Transcript 1. Crystal Properties and Growth of Semiconductors

2. Atoms and Electrons
How to describe a new physical phenomenon?
New natural phenomenon
Previously existing theory
Explained
Experiments confirm
new phenomena
Not explained
New theory
Predicts new phenomena
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How to describe a new physical phenomenon?
New phenomenon
Previous Theory
New comprehensive theory
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Shortest Course in Quantum Mechanics
Observation: Electrons and atoms did not obey the classical
laws of mechanics.
New theory: Quantum mechanics predicts the way in which
electrons behave in solids..
Postulate: The light is quantized. The smallest discrete
unit of energy is photon.
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E=h·f
h=6.625*10 Js Planck constant
E – Energy of photon
f – Frequency of light
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Shortest Course in Quantum Mechanics, Cont.
Nobel Prizes: 1918 Planck for the discovery of energy quanta
1921 Einstein for the law of the photoelectric effect
Dual nature:
Wave
Particle
Light:
Wave nature: electromagnetic wave
f=1/ T (Hz) =c/f (m) wavelength
Particle nature : photon
p=h/ momentum of a photon
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Shortest Course in Quantum Mechanics, Cont.
Atomic spectra: Bohr model of atom
Nobel prize 1922 Niels Bohr for structure of atoms and
radiation emanating from them
Bohr postulates:
1) Electron exists in certain stable circular orbits about
the nucleus and does not give off radiation
2) Electron may shift to an orbit of higher or lower
energy by absorbing or emitting a photon of energy hf
3) Angular momentum is quantized p =m v r = n h/2

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Shortest Course in Quantum Mechanics, Cont.
Atomic spectra: Bohr model of atom
E3
e-
E2
hf31 = E3-E1 Emission
E1
e-
hf12 =E2-E1 Absorption
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Shortest Course in Quantum Mechanics, Cont.
Heisenberg Uncertainty Principle (Nobel prize 1932
for the creation of quantum mechanics)
The more precise you know the position of a particle ,
the less precise you know the momentum of the
particle:
x px ≥ h/2
The more precise you know the time, the less precise
you know the energy:
E t ≥ h/2
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Shortest Course in Quantum Mechanics, Cont.
Schrodinger Wave Equation
Dual nature of Electron :
Wave:
• Wave function (x)
• Schrodinger Wave Equation
• (x) *(x) dx is probability
that the position of electron is
within (x, x+x)
Particle:
•Mass
•Position
•Momentum
•Energy
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Shortest Course in Quantum Mechanics, Cont.
Schrodinger equation and solution for the potential well
problem will be presented in class.
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