Find dispersion relation for free electron, Electrical Engineering

Find Dispersion Relation for Free Electron

Question: Find the dispersion relation for a free electron, and, thus, observe the relation between its rest mass and effective mass.

Solution: For a free electron, the electron momentum is  p =m0v = hk. Thus, E=m0V2/2=p2/ (2m0) = h2k2/(2m0). Therefore, the dispersion relation, i.e., E-k relation is parabolic. Hence, mx = h2/∂2Ε/∂K2=m0. This is a very interesting relation that says states that for a free electron, the rest mass and effective mass are one and similar, which is because of the parabolic band structure. Several materials have non-parabolic E-k relation, and, so they have quite different rest mass and effective mass for electrons.

Note: the effective mass may become a function of energy, for severely non-parabolic band structures, however, near the minima of the conduction band and towards the maxima of the valence band, the band structure can be taken to be parabolic, and, thus, an effective mass, which is independent of energy, may be obtained.

  • Thus, the effective mass is an inverse function of the curvature of the E-k diagram: weak curvature gives large mass, and strong curvature gives small mass.
  • Note that in general, the effective mass is a tensor quantity, however, for parabolic bands, it is a constant.
  • Another interesting feature is that the curvature d2E/dk2 is positive at the conduction band minima, however, it is negative at the valence band maxima.
  • Thus, the electrons near the top of the valence band have negative effective mass.
  • Valence band electrons with negative charge and negative mass move in an electric field in the same direction as holes with positive charge and positive mass.
  • Thus, the charge transport in the valence band can be fully accounted for by considering hole motion alone.
  • The electron and hole effective masses are denoted by m*n and m*p  respectively.

 

Table: the effective mass for electrons and holes (Χ m0, where m0 is the rest mass for electrons)311_Find Dispersion Relation for Free Electron.png

Posted Date: 1/11/2013 4:39:47 AM | Location : United States







Related Discussions:- Find dispersion relation for free electron, Assignment Help, Ask Question on Find dispersion relation for free electron, Get Answer, Expert's Help, Find dispersion relation for free electron Discussions

Write discussion on Find dispersion relation for free electron
Your posts are moderated
Related Questions
Q. What is Non-Folded Network? Non-Folded Network: In a switching network, all outlet/inlet connection may be used for inter exchange transmission. In such a case, exchange d

Aims of the Tariff Policy - electricity policies: The aims of the National Tariff Policy are to: 1. Ensure availability of electricity to consumers at reasonable and compet

WHAT ABOUT THE STABILITY IF WE USE COMPENSATOR

Q. Physical operation of the junction of diode? The physical operation of the junction can be described in terms of the charge-flow processes. Usually there is a greater concen

Which clipper would you prefer between the series and the shunt clipper? Why?

5 page paper on matrix and computer methods applied to Linear Gear trains

Define real time operating system. Real time operating system (RTOS): The real operating system is an operating system used in embedded applications which performs tasks in a

Q. What is power gain? Power gain is the ratio of power delivered to the load to power delivered to the amplifier is the power gain. A p =P o /P i     =V o I o /V i I s

Interrupt Signals There are five  interrupt  signals in 8085 microprocessor.  These  signals  are used to inter rut the  current  program  under  execution and  transfer the ex

#question.classification of conducting material.