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Density of states The number of energy states per unit volume and unit energy is termed Density of States (DOS). Assumptions for simplified calculations: Potential energy of crystal is an infinite quantum well in which electrons have effective mass m*; - Electrons are free to move; The ground energy in the well is set to zero; Crystal is assumed a cube with side L. 4x= A exp(±kxx) kx = nïIL, n = 1, 2, 3, ... Kmax = ±л/α (λ = 2a) kmin π/L (quantum of wavenumber) ky Calculation of the number of states with wavenumber less than k. E E kx 8√√2π g(E): = h³ - m*3/2√√E Density of states of electrons per unit volume per unit energy. Density of states in semiconductor Egap Density of states 8mm√√2m(E-E) 8.(E)= n h³ 8,(E)= 8mm 2m (E-E) P√ 3 h³ Ę is the energy of the bottom of the conduction band E, is the energy of the top of the valence band Density of states in silicon and germanium 1. Calculate density of states of free electrons and holes* of energy** 0.01 eV in Si. 2. Calculate density of states of free electrons and holes* of energy** 0.1 eV in Ge. *Note that the energy of holes is negative with respect to the energy of electrons. **Note that the energy of free electrons is measured up from the bottom of the conduction band, whereas the energy of free holes is measured down from the top of the valence band.

Density of states The number of energy states per unit volume and unit energy is termed Density of States (DOS). Assumptions for simplified calculations: Potential energy of crystal is an infinite quantum well in which electrons have effective mass m*; - Electrons are free to move; The ground energy in the well is set to zero; Crystal is assumed a cube with side L. 4x= A exp(±kxx) kx = nïIL, n = 1, 2, 3, ... Kmax = ±л/α (λ = 2a) kmin π/L (quantum of wavenumber) ky Calculation of the number of states with wavenumber less than k. E E kx 8√√2π g(E): = h³ - m*3/2√√E Density of states of electrons per unit volume per unit energy. Density of states in semiconductor Egap Density of states 8mm√√2m(E-E) 8.(E)= n h³ 8,(E)= 8mm 2m (E-E) P√ 3 h³ Ę is the energy of the bottom of the conduction band E, is the energy of the top of the valence band Density of states in silicon and germanium 1. Calculate density of states of free electrons and holes* of energy** 0.01 eV in Si. 2. Calculate density of states of free electrons and holes* of energy** 0.1 eV in Ge. *Note that the energy of holes is negative with respect to the energy of electrons. **Note that the energy of free electrons is measured up from the bottom of the conduction band, whereas the energy of free holes is measured down from the top of the valence band.

Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
7th Edition
ISBN:9781337900348
Author:Stephen L. Herman
Publisher:Stephen L. Herman
Chapter1: Atomic Structure
Section: Chapter Questions
Problem 6RQ: How many valence electrons are generally contained in materials used for insulators?
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Density of states The number of energy states per unit volume and unit energy is termed Density of States (DOS). Assumptions for simplified calculations: Potential energy of crystal is an infinite quantum well in which electrons have effective mass m*; - Electrons are free to move; The ground energy in the well is set to zero; Crystal is assumed a cube with side L. 4x= A exp(±kxx) kx = nïIL, n = 1, 2, 3, ... Kmax = ±л/α (λ = 2a) kmin π/L (quantum of wavenumber) ky Calculation of the number of states with wavenumber less than k. E E kx 8√√2π g(E): = h³ - m*3/2√√E Density of states of electrons per unit volume per unit energy. Density of states in semiconductor Egap Density of states 8mm√√2m(E-E) 8.(E)= n h³ 8,(E)= 8mm 2m (E-E) P√ 3 h³ Ę is the energy of the bottom of the conduction band E, is the energy of the top of the valence band Density of states in silicon and germanium 1. Calculate density of states of free electrons and holes* of energy** 0.01 eV in Si. 2. Calculate density of states of free electrons and holes* of energy** 0.1 eV in Ge. *Note that the energy of holes is negative with respect to the energy of electrons. **Note that the energy of free electrons is measured up from the bottom of the conduction band, whereas the energy of free holes is measured down from the top of the valence band.
Transcribed Image Text:Density of states The number of energy states per unit volume and unit energy is termed Density of States (DOS). Assumptions for simplified calculations: Potential energy of crystal is an infinite quantum well in which electrons have effective mass m*; - Electrons are free to move; The ground energy in the well is set to zero; Crystal is assumed a cube with side L. 4x= A exp(±kxx) kx = nïIL, n = 1, 2, 3, ... Kmax = ±л/α (λ = 2a) kmin π/L (quantum of wavenumber) ky Calculation of the number of states with wavenumber less than k. E E kx 8√√2π g(E): = h³ - m*3/2√√E Density of states of electrons per unit volume per unit energy. Density of states in semiconductor Egap Density of states 8mm√√2m(E-E) 8.(E)= n h³ 8,(E)= 8mm 2m (E-E) P√ 3 h³ Ę is the energy of the bottom of the conduction band E, is the energy of the top of the valence band Density of states in silicon and germanium 1. Calculate density of states of free electrons and holes* of energy** 0.01 eV in Si. 2. Calculate density of states of free electrons and holes* of energy** 0.1 eV in Ge. *Note that the energy of holes is negative with respect to the energy of electrons. **Note that the energy of free electrons is measured up from the bottom of the conduction band, whereas the energy of free holes is measured down from the top of the valence band.
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