Analytic Solutions of Drift-Diffusion Equations and Mobility of Organic Semiconductors

Although the drift-diffusion model (DDM) is fundamental in semiconductor physics and related fields, the accurate solution of the DDM is unavailable over a long period of time. The DDM is accurately and analytically solved based on the Fermi-Dirac statistics and general mobility model. The differences in current values, carrier density, and electric field functions between the accurate solution, other solutions, and the standard Scharfetter-Gummel (SG) scheme are evident. The results for mobility extracted from the accurate solution are larger and evidently different from those of the SG scheme, Mott-Gurney equation, and the analytic solution under the uniform-electric-field approximation.