Tham khảo tài liệu 'mosfet modeling for vlsi simulation - theory and practice episode 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 216 5 Threshold Voltage distribution of the potential Ộ. Physically speaking Eq. means that the influence of the lateral drain-source field on the potential barrier height is equivalent to and can be replaced by the reduction in the doping concentration 50 Although Eq. could be solved for any doping profile assuming a step doping profile one obtains 49 Kfci vfb ộsi - V2eữ siqNeff ộsi - Psfc when XJm X ox while Ka2 - ox yựộsi X2 Neff Nb when xdm X where N ff ir 2eoes E AL------0 ds qL2 and V ds is given by Eq. . The above model for vth shows an approximately inverse quadratic dependence on channel length L and an inverse dependence on oxide capacitance Cox. It should be pointed out that the weak dependence of the short-channel effect on the junction depth Xj has not been taken into account. In normal enhancement devices this effect is small. Figure shows the Vtll variation with drain bias for two different back bias ov and Kh 2V . Continuous lines are experimental data while dashed lines are based on Eq. . As can be seen agreement between the experimental data and the model is fairly good. Empirical Approach. Very often in actual devices the exponential dependence of the DIBL effect on L is not observed. In such cases an empirical approach is often used assuming the surface potential to be constant along the length of the channel even for short channel devices. This assumption results in a very simple expression for Ơ which can be derived as follows 79 . When vds is small V the substrate depletion region width Xdm may be calculated using the Poisson equation. When vds is large an additional potential will be imposed in the region already depleted. Since no additional charge appears in Poisson s equation this additional potential satisfies the Laplace equation d2v. A o. dx2 Threshold Voltage Variations with Device Length and Width 217 Under the simplifying assumptions that 1 source drain junction depths are .
