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Detection of Light
I. Introduction II. Solid State Physics
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Blabla Recommended
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Information Carriers in Astronomy
• In situ (planetary spacecraft)
• Gravitational Waves
• Neutrinos
• Photons / electromagnetic waves
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The Electromagnetic Spectrum
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Photons Waves
Light as a Wave
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( ) ( )00 rksinr1,r φω +⋅−⋅= tEtE
Angular frequency Wavenumber Intensity
ck ω
λπ==
2
fπω 2=
( )20E∝
Phase angle
Space Time
Manifestation as Wave
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1
2
2
1
2
1
vv
sinsin
:law sSnell'
nn
==θθ
+=
+=
cvv
cv1or v1 00λλ
Refraction
Doppler effect (non-relativistic)
Diffraction & interference
Light as a Particle
Energy Momentum
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λν hchE ==
λν hc
hp ==( )
1exp
125
2
−
=
kThc
hcTI
λλλ
Max Planck (1858 – 1947)
Photoelectric effect –observed by Hertz (1887) and explained by Einstein (1905): light comes in “quanta”:
Information carried by Light …
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… and Measurements of that Information
10
Detector Technology Astronomy
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Two Fundamental Principles of Detection
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Photons
Waves
Respond to electrical field strength and preserve phase
Respond to individual photon energy
Two Types of Direct Detection
Based on photoelectric effect (release of bound charges)
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Thermalize photon energy
Wavelength Technology
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Quantum
Thermal Coherent
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Lecture slides (“handouts”) will be posted on the site Homework and solutions will be posted on the site 4-2-2015 Detection of Light – Bernhard Brandl 17
Course Topics & Lectures
Literature Main resource:
Detection of Light - from the Ultraviolet to the Submillimeter, by George Rieke, 2nd Edition, 2003, Cambridge University Press, ISBN 0-521-01710-6.
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Further reading: • Introduction to Solid State Physics (8th Edition)
by Charles Kittel; • Electronic Imaging in Astronomy: Detectors and
Instrumentation (2nd Edition) by Ian S. McLean; • Observational Astrophysics by P. Lena, Francoise Lebrun &
Francois Mignard;
Course Organization
• 3 ECTS, Level 500 – you need to register in uSis
• Lecture room: Huygens #106/7 from 9:00 - 10:45 hr
• Lecture period: 4 February – 1 April
• Lecturer: Dr. Bernhard Brandl, office: #535
• TA: Michael Wilby, office: #570
• Grade = 80% written exam + 20% mandatory homeworks
• Exam date: 13 April, 14:00 - 16:00 hr.
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Course Website http://home.strw.leidenuniv.nl/~brandl/DOL/Detection_of_Light.html
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Nucleons define the Period Table of the Elements
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Electrons lead to Atomic Lines and Bands
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• Electrons are described by probability clouds (“orbitals”) with specific energies.
• An electron around a positively charged nucleus has one unique set of four quantum numbers (QN).
Principal QN (n) = electron shell
Orbital QN (l) = angular momentum
Magnetic QN (ml)
Spin QN (ms)
Electronic Energy Levels
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• An atom can absorb or emit photons of specific energies • In this process, electrons change their energy levels (“orbitals”)
Example: hydrogen atom with one electron
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Electronic Bonding
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This can lead to transfer of electrons ( salts) or sharing of electrons ( covalent bonds)
Atoms with “incomplete” (= less than eight electrons) outer shells want to form a stable configuration
The Diamond Lattice Elements with 4 e– (e.g., C, Si, Ge) form crystals with a diamond lattice structure (each atom bonds to four neighbors).
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III – IV Semiconductors A diamond lattice can not only be formed by IV elements (C, Si, Ge) but also by elements from the 3rd and 5th group of elements.
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Gallium has 3 electrons, Arsenic has 5 electrons:
Si GaAs
Common Semiconductor Materials
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Metals, Semiconductors and Insulators
Metals have high electrical conductivity and consist of positive ions in a crystal lattice surrounded by delocalized electrons. Semiconductors have electrical resistivity between metals and insulators, which is temperature dependent. Insulators (also called dielectrics) resist the flow of electric current.
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Metals
Semimetals
Semiconductors
Animation: Electronic States and Bands Link to file
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http://en.wikipedia.org/wiki/Electronic_band_structure
Atomic Orbitals overlap Electronic Bands
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Isolated atoms Lattice spacing Decreasing atomic separation
VALENCE BAND
CONDUCTION BAND
Energy Outermost orbitals begin to
overlap.... ...bands form at crystal spacing
Bands in a periodic Crystal Lattice
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*note that even in a crystal with T=0, the electrons have momentum
The so-called k-vector of an electron or hole in a crystal is the wave-vector of its quantum-mechanical wavefunction
The electron moves* with momentum in a periodic lattice with lattice constant a and potential U.
kp =
Atom Crystal
Real Band Structures
"Bulkbandstructure" by Saumitra R Mehrotra & Gerhard Klimeck - Bandstructure Lab on nanoHUB.org Link: http://nanohub.org/resources/8814. Licensed under CC BY 3.0 via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:Bulkbandstructure.gif#mediaviewer/File:Bulkbandstructure.gif
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Band Gaps of Isolators, Metals and Semiconductors
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Energy CONDUCTION BAND
VALENCE BAND
BAND GAP
Insulator Metal Intrinsic Semiconductor
What makes a Detector work …:
That photon of energy may be our astronomical signal.
However, note that electrons can also get thermally excited cooling 4-2-2015 Detection of Light – Bernhard Brandl 39
Energy CONDUCTION BAND
VALENCE BAND
BAND GAP
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The Fermi Energy In a 1D, periodic potential, the electronic energy states are given
by
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At T = 0 K the Fermi energy is the same as the chemical potential µ.
22
2
=
an
mEn
π
The Pauli principle requires that no two electrons have exactly the same quantum numbers.
The energy corresponding to the highest occupied quantum state in a system of N electrons is the Fermi energy:
22
22
=
aN
mEF
π
The Energy Distribution of Electrons (1) In the classical picture, the energetic distribution of electrons would be given by the Maxwell-Boltzmann statistics:
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In the QM picture the concentration of electrons in the conduction
band is given by:
...where N(E) dE is the density of states and f(E) the Fermi distribution
(Fermi-Dirac statistics):
Fermi Energy and Distribution
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Fermi Distribution and Temperature At T = 0 K, the Fermi distribution is a step function
At T >> 0 K, the Fermi distribution flattens electrons may reach the conduction band by thermal excitation.
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The Energy Distribution of Electrons (2) Even at room temperature, the conduction electrons occupy typically only the lowest states in the conduction band.
If f(E)N(E) is close to zero at E > Ec, it can be described by an average “effective density of states Nc” near E ~ Ec:
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Hence the Fermi-Dirac statistics becomes:
…and we get:
Fermi Energy Chemical Potential
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What can we do to reduce the Bandgap? Goal: smaller bandgap = lower excitation energy = detection of lower energies = detection of longer wavelengths photons
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Consider “doping” a pure silicon crystal with small amounts of Group V or Group III elements:
Adding a Group V element (“donor”) adds conduction electrons n-type Si
Adding a Group III element (“acceptor”) adds a missing electron = “hole” p-type Si
Energy Bandgaps at T = 0 K
Note: pure semiconductors are called intrinsic, doped semiconductors are called extrinsic.
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Energy CONDUCTION BAND
VALENCE BAND
BAND GAP
Intrinsic Semiconductor
Extrinsic n-type Semiconductor
Extrinsic p-type Semiconductor
Energy Bandgaps at T > 0 K
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Energy CONDUCTION BAND
VALENCE BAND
BAND GAP
Intrinsic Semiconductor
Extrinsic n-type Semiconductor
Extrinsic p-type Semiconductor
Bandgaps in extrinsic Semiconductors Measured donor Ed and acceptor Ea ionization energies:
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Donor Si (meV) Ge (meV) intrinsic 1100 700 P 45 12 As 49 13 Sb 39 10 B 45 10 Ga 65 11 In 157 11
Note: 25 × smaller bandgap means 25 × longer wavelength coverage of the detector!
Note: for T = 300K, kT ~ 26 meV cooling of detector is crucial
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