This website uses cookies to ensure you have the best experience. Learn more

Band Theory Essay

2315 words - 10 pages

According to quantum free electron theory of metals, a electron in a metal experiences constant(or zero) potential and free to move inside the crystal but will not come out of the metal because an infinite potential exists at the surface.
Bloch Theorem: According to this theorem, the periodic potentials due to the positive ions in metal have been considered. (i.e. the electrons moves in a periodic potential provided by lattice). If the electron moves through these ions, it experiences varying potentials. The potential of an electron at the positive ion site zero and is maximum in between two ions. i.e. the potential experienced by an electron varies periodically ...view middle of the document...

The potential of electron varies periodically with periodicity of ion core ‘a’ which is nothing but inter-atomic spacing. It is assumed that the potential energy of the electrons is zero near nucleus of the positive ion core and maximum when it is lying between the adjacent nuclei as shown fig.

Fig. One dimensional periodic potential
The width of the potential well and barrier are ‘a’ and ‘b’ respectively. The potential energy of an electron in the well is zero and in the barrier is V0. The periodicity of the potential is a+b. This model is an highly artificial, but it illustrates many of the characteristics features of the behavior of electrons in periodic lattice. The energies and wave functions of electrons associated with model can be calculated by solving the Schrödinger’s wave equation for two regions I and II.

The Schrödinger’s equations are
for region-I 0 < x < a
and for region-II -b < x < a
Since E less than Vo, define two +ve quantities, α2 = 2mE/ ħ2 and β2 = 2m(V0– E )/ħ2 for region 0 < x < a
for region -b < x < a
According to Bloch Theorem, the solutions of above equations can be written as
Ψ(x) = uK (x) eiKx
The consists of a plane wave eiKx modulated by the periodic function uK(x), where this UK(x) is periodic with the periodicity of the lattice.
uK(x) = uK(x+a)
where K is propagating constant along x-direction and is given by K =2π/λ is a Propagation wave vector. In order to simplify the computations, an assumption made regarding the potential barrier. As Vo increases the width of the barrier ‘b’ decreases so that the product Vob remains constant. After tedious calculations, the possible solutions for energies are obtain from the relation
Psin∝aαa+cos∝a=cosKa ------------ (1)
where P = mVo ab /ħ2 is scattering power of the potential barrier. It is a measure with which electrons in a crystal are attracted to the ions on the crystal sites.
The left hand side of the equation (1) is plotted as a function of αa for the value of P=3π/2. The right side of the equation imposes a limitations on the values of left side function, i.e., between -1 to +1 as indicated by the horizontal lines in fig. Hence only certain range of α are allowed.

Fig. a) For large value of P b) P⟶∞ c) P⟶0
The permitted values of energy are shown as solid lines between white portions. This gives rise to the concept of ranges of permitted values of for a given ion lattice spacing a.
1. The energy spectrum of electron consists of alternate regions of allowed energy and un allowed regions i.e. The motion of electrons in a periodic lattice is characterized by the bands of allowed energy separated by forbidden regions.
2. As the value of a increases, the width of allowed energy bands also increases and the...

Other assignments on Band Theory

Chet Baker Essay

1522 words - 7 pages fact that the trombone being huge. Even though Baker received musical education at Glendale Junior High School, he left school at the age of 16 to join the United States Army where and joined the army band. In his transition period, he left the army in 1948 and attended El Camino College in Los Angeles where he studied theory and harmony. But he was dropped out again and joined the army again in 1950. The he became a member of the sixth army

Data Communication Theory Essay

2643 words - 11 pages [pic] DATA COMMUNICATION THEORY LAB REPORT Report on Digital Transmission of Analogue Signals Pulse Amplitude Modulation INTRODUCTION: The experiment uses the L.J.Electronics Modicom-1 board to investigate the sampling of signals, and the filter effects on the reconstruction of the original signal from the sampled input. The sample/Hold operation is also investigated in

Hickman And Cuoto

661 words - 3 pages Causality, Change, and Leadership Gill Robinson Hickman Hickman, G. & Cuoto, R. (2006) Causality, Change, and Leadership. Chapter in Goethals, G. & Sorenson, G. The quest for a general theory of leadership. Northhampton, MA: Edward Elgar Publishing, Inc. The chapter will be posted in the Course Resources section of this course. We will discuss this case as part of our Unit 4 cohort meeting. The key question to discuss is, "What two

The Sun Our Star

1628 words - 7 pages . | |e. |magnetic field. | ____ 4. A filtergram is a photograph of the sun's surface made |a. |in a band of wavelengths in the infrared. | |b. |in a band of wavelengths in the ultraviolet

Cfa- Test 2010

1746 words - 7 pages performance each year going forward up to a maximum of 10 years. Answer: C A firm is initially required to present at least five years of compliant history and must add annual performance each year going forward up to 10 years at a minimum. 3. A rock band plans to visit 15 cities all over the world in one year. They will visit 3 of these 15 cities in January. The number of possible combinations of venues for January is closest to: A. 455 B

2g Scam

5398 words - 22 pages , you don’t get the ticket. This also leads to ticket black-marketing, for example, I come early, buy all the tickets. You come late, all the tickets are sold, I offer my tickets to you at higher price and make huge profit. This is not good for economy because I’m making money without producing any new goods/services which will lead to inflation. But according to a theory propounded by Mr.Sibal, this is “zero loss” because cinema hall did receive

My Personal Learning Style

2382 words - 10 pages relies on his or her hearing to succeed in the classroom. These students are very particular about their choice of words when speaking inside the classroom. They excel more with musical tasks and extra-curricular activities such as band. Teaching equipment such as CD-ROMs, audio cassettes, and guest speakers are highly beneficial to these types of learners (Gardner, 1985). Just as with a “verbal-linguistic” learner there can be many difficulties

Sociology Essay Structure

3978 words - 16 pages /categorising responses; lack of reliability; small scale; lack of representativeness; qualitative data; grounded theory; informed consent. Note: In any mark band, students will be rewarded for making relevant reference to their own research experiences or to sociological studies using the selected method, when such material is applied appropriately to the set question. * Using material from Item B and elsewhere, assess the strengths


1404 words - 6 pages . You may not see it. You may not recognize it if you do see it, but it must be there somewhere. The antenna does only one thing: It converts electrical signals coming from a conductor into airborne waves, or it converts airborne waves into electrical signals to be sent down a conductor. Being a resonant device, it operates efficiently over a narrow frequency band. The real way that an antenna does its work is somewhat complex, but for this

Law/421 Final Examination Study Guide

2675 words - 11 pages , privacy, ethics, and security. 12. Which of the following is not an example of a trademark lost, or in danger of losing protection, due to its becoming a generic term? a. Kleenex b. Band-Aid c. Ford d. Aspirin Week Three: Contracts Objective: Analyze the elements necessary to form valid contracts. 13. Mike is walking through a parking lot and finds Kathy lying unconscious. He puts her in his car and takes her to the

Frustration Of Contracts

4948 words - 20 pages  of a party, due to death, illness, or other exceptional circumstances. E.g. you hire a famous band to play at a party, but the lead singer is taken ill and can’t perform. Thus, doctrine of frustration comes into play in two cases i.e when the performance is physically cut off and when the object fails. Supreme court has held that sec.56 can be applied to both kinds of frustration. In Satyabrata Ghose v. Mugneeram Bangur & Co [24], the

Similar Documents

No It Isnt Essay

358 words - 2 pages June 2011 PSYB3 Cog.Dvlpt essay qu. Describe and evaluate the information processing approach to children’s cognition. In your answer, you should explain how the information processing approach differs from at least one other approach to cognitive development. (12 marks) [AO1 = 4 marks, AO2 = 8 marks] Examiners must read the whole response prior to marking in order to make a band judgement about whether the response is Very

Diode Essay

2753 words - 12 pages 1. INTRODUCTION This piece of work is the further investigation of the 3B5 - Schottky Barrier Diode (SBD) experiment. It involves a comprehensive data error analysis to both the raw data from the experiment and the parameters derived from them. An in-depth probe to the SBD is also done by examining the fundamental theory of SBD with illustrative band diagrams and reference to the thermionic emission theory. The ideal SBD model is then compared

Case Study For Play Station 3

2128 words - 9 pages , information theory, radio communications, signal processing, and spectroscopy. A key characteristic of bandwidth is that a band of a given width can carry the same amount of information, regardless of where that band is located in the frequency spectrum (assuming equivalent noise level). For example, a 5 kHz band can carry a telephone conversation whether that band is at baseband (as in your POTS telephone line) or modulated to some higher (passband

Proof's Summary Essay

379 words - 2 pages Robert did his best work by the time he was in his mid-twenties. After that, he became mentally ill. Catherine is worried that she will inherit the illness. It then transpires that Robert died a week before, of heart failure, and the funeral is the next day. Hal, a former student of Robert’s, enters. He has been working on Robert’s notebooks, but Catherine says there is nothing valuable in them. Hal invites her to hear him play in a rock band, but