Can anyone Tell me what is the model relation between resistivity and the temperature for a extrinsic semiconductor. Kindly provide with summarized clarification & model equation between resistivity and temperature for extrinsic semiconductor.
Whether will it be p=p0 exp(Ei/kT) or will it be p=p0 exp(Ei/2kT) for extrinsic semiconductor where Ei is the activation energy???? Kindly confirm.
Dear Sabyasachi Sen,
I think the same model equation of intrinsic semiconductor, only the bandgap energy (Eg) in the equation of intrinsic semiconductor becomes activation energy (∆E) in the equation of extrinsic.
Best Regards
It's quite ok for intrinsic semiconductor! It will be p=p0 exp(Eg/2kT) for intrinsic semiconductor.
However, I have some confusion regarding the model equation for extrinsic semiconductor!
Whether will it be p=p0 exp(Ei/kT) or will it be p=p0 exp(Ei/2kT) for extrinsic semiconductor where Ei is the activation energy???? Kindly confirm.
Dear Sabyasachi,
The first thing to do is to know about the defect chemistry of your material and the ionization energies involved. Having these, you can calculate the concentration of holes (I presume you wrote 'p' for the concentration of holes) at any temperature and, then, it is not relevant which is the 'correct' equation (you use the Fermi energy for those calculations).
Perhaps you want to get the activation energy instead of calculating p. If the measuring temperature range is low for your system, as an approximation you can assume a kind of band gap between VB (valence band) and the energy of the acceptor, which you wrote as Ei. Therefore, in that case, use equation p=p0 exp(-Ei/2kT) and you assess that activation energy. Do not forget this is an approximation; for high temperature ranges or for low acceptor concentrations, you cannot use this equation. The same answer was already given by Dr. Abdu; I hope your doubts could be dissipated now. Good work for you.
With my best regards,
For higher temp range, it will be either p=p0 exp(Ei/kT) or p=p0 exp(Ei/2kT) not in the one with p=p0 exp(-Ei/2kT) manner since for a semiconductor resistivity always decreases exponentially with increase in temperature.
Therefore, I want to know which one is true for the temperature dependence of resistivity?? Either p=p0 exp(Ei/kT) or p=p0 exp(Ei/2kT)?? Kindly specify.
In that case, none of them. As you can see, both your equations mean a decrease of carrier concentration upon increasing the temperature, which means increasing resistivity; but, as you wrote, for a semiconductor resistivity always exponential decreases with increasing temperature. Therefore, none of the proposed equations could account for the variation of the resistivity with temperature for your material.
Here for p=p0 exp(Ei/2kT), p is not carrier/hole concentration...it is basically rho (resistivity) here. Since semiconductor resistivity always decreases exponentially with increase in temperature, therefore it will be p=p0 exp(Ei/2kT) rather than p=p0 exp(-Ei/2kT).
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Materials Science
- Materials
- Semiconductor