The modern electronic devices have been scaled down significantly. The scaling rules would dictate higher doping concentrations which lead us to consider the degeneracy in the calculations. One of the semiconductor device quantities that would be impacted by considering the degeneracy is the Einstein Relation. The commonly used formula of Einstein Relation assumes that it is constant and independent of doping. The doping-independent Einstein Relation would cause serious inaccuracy in the calculations. This paper offers a closed-form solution fordoping-dependent Einstein Relation. The proposed expression employs approximations of Fermi-Dirac Integrals (FDI) needed in the Einstein Relation. The quality and accuracy of the proposed approximations have been determined.

现代电子设备已大大缩小。缩放规则将要求较高的掺杂浓度，这导致我们在计算中考虑简并性。爱因斯坦关系是受简并性影响的半导体器件数量之一。爱因斯坦关系的常用公式假定它是恒定的并且与掺杂无关。独立于掺杂的爱因斯坦关系会在计算中引起严重的误差。本文为依赖掺杂的爱因斯坦关系提供了一种封闭形式的解决方案。拟议的表达式采用了爱因斯坦关系中所需的费米-狄拉克积分（FDI）的近似值。已经确定了所提出的近似值的质量和准确性。