Extract threshold voltage and hole mobility uβ of organic PMOS

This week the supervisor provided data of PMOS inverter including the form of  value of Drain Current ID change with Gate voltage Vg (as shown in Table 1), fixed Drain voltage, oxide capacitance Cox, constant temperature Tc, aspect ratio, SI unit K and silicon permittivity εs. In order to extract Vt and uβ, the following equation are needed:

Then,the experimenters get the following equation:

It is obvious that Vt can be extracted by calculating the intercept of ID^0.5 against Vg and hole mobility uβ can be extracted by calculating the slope of the equation above. Moreover, the values of parameters mentioned above are listed as follow:

1.Drain voltage = -10  V

2.W/L = 400 mm/3mm

3.Cox = 2 x 10 -3 F/m2

4.TC  =  450 K

5.K = 7.9 x 10 -16 (SI Unit)

6.εs = 2.5

And the the form of  value of Drain Current ID and ID^0.5 change with Gate voltage Vg is show in Table 1:

Vg	ID	Square root of ID
4.1	2.41E-11	4.91E-06
4	2.31E-11	4.80E-06
3.9	2.49E-11	4.99E-06
3.8	2.21E-11	4.70E-06
3.7	2.16E-11	4.65E-06
3.6	2.06E-11	4.54E-06
3.5	2.27E-11	4.77E-06
3.4	1.75E-11	4.19E-06
3.3	1.54E-11	3.92E-06
3.2	2.21E-11	4.70E-06
3.1	1.62E-11	4.03E-06
3	1.70E-11	4.12E-06
2.9	1.78E-11	4.22E-06
2.8	1.13E-11	3.36E-06
2.7	1.62E-11	4.02E-06
2.6	1.76E-11	4.20E-06
2.5	1.36E-11	3.69E-06
2.4	1.62E-11	4.03E-06
2.3	1.72E-11	4.15E-06
2.2	1.19E-11	3.45E-06
2.1	1.62E-11	4.02E-06
2	1.47E-11	3.83E-06
1.9	1.21E-11	3.48E-06
1.8	1.86E-11	4.32E-06
1.7	1.37E-11	3.70E-06
1.6	1.40E-11	3.75E-06
1.5	1.32E-11	3.63E-06
1.4	1.49E-11	3.87E-06
1.3	1.47E-11	3.84E-06
1.2	1.67E-11	4.08E-06
1.1	1.62E-11	4.03E-06
1	1.01E-11	3.18E-06
0.9	1.83E-11	4.27E-06
0.8	1.51E-11	3.89E-06
0.7	1.30E-11	3.61E-06
0.6	1.80E-11	4.25E-06
0.5	1.71E-11	4.13E-06
0.4	1.00E-11	3.17E-06
0.3	1.70E-11	4.12E-06
0.2	1.52E-11	3.89E-06
0.1	1.42E-11	3.77E-06
0	1.56E-11	3.94E-06
-0.1	1.55E-11	3.94E-06
-0.2	1.60E-11	4.00E-06
-0.3	1.86E-11	4.31E-06
-0.4	1.52E-11	3.90E-06
-0.5	2.03E-11	4.51E-06
-0.6	1.49E-11	3.86E-06
-0.7	1.86E-11	4.31E-06
-0.8	2.24E-11	4.73E-06
-0.9	1.83E-11	4.28E-06
-1	2.07E-11	4.55E-06
-1.1	1.74E-11	4.17E-06
-1.2	2.33E-11	4.83E-06
-1.3	2.39E-11	4.89E-06
-1.4	2.47E-11	4.97E-06
-1.5	3.15E-11	5.61E-06
-1.6	3.21E-11	5.66E-06
-1.7	4.40E-11	6.63E-06
-1.8	5.63E-11	7.50E-06
-1.9	6.92E-11	8.32E-06
-2	9.15E-11	9.57E-06
-2.1	1.19E-10	1.09E-05
-2.2	1.58E-10	1.26E-05
-2.3	2.07E-10	1.44E-05
-2.4	2.65E-10	1.63E-05
-2.5	3.35E-10	1.83E-05
-2.6	4.30E-10	2.07E-05
-2.7	5.42E-10	2.33E-05
-2.8	6.74E-10	2.60E-05
-2.9	8.40E-10	2.90E-05
-3	1.04E-09	3.22E-05
-3.1	1.26E-09	3.55E-05
-3.2	1.54E-09	3.93E-05
-3.3	1.87E-09	4.32E-05
-3.4	2.24E-09	4.73E-05
-3.5	2.67E-09	5.16E-05
-3.6	3.16E-09	5.62E-05
-3.7	3.73E-09	6.11E-05
-3.8	4.37E-09	6.61E-05
-3.9	5.08E-09	7.13E-05
-4	5.89E-09	7.67E-05
-4.1	6.79E-09	8.24E-05
-4.2	7.78E-09	8.82E-05
-4.3	8.91E-09	9.44E-05
-4.4	1.02E-08	1.01E-04
-4.5	1.15E-08	1.07E-04
-4.6	1.30E-08	1.14E-04
-4.7	1.47E-08	1.21E-04
-4.8	1.65E-08	1.29E-04
-4.9	1.85E-08	1.36E-04
-5	2.07E-08	1.44E-04
-5.1	2.29E-08	1.51E-04
-5.2	2.55E-08	1.60E-04
-5.3	2.82E-08	1.68E-04
-5.4	3.10E-08	1.76E-04
-5.5	3.43E-08	1.85E-04
-5.6	3.76E-08	1.94E-04
-5.7	4.11E-08	2.03E-04
-5.8	4.50E-08	2.12E-04
-5.9	4.91E-08	2.22E-04
-6	5.35E-08	2.31E-04
-6.1	5.82E-08	2.41E-04
-6.2	6.31E-08	2.51E-04
-6.3	6.84E-08	2.62E-04
-6.4	7.38E-08	2.72E-04
-6.5	7.96E-08	2.82E-04
-6.6	8.60E-08	2.93E-04
-6.7	9.25E-08	3.04E-04
-6.8	9.93E-08	3.15E-04
-6.9	1.06E-07	3.26E-04
-7	1.14E-07	3.37E-04
-7.1	1.22E-07	3.49E-04
-7.2	1.30E-07	3.61E-04
-7.3	1.38E-07	3.72E-04
-7.4	1.47E-07	3.84E-04
-7.5	1.57E-07	3.96E-04
-7.6	1.66E-07	4.07E-04
-7.7	1.76E-07	4.19E-04
-7.8	1.87E-07	4.32E-04
-7.9	1.97E-07	4.44E-04
-8	2.08E-07	4.56E-04
-8.1	2.19E-07	4.68E-04
-8.2	2.32E-07	4.81E-04
-8.3	2.44E-07	4.94E-04
-8.4	2.58E-07	5.08E-04
-8.5	2.72E-07	5.22E-04
-8.6	2.88E-07	5.36E-04
-8.7	3.03E-07	5.51E-04
-8.8	3.19E-07	5.65E-04
-8.9	3.36E-07	5.80E-04
-9	3.53E-07	5.94E-04
-9.1	3.70E-07	6.08E-04
-9.2	3.88E-07	6.23E-04
-9.3	4.06E-07	6.37E-04
-9.4	4.25E-07	6.52E-04
-9.5	4.44E-07	6.66E-04
-9.6	4.65E-07	6.82E-04
-9.7	4.85E-07	6.96E-04
-9.8	5.06E-07	7.11E-04
-9.9	5.26E-07	7.26E-04
-10	5.48E-07	7.40E-04
-10.1	5.70E-07	7.55E-04
-10.2	5.92E-07	7.70E-04
-10.3	6.15E-07	7.84E-04
-10.4	6.39E-07	7.99E-04
-10.5	6.62E-07	8.14E-04
-10.6	6.86E-07	8.28E-04
-10.7	7.10E-07	8.43E-04
-10.8	7.37E-07	8.58E-04
-10.9	7.62E-07	8.73E-04
-11	7.86E-07	8.87E-04
-11.1	8.12E-07	9.01E-04
-11.2	8.39E-07	9.16E-04
-11.3	8.66E-07	9.31E-04
-11.4	8.93E-07	9.45E-04
-11.5	9.20E-07	9.59E-04
-11.6	9.48E-07	9.74E-04
-11.7	9.75E-07	9.88E-04
-11.8	1.00E-06	0.001
-11.9	1.03E-06	0.00102
-12	1.06E-06	0.00103
-12.1	1.09E-06	0.00104
-12.2	1.12E-06	0.00106
-12.3	1.14E-06	0.00107
-12.4	1.17E-06	0.00108
-12.5	1.20E-06	0.00109
-12.6	1.23E-06	0.00111
-12.7	1.26E-06	0.00112
-12.8	1.29E-06	0.00114
-12.9	1.32E-06	0.00115
-13	1.36E-06	0.00116
-13.1	1.39E-06	0.00118
-13.2	1.42E-06	0.00119
-13.3	1.45E-06	0.0012
-13.4	1.48E-06	0.00122
-13.5	1.51E-06	0.00123
-13.6	1.55E-06	0.00124
-13.7	1.58E-06	0.00126
-13.8	1.61E-06	0.00127
-13.9	1.64E-06	0.00128
-14	1.67E-06	0.00129
-14.1	1.68E-06	0.0013
-14.2	1.71E-06	0.00131
-14.3	1.72E-06	0.00131
-14.4	1.73E-06	0.00132
-14.5	1.75E-06	0.00132
-14.6	1.77E-06	0.00133
-14.7	1.79E-06	0.00134
-14.8	1.81E-06	0.00134
-14.9	1.83E-06	0.00135
-15	1.84E-06	0.00136
-15.1	1.86E-06	0.00137
-15.2	1.88E-06	0.00137
-15.3	1.91E-06	0.00138
-15.4	1.93E-06	0.00139
-15.5	1.95E-06	0.0014
-15.6	1.97E-06	0.0014
-15.7	1.99E-06	0.00141
-15.8	2.03E-06	0.00143
-15.9	2.08E-06	0.00144
-16	2.12E-06	0.00146
-16.1	2.16E-06	0.00147
-16.2	2.20E-06	0.00148
-16.3	2.24E-06	0.0015
-16.4	2.28E-06	0.00151
-16.5	2.32E-06	0.00152
-16.6	2.36E-06	0.00153
-16.7	2.39E-06	0.00155
-16.8	2.43E-06	0.00156
-16.9	2.46E-06	0.00157
-17	2.50E-06	0.00158
-17.1	2.53E-06	0.00159
-17.2	2.57E-06	0.0016
-17.3	2.60E-06	0.00161
-17.4	2.63E-06	0.00162
-17.5	2.66E-06	0.00163
-17.6	2.70E-06	0.00164
-17.7	2.73E-06	0.00165
-17.8	2.76E-06	0.00166
-17.9	2.79E-06	0.00167
-18	2.82E-06	0.00168
-18.1	2.84E-06	0.00169
-18.2	2.87E-06	0.00169
-18.3	2.90E-06	0.0017
-18.4	2.92E-06	0.00171
-18.5	2.95E-06	0.00172
-18.6	2.98E-06	0.00173
-18.7	3.00E-06	0.00173
-18.8	3.03E-06	0.00174
-18.9	3.05E-06	0.00175
-19	3.07E-06	0.00175
-19.1	3.10E-06	0.00176
-19.2	3.12E-06	0.00177
-19.3	3.14E-06	0.00177
-19.4	3.17E-06	0.00178
-19.5	3.19E-06	0.00179
-19.6	3.21E-06	0.00179
-19.7	3.23E-06	0.0018
-19.8	3.25E-06	0.0018
-19.9	3.27E-06	0.00181
-20	3.29E-06	0.00181
-20.1	3.30E-06	0.00182
-20.2	3.33E-06	0.00182
-20.3	3.34E-06	0.00183
-20.4	3.36E-06	0.00183
-20.5	3.38E-06	0.00184
-20.6	3.39E-06	0.00184
-20.7	3.41E-06	0.00185
-20.8	3.43E-06	0.00185
-20.9	3.45E-06	0.00186
-21	3.46E-06	0.00186
-21.1	3.48E-06	0.00186
-21.2	3.49E-06	0.00187
-21.3	3.51E-06	0.00187
-21.4	3.52E-06	0.00188
-21.5	3.54E-06	0.00188
-21.6	3.55E-06	0.00188
-21.7	3.56E-06	0.00189
-21.8	3.58E-06	0.00189
-21.9	3.59E-06	0.00189
-22	3.60E-06	0.0019
-22.1	3.61E-06	0.0019
-22.2	3.63E-06	0.0019
-22.3	3.64E-06	0.00191
-22.4	3.65E-06	0.00191
-22.5	3.66E-06	0.00191
-22.6	3.67E-06	0.00192
-22.7	3.69E-06	0.00192
-22.8	3.69E-06	0.00192
-22.9	3.71E-06	0.00193
-23	3.72E-06	0.00193
-23.1	3.73E-06	0.00193
-23.2	3.74E-06	0.00193
-23.3	3.75E-06	0.00194
-23.4	3.75E-06	0.00194
-23.5	3.76E-06	0.00194
-23.6	3.77E-06	0.00194
-23.7	3.78E-06	0.00194
-23.8	3.79E-06	0.00195
-23.9	3.79E-06	0.00195
-24	3.81E-06	0.00195
-24.1	3.81E-06	0.00195
-24.2	3.83E-06	0.00196
-24.3	3.83E-06	0.00196
-24.4	3.84E-06	0.00196
-24.5	3.85E-06	0.00196
-24.6	3.85E-06	0.00196
-24.7	3.86E-06	0.00196
-24.8	3.86E-06	0.00197
-24.9	3.87E-06	0.00197
-25	3.88E-06	0.00197

             Table 1

Then,the experimenters plot the sub-threshold plot is shown in below:

Figure 1 The Sub-threshold Plot

Then, select part of the data above to draw a fitting straight line to get the intercept and slope of the curve. And the figure is shown in Figure 2

Figure 2 Fitting Straight Line of Sub-threshold Plot

According to the figure above, the experimenter find the slop of the straght line is -1.22*10^-4 and the constant of the equation of straight line is 4.77*10^-4. Therefore, the hole mobility uβ of the organic PMOS is:

1.1163*10^-4 cm²/V*s    

and the threshold voltage of the organic inveter is :

Vt = 4.77*10^-4 / -1.22*10^-4 ≈ -3.9V

which is similar to the value of intercept of square root of  drain current againist gate voltage.