Quantum wells
en
modern electronics
Annalisa Fasolino
Theoretische Fysica, Nijmegen
Here you find the slides of the talk given October 24th
in Nijmegen. If you wish you can find more information
and addresses of many useful internet sites in the slides
of my lectures for the course
“Natuurkunde in de praktijk: nanotechnologie”
at http://www.sci.kun.nl/tvs/people/fasolino.html/teaching.shtml
Quantum wells
en
modern electronics
Annalisa Fasolino, Theoretische Fysica, Nijmegen
•
•
•
•
which are the effects needed
basic function of device elements
electrons in solids are the players in the game
how can we use their quantum mechanical nature to
achieve new effects
• the need for new artificial materials
• a success story till now but new ideas are needed if we
want to keep the pace we have witnessed in the last
ten years
Wishes for devices
•
•
•
•
as small as possible
as fast as possible
low operating costs, small consumption
cheap
Which applications
• fast electronics: high frequency
GHz
– mobile telephones, satellite receivers (TV), computers
• optoelectronics :
current  light
– lasers, LED, telecommunications (light through fibres)
– solar cells, photocells, light detectors
Basic function
• Switch current on/off
• amplification of signals
– small action, big effect
Vmod~100mV
Vout
r
R
Vext= 9V
r varied by external bias
= device
With it you can
-Switch on/off
- Amplify Vmod to Vout
Vout= Vext r/(r+R)
Variable resistance
l m
R
2
A ne 
L=length
A=surface
n=number of charge carriers
e=electron charge
=time between collisions
m=mass
in practice
n is the only parameter
which can be changed
but in metals n is fixed (~1 electron per atom),
in semiconductors it can be changed by doping
Crystals
Regular periodic arrangement of atoms in a lattice
Simple cubic
Face centered
cubic
fcc
From http://www.lassp.cornell.edu/sethna/Tweed/Cubic_Crystals.html
fcc unit cell
From http://www.jwave.vt.edu/crcd/farkas/lectures/structure/tsld001.htm
Effects of periodicity (formal)
a  0.1 nm
            
L  cm
 Wavefunction must be the same at symmetric positions
 ( x)   ( x  a )
2
2
  k  u k ( x )e
Periodic with
period a
ikx
Plane
wave
 This condition is satisfied only for some values of energy
Effects of periodicity (intuitive)
 Waves do not scatter (as particles do) if the order is perfect
mean free path in metals can be cm,
electrons behave almost as if the periodic potential
did not exist
Constructive
interference
for some
wavelengths,
destructive for
others
In Crystals: atomic energy levels -> bands
Metals, semiconductors and insulators
Energy of electrons
Fermi
energy
empty
empty
empty
filled
insulator
filled
semiconductor
filled
metal
GaAs band structure
Conduction band
(empty)
gap Eg
Valence band
(full)
2 2
E k  2m* k
Cu 4s1
Metals
Insulators
electrons loosely bound to
nuclei , “electron gas”
C 2s22p2
electrons form strong
covalent bonds
energy gap between occupied and empty states
NO
YES
Periodic table around semiconductors
III
IV
V
s 2p 1 s 2p 2 s 2p 3
Valence
electrons
B
C
N
Al
Si
P
Ga
Ge
As
In
Sn
Sb
Doping
The most important property of semiconductors is represented by the
possibility of doping with atoms with one electron more or one electron
less than what is needed for covalent bonds
Typical concentrations 1 atom every 100 million
One electron too much (too little). Extra electron does not
participate to bonding but remains nearly free
empty
doped
Doped + Interaction
with extra proton
filled
filled
filled
good and bad of doping
+ allows to control amount of free carriers, low density
- ionized impurities cause scattering, reduce mobility
p-n junction
Effect of external voltage (bias)
Equilibrium:
Coulomb force from ions
prevents migration across junction
Reverse bias:
applied electric field further
prevents flow across junction
Forward bias:
applied electric field assists
electrons in overcoming the
Coulomb barrier of the space
charge in depletion region
I-V characteristic
Diodes used for rectification, AM-FM detector, ...
Metal Oxide Semiconductor Field Effect
Transistor (MOSFET)
1 cm
First metal-insulator-semiconductor
Field Effect Transistor (~1960)
Present day dimensions
0.4 m (2000 lattice parameters) wide
10 nm (50 lattice parameters) thick active layer
Metal Oxide Field Effect Transistor (MOS)
V=0
V>Vth
 V between metal gate and p-substrate creates n-conducting
channel -> source-drain resistance decreases dramatically
 Almost no current passes (vertically) through oxide
 But many impurities in conducting channel (dissipation, ‘slow’)
Near the SiO2-Si interface
Classical
SiO2
Quantum Mechanical
SiO2
p-Si
10nm
p-Si
10nm
E1
 maximal
But such short and steep
variations of the potential
require a Q.M.
description.
H=(p2/2m + eFx) =E 
distance
Electron
density 
Electron
density 
E2
 minimal
=  *
distance
Getting rid of impurities: selective doping

- -- -- -- -- -- -- doped
layer
undoped
sc 1
Conducting
channel
undoped
sc 2 with
smaller
gap
Unstable: charge transfer --->
band bending
Heterostructures: Two layers of different semiconductors
with different bandgaps. Separate electrons from ionized
impurities !
Molecular Beam Epitaxy (MBE)
Typical MBE growth chamber
Mechanism for RHEED
specular spot oscillations
during growth
Atomic layer by layer growth
Mobility
e
 *
m
el
drift
v
 E
High  -> high speed

optical transitions
Absorption or emission of photons between full and empty states
ph
Needs photon energy E  hf equal to the energy
separation E of electronic levels
absorption
hf
E  hf 
emission
E
hc

hf
6.63 10-34 Js 3 10 8 m/s
hc


E
E(eV) 1.6 10-19 J/eV
E=1eV -> =1.243 m
Some frequencies are more useful than others
Transmission of light in air: best between 3 and 4 m
Attenuation in optical fibers
Glass fibers
for telecommunication,
best between 1.3-1.55 m
Attenuation less than
0.1 db/km
Energy gaps and lattice parameters
Quantum well (QW)
width L, infinite barriers
 ( x) 
2
 n 
sin 
x
L  L 
 (0)   ( L)  0
h
  n 
2
E n  8mL2 n  2m  L 
2
2
2
2 2

k
2m
E
2D: electrons
are bound
along x, free
to move
perpendicularly
parabolic
dependence
k
n
L
The principle of a semiconductor QW
New artificial material formed by thin layers of semiconductors
with different energy gaps
Ga
Al
As
AlAs
E
AlAs
g
GaAs
E
AlAs
GaAs
g
E
AlAs
g
a QW !
Bound states electron
Bound states holes
new, larger gap
400 nm
21 nm
10 meV
14 nm
Norm. PL intensity (arb. units)
Absorption from 3D to 2D
1
2
3
1.53 1.54 1.55 1.56 1.57 1.58
4
1.65 1.66
Photon energy (eV)
From
R. Dingle
Festkoerperprobleme
15,21 (1975)
1
2
3
4
well width
19.8 nm
12.2 nm
8.3 nm
5.1 nm
linewidth
0.25 meV
0.4 meV
1.0 meV
~ 5 meV
F. Pulizzi et al., Magnet Lab Nijmegen, 2001
The philisophy of semiconductor technology,
a success story
• Let’s make existing material smaller and smaller
• If the material we need does not exist let’s make it
ourselves
• use quantum confinement to tune electronic and optical
properties
• new things happen on the nanometer scale
• look for new fundamental physics AND for
applications/devices
Present technology based on miniaturization and
layer by layer growth
So successful that also Britney Spears
knows a lot about semiconductors
And now?
• Present technology based on scaling down from
`big` to small, is reaching its limits.
–
–
–
–
–
–
Limits of lithography, structures and contacts
Dissipation
Interconnects
Effect of interfaces
Quantum wires and quantum dots
QW are by now used in many commercial devices.
Why not try and confine electrons also in the other one or two
directions?
Quantum wires: etch selectively
with chemicals to create 1D structures.
Confinement effects need wires about
10 nm wide
(1000 thinner than a hair).
It turns out that it is very difficult
(and expensive) to create 1D (wires)
and 0D (dots) structures on nm scale
by chemical etching
Let’s nature help: look for self-organization
Growth on non-planar
grooved structures
From
http://imowww.epfl.ch/Nanoweb/default.htm
Thicker GaAs (the wire) at the bottom of the groove results from
the competition between the growth rate anisotropy on the
different facets of the groove and the surface diffusion of adatoms.
Wavefunction in quantum wires
From
http://www.ifm.liu.se/Matephys/
AAnew/research/iii_v/qwr.htm#S1.2
Turn a failure into a success
When the lattice mismatch is too big, layers turn into dots
Self-organized InAs quantum dots
From
http://www.ifm.liu.se/Matephys/AAnew/research/iii_v/qwr.htm#S1.2
The dots are formed during
spontaneous reorganisation of a sequence of AlGaAs and strained
InGaAs epitaxial films grown on GaAs (311)B substrates.
The size of the quantum dots are as small as 20 nm
Future
• Semiconductor technology based of sophisticated
techniques and concepts has been very successful
but is reaching its limits.
• New technology based on ‘bottom up’ is being
developed but far from maturity
– Molecular electronics (switching one molecule)
– Self-organisation of molecules, clusters, carbon
nanotubes.
• As Feynman said ‘there is plenty of room at the
bottom’ but:
• Almost everything needs to developed from
scratch again.