Yes Sen. It is okay. All you need now is to show of Ei us the factor 2 in the denominator of Ei. I know that my derivations are not erogenous at low temperatures. Now present the derivation to verify it.

Best wishes

Dear Sen,

you can find an answer to your question-solving temperature temperature-dependent carrier density in the semiconductor. If there is a single dopant or ionization energy, the equation for temperature-dependent temperature carrier density can satisfy the relation as p0 exp(-Ei/2kT). It is equation is also suitable for intrinsic semiconductor.

If there is double dopant energy or double ionization energy (one of them is a shallow donor/defect, and the other is the deep donor/defect), the equation for temperature-dependent carrier density can satisfy a relation as p=p0 exp(-Ei/kT), under some conditions. The equation (p=p0 exp(-Ei/kT) can also satisfy for compensated semiconductors. Then you can obtain the resistivity equation by using temperature-dependent carrier density with fundamental relation.

You can find a detailed answer in the book "Physical Foundations of solid-state devices" (chapter 14) by E.F. Schubert. (If you do a quick search in google, you can find a limited free version of the book )

I think the equation will be p=p0 exp(Ei/2kT) rather than p0 exp(-Ei/2kT) since resistivity decreases with increase in temp in case of semiconductor.

Basically in my material there are dual bands i.e. a shallow acceptor level due to defects in the semiconducting material & another one is deep donor/acceptor level due to specified dopants. Kindly suggest which one will be suitable: p=p0 exp(Ei/2kT) or p=p0 exp(Ei/kT).

There is nothing specified about resistivity of Extrinsic semiconductor in the 14th chapter of the book " Physical Foundations of solid-state devices". Only there is specifications regarding carrier concentration in extrinsic semiconductor in 14th chapter.

Dear S.Sen,

I guessed you can directly obtain the resistivity equation by using fundamental physics equation, given in chater 14th by Schubert, as fundamental information is given there.

(Minus sign in previous answer equation should appear all temperature-dependent carrier density equation. If it is not written, it is coming from typos error.)

Right! But, I am not asking for carrier concentration. I am asking for resistivity. P denotes rho which nothing but resistivity. Therefore, I think the resistivity model equation will be, p=p0 exp(Ei/2kT) rather than p=p0 exp(-Ei/2kT) since resistivity decreases with increase in temp in case of semiconductor.

One more query! Are you sure that the resistivity variation with temp can be denoted as p=p0 exp(Ei/kT) instead of p=p0 exp(Ei/2kT) in case of dual band model i.e. a shallow acceptor level due to defects in the semiconducting material & another one is deep donor/acceptor level due to specified dopants???????

Dear Sen,

welcome,

I would like to bring some systematic in your answer.

The resistivity roh = 1/ conductivity sigma,

sigma= q(un n +up p)

un and up are the mobilities of electrons and holes respectively,

n is the electron concentration and p is the hole concentarion.

If the material is doped say n type, then ,

n= Nd exp - Ei/kT where Nd is the doping concentration, Ei is the ionization energy

of the donors.

p=ni^2/n,

At low temperatures p is negligible and

sigma=q un Nd exp - Ei/kT

If one assumes that un is weakly independent on temperature,

Than sigma is proportional to exp -Ei/kT

And roh is proportional to exp Ei/kT

Best wishes

Dear Dr. Zekry,

Thanks for your suggestion. I have already performed all those calculations previously & come to conclusions that Rho (P)=1/nqun where un is the mobility of electron in n-type semiconductor (Neglecting minority carrier hole concentration p at low temp). Therefore, Resistivity P=1/[Nd exp(-Ei/2kT)qun] since at low temperature n is not Nd exp (- Ei/kT), it will be n=Nd exp (-Ei/2kT) in case of dual band model i.e. for double dopant energy or double ionization energy. However, there is a doubt since un at low temperature is dependent on impurity ionization scattering i.e. un is proportional to T3/2/NI. Therefore, Resistivity P should be equal to 1/[Nd exp(-Ei/2kT)qT3/2/NI] at low temp. Kindly verify.

Yes Sen. It is okay. All you need now is to show of Ei us the factor 2 in the denominator of Ei. I know that my derivations are not erogenous at low temperatures. Now present the derivation to verify it.

Best wishes

I have quite a bit confusion that as per the 14th chapter of the book "Physical Foundations of solid-state devices" by E.F. Schuber the Hall concentration dependence on temperature at high temperature has been depicted as n=n0exp(- Ei/kT) for free electrons as per dual band model i.e. for double ionization energy whereas the temperature dependence has been scripted as p=p0exp(- Ei/2kT) in the paper "Impurity band in p-type beta-FeSi2" at high temperature for hole as per the similar dual band model. If someone resolve this confusion out by suggesting correct suggestion then it would be helpful for me.

For your kind convenience I am attaching both the documents with this message. Kindly suggest the correct one for me.

There are distinct different between Chapter 14 results and paper "impurity band in FeSi2". In the chapter 14, the defect level behave as localized state, but in the paper, it is a new band. As you see in the paper figure, there are parallel conduction, but there is no parallel conduction in chapter 14. I recommend you can exploit further fundamental paper, if you interest temperature dependent resistance or conductivity. If it is your problem is similar to the paper on FeSi2, you can benefit Kane paper (M J Kane et al 1985 J. Phys. C: Solid State Phys. 18 5629 or C. Kittle book on semiconductor as Introduction to Solid State Physics). For this case, forgot what I recommend before.