Modeling of the effective field dependent mobility for the random discrete dopant simulation

Abstract

In the thesis, an effective field dependent mobility model, which can be applied to the random discrete dopants (RDD) simulation of the current variation, is proposed. In order to evaluate the characteristics of the silicon devices considering the RDD, the proper electrostatic and mobility model should be used simultaneously. To deal with the discrete dopants, the electrostatic effect can be modeled by the density gradient (DG) methods, but the appropriate mobility model for the RDD simulation has not been fully exploited. The conventional doping-dependent mobility model such as the Masetti model has been widely used because the device sizes are relatively larger than the varying range of the doping concentration. However, if one applies this Masetti model to the RDD simulation, it leads to incorrectly high terminal currents, since the mobility values of each mesh are determined abnormally. By the doping-dependent nature of the Masetti model, the meshes with the extremely high doping concentrations (representing the individual dopants) have very low mobility values. But, the remaining intrinsic meshes have the maximum mobility, and it leads to the incorrect high terminal currents. In order to reproduce the target current in the RDD simulation, the proper mobility model for the RDD simulation should be available. First, a new quantity called mobility field is defined in each mesh. The mobility field is derived from the definition of the renowned effective field of the Takagi et al., considering the analogy between the inversion layer in the MOS surfaces and the vicinity of the discrete dopants. This new mobility field still includes the physical consistency with the conventional effective field which determines the mobility of the devices. The consistency is confirmed using the MOS simulation. Second, the formula of the mobility value in each mesh is established using this mobility field, and the model parameters is found to make the resultant currents of the RDD simulation reproduce the correct current targets. Using the proposed mobility model and the model parameters, the terminal currents of the RDD simulation successfully reproduce the target currents with the linear error rate of < 1% for the wide range of doping concentrations and temperatures simultaneously. The determined model parameters have intriguing properties. The coefficients in the mobility formula have the linear and the exponential dependence to the inverse of the temperature, respectively. The exponents in the formula have the values near 1/3 and 3/2, respectively. These quantities are related to the conventional surface mobility degradation models such as the Lombardi model, which includes the linearity to 1/T and 1/3-dependence to the transverse electric fields. It can be considered that the same physical scattering effects are governed near the surface channel region and the discrete dopants.