Charge-Dipole Model for the Universal Field Dependence of Mobilities in Molecularly Doped Polymers

Abstract

Using the general result that the mobility m of charge carriers driven in a spatially correlated random potential by an electric field E can be expressed in terms of the Laplace transform of a particular correlation function related to the random potential, we demonstrate that the exponential dependence of m on p E universally observed in molecularly doped polymers arises naturally from the interaction of charge carriers with randomly distributed permanent dipoles. [S0031-9007(96)00689-8] PACS numbers: 72.10.Bg, 72.80.Le High-field time-of-flight experiments have been used for over two decades to characterize carrier mobilities in photoexcited molecularly doped polymers and amorphous molecular glasses [1-3]. Numerous measurements over a large range of fields E and temperatures T have established that, in many materials, the carrier mobility m exhibits a universal Poole-Frenkel behavior [4]where m 0 is a temperature independent prefactor and k is Boltzmann's constant. In a particular form of this phenomenological expression proposed by Gill [5], the activation energy Q is temperature independent, and the Poole-Frenkel factor is written g B͑b 2 b 0 ͒, where b 1͞kT , and B and b 0 1͞kT 0 are constants. In a second form, motivated by extensive numerical simulations on the Gaussian disorder model (GDM) of Bässler and coworkers [2], Q͞kT ͑2s͞3kT͒ 2 , and g C͑b 2 s 2 2 S 2 ͒, where s is the width of the energetic disorder, and C and S are constants. Many recent theoretical attempts to explain this observed proportionality between lnm and p E have focused on the role played by spatial and energetic disorder [2,6-8]. The GDM, for example, describes transport as a biased random walk among dopant molecules with Gaussian-distributed random site energies [2]. Of the various mechanisms proposed as the source of this disorder, it has been shown that the interaction of charge carriers with permanent dipoles (located on either dopant or host molecules) can give rise to a Gaussian-like density of states of the type assumed in the GDM [9,10]. Considerable data establishing a relationship between carrier mobilities and group dipole moments of molecular constituents support this view of charge-dipole interactions as the source of energetic disorder in these systems [9,[11][12][13][14][15].Unfortunately, although the standard GDM satisfactorily explains many features of experiment, such as the time-of-flight transients, it displays a field dependence similar to (1) only in a relatively narrow range and only at large fields (E . 10 5 V͞cm). Indeed, a general feature of Monte Carlo simulations [2,6] and other numerical work [8] on this problem is a significant regime at low fields in which the field dependence is much weaker than that described by (1). In experiments, by contrast, the linear dependence of lnm on p E often [16] persists down to the lowest fields probed (8 3 10 3 V͞cm).In this Letter we develop an analytical theory for the field dependence based upon an idea introduced recently by Gartstein and Conwell [17]. We show, usin...

Electron-hole recombination in disordered organic semiconductors: Validity of the Langevin formula

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