Question 9.6: Parameter Extraction To extract the threshold voltage and m...
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.
V_G = 1 \ V V_G=2 \ V
V_D=0.05 \ V \ \ \ \ \ \ I_D=14 \ μA \ \ \ \ \ \ \ I_D=34 \ μA
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 x_{ox} = 45 nm, W = 10 μm, and L = 1.0 μm.
At very small drain voltages V_D , Equation 9.2.9 can be used. From the values given in the table,
I_D=\mu _{eff}C_{ox}\frac{W}{L} \left(V_G-V_T-\frac{V_D}{2} \right) V_D\frac{1}{1+(V_D/\xi _{sat}L)} (9.2.9)
14 \mu A\approx \mu _{eff}C_{ox}\frac{W}{L} (1-V_T)V_D (1)
34 \mu A\approx \mu _{eff}C_{ox}\frac{W}{L} (2-V_T)V_D (2)
Dividing Equation (2) by Equation (1) , we have \frac{2-V_T}{1-V_T} \approx \frac{34}{14} \Rightarrow V_T=0.3 \ V
Knowing V_T . we can use Equation 9.2.9 to find
\mu _{eff}\approx \frac{I_DL}{WC_{ox}(V_G-V_T)V_D} \\ =\frac{14\times10^{-6}\times1\times10^{-4}}{10\times10^{-4}\times\left(\frac{3.9\times8.85\times10^{-14}}{45\times10^{-7}} \right) (1-0.3)0.05} \\ = 521 \ cm^2V^{-1}s^{-1}