Quasi Two-dimensional MOSFET Threshold Voltage Model Of Considering The Source And Drain Field

The rapid development of semiconductor technology has brought about great changes to all walks of life, greatly improving labor productivity and the quality of people’s lives. At the same time it also brings serious challenges to the semiconductor and integrated circuit itself, that is there are a great variety of products and they renew rapidly, therefore it requires researchers and the industry develop new technologies continually to keep up with the pace of development. Bulk silicon CMOS technology has become the dominant technology of microelectronics products.According to the theory of scaling down, generations of new products have been developed by the CMOS technology, every three years, the integration density and circuit performance is increased by times, Now CMOS technology has come to deep submicron and even nano era, the size of MOS device are getting smaller and smaller, its device physics and technology has become more and more complex, which need people keep using the new device structure, new materials and new working principle to break through the limits of the original.Now, as device sizes scaling down, a series of physical effects influencing the performance of the devices are produced, Some people think that CMOS technology has getting more and more close to the basic physical limits, therefore, it is necessary to consider the potential ability CMOS, and the development direction of CMOS into the nano range, although we have gained tremendous benefits from the conventional scaled-down law, the cost is also more and more expensive. In this case, improving structure design and using new materials may play a huge role.The threshold voltage is the important parameters to descript the switching characteristics of the MOSFET devices.One of the basic requirements for the analysis of MOS transistor is to get surface potential. For a long-channel device, the junction depletion layers along the channel due to the source-substrate and drain-substrate junctions constitute a negligible portion of the channel. In weak inversion or depletion regime, the surface potential may be considered to constant over the large portion of the channel, constituting the entire channel minus the above two junction depletion layers.We need to consider the surface potential only over this portion to compute. However, in the case of short channel devices, the electric field effect of source and drain junction regions is very important to surface potential.The junction regions constitute a signifc ant portion of the channel can not be neglected compared to the small channel length.The conventional threshold voltage model does not consider the source and drain p-n junction electric field, when the size decreases, effect of source and drain p-n junc tion electric field to the threshold voltage can not be ignored. In this paper, according to the Gauss theorem, combined with numerical simulation, a quasi-one dimensional threshold voltage model is established. Firstly, p-n junction of source and drain side are approximately regarded as the abrupt junction, calculating the electric field intensity of the source and drain side in p-n junction space charge region. By applying Gauss’s law and neglecting the mobile carrier charge, considering the source and drain p-n junction electric field and fitting a parameter relevant to them, the Quasi two-dimensional MOSFET threshold voltage model can be established. According to classic model, the depletion layer thickness can be gained by the surface potential, in the model for this paper, the relation of the surface potential and the depletion layer thickness also can be got, we assume when the depletion thickness is equal to the classical model’s, the device is inversion, then the gate voltage is threshold voltage. We can obtain the threshold voltage by using the classical threshold voltage expression.For the assumptions above, the result can be verified through numerical simulation and theoretical calculation, Firstly source and drain junction electric field related parameters can be fitted into a function,then change different parameters to simulate by the Medici and to caculate by MATLAB,comparing the theoretical and simulation value, so as to prove the threshold voltage expression is correct.