# why the equation density carrier electron vs temperature don't fit with the graph of book?

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#### stackprogramer

##### Full Member level 3
why the equation density carrier electron vs temprature don't fit with graph of book?

hi,in link https://www.iue.tuwien.ac.at/phd/wittmann/node7.html that it is too there is in yang micro device,there is a graph that can see below: the equation of carrier is below our default is NA=0 and we have n-type silicon, when i plot this equation in matlab we don't arrive this graph!!11
clc
clear
Nd=10^16;
Eg=1.4;%ev
K=8.6173324*10^(-5);%ev
m0=9.109*10^-31;
me=1.08*m0;
mh=.56*m0;
h=4.135667662*10^(-15);%ev

y=@ (T) 1/2+1/2*(1+16*(6.28*K*T*(me*mh)^.5*(1/h^2))^3*exp(-Eg/K*T)*1/Nd^2)^.5;
fplot(y,[1,2]);
the output from matlab is here: Last edited:

Re: why the equation density carrier electron vs temprature don't fit with graph of b

Are You sure that every number used in your formula is float?

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Re: why the equation density carrier electron vs temprature dosn't fit with graphof b

why i do wrong?

Apart from the fact that I cannot judge if

1. this equation can really regenerate the graph
2. NA=0 is a valid assumption for this calculation
3. your MATLAB command file is correct

In any case I'd suggest to use a log scale for the y-axis.

Re: why the equation density carrier electron vs temprature don't fit with graph of b

i talk that this post is from microelectronic devices s.yang is about semiconductor,fabrication,inetgrated circuit is not phyisics it is physics of semiconductor in engineer electronic.please change to my category.
thanks

- - - Updated - - -

this equation can really regenerate the graph
i suspect my wrong is here,but i think that how i find and calculate equation
thanks for replay

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Re: why the equation density carrier electron vs temprature don't fit with graph of b

... is from microelectronic devices s.yang is about semiconductor,fabrication,inetgrated circuit is not phyisics it is physics of semiconductor in engineer electronic.please change to my category.

... is not physics (!) it is physics of semiconductor ...

Right: it is physics, but has nothing to do with IC design, layout & fabrication, that's why I had transferred it to the math & physics section. I think you've more chances to get help here.

Re: why the equation density carrier electron vs temprature don't fit with graph of b

Checking the equation parts shows that exp(-Eg/K*T) is effectively zero, so the constant 1 output is expectable.

Don't see how you arrived at the equation. Maybe just a typo.

Re: why the equation density carrier electron vs temprature don't fit with graph of b

Those equations do not describe carrier freeze-out effect - they are applicable only for temperature above freeze out.
The plot is correct, but it does not correspond to those equations.

Equations accounting for carrier freeze out effect should involve impurity activation energy.
Under carrier freeze-out, ionized impurity concentration is lower than the total impurity concentration, so the equation (2.19) is not valid.

I think the physics of semiconductor devices is directly related to analog circuits...

Re: why the equation density carrier electron vs temprature don't fit with graph of b

Checking the equation parts shows that exp(-Eg/K*T) is effectively zero, so the constant 1 output is expectable.
you are right,but i conclude that this equation is n't for curve.
Equations accounting for carrier freeze out effect should involve impurity activation energy.
Under carrier freeze-out, ionized impurity concentration is lower than the total impurity concentration, so the equation (2.19) is not valid.
yes,i should find the equation for ionization,extrinsic,intrinsic state and i plot.
but where is these equations!its not in refrence s.yang ben G streetman,
i am searching.............
Right: it is physics, but has nothing to do with IC design, layout & fabrication, that's why I had transferred it to the math & physics section. I think you've more chances to get help here.
A PhD of physics can't answer of these question ,a electronic guy can solve it.but you are moderator and you should decide
thanks for accessing my post in analog circuit

I think the physics of semiconductor devices is directly related to analog circuits...
i am unanimous you.

Re: why the equation density carrier electron vs temprature don't fit with graph of b

i conclude that this equation is n't for curve.
The subexpression doesn't seem right for any meaningful equation, I guess either the parameter values or the equation has a typo.

Re: why the equation density carrier electron vs temprature don't fit with graph of b

I found many errors in your matlab code and in your math. First of all I think is better to have anything in MKS system, then:

h=6.626e-34
K=1.38e-23
1eV = 1.6e-19J that means Eg=1.12*1.6e-19

In the exponential you wrote exp(-Eg/K*T) that due to the precedence of the operators T is at the numerator. The correct code is instead exp(-Eg/(K*T)).

However ni2=Nc*Nv*exp(-Eg/(K*T)) where

Nc=2*(2*pi*me*K*T/h2)3/2
Nv=2*(2*pi*mh*K*T/h2)3/2

then Nc*Nv=4*(4*pi2*me*mh*K2*T2/h4)3/2

that is: Nc*Nv=32*(pi*sqrt(me*mh)*K*T/h2)3

so: ni2=32*(pi*sqrt(me*mh)*K*T/h2)3*exp(-Eg/(K*T))

this result can be used in the main equation:

nn = 0.5*{ND-NA+sqrt[(ND-NA)2+4*ni2]}

I hope now it's correct. Please check.

However I don't think you can see the freeze-out region from this equation, but you should see the extrinsic as well as the intrinsic region.

Pay attention to the measurement units: the result of the equation is in m-3 while the graph is in cm-3 so you have to multiply by 106. The same apply to ND that has to be set in m-3

A question: why do you assume NA=0 ?

• FvM

### FvM

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Re: why the equation density carrier electron vs temprature don't fit with graph of b

I hope now it's correct. Please check.
but my code run in matlab 2015 and no have errors!

Pay attention to the measurement units: the result of the equation is in m-3 while the graph is in cm-3 so you have to multiply by 106. The same apply to ND that has to be set in m-3
i am know this rule.thanks for reply.
A question: why do you assume NA=0 ?
because we have n-type semiconductor.thanks for attention.

finally i conclude this equation is not for this curve the equation i find in Robert F. Pierret-Advanced Semiconductor Fundamentals-Prentice Hall (2002).pdf page 122

the equation image is in below. Re: why the equation density carrier electron vs temprature don't fit with graph of b

i finally succeed i ploted density of electron /ND vs temprature ,these are output,
the equations i found in Robert F. Pierret-Advanced Semiconductor Fundamentals-Prentice Hall (2002).pdf page 122   if we increase ND=10^16 1/cm^3 to ND=10^17,10^18,10^19 the curve chnages according:
1)the graph shifts to right,ionization donor temprature increase
too instrinsic region shifts a little right.
2)the linear region(Exrinsic region) decrease in semiconductor,it is not good for us or semiconductor industrial. soon source and files will be shared.thanks

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