σ, tend to increase together over the whole range of organic semiconductors. They fall into a broad band of values confined roughly between two lines given by log σ 0 = αΔε + β, the compensation rule, with log σ 0 varying from 5 ± 4 for Δε equal to 1.0 e.v., to 14 ± 2 for Δε = 4.0 e.v. The parameter σ 0 is related to the mobility of charge carriers μ, and the present paper attempts a broad qualitative discussion of the factors determining μ. The following mechanisms are considered to apply for the origin and motion of the charge carriers in order of increasing Δε and log σ 0 : ( a ) intrinsic bulk thermal generation, transport by hopping over intermolecular barriers, ( b ) bulk generation, with tunnelling through intermolecular barriers going over to, ( c ) narrow‐band theory, ( d ) electron or hole injection from the electrodes into the conductivity band for high energy gap substances. It is shown that process ( b ) can only account for a restricted range of log σ 0 , from 4 to 1.0, except perhaps for proteins where log σ 0 = 4, may reflect a high mobility along the C0 … HN network. Electron injection may give rise to log σ 0 = 1.6 and it seems possible that very much higher apparent values may arise from a temperature‐variable adsorbed film, on the semiconductor or the metal. Somewhat scanty evidence suggests that while atactic polymers may have low Δε values they may also have low values of log σ 0 . Going over to isotactic polymers may lower Δε somewhat, and increase σ 0 by a factor of 10. It is suggested that to achieve high mobility values, e.g., μ = 10 4 cm. 2 v. −1 sec. −1 , it will be necessary to develop intermolecular bridging by metal atoms or hydrogen bonds, to assist charge‐carrier transport through the crystal.