Download 3PNT_L1

3PNT – Photonics and
Nanotechnology
• Part I Quantum electronic and
optical confinement (6 lectures,
Prof BN Murdin)
– Recap of basic semiconductor
physics
– Semiconductor quantum
structures
• Wells, wires, dots
– Photonic bandgap structures
– Fabrication of nanostructures
• Part II Advanced Lasers and
optical communications (6
lectures, Dr SJ Sweeney)
–
–
–
–
Semiconductor lasers
Optical amplifiers
Optical fibres
Telecommunications
• Part III Modern Nanophotonics
(8 lectures, Profs J Allam and
BN Murdin)
– Including:
•
•
•
•
Spintronics
Microcavities
Polymer photonic devices
Biophotonics
Take a strip off the bottom of a piece of A4
paper and cut it in half, then half again…..
No Cuts
Length
Objects on that scale
0
21.0 cm
Red blood cell
2
5.25 cm
Diameter of a human hair
4
1.31 cm
Bacteria
6
3.28 mm
8
820 mm
Toothpick
10
205 mm
Cluster of atoms, a nanoparticle
12
51.2 mm
Pencil
14
12.8 mm
Diameter of a finger
16
3.2 mm
Eight hydrogen atoms lined up
18
801 nm
Kernel of corn
20
200 nm
Silt
22
50.0 nm
Gnat
24
12.5 nm
Resolution of optical microscope
26
3.13 nm
Virus, Intel’s smallest transistor
28
7.82 Å
Thickness of a cell wall
Tip of a needle, bee sting
Take a strip off the bottom of a piece of A4
paper and cut it in half, then half again…..
No
Cuts
Length
0
21.0 cm
2
5.25 cm
4
1.31 cm
6
3.28 mm
8
820 mm
10
205 mm
12
51.2 mm
14
12.8 mm
16
3.2 mm
18
801 nm
20
200 nm
22
50.0 nm
24
12.5 nm
26
3.13 nm
28
7.82 Å
Objects on that scale
Objects on that scale
Pencil
Toothpick
Diameter of a finger
Kernel of corn
Gnat
Tip of a needle , bee sting
Diameter of a human hair
Silt
Red blood cell
Bacteria
Resolution of optical microscope
Virus, Intel’s smallest transistor
Thickness of a cell wall
Cluster of atoms, a nanoparticle
Eight hydrogen atoms lined up
Nanophotonics: Nobel Prizes in
Physics 1991 & 2000
• 2000
• ZI Alferov Russia, H Kroemer,
Germany, JS Kilby USA
• for the invention of integrated
circuit, and for developing
semiconductor
heterostructures, including:
– The heterojunction laser
• 1991
• PG de Gennes, France
• for generalizing the theory of
order/disorder in simple
systems (e.g. magnets) to
complex forms of matter, in
particular:
– Liquid crystals
Other nanotechnology Nobel prizes
• 1973 tunnelling phenomena
– L Esaki Japan, I Giaever USA (b.
Norway) BD Josephson United
Kingdom
• 1985 quantum Hall effect
– K von Klitzing Germany
• 1986 electron microscope
– E Ruska, G Binnig, Germany and H
Rohrer, Switzerland
Other photonics Nobel prizes
• 1964 the maser/laser
– CH Townes USA, NG Basov
USSR, AM Prokhorov USSR
• 1971 holography
– D Gabor, United Kingdom (b.
Hungary)
• 1981 laser and electron
spectroscopy
– N Bloembergen USA (b
Netherlands), AL Schawlow
USA, KM Siegbahn Sweden
• 2005 quantum theory of optical
coherence and laser-based
precision spectroscopy
– RJ Glauber USA, JL Hall USA,
TW Hänsch Germany
Challenges for Nanotechnology
• Nanomanufacturing
– Incorporating nanoscale materials into larger scale devices (e.g.
heterostructure lasers)
– Designing materials with nanoscale structure (e.g. synthetic
opals)
– Nanomachines (microcraft and robotics)
• Nanophysics
– Investigation of Nano-Electronics, -Photonics, and -Magnetics
• Nanotechnology applications
–
–
–
–
Detection of chemical-biological-radiological-medical compounds
Therapeutics (e.g. drug delivery)
Instrumentation, and Metrology (e.g. gyros)
Energy Conversion (e.g. solar cells, suncream) and storage (e.g.
zeolytes)
– Processes for environmental improvement
Current photonics industries
• Products in the Growing Period: commercially available
technology and expanding market scale
– TFT-LCD (TV, Monitor), PDP
– DVD Player (Audio, Video),CD/DVD Recorder (Burner), Discs
– Imaging devices (DSC, image sensor)
• Products in the Emerging Period: technology under
development with high market potential
– Organic-EL, high brightness LED, LD
– High-Density Optical Discs (bluray), LCD (LTP-Si, reflective, low
power consumption), Projectors (DLP, LCoS, LCD , VR)
– Advanced networking systems (Local LAN, all-optical networks)
Overview of global photonics market
What is Nano-Photonics?
• Information technology: storage and processing
(Moore’s Law), transmission and reception,
displays
• Sensors: identification of compounds
(bio/chem/medical), nondestructive testing and
evaluation
• Nanomedicine: microscopy, disease detection
and treatments
• Power generation and efficient utilization: solar
cells, Thermo-photovoltaics (TPVs), lasers, LED
lighting
What’s So Great About
Semiconductors?
• The resistance of a semiconductor structure may be fixed within a
range of many orders of magnitude by various means:
– Impurities (doping), homostructure design, heterostructure design etc….
• Once produced, the resistance of the structure my then also be
varied over a range of many orders of magnitude by various means:
– Light, electric field, current, temperature, magnetic fields, etc…
Photo-Diodes
Resistance =
f(incident light)
Transistors
Resistance =
f(V) or f(I)
Thermo-resistors
Resistance =
f(Temperatur)
• Finally, semiconductors can actively produce, modulate, switch and
recolour light beams, and are the basis of a huge variety of useful
“photonic” devices.
Things that can’t be made from Si
• Light emitters and optical modulators (it’s “indirect”)
– Light emitting diodes, Laser diodes (any wavelength)
– Amplitude modulation of light for fibre telecoms
• Mid-IR, far-IR, UV detectors (interband absorption is 0.5 to1.1 μm)
–
–
–
–
–
Fibre communication receivers (l = 1.3 and 1.55 μm)
Atmospheric “windows” (l = 3 to 5 μm and 8 to 12 μm)
Infrared imaging arrays (responding to 500 K black bodies)
Solar blind detectors (l ≤ 0.5 μm)
Efficient solar cells
• Very-high speed electronics (its “effective mass” is high)
– Operating at 40 GHz and above for mobile phones and fibre telecoms
• High temperature electronics (bandgap and melting point too low)
– Operable at temperatures above 200˚C for process monitoring
What is a heterostructure ?
• A device built from different semiconductor
materials, thus exploiting the differences in
electronic level structure.
Ohm’s Law for grown-ups
1
I V
R
j  sF
s  enm
• The response (j) to the drive (F) is a material property
(s), which is independent of size and determined by the
number of mobile charges, and the charge and the
“mobility” of each.
Metal
semicond
Insulator
s (W-1m-1)
>106
105-10-7
<10-8
n (m-3)
1028
1027-1016
<1015
m (mV-1s-1) 10-3
10-3-102
Why such big variation in s?
• Metal
s  enm
• Semiconductor
– Continuous DoS
– DoS has gap
• n ≠ n(T)
• n = n(EF,T)
depends very
sensitively on
both on doping
and
temperature
E
– Drude mobility:
• m = et(T)/m
– Temp. dep. of s
comes from t
the electron
scattering time
EF
r
f
r
Fermi
occupation
function
In the metal the charges that can take part in the transport are all those near
EF. This number is not very sensitive to T. In the semiconductor most states
near EF are missing, and the occupation of the remainder is very sensitive to T.
How do we control n?
• The Fermi level (or chemical potential) of the electrons
falls in a gap of the band structure.
• Doping allows us to control the position of EF in the gap.
– Either electrons (n-type) or holes (p-type) act as carriers of
charge.
• We can also optically excite electron-hole pairs.
• How do we calculate n? This requires knowing the
Density of States (DoS) – see homework.
Schroedinger Eqn in 1D
E
 2 2

  V (r) (r)  E(r)

 2m

n=3
10
5
• … the energy of a state is related
to the curvature of the
wavefunction
C
n=2
5
0
• Tighter confinement → Higher
Energy
0
z/L
1
0
•Fixed box boundary
conditions give standing
waves
•Periodic b.c.’s allow
travelling waves
• Nodes in wavefunction → Higher
Energy
kn  n
10
n=1
0
( z )  A sin kn z 
Ψ2(z)
Ψ(z)
• Schrodinger’s Equation…

L
 2 k n2
En 
2m
1
Energy bands for 1-D, one atom lattice
• 1D, one atom basis: each s & p forms one band.
– Two atom basis: each s & p forms two bands.
– 3D: p-orbitals are 3-fold degenerate, px, py, pz.
Crystal structure of GaAs
• FCC lattice with two atom
basis:
• 1 Ga & 1 As atom per lattice
site
– Tetrahedrally coordinated
– Ga: [Ar] 3d10 4s24p1
– As: [Ar] 3d10 4s24p3
– 3 valence e- per gallium atom
– 5 valence e- per arsenic atom
• Germanium:
– Both sites still different
(different coordination) but
both atoms same species
– Ge: [Ar] 3d10 4s24p2
• total: 8 valence e- per unit cell
– 4 bands full (x2 for spin)
Bandstructure of GaAs
EF
4s2
Bonding
Isolated
atom
Two Two atom
lattice
atoms
Energy (eV)
Anti-bonding
Full
valence bands
4p2
Empty
conduction
bands
L-valley G-valley X-valley
000
100
111
kz
G
L
X
ky
kX
wavevector, k
E
Effective mass
• For almost all properties of
semiconductors the most
important states are the ones
near the band edges, because
that’s where the electrons and
holes collect.
• The bottom of the conduction
band is a turning point, so odd
k terms are zero :
E  c0  c2 k 2  c4 k 4  
• We (usually) neglect higher
terms (small k, small E), so we
write:
k
 2k 2
E  E0 
2m 
G
• Electrons move as if in free
space, but with a mass
determined by curvature: the
"effective mass".
1
1  E (k )
 2
2
m *  k
2
Optical transitions
• Interband transitions
• Intraband
transitions
n-type
h  E g
h  E g
p-type
t  nanoseconds in GaAs
t  < ps in GaAs
Direct and indirect gap
transitions
Direct bandgap
a~104 cm-1
h
E
k
• G valley is lowest
• optical transitions are direct
• ~zero momentum transfer
• optical absorption length ~ 1mm
Indirect bandgap
a~102 cm-1
h
phonon-assisted
absorption
•X or L valley is lowest
• optical transitions are indirect
• momentum supplied by phonon
• optical absorption length ~ 100mm
Photons carry virtually no momentum
E
Conduction band
 2k 2
E (k ) 
2mc
Eg
k
Valence band
• Q: how much is k for absorption in GaAs 5%
above gap?
mc=0.07 me, mv>>me EG = 1.5eV GaAs
period
group
2
3
4
5
6
II III IV V VI
B C N O
Al Si P S
Zn GaGe As Se
Cd In Sn Sb Te
Hg
larger atoms
larger atoms
Bandstructure of Ge and GaAs
Band edges and vacuum level
• Band edge energies
•
– The band edge energies relative to the
vacuum reference level and to each
vacuum reference level
other are a property of the
semiconductor
0
– Energy gap, EG: Valence band edge
to conduction band edge
Electron
eF
Fermi level
energy
– Depends additionally on doping
Ec
– n-type
EF
n  N C exp -eEC -E F  / kT 
 EC -E F  (kT/e) ln ( N C /n)
– p-type
p  NV exp -eEV -E F  / kT 
 EF -EV  (kT/e) ln ( NV /p)
– Work function, F: Fermi level to
vacuum ref.
EG
EG
Ev
Distance, z
n-type: EF is
near c.b. edge
Homojunctions
•
•
i.e. joining two pieces of same material, different doping
Isolated n- and p-type:
vacuum reference level
0
qF
Ec
EF
qF
vacuum
Ec
Ev
n-type
•
•
•
0
i. Have same vacuum ref.,
ii. Fermi levels differ
iii. Both materials neutral
EF
Ev
p-type
Homojunctions
•
Electrically connected:
0
qF
0
qF
Ec
EF
Ec
+++
n-type
- - p-type
EF
Ev
Ev
•
•
•
i. Charge diffuses from high concentration to low across the boundary
ii. Ionised dopants left behind change potential
iii. Fermi levels shift until equal
Growth of Heterostructures:
Molecular Beam Epitaxy of GaAs/AlGaAs
Heterostructures: Bandgaps/misfits
•
Epitaxial films may only have small lattice mismatch
– the bigger the mismatch the smaller the thickness
that can be grown without dislocations
1D P.E. landscapes: step
• Classically, electrons with
0 < E < DE cannot pass x
= 0, while all those with E
> DE can.
• Quantum mechanically,
electrons with 0 < E < DE
penetrate the barrier with
an exponential depth,
and those with E > DE
have a finite probability of
being reflected by the
step.
• Such a step can be
created by laying a wide
gap semiconductor on
top of a narrow gap
semiconductor
DE
E
Potential energy landscape
model
• In heterojunctions electrons and holes
can be modelled by the effective mass
theory, even though perfect periodicity
is destroyed.
• In this case, the potential energy
profile, V(x), seen by electrons is Ec(x)
and that seen by holes is Ev(x).
Heterojunctions
• i.e. joining two pieces of different materials, (maybe different doping)
vacuum reference level
0
0
qFn
vacuum
Ec
EF
qFp
Ec
EF
Ev
intrinsic narrow gap
Ev
n-type wide gap
Heterojunctions
•
Electrically connected:
0
qF
0
qF
Ec
EF
Ec
+++
n-type
p-type
EF
Ev
Ev
Discontinuity forms potential well
in narrow gap material (which
band depends on doping)
• Q: draw band diagram for p-type wide gap
and n-type narrow gap
Homework
• Revise Density of States for 3D system
(see level 2 semiconductors 2SP, level 3
Physics of Stars 3PS etc)
• Find out Density of states for 2D, 1D and
0D system.
• Bring drawings and formulas to lecture