Tham khảo tài liệu 'mosfet modeling for vlsi simulation - theory and practice episode 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 296 6 MOSFET DC Model where p is the charge density in the pinch-off region. This equation can only be solved by using numerical techniques. In order to obtain an approximate analytical solution for V x y various simplifying assumptions are made. The method most widely used to solve Eq. is to ignore the field gradient in the X direction so that Eq. is reduced to Õ2V p y Sy2 eoesi Assuming uniform doping in the substrate the charge density p can be replaced by the sum of the depletion charge density qNb and mobile charge density Qị. Recall that while calculating vdsat for long channel devices we had assumed that Qi was zero in the pinch-off region. Thus following the long channel approximation one assumes that no mobile carriers are present in the pinch-off region and only depletion charge exists that is p qNb so that Eq. becomes 02V_qNb Sy2 si Integrating this equation under the following boundary conditions JZ V JVdsat at y L ld w K at y L . dv . y y J. 0 at y L ld dy we get13 where ữ 1 2eoesi Note that Eq. is the same equation as that obtained for the depletion layer width in a step pn junction with a voltage Vds Vdsat dropped across the junction. This is the model for the CLM effect first proposed by Reddi and Sah 94 to account for non-zero output conductance. However this 13 Integration can easily be performed by redefining the coordinate system such that ý 0 at y L ld and ý ld at y L so that the limits of integration are from ý 0 to h. Short-Geometry Models 297 formulation overestimates the output conductance 95 - 96 . This is because the approach completely ignores the presence of a gate electrode and treats the field problem along the channel the same as that of a pn junction between the substrate and drain regions. Further this simple approach results in a discontinuity of the field at y L ld. This is because while deriving Eq. we assumed that 0 at y L ld we also assumed that Qi 0 in the pinch-off .
