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
MOV Instruction Op code  format  of MOV  instruction is as follows : Replace the  codes of destination register and source  register with code of  required  register from.

Current  Source Inverter (CSI) Current  source  inverter has constant  input  but it  can be  adjusted. In CSI  the amplitude of output  current is  independent of load. The lo


Q. Frequency stability of quartz crystals ? The amount of frequency deviation from the ambient temperature frequency over the operating temperature range. This deviation is ass

Explain the Johnson Counters? The Johnson counters are a variation of standard ring counters with the inverted output of the last stage fed back to the input of the first stage

Standard Color-Coded Bands for Evaluating Resistance Practical resistors are manufactured in standard values, various resistance tolerances, several power ratings (as will be e

Explain the meaning of Synchronous Counters? In the synchronous counters the clock inputs of all the flip-flops are connected together and are triggered by the input pulses, the

Q. Explain, with the help of structure, the working of UJT? List its applications One of the oddest semiconductor devices in use is the unijunction transistor (UJT). As its nam

List the addressing modes supported by 8051. 1. Register addressing  2. Direct  addressing 3. Register indirect addressing 4. Immediate addressing 5.Register addres

how does creating a supernode helps solve the problems?