Parameter Extraction To extract the threshold voltage and mobility of the n-channel MOSFETs obtained from a foundry, test devices are measured by applying two different gate voltages with the drain voltage kept at 0.05 V. The measured drain currents are shown in the following table. VG = 1 V VG=2

Question

Parameter Extraction

To extract the threshold voltage and mobility of the n-channel MOSFETs obtained from a foundry, test devices are measured by applying two different gate voltages with the drain voltage kept at 0.05 V. The measured drain currents are shown in the following table.

[latex] V_G = 1 \ V [/latex] [latex] V_G=2 \ V [/latex]

[latex] V_D=0.05 \ V \ \ \ \ \ \ I_D=14 \ μA \ \ \ \ \ \ \ I_D=34 \ μA[/latex]

We assume that mobility degradation is not important and that the source/drain resistance is negligibly small compared to the channel resistance. Use the measurements to obtain the low-field threshold voltage and the mobility in the MOSFET if the known parameters describing it are [latex] x_{ox} [/latex] = 45 nm, W = 10 μm, and L = 1.0 μm.

Accepted Answer

At very small drain voltages [latex] V_D [/latex], Equation 9.2.9 can be used. From the values given in the table,

[latex] I_D=\mu _{eff}C_{ox}\frac{W}{L} \left(V_G-V_T-\frac{V_D}{2} ight) V_D\frac{1}{1+(V_D/\xi _{sat}L)} [/latex] (9.2.9)

[latex] 14 \mu A\approx \mu _{eff}C_{ox}\frac{W}{L} (1-V_T)V_D [/latex] (1)

[latex] 34 \mu A\approx \mu _{eff}C_{ox}\frac{W}{L} (2-V_T)V_D [/latex] (2)

Dividing Equation (2) by Equation (1) , we have [latex] \frac{2-V_T}{1-V_T} \approx \frac{34}{14} \Rightarrow V_T=0.3 \ V [/latex]

Knowing [latex] V_T [/latex]. we can use Equation 9.2.9 to find

[latex] \mu _{eff}\approx \frac{I_DL}{WC_{ox}(V_G-V_T)V_D} \ =\frac{14 imes10^{-6} imes1 imes10^{-4}}{10 imes10^{-4} imes\left(\frac{3.9 imes8.85 imes10^{-14}}{45 imes10^{-7}} ight) (1-0.3)0.05} \ = 521 \ cm^2V^{-1}s^{-1}[/latex]

Question 9.6: Parameter Extraction To extract the threshold voltage and m...

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