Tham khảo tài liệu 'mosfet modeling for vlsi simulation - theory and practice episode 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 176 5 Threshold Voltage Fig. Calculated threshold voltage for n- and p-channel MOSFETs as a function of substrate doping Nb for n polysilicon gate left scale and p polysilicon gate right scale for three different oxide thickness. After Sze 5 curves are based on the assumption that Qo 0 a reasonable assumption for modern VLSI processes. The temperature through the ộf term the higher the temperature the lower the Vlh for details see section The body bias Vsb the higher the Vsb the higher the Vth. The increase in vth due to an increase in Vsb can be obtained from Eq. as vth - VT0 y 2ộf vsb - ựĩộpY Body-Effect. The variation of vth with Vsb is often called the substrate bias sensitivity or body-effect. Differentiating Eq. with respect to Vsb we get 7 - dvsb 2y 2ộf vsb where the and the signs are for n- and p-channel devices respectively. This equation shows that the body-effect increases as the body factor 7 Nonuniformly Doped MOSFET 177 increases and body bias Vsb decreases. For circuit design it is often desirable to lower the body effect 3 which means the body factor y should be reduced. From Eq. it is evident that y can be reduced with lower doping concentration Nb and or lower oxide thickness tox. However lowering Nb for example conflicts with the scaling rule cf. section . In fact the choice of process or circuit parameters is a trade off between various parameters involved in device design. SPICE Implementation. Note that Eq. becomes invalid for Vsb 2ộf . when the S D diodes become forward biased by an amount 2ộf. Although during normal operation of the device the S D diodes will not be forward biased however in SPICE during Newton-Raphson iterations it is possible to encounter Ps6 2 f f. This is just an artifact of the iteration solution process and convergence to a proper solution requires the model to behave well even in such invalid operating regions. Therefore to use Eq. or in the forward biased .
