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Vth nmos transistor8/11/2023 ![]() How CMOS leverages the advantages of PMOS and NMOS for a superior switching device.ĬMOS technology (shown above in an image sensor) marked the end of the PMOS vs. ![]() The early manufacturing difficulties of NMOS and its growth to prominence. The threshold voltages for the different substrate voltages are listed in the table below.The beginning of active switching elements and the transition to PMOS. The body effect parameter was obtained from: Where the flatband voltage without substrate bias, V T0, was already calculated in example 6.2. The threshold voltage at V BS = -2.5 V equals: Assume there is no fixed charge in the oxide or at the oxide-silicon interface. The capacitor has a substrate doping N a = 10 17 cm -3, a 20 nm thick oxide (ε ox = 3.9 ε 0) and an aluminum gate (Φ M = 4.1 V). This is due to the larger depletion layer width, which reduces the relative variation of the depletion layer charge along the channel.Ĭalculate the threshold voltage of a silicon nMOSFET when applying a substrate voltage, V BS = 0, -2.5, -5, -7.5 and -10 V. The difference however reduces as a more negative bulk-source voltage is applied. As the drain-source voltage at saturation is increased, there is an increasing difference between the drain current as calculated with each model. For a device biased at the threshold voltage, drain saturation is obtained at zero drain-to-source voltage so that the depletion layer width is constant along the channel. Square root of I D versus the gate-source voltage as calculated using the quadratic model (upper curves) and the variable depletion layer model (lower curves).įirst, we observe that the threshold shift is the same for both models. The expected characteristics, as calculated using the quadratic model and the variable depletion layer model, are shown in Figure 7.4.2. The variation of the threshold voltage with the applied bulk-to-source voltage can be observed by plotting the transfer curve for different bulk-to-source voltages. Where Γ is the body effect parameter given by: The threshold difference due to an applied source-bulk voltage can therefore be expressed by: This results in a modified expression for the threshold voltage, as given by: ![]() The voltage difference between the source and the bulk, V BS changes the width of the depletion layer and therefore also the voltage across the oxide due to the change of the charge in the depletion region. The voltage applied to the back contact affects the threshold voltage of a MOSFET. A variation of the flatband voltage due to oxide charge will cause a reduction of both threshold voltages if the charge is positive and an increase if the charge is negative. The threshold of nMOSFETs increases with doping while the threshold of pMOSFETs decreases with doping in the same way. The threshold of both types of devices is slightly negative at low doping densities and differs by 4 times the absolute value of the bulk potential. Threshold voltage of n-type (upper curve) and p-type (lower curve) MOSFETs versus substrate doping density. The threshold voltage dependence on the doping density is illustrated with Figure 7.4.1 for both n-type and p-type MOSFETs with an aluminum gate metal. The threshold voltage of a p-type MOSFET with an n-type substrate is obtained using the following equations: Where the flatband voltage, V FB, is given by: The threshold voltage equals the sum of the flatband voltage, twice the bulk potential and the voltage across the oxide due to the depletion layer charge, or: In this section we summarize the calculation of the threshold voltage and discuss the dependence of the threshold voltage on the bias applied to the substrate, called the substrate bias effect. 7.4 Threshold voltage 7.4.1. Threshold voltage calculation 7.4.2. The substrate bias effect
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