Explain einstein relation, Electrical Engineering

Assignment Help:

Explain Einstein relation.

Einstein relation:

There exists a significant relation between the diffusion constant and the mobility. It is termed as the Einstein relation and may be deduced as given below:

Consider a semiconductor wherein there exists an electric field Ex and a concentration gradient as the current is zero. In these conditions the system is in the Boltzmann statistics and thermal equilibrium applies. Consider a potential V(x) producing at x an electric field E(x)= -dV/dx.

For the density of holes the Boltzmann expression as a function of x in thermal equilibrium is as

p(x) = Ce-eV/KT

Here C is a constant.

Therefore the gradient of the hole density is given by

dp/dx = (-e/KT)p.(dv/dx)

= (e/KT)p.E

The hole current vanishes in thermal equilibrium. Therefore,

O=peup Ex-eDp  dp/dx

=peup Ex-(e2 /KT)Dp . Ex

Dp = (KT/e) Up (i.e. the Einstein relation).


Related Discussions:- Explain einstein relation

Obtain the laplace transform of the waveform, Q. Use MATLAB to obtain the L...

Q. Use MATLAB to obtain the Laplace transform of the waveform f(t) = [200t e -25t + 10 e -50t sin(25t)]u(t) which consists of a damped ramp and a damped sine. Also show the

Effective mass, Effective Mass The electrons' "wave-particle" motio...

Effective Mass The electrons' "wave-particle" motion in a lattice is not the same as that for a free electron, because of the interaction with the periodic potential of the

What do you mean by capacitance, Q. What do you mean by Capacitance? An...

Q. What do you mean by Capacitance? An ideal capacitor is an energy-storage circuit element (with no loss associated with it) representing the electric-field effect. The capaci

Microprocessor development system, Write explanatory notes on  Microprocess...

Write explanatory notes on  Microprocessor development system. Microprocessor development system : Computer systems have undergone several changes recently. Machines which

Electromechanical and electronic switching system, Q. Compare electromechan...

Q. Compare electromechanical switching system with electronic switching system. Sr. No Electromechanical switching System Electroni

Show proper cash management, Q. Show Proper cash management? Proper cas...

Q. Show Proper cash management? Proper cash management: cash management is a important task of finance management he has to access to various cash needs at the difference time

Electricity and gas hazards, Electricity beyond doubt is very useful and es...

Electricity beyond doubt is very useful and essential for us; but if dealt with carelessly, it can prove to be very fatal. It is compulsory for a laboratory assistant to be sure of

In given block diagram find geq, Q. Show that the block diagram of Figure c...

Q. Show that the block diagram of Figure can be reduced to the form of Figure. Find G eq (s) and H eq (s).

Illustrate the basic concept of machine cell design, a) Write short notes o...

a) Write short notes on part feeding devices and transfer mechanism. b) Explain with example automation for machining operation with relevant diagrams. c) discuss different p

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd