Short-Channel Model Use the short-channel model to find values for VDsat and IDsat for a MOSFET with the following parameters: xox = 20 nm, W = 50 μm, L = 0.5 μm, VT = 0.7 V when its source is at zero potential, and with bias voltages VG = 3 V and VD = 1.5 V . Compare these results to the

Question

Short-Channel Model

Use the short-channel model to find values for [latex] V_{Dsat} [/latex] and [latex] I_{Dsat} [/latex] for a MOSFET with the following parameters: [latex] x_{ox} = 20 \ nm, W = 50 \ μm, L = 0.5 \ μm, V_T = 0.7 \ V [/latex] when its source is at zero potential, and with bias voltages [latex] V_G = 3 \ V [/latex] and [latex] V_D = 1.5 \ V [/latex]. Compare these results to the predictions of the long-channel model.

Accepted Answer

From Equation 9.2.3 with [latex] V_Z = 0.5 V [/latex],

[latex] \xi _{eff}=\frac{(V_G-V_T)}{6x_{ox}} +\frac{(V_T+V_Z)}{3x_{ox}} =3.92 imes10^5 \ Vcm^{-1} [/latex]

From Equation 9.2.4 and Table 9.3

[latex] \mu _{eff}=\frac{\mu _0}{1+(\xi _{eff}/\xi _0)^ u } [/latex] (9.2.4)

	Unit	Electron (surface)	Hole (surface)	Hole (subsurface)
[latex] \mu _0 [/latex]	cm²/V-s	670	160	290
[latex] \xi _0 [/latex]	MV/cm	0.67	0.7	0.35
[latex] u [/latex]		1.6	1.0	1.0

[latex] \mu _{eff}=\frac{\mu _0}{1+(\xi _{eff}/\xi _0)^ u } =470 \ cm^2 \ V^{-1} \ s^{-1} [/latex]

Taking [latex] v_{sat} = 8 imes 10^6 cm s^{-1} [/latex], we calculate [latex] \xi _{sat} = 2\frac{v_{sat}}{\mu _{eff}} = 3.4 imes 10^4 \ Vcm^{-1} [/latex]

From Equation 9.2.11, [latex] V_{Dsat} = \frac{\xi _{sat}L(V_G-V_T)}{\xi _{sat}L+(V_G-V_T)} =0.98 \ V [/latex]

Because the applied drain voltage is 1.5 V (> [latex] V_{Dsat} [/latex]), the MOSFET is in the saturated-drain-current region; hence, using Equation 9.2.10,

[latex] I_{Dsat}=WC_{ox}(V_G-V_T-V_{Dsat})v_{sat}=9 \ mA [/latex]

To compare these results to those from the long-channel theory, we first calculate [latex] V_{Dsat} = V_G - V_T = 2.3 \ V [/latex] so that the MOSFET is operating below the saturation region. From Equation 9.1.5 we find

[latex] I_D=\mu _nC_{ox}\frac{W}{L} \left[\left(V_G-V_T-\frac{1}{2}V_D ight)V_D ight] \ \ \ \ \ ext{ or } \ \ \ \ \ I_D=24 \ mA [/latex]

using a typical low-field mobility value of [latex] 600 cm^2 V^{-1} s^{-1} [/latex]. The very different results obtained using these two models show the degree to which the MOSFET behavior is influenced by short-channel effects.

Question 9.4: Short-Channel Model Use the short-channel model to find valu...

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