Departamento de Física, Universidade Federal do Paraná, Curitiba-PR, Brazil.
J Chem Phys. 2011 Feb 28;134(8):084112. doi: 10.1063/1.3548884.
We have reformulated a traditional model used to describe the current-voltage dependence of low mobility materials sandwiched between planar electrodes by using the quasi-electrochemical potential as the fundamental variable instead of the local electric field or the local charge carrier density. This allows the material density-of-states to enter explicitly in the equations and dispenses with the need to assume a particular type of contact. The diffusion current is included and as a consequence the current-voltage dependence obtained covers, with increasing bias, the diffusion limited current, the space-charge limited current, and the injection limited current regimes. The generalized Einstein relation and the field and density dependent mobility are naturally incorporated into the formalism; these two points being of particular relevance for disordered organic semiconductors. The reformulated model can be applied to any material where the carrier density and the mobility may be written as a function of the quasi-electrochemical potential. We applied it to the textbook example of a nondegenerate, constant mobility material and showed how a single dimensionless parameter determines the form of the I(V) curve. We obtained integral expressions for the carrier density and for the mobility as a function of the quasi-electrochemical potential for a Gaussianly disordered organic material and found the general form of the I(V) curve for such materials over the full range of bias, showing how the energetic disorder alone can give rise, in the space-charge limited current regime, to an I∝V(n) dependence with an exponent n larger than 2.
我们重新制定了一个传统的模型，用于描述夹在平面电极之间的低迁移率材料的电流-电压依赖性，该模型使用准电化学势作为基本变量，而不是局部电场或局部载流子密度。这使得材料的态密度可以明确地包含在方程中，并避免了需要假设特定类型的接触。扩散电流被包含在内，因此获得的电流-电压依赖性随着偏压的增加，涵盖了扩散限制电流、空间电荷限制电流和注入限制电流区域。广义的爱因斯坦关系和场依赖的和密度依赖的迁移率自然地被纳入到形式主义中；这两点对无序有机半导体特别重要。重新制定的模型可以应用于任何载流子密度和迁移率可以表示为准电化学势函数的材料。我们将其应用于非简并、恒迁移率材料的典型示例，并展示了一个单一的无量纲参数如何决定 I(V)曲线的形式。我们获得了高斯无序有机材料中载流子密度和迁移率作为准电化学势函数的积分表达式，并找到了此类材料在整个偏压范围内的 I(V)曲线的一般形式，展示了仅能量无序如何在空间电荷限制电流区域中导致 I∝V(n)的依赖性，其中指数 n 大于 2。
