A2-D Semi Analytical Model For Ultra-Short Channel MOSFET Taking Into Account The Junctions Depth

With the development of semiconductor preparation technology,the gate length of MOSFETs decreases rapidly and the number of devices on a chip increases exponentially. Presently, the gate length of MOSFETs has scaled down to10-20nm, these aggressive scaling gives rise to various undesirable short-channel effects(SCEs), which will affect the device characteristics seriously and bring a series of new challenges in simulation. At the same time, high speed and accurate model is of great value in improving the performance of integrated circuits and shortening the development cycle. Therefore, the ultra short channel transistors need to be modeled so as to adapt to the development of semiconductor technology.Simulation model can be divided into two kinds. One is the analytical model in circuit simulation, which has a set of analytical functions with some fitting parameters, small calculation and low accuracy, such as SPICE model. Another kind is the numerical model of device simulation, which is characterized by high precision, heavier calculation, such as MEDICI, ATLAS TCAD, etc. In order to take the advantages of analytic model and numerical model, a Semi-Analytical Method (SAM)is proposed for the deep junctions MOSFET and shallow junctions MOSFET modeling in this paper. The SAM is derived from the theory of generalized multilevel, but differs on the solution of undetermined coefficient. The concrete process of SAM is:determining the coordinate system of MOS devices and listing the oxide layer and space charge definite solutions including Poisson equation and boundary conditions, solving the problem to get two-dimensional potential with a series of undetermined coefficients, then expansion the equations of different regions boundary connection with characteristic function and finally we get the matrix of undetermined coefficients.In order to simplify the boundary condition, the current model does not consider the effects of junction depth, but the truth is just the opposite. Therefore, on the basis of deep junctions semi-analytical model, we propose the potential definite solutions and corresponding boundary conditions taking into account the depth of source and drain junctions in this paper, and solve the two-dimensional potential model by using SAM for the first time. The results show that our proposed SAM is a kind of new modeling method, not only has contract analytical expression, but also has high accuracy with certain number of undetermined coefficients.Due to the potential model contains depletion depth which calculated by the potential, it is clear that an accurate modeling of potential is possible only when an appropriate model for the depletion depth is used for ultra short channel device. But the previous depletion depth models don’t apply the ultra-shallow junctions short-channel MOSFET which cause a decline in the model accuracy. A self-consistent solution of depletion depth and iteration calculation of potential is proposed in this paper according to the boundary conditions at the bottom of depletion region. Compared with MEDICI numerical calculation, I find that the self-consistent iteration solution has faster convergence speed and less amount of calculation. I also discuss the sub-threshold current based on the two-dimensional potential model. Finally, potential distribution, depletion depth, the sub-threshold current and threshold voltage have been verified. The comparison results show that, this model, which can be directly used in circuit simulation, has the characteristics of its expression without fitting parameter and small calculating amount.