# Help me to calculate Kn Cox

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#### shaq

##### Full Member level 5
Which one is correct?

Dear all,

When I calculate K'n=(0.5)µnCox, I have a problem.

By TSMC 0.35µm SPICE model, I know these parameters (TT case):

(1) U0=0.04660162 (NMOS)
(2) tox=toxn=7.5e-9
(3) λ=DELTA= 0.01
(4)Vth0=0.536027

And, we know that ε=εox*ε0=3.9*8.854e-14F/cm=3.46e-11F/m
also know that Cox= ε/tox
so, we can get K'n=(0.5)*U0*Cox=0.5*0.04660162 *3.46e-11/7.5e-9=107.49µA/V

But, I use hspice to simulate a NFET which the result does not match to 107.49µA/V
Code:
Vgs g 0 1V
Vds d 0 0V
Vbs b 0 0V
*NFET

M1 d g 0 b NCH L=1u W=1u

.LIB 'mm0355v.l' TT
.options post probe

*For I-V Curve Id vs Vds with Vgs = 1V
.dc vds 0 3.3 0.01
.probe Id(M1)
.end

The figure of the result is shown below.

Because Vgs=1v and (W/L)=1, we can get Id=17µA

17µA=K'n(1-0.536027)^2*(1+0.01*3) , so we can get K'n=76.67µA/V

Can anyone tell me which K'n is correct?:?:

#### pthoppay

##### Member level 5
Re: Which one is correct?

Hi,

In my opinion the difference could be due to the variation in the mobility between the theoritical and simulated one.

Although 466 cm2/Vsec is a good assumption but working in the deep saturation might reduce the mobility ( I guess).

For further knowledge on dependence of mobility on gate volatge, please refer to

https://www.research.ibm.com/journal/rd/342/ibmrd3402a3J.pdf

Regards,
Prakash.

mostafah67

### mostafah67

Points: 2

#### Amuro

##### Full Member level 4
Which one is correct?

I think the simulation results would be more precise, since it include many second order effects.

mostafah67

### mostafah67

Points: 2

#### wjxcom

##### Full Member level 5
Which one is correct?

I do agree with Amuro!!
I design OP examples writed by Allen and I use library CSMC. But the parameters such as gain is not like the parameters in the examples writed by Allen.

mostafah67

### mostafah67

Points: 2

#### flushrat

##### Full Member level 3
Re: Which one is correct?

Hand calculation is a rough estimation. Simulation is more accurate.

And how do you get λ= 0.01 ? λ is different with different L.

mostafah67

### mostafah67

Points: 2

#### nxing

Which one is correct?

the traditional square-law model is not correct for sub-micro devices

mostafah67

### mostafah67

Points: 2
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