I. Introduction II. Solid State Physics Detection of Light Bernhard Brandl 1

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1 Detection of Light I. Introduction II. Solid State Physics Detection of Light Bernhard Brandl 1

2 Detection of Light Bernhard Brandl 2

3 Blabla Recommended Detection of Light Bernhard Brandl 3

4 Information Carriers in Astronomy In situ (planetary spacecraft) Gravitational Waves Neutrinos Photons / electromagnetic waves Detection of Light Bernhard Brandl 4

5 The Electromagnetic Spectrum Photons Waves Detection of Light Bernhard Brandl 5

6 Light as a Wave E 1 r Time Space ( r, t) = E sin( ω t k + φ ) 0 r 0 Phase angle Angular frequency ω = 2πf Wavenumber k 2π ω = = λ c Intensity ( ) 2 E Detection of Light Bernhard Brandl 6

7 Manifestation as Wave Diffraction & interference Refraction Snell's law : sinθ1 sinθ 2 = v v 1 2 = n n 2 1 Doppler effect (non-relativistic) v v λ = λ or v = v0 1 + c c Detection of Light Bernhard Brandl 7

8 Light as a Particle Photoelectric effect observed by Hertz (1887) and explained by Einstein (1905): light comes in quanta : Max Planck ( ) I λ ( T ) = 2hc 5 λ 2 1 hc exp λkt 1 Energy Momentum hc E = hν = λ hν p = = c h λ Detection of Light Bernhard Brandl 8

9 Information carried by Light Detection of Light Bernhard Brandl 9

10 and Measurements of that Information 10

11 Detector Technology Astronomy

12 Detection of Light Bernhard Brandl 12

13 Two Fundamental Principles of Detection Respond to individual photon energy Photons Waves Respond to electrical field strength and preserve phase Detection of Light Bernhard Brandl 13

14 Two Types of Direct Detection Based on photoelectric effect (release of bound charges) Thermalize photon energy Detection of Light Bernhard Brandl 14

15 Wavelength Technology Quantum Thermal Coherent Detection of Light Bernhard Brandl 15

16 Detection of Light Bernhard Brandl 16

17 Course Topics & Lectures Lecture slides ( handouts ) will be posted on the site Homework and solutions will be posted on the site Detection of Light Bernhard Brandl 17

18 Main resource: Literature Detection of Light - from the Ultraviolet to the Submillimeter, by George Rieke, 2 nd Edition, 2003, Cambridge University Press, ISBN Further reading: Introduction to Solid State Physics (8 th Edition) by Charles Kittel; Electronic Imaging in Astronomy: Detectors and Instrumentation (2 nd Edition) by Ian S. McLean; Observational Astrophysics by P. Lena, Francoise Lebrun & Francois Mignard; Detection of Light Bernhard Brandl 18

19 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 Detection of Light Bernhard Brandl 19

20 Course Website Detection of Light Bernhard Brandl 20

21 Detection of Light Bernhard Brandl 21

22 Detection of Light Bernhard Brandl 23

23 Nucleons define the Period Table of the Elements Detection of Light Bernhard Brandl 24

24 Electrons lead to Atomic Lines and Bands 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 (m l ) Spin QN (m s ) Detection of Light Bernhard Brandl 25

25 Electronic Energy Levels 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 Detection of Light Bernhard Brandl 26

26 Detection of Light Bernhard Brandl 27

27 Electronic Bonding Atoms with incomplete (= less than eight electrons) outer shells want to form a stable configuration This can lead to transfer of electrons ( salts) or sharing of electrons ( covalent bonds) Detection of Light Bernhard Brandl 28

28 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) Detection of Light Bernhard Brandl 29

29 III IV Semiconductors A diamond lattice can not only be formed by IV elements (C, Si, Ge) but also by elements from the 3 rd and 5 th group of elements. Gallium has 3 electrons, Arsenic has 5 electrons: Si GaAs Detection of Light Bernhard Brandl 30

30 Common Semiconductor Materials Detection of Light Bernhard Brandl 31

31 Detection of Light Bernhard Brandl 32

32 Metals, Semiconductors and Insulators Metals Semimetals Metals have high electrical conductivity and consist of positive ions in a crystal lattice surrounded by delocalized electrons. Semiconductors Semiconductors have electrical resistivity between metals and insulators, which is temperature dependent. Insulators (also called dielectrics) resist the flow of electric current Detection of Light Bernhard Brandl 33

33 Animation: Electronic States and Bands Link to file Detection of Light Bernhard Brandl 34

34 Atomic Orbitals overlap Electronic Bands Energy Outermost orbitals begin to overlap......bands form at crystal spacing CONDUCTION BAND VALENCE BAND Isolated atoms Lattice spacing Decreasing atomic separation Detection of Light Bernhard Brandl 35

35 Bands in a periodic Crystal Lattice The so-called k-vector of an electron or hole in a crystal is the wavevector of its quantum-mechanical wavefunction The electron moves* with momentum p = k with lattice constant a and potential U. in a periodic lattice Atom Crystal *note that even in a crystal with T=0, the electrons have momentum Detection of Light Bernhard Brandl 36

36 Real Band Structures "Bulkbandstructure" by Saumitra R Mehrotra & Gerhard Klimeck - Bandstructure Lab on nanohub.org Link: Licensed under CC BY 3.0 via Wikimedia Commons Detection of Light Bernhard Brandl 37

37 Band Gaps of Isolators, Metals and Semiconductors Energy CONDUCTION BAND Insulator Metal Intrinsic Semiconductor BAND GAP VALENCE BAND Detection of Light Bernhard Brandl 38

38 What makes a Detector work : Energy CONDUCTION BAND BAND GAP VALENCE BAND That photon of energy may be our astronomical signal. However, note that electrons can also get thermally excited cooling Detection of Light Bernhard Brandl 39

39 Detection of Light Bernhard Brandl 40

40 The Fermi Energy In a 1D, periodic potential, the electronic energy states are given 2 2 by nπ E n = 2m a 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: E F = 2 2m Nπ 2a 2 At T = 0 K the Fermi energy is the same as the chemical potential µ Detection of Light Bernhard Brandl 41

41 The Energy Distribution of Electrons (1) In the classical picture, the energetic distribution of electrons would be given by the Maxwell-Boltzmann statistics: 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): Detection of Light Bernhard Brandl 42

42 Fermi Energy and Distribution Detection of Light Bernhard Brandl 43

43 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 Detection of Light Bernhard Brandl 44

44 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 > E c, it can be described by an average effective density of states N c near E ~ E c : Hence the Fermi-Dirac statistics becomes: and we get: Detection of Light Bernhard Brandl 45

45 Fermi Energy Chemical Potential Detection of Light Bernhard Brandl 46

46 Detection of Light Bernhard Brandl 47

47 What can we do to reduce the Bandgap? Goal: smaller bandgap = lower excitation energy = detection of lower energies = detection of longer wavelengths photons 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 Detection of Light Bernhard Brandl 48

48 Energy Bandgaps at T = 0 K Energy Intrinsic Semiconductor CONDUCTION BAND Extrinsic n-type Semiconductor Extrinsic p-type Semiconductor BAND GAP VALENCE BAND Note: pure semiconductors are called intrinsic, doped semiconductors are called extrinsic Detection of Light Bernhard Brandl 49

49 Energy Bandgaps at T > 0 K Energy Intrinsic Semiconductor CONDUCTION BAND Extrinsic n-type Semiconductor Extrinsic p-type Semiconductor BAND GAP VALENCE BAND Detection of Light Bernhard Brandl 50

50 Bandgaps in extrinsic Semiconductors Measured donor E d and acceptor E a ionization energies: Donor Si (mev) Ge (mev) intrinsic P As Sb B Ga In Note: 25 smaller bandgap means 25 longer wavelength coverage of the detector! Note: for T = 300K, kt ~ 26 mev cooling of detector is crucial Detection of Light Bernhard Brandl 51

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