FYS3410 - Vår 2017 (Kondenserte fasers fysikk) · 3) + (0.5 to 2) at% Cr 2 O 3 -- Sapphire is...
Transcript of FYS3410 - Vår 2017 (Kondenserte fasers fysikk) · 3) + (0.5 to 2) at% Cr 2 O 3 -- Sapphire is...
FYS3410 - Vår 2017 (Kondenserte fasers fysikk) http://www.uio.no/studier/emner/matnat/fys/FYS3410/v16/index.html
Pensum: Introduction to Solid State Physics
by Charles Kittel (Chapters 1-9, 11, 17, 18, 20)
Andrej Kuznetsov
delivery address: Department of Physics, PB 1048 Blindern, 0316 OSLO
Tel: +47-22857762,
e-post: [email protected]
visiting address: MiNaLab, Gaustadaleen 23a
2017 FYS3410 Lectures and Exam (based on C.Kittel’s Introduction to SSP, Chapters 1-9, 11, 17,18,20)
Module I – Periodic Structures and Defects (Chapters 1-3, 20)
T 17/1 12-15 Introduction. Crystal bonding. Periodicity and lattices. Lattice planes and Miller indices. Reciprocal space. 3h
W 18/1 09-10 Bragg diffraction and Laue condition 1h
T 24/1 12-14 Ewald construction, interpretation of a diffraction experiment, Bragg planes and Brillouin zones 2h
W 25/1 08-10 Surfaces and interfaces. Elastic strain in crystals 2h
T 31/1 12-14 Point defects and atomic diffusion in crystals 2h
W 01/2 08-10 Summary of Module I 2h
Module II – Phonons (Chapters 4, 5, and 18 pp.557-561)
T 07/2 12-14 Vibrations in monoatomic and diatomic chains of atoms; examples of dispersion relations in 3D 2h
W 08/2 08-10 Periodic boundary conditions (Born – von Karman); phonons and its density of states (DOS) 2h
T 14/2 12-14 Effect of temperature - Planck distribution; lattice heat capacity: Dulong-Petit, Einstein, and Debye models 2h
W 15/2 08-10 Comparison of different lattice heat capacity models 2h
T 21/2 12-14 Thermal conductivity and thermal expansion 2h
W 22/2 08-10 Vibrational and thermal properties of nanostructures 2h
T 28/2 12-14 Summary of Module II 2h
Module III – Electrons (Chapters 6, 7, 11 - pp 315-317, 18 - pp.528-530, and Appendix D)
W 01/3 08-10 Free electron gas (FEG) versus free electron Fermi gas (FEFG) 2h
T 07/3 12-14 DOS of FEFG in 3D; Effect of temperature – Fermi-Dirac distribution; heat capacity of FEFG in 3D 2h
W 08/3 08-10 Transport properties of electrons electrons – examples for thermal, electric and magnetic fields 2h
T 14/3 12-14 DOS of FEFG in 2D - quantum wells 2h
W 15/3 08-10 DOS in 1D – quantum wires, and in 0D – quantum dots 2h
T 21/3 12-14 Origin of the band gap; Nearly free electron model 2h
W 22/3 08-10 Kronig-Penney model; Empty lattice approximation; Number of orbitals in a band 2h
T 28/3 12-14 no lecture
W 29/3 08-10 no lecture
T 4/4 12-14 Effective mass method 2h
W5/4 08-10 Summary of Module III 2h
Easter break
Module IV – Semiconductors and Metals (Chapters 8, 9 pp 223-231, and 17)
T 18/4 12-14 Fermi surfaces in metals; approaches for energy band calculations 2h
W 19/4 08-10 Effective mass method for calculating localized energy levels for defects in crystals 2h
T 25/4 12-14 Intrinsic and extrinsic electrons and holes in semiconductors; carrier statistics 2h
W 26/4 08-10 p-n junction and metal-semiconductor contact 2h
T 02/5 12-14 Optical properties of metals and semiconductors 2h
W 03/5 08-10 Optoelectronic device demonstrations with Randi Haakenaasen 2h
T 09/5 12-14 Summary of Module IV 2h
Summary and repetition
T 16/5 12-14 Repetition - the course in a nutshell 2h
Exam
Week 22 , June 1-2, your presence is required for 1 h – please book your time in advance
Optical properties of solids
• Recap of the hydrogen optical spectrum and optical process in solids
• Absorption and reflection of light in metals
• Light absorption semiconductors
• Photoluminecence: 3D versus 2D semiconductors
• Use of p-n junctions in optics: LEDs and solar cells
Optical properties of solids
• Recap of the hydrogen optical spectrum and optical process in solids
• Absorption and reflection of light in metals
• Light absorption semiconductors
• Photoluminecence: 3D versus 2D semiconductors
•Use of p-n junctions in optics: LEDs and solar cells
ENG2000: R.I. Hornsey Optic: 5
Absorption or emission due to excitation or relaxation of
the electrons in hydrogen atom
Light that can be detected by the human eye has
wavelengths in the range λ ~ 450nm to 650nm &
is called visible light:
• The human eye can detect light
of many different colors.
• Each color is detected with
different efficiency.
3.1eV 1.8eV
Spectral Response of Human Eyes
Eff
icie
ncy
, 100%
400nm 600nm 700nm 500nm
Chapter 21 -
• Incident light is reflected, absorbed, scattered, and/or
transmitted:
Light interactions with solids
• Optical classification of materials:
Transparent Translucent
Opaque
Incident: I0
Absorbed: IA
Transmitted: IT
Scattered: IS
Reflected: IR
Chapter 21 - 8
Light Absorption
e0IIT
The amount of light absorbed by a material is
calculated using Beer’s Law
= absorption coefficient, cm-1
= sample thickness, cm
= incident light intensity
= transmitted light intensity
0I
TI
ln
0I
IT
Rearranging and taking the natural log of both sides
of the equation leads to
Optical properties of solids
• Recap of the hydrogen optical spectrum and optical process in solids
• Absorption and reflection of light in metals
• Light absorption semiconductors
• Photoluminecence: 3D versus 2D semiconductors
• Use of p-n junction in optics: LEDs and solar cells
Chapter 21 -
• Absorption of photons by electron transitions:
• Unfilled electron states are adjacent to filled states
• Near-surface electrons absorb visible light.
Light absorption in metals
Energy of electron
Planck’s constant
(6.63 x 10-34 J/s)
freq. of incident light
filled states
unfilled states
DE = h required!
Chapter 21 - 11
Light reflection in metals
• Electron transition from an excited state produces a photon.
photon emitted
from metal
surface
Energy of electron
filled states
unfilled states
Electron transition
IR “conducting” electron
Chapter 21 - 12
• Reflectivity = IR /I0 is between 0.90 and 0.95.
• Metal surfaces appear shiny
• Most of absorbed light is reflected at the
same wavelength
• Small fraction of light may be absorbed
• Color of reflected light depends on
wavelength distribution
– Example: The metals copper and gold absorb light
in blue and green => reflected light has gold color
Light reflection in metals
Chapter 21 -
Optical properties of solids
• Recap of the hydrogen optical spectrum and optical process in solids
• Absorption and reflection of light in metals
• Light absorption semiconductors
• Photoluminecence: 3D versus 2D semiconductors
• Use of diodes in optics: LEDs and solar cells
Chapter 21 -
Absorption of light of frequency by by electron transition
occurs if h > Egap
• If Egap < 1.8 eV, all light absorbed; material is opaque (e.g., Si, GaAs)
• If Egap > 3.1 eV, no light absorption; material is transparent and
colorless (e.g., diamond)
Light absorption in semiconductors
• If 1.8 eV < Egap < 3.1 eV, partial light absorption; material is colored
blue light: h = 3.1 eV
red light: h = 1.8 eV
incident photon
energy h
Energy of electron
filled states
unfilled states
Egap
Examples of photon energies:
Chapter 21 -
Valence Band – Conduction Band Absorption
(Band to Band Absorption)
Conduction Band, EC
Valence Band, EV
Egap h = Ephoton
This process obviously requires that the minimum energy of a
photon to initiate an electron transition must satisfy
EC - EV = h = Egap
If h > Egap then obviously a transition
can happen. Electrons
are then excited to the
conduction band.
Chapter 21 - 16
Ge (min)hc
Eg (Ge)
(6.63 x 1034 J s)(3 x 108 m/s)
(0.67 eV)(1.60 x 1019 J/eV)
Computations of Minimum
Wavelength Absorbed
Note: the presence of donor and/or acceptor states allows for light
absorption at other wavelengths.
Solution:
(a) What is the minimum wavelength absorbed by
Ge, for which Eg = 0.67 eV?
Ge (min)1.86 x 10 -6 m 1.86m
(b) Redoing this computation for Si which has a band gap
of 1.1 eV
Si(min)1.13m
ENG2000: R.I. Hornsey Optic: 17
• Hence, the absorption coefficients of various
semiconductors look like:
Direct Indirect Band Gap Semiconductors
E
CB
k–k
Direct Bandgap
(a) GaAs
E
CB
VB
Indirect Bandgap, Eg
k–k
kcb
(b) Si
E
k–k
Phonon
(c) Si with a recombination center
Eg
Ec
Ev
Ec
Ev
kvb VB
CB
Er
Ec
Ev
Photon
VB
(a) In GaAs the minimum of the CB is directly above the maximum of the VB. GaAs istherefore a direct bandgap semiconductor. (b) In Si, the minimum of the CB is displaced fromthe maximum of the VB and Si is an indirect bandgap semiconductor. (c) Recombination ofan electron and a hole in Si involves a recombination center .
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Chapter 21 - 19
• Color determined by the distribution of wavelengths: -- transmitted light
-- re-emitted light from electron transitions
• Example 1: Cadmium Sulfide (CdS), Eg = 2.4 eV
-- absorbs higher energy visible light (blue, violet)
-- color results from red/orange/yellow light that is transmitted
Color of Nonmetals
• Example 2: Ruby = Sapphire (Al2O3) + (0.5 to 2) at% Cr2O3
-- Sapphire is transparent and
colorless (Eg > 3.1 eV)
-- adding Cr2O3 : • alters the band gap
• blue and orange/yellow/green
light is absorbed
• red light is transmitted
• Result: Ruby is deep
red in color
Adapted from Fig. 21.9, Callister & Rethwisch 8e.
(Fig. 21.9 adapted from "The Optical Properties of
Materials" by A. Javan, Scientific American, 1967.)
40
60
70
80
50
0.3 0.5 0.7 0.9
Tra
nsm
itta
nce (
%)
ruby
sapphire
wavelength, (= c/)(m)
Some of the many applications
– Emission:
light emitting diodes (LED) & Laser Diodes (LD)
– Absorption:
– Filtering: Sunglasses, ..
Si filters (transmission of infra red light with simultaneous
blocking of visible light)
Optical properties of solids
• Recap of the hydrogen optical spectrum and optical process in solids
• Absorption and reflection of light in metals
• Light absorption semiconductors
• Photoluminecence: 3D versus 2D semiconductors
• Use of p-n junctions in optics: LEDs and solar cells
Chapter 21 - 22
Photoluminescence
• Luminescence – reemission of light by a material
– Material absorbs light at one frequency and reemits it at another
(lower) frequency.
– Trapped (donor/acceptor) states introduced by impurities/defects
activator level
Valence band
Conduction band
trapped states Eg
Eemission
Multiple Quantum Wells (MQWs)
repetitions of
ZnO/ZnCdO/ZnO
1.5nm
Quantum properties electrons at the excited state
Bulk properties electrons at the ground state
hν
”blue shift”
Vishnukanthan, et.al Solar Energy, 106, 82(2014)
”blue shift”
PL: optical excitation and subsequent radiative carrier
recombination
Photoluminecence: 3D versus 2D semiconductors
Photoconductivity • Charge carriers (electrons or
holes or both) created in the
corresponding bands by
absorbed light can also
participate in current flow,
and thus should increase the
current for a given applied
voltage, i.e., the conductivity
increases
• This effect is called
Photoconductivity
• Want conductivity to be controlled by
light. So want few carriers in dark → A
semiconductor
• But want light to be absorbed, creating
photoelectrons
• → Band gap of intrinsic
photoconductors should be smaller than
the energy of the photons that are
absorbed
Optical properties of solids
• Recap of the hydrogen optical spectrum and optical process in solids
• Absorption and reflection of light in metals
• Light absorption semiconductors
• Photoluminecence: 3D versus 2D semiconductors
• Use of p-n junctions in optics: LEDs and solar cells
LEDs
From Light-Emitting Diodes, Fred Schubert
Chapter 21 - 27
Solar Cells
• Solar cell operation - incident photons generate elecron-hole pairs.
- internal p-n junction field drive the current
- current increases with light intensity.
n-type Si
p-type Si
p-n junction
light
+
-
+ + +
- - -
creation of
Electron-hole pair
Solar Cells
Conventional pyramid textures can be readily obtained via anisotropic etching of (100)-oriented c-Si in alkaline
solutions, which is widely used in c-Si PV cell manufacturing.
Y.Wang, L.Yang, Y. Liu, Z.X Mei, W.Chen, J. Li, H.L.Liang, A.Yu.Kuznetsov and X.L.Du
Scientific Reports 5, 10843 (2015)
Maskless inverted pyramid texturization of silicon
Conventional pyramid textures can be readily obtained via anisotropic etching of (100)-oriented c-Si in alkaline
solutions, which is widely used in c-Si PV cell manufacturing.
So-called inverted pyramid (IP) arrays, outperform conventional textures of their superior structure and light-
trapping characteristics
Inverted
pyramid
Y.Wang, L.Yang, Y. Liu, Z.X Mei, W.Chen, J. Li, H.L.Liang, A.Yu.Kuznetsov and X.L.Du
Scientific Reports 5, 10843 (2015)
Maskless inverted pyramid texturization of silicon
Y.Wang, L.Yang, Y. Liu, Z.X Mei, W.Chen, J. Li, H.L.Liang, A.Yu.Kuznetsov and X.L.Du
Scientific Reports 5, 10843 (2015)
Maskless inverted pyramid texturization of silicon