Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 10, Problem 26P
(a)
To determine
The graph of
(b)
To determine
The graph of
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The Fermi-Dirac statistic describes the probability of occupation of an energy state E, as a function of temperature and of the parameter Ef, the Fermi energy.a) What is the physical interpretation for the result obtained when E = Ef?b) Under which conditions of temperature and position of the Fermi level, Ef, can the Fermi-Dirac statistic be written as a simple exponential? Justify your answer.
To improve the semiconducting characteristics of GaAs, 1.31 x 10^15 atoms of Be are incorporated into the material. Be has an ionization energy of 0.6eV.
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After the doping process, where can you find the Fermi energy level?
Volume
2. a) The intrinsic carrier concentration in GaAs at 300 K is 1.8 x 106 cm³. What is the carrier concentration in fm³
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b) The mobility of holes in GaAs at 300 K is 400 cm²/V-s. What is the mobility in m²/V-s?
Chapter 10 Solutions
Modern Physics
Ch. 10 - Prob. 1QCh. 10 - Prob. 2QCh. 10 - Prob. 1PCh. 10 - Prob. 2PCh. 10 - Prob. 3PCh. 10 - Prob. 4PCh. 10 - Prob. 5PCh. 10 - Prob. 6PCh. 10 - Prob. 8PCh. 10 - The light from a heated atomic gas is shifted in...
Ch. 10 - Prob. 10PCh. 10 - To obtain a more clearly defined picture of the...Ch. 10 - Prob. 12PCh. 10 - Prob. 14PCh. 10 - Prob. 15PCh. 10 - Prob. 16PCh. 10 - Prob. 17PCh. 10 - Prob. 18PCh. 10 - Prob. 19PCh. 10 - Prob. 20PCh. 10 - Prob. 21PCh. 10 - Prob. 22PCh. 10 - Prob. 23PCh. 10 - Prob. 24PCh. 10 - Prob. 26P
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- To obtain a more clearly defined picture of the FermiDirac distribution, consider a system of 20 FermiDirac particles sharing 94 units of energy. By drawing diagrams like Figure P10.11, show that there are nine different microstates. Using Equation 10.2, calculate and plot the average number of particles in each energy level from 0 to 14E. Locate the Fermi energy at 0 K on your plot from the fact that electrons at 0 K fill all the levels consecutively up to the Fermi energy. (At 0 K the system no longer has 94 units of energy, but has the minimum amount of 90E.) 1 Microstate8 others? One of the nine equally probable microstates for 20 FD particles with a total energy of 94E.arrow_forwardQ3/ An experiment was conducted to find the relationship between the specific heat of potassium metal and the temperature, and it was found that this relationship takes the following formula at low temperatures 2.08 +2.57 T2 What is the value of each of: (1) the fermi temperature of potassium? (b) Debye temperature of potassium? Note that specific heat is measured in units of mj / mol / K.arrow_forwardSuppose we have an ideal fermion gas of identical particles in a "box" at T = 0 K. Which of the following statements are true? a. The multiplicity of the gas is =1 b. The multiplicity of the gas is =N! C. If the gas consists of electrons with densities that correspond to the typical densities of conduction electrons in metals, only a part of the electrons can contribute to the heat capacity of the system as the temperature rises. d. If the gas consists of electrons with densities corresponding the typical densities of conduction electrons in metals, all electrons can easily contribute to the heat capacity of the system as the temperature rises.arrow_forward
- What is the Fermi wavevector (kF) and the displacement of the Fermi sphere (delta kF) if a field of E = 1,000 V/cm is applied? The low temperature conductivity is 1x108 (Ω-cm)-1 and the Hall coefficient is -1x10-24 (in CGS units). Assume that the metal exhibits free electron characteristics. fasr in 30 minutesarrow_forwardThe diffusion constant for injected electrons in a molecular crystal is 1x10^-2 cm^2/s at room temp. What is the mobility? What is the drift velocity in n electric field of 1x10^5 Volts/cm?arrow_forwardThe Fermi energy level for a particular material at T = 300 K is 5.50 eV. The electrons in this material follow the Fermi-Dirac distribution function. a) Find the probability of an energy level at 5.50 eV being occupied by an electron. b) Repeat part (a) if the temperature is increased to T = 600 K. (Assume that EF is a constant.). c) Calculate the energy level where probability of finding an electron at room temperature is 70%. d) Calculate the temperature at which there is a 7 percent probability that a state 0.4 eV below the Fermi level will be empty of an electron.arrow_forward
- 6.9 Show that the fraction of electrons within kBT of the Fermi level is equal to 3kB T/2&F, if D(ɛ) ~ €¹/2arrow_forwardH.W(1); Derive the Fermi momentum (pF) and the Fermi energy (EF), then calculated the amount?arrow_forwardSilicon is doped with phosphorus atoms (column V of Mendeleev table) with a concentration of 1018 cm-3 a- What is, at 27 °C, the electron density in doped Si. Use this result to derive the hole density. Which type of semiconductor is obtained? b- Calculate, at 27 °C, the position of the Fermi level EF and plot the band diagram.arrow_forward
- For a gas trapped in a two-dimensional harmonic oscillator, E = hf (nx+ny), sketch the positions of states in the n-plane and draw a couple of curves of constant energy. Calculate U/N at T = 0 and express it as a multiple of the Fermi energy. What is the density of states?arrow_forwardSilver contains 5.8 * 1028 free electrons per cubic meter. At absolute zero, what is the density of states (in states>J and states>eV) at the Fermi energy for a block of silver of volume 1.0 cm3?arrow_forwardPlot the Fermi function Vs. Energy at the temperature of 500 K, when EF = 2 eVarrow_forward
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