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Fundamentals Of Physics
Found in: Page 1272
Fundamentals Of Physics

Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

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Short Answer

In a silicon lattice, where should you look if you want to find (a) a conduction electron, (b) a valence electron, and (c) an electron associated with the 2p subshell of the isolated silicon atom?

  1. The conduction electron in a silicon lattice is found in the conduction band.
  2. The valence electron in a silicon lattice is found in the outermost occupied shells of the atoms which is at the top of the valence band.
  3. The electron associated with the 2p subshell is found above the Fermi level and below the bottom of the conduction band.
See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: The given data

A silicon lattice is given.

Step 2: Understanding the concept of band structure

Usually, the free electrons responsible for the conduction are called the conduction electrons that flow from the top of the valence band to the bottom of the conduction band. Generally, the electrons present in the valence band, absorb energy from the environment and jump to the conduction band. Now, using the band structure concept, we can get that the 2p-orbital of the silicon lattice structure is a closely packed shell with a location above the Fermi level and below the conduction band. Fermi level is at the middle of both the bands for undoped silicon.

Step 3: a) Calculation of the location of conduction electron

As per the concept, the conduction electrons which are responsible for the conduction of electricity are present in the conduction band.

Step 4: b) Calculation of the location of valence electron

the energy band present just below the conduction band is known as a valence band.

The electrons present in the highest occupied level of the band are called valence electrons.

Step 5: c) Calculation of the location of the 2p electron  

Using the concept of the band structure of the silicon lattice, we can see that the band structure is composed of closely packed lines. This also shows that the 2p-orbital of the silicon atom is located between the valence band and the conduction band that is more close to the conduction band.

Hence, the electrons present in 2p-orbital is found between the Fermi level and the bottom of the conduction band.

Most popular questions for Physics Textbooks

At 1000K, the fraction of the conduction electrons in a metal that have energies greater than the Fermi energy is equal to the area under the curve of Fig. 41-8b beyond EF divided by the area under the entire curve. It is difficult to find these areas by direct integration. However, an approximation to this fraction at any temperature T is frac=3kT2EF .

Note that frac = 0 for T = 0 K, just as we would expect. What is this fraction for copper at (a) 300 K and (b) 1000 K? For copper EF=7.0 eV . (c) Check your answers by numerical integration using Eq. 41-7.

(a) Show that the density of states at the Fermi energy is given by

N(EF)=4(31/3)(π2/3)(mn1/3)h2 =(4.11×1018m-2eV-1)n1/3

in which n is the number density of conduction electrons.

(b) Calculate N(EF) for copper, which is a monovalent metal with molar mass 63.54g/mol and density 8.96g/cm3.

Verify your calculation with the curve of Fig. 41-6, recalling that EF=7.0eV= for copper.

In a simplified model of an undoped semiconductor, the actual distribution of energy states may be replaced by one in which there are NV states in the valence band, all having the same energy EV, and NC states in the conduction band all these states having the same energy Ec. The number of electrons in the conduction band equals the number of holes in the valence band.

  1. Show that this last condition implies that Ncexp(∆Ec / kT)+1=Nv exp(∆Ev / kT)+1 in which ∆Ec=∆Ec-∆EF and ∆Ev=-(∆Ev-∆EF).
  2. If the Fermi level is in the gap between the two bands and its distance from each band is large relative to kT then the exponentials dominate in the denominators. Under these conditions, show that EF=(Ec+Ev)2+kTIn(Nv+Nc)2 and that if Nv≈Nc , the Fermi level for the undoped semiconductor is close to the gap’s center.

Figure 41-21 shows three leveled levels in a band and also the Fermi level for the material. The temperature is 0K. Rank the three levels according to the probability of occupation, greatest first if the temperature is (a) 0K and (b) 1000K. (c) At the latter temperature, rank the levels according to the density of states N(E) there, greatest first.

Show that Eq. 41-9 can be written as EF=An2/3where the constant A has the value role="math" localid="1661507403881" 3.65×10-19 m2eV.
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