Analytical evaluation of the charge carrier density of organic materials with a Gaussian density of states revisited

作者：Selvaggi Jerry P.^*

来源：Journal of Computational Electronics, 2018, 17(1): 61-67.

DOI：10.1007/s10825-017-1113-5

• Organic materials
• Charge carrier density
• Gaussian distribution
• Fermi-Dirac integral
• Error functions
• Density of states

An analytical solution for the calculation of the charge carrier density of organic materials with a Gaussian distribution for the density of states is presented and builds upon the ideas presented by Mehmetoglu (J Comput Electron 13: 960-964, 2014) and Paasch et al. (J Appl Phys 107: 104501-1-104501-4, 2010). The integral of interest is called the Gauss-Fermi integral and can be viewed as a particular type of integral in a family of the more general Fermi-Dirac-type integrals. The form of the Gauss-Fermi integral will be defined as
G (alpha, beta, xi) = integral(infinity)(-infinity) e-alpha(x-beta)(2)/1 + e(x-xi)dx,
where G (alpha, beta, xi) is a dimensionless function. This article illustrates a technique developed by Selvaggi et al. [3] to derive a mathematical formula for a complete range of parameters alpha, beta, and xi valid for all alpha epsilon R >= 0, beta epsilon R, and for all xi epsilon R.

• 出版日期2018-3