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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

If the temperature of a piece of a metal is increased, does the probability of occupancy 0.1 eV above the Fermi level increase, decrease, or remain the same?

The increase in temperature increases the probability of the occupancy above the Fermi level.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: The given data

  1. Temperature is increased.
  2. Fermi energy of the material, ∆E=0.1 eV

Step 2: Understanding the concept of occupancy probability

Using the basic concept of the probability of occupied states, we can get the required occupancy probability change of the material. Thus, this helps in determining energy change as per the given condition.

Formula:

The probability of the condition that a particle will have energy E according to Fermi-Dirac statistics, PE=1eE1-EF/kT+1 (i)

Step 3: Calculation of the energy change

Using the occupancy probability equation (i), we can get that for increased temperature, the exponential term decreases. This in turn increases the probability value.

Hence, for the given energy above the Fermi level and for the temperature increase, the occupancy probability increases.

Most popular questions for Physics Textbooks

Calculate the number density (number per unit volume) for (a) molecules of oxygen gas at 0.0°Cand 1.0 atm pressure and (b) conduction electrons in copper. (c) What is the ratio of the latter to the former? What is the average distance between (d) the oxygen molecules and (e) the conduction electrons, assuming this distance is the edge length of a cube with a volume equal to the available volume per particle (molecule or electron)?

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?

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.

Show that Eq. 41-5 can be written as N(E)=CE1/2. (b) Evaluate in terms of meters and electron-volts. (c) Calculate N(E) for E=5.00eV for .

A certain computer chip that is about the size of a postage stamp 2.54 cm×2.22 cm contains about 3.5 million transistors. If the transistors are square, what must be their maximum dimension? (Note: Devices other than transistors are also on the chip, and there must be room for the interconnections among the circuit elements. Transistors smaller than 0.7μm are now commonly and inexpensively fabricated.)
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