Observing the effects of changing tox to the gain of a simple

amplifierBy R. E. Evans

tox

• Process parameter

• Thickness of the gate oxide

• Cox = εox/tox -> As tox increases, Cox decreases

• Cox affects ß, gate capacitance

Why vary tox?

• Because fabrication process is not perfect• Variation in tox will vary from wafer to wafer and

slight variation on the same platter• This experiment varies tox beyond tolerances to

make the results look good, but the same experiment can be done with actual variations from a given process and foundry which usually go between 0.1nm to 1nm

My experiment

• Make a schematic of a simple amplifier

• Alter the sized pair model to allow for variation of tox

• Use previous test circuits to find gm, gds

• Find an equation for gain in terms of tox

• Show theoretical versus simulated

Simple amplifier circuit

Simulation parameters

• Changed TOX to TOX = {tox + 1.41E-8}

• Will vary tox from -7nm to 49 nm in 7nm steps

• Sweep Vin from 0 to 2 volts, Ix = 100 uA

Results

• Gain = -gm1/(gds1+gds2)

• gm is in terms of beta, which is dependent on Cox, which is dependent on tox

• Use our level-1 approximation for gm1, gds1, gds2

• gds1 = I+Ino/Va gds2=I+Ipo/Va gm1=SQRT(2*eox/tox*uo*W/L*(I+I1))

Results - Gain

Results – Max Gain vs. Tox

Results – Max Gain vs. Tox from -1nm to +1nm

Results – gds1, gds2, gm1

• From previous exercises: gds1 = 3.68 V, gds2 = 6.4 V

• gm1 = SQRT(B*(100+45))

• Theoretical gain =

-SQRT(2*0.6*B*(100+45))/(3.68+6.4)

Curve Fit

• Difference between my theoretical values and simulated values were off by a small factor

• Added a shift element to the equation

• New Theoretical gain =

-SQRT(2*0.6*B*(100+45))/(3.68+6.4)*-12

Results - Curve

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

0.00E+00

1.00E-02

2.00E-02

3.00E-02

4.00E-02

5.00E-02

6.00E-02

7.00E-02

Simulation

Theory

Conclusion

• Saw the overall effect of changing tox, did get my expected results: which means I had a good equations and tox vs. gain can be modeled in level-1 terms

• Reported tolerances in tox can shift the peak gain by 6 which needs to be at least noted when designing analog IC’s