1. 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

2. 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

3. Wishes for devices Which applications 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

4. Basic function Switch current on/off amplification of signals
small action, big effect
r varied by external bias
= device
Vmod~100mV
Vout
With it you can
-Switch on/off
- Amplify Vmod to Vout r R
Vout= Vext r/(r+R)
Vext= 9V

5. Variable resistance in practice n is the only parameter
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

6. Regular periodic arrangement of atoms in a lattice
Crystals
Regular periodic arrangement of atoms in a lattice
Simple cubic
Face centered
cubic
fcc
From
fcc unit cell
From

7. Effects of periodicity (formal)
L  cm
a  0.1 nm
            
 Wavefunction must be the same at symmetric positions
Periodic with
period a
Plane
wave
 This condition is satisfied only for some values of energy

8. 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

9. In Crystals: atomic energy levels -> bands

10. Metals, semiconductors and insulators
Energy of electrons
Fermi
energy
empty
empty
filled
empty
filled
filled
metal
insulator
semiconductor

11. GaAs band structure
Conduction band
(empty)
gap Eg
Valence band
(full)

12. Metals Insulators Cu 4s1 C 2s22p2 electrons loosely bound to
nuclei , “electron gas”
electrons form strong
covalent bonds
energy gap between occupied and empty states
NO YES

13. Periodic table around semiconductors
Valence
electrons

14. 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

15. + allows to control amount of free carriers, low density
One electron too much (too little). Extra electron does not
participate to bonding but remains nearly free
filled
empty
doped
Doped + Interaction
with extra proton
good and bad of doping
+ allows to control amount of free carriers, low density
- ionized impurities cause scattering, reduce mobility

16. p-n junction

17. 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

18. I-V characteristic
Diodes used for rectification, AM-FM detector, ...

19. 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

20. 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’)

21. Near the SiO2-Si interface
Classical
Quantum Mechanical
CB-edge
E=eFx
SiO2
p-Si
10nm
CB-edge
E=eFx
SiO2
p-Si
10nm E1 E2
But such short and steep
variations of the potential
require a Q.M. description.
H=(p2/2m + eFx) =E 
Electron
density 
Electron
density 
=  *
 maximal
 minimal
distance
distance

22. Getting rid of impurities: selective doping
doped
layer
undoped
sc 2 with
smaller
gap
sc 1
Conducting
channel
Unstable: charge transfer ---> band bending
Heterostructures: Two layers of different semiconductors with different bandgaps. Separate electrons from ionized impurities !

23. Molecular Beam Epitaxy (MBE)
Mechanism for RHEED
specular spot oscillations
during growth
Typical MBE growth chamber

24. Atomic layer by layer growth

25. Mobility
High  -> high speed

26. optical transitions
Absorption or emission of photons between full and empty states
Needs photon energy equal to the energy
separation of electronic levels
absorption emission
Js m/s
E(eV) J/eV
E=1eV -> =1.243 m

27. Some frequencies are more useful than others
Transmission of light in air: best between 3 and 4 m

28. Attenuation in optical fibers
Glass fibers
for telecommunication,
best between m
Attenuation less than
0.1 db/km

29. Energy gaps and lattice parameters

30. Quantum well (QW) width L, infinite barriers E 2D: electrons are bound
along x, free
to move
perpendicularly
parabolic
dependence

31. The principle of a semiconductor QW
New artificial material formed by thin layers of semiconductors
with different energy gaps Ga Al As
AlAs
GaAs
AlAs
a QW !
Bound states electron
Bound states holes
new, larger gap

32. Absorption from 3D to 2D 400 nm 21 nm 14 nm well width linewidth From
10 meV
well width linewidth
nm meV
nm 0.4 meV
3 8.3 nm 1.0 meV
4 5.1 nm ~ 5 meV
F. Pulizzi et al., Magnet Lab Nijmegen, 2001
From
R. Dingle
Festkoerperprobleme
15,21 (1975)

33. 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

34. So successful that also Britney Spears knows a lot about semiconductors

35. 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

36. 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

37. Let’s nature help: look for self-organization
Growth on non-planar
grooved structures
From
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.

38. Wavefunction in quantum wires
From
AAnew/research/iii_v/qwr.htm#S1.2

39. Turn a failure into a success
When the lattice mismatch is too big, layers turn into dots

40. Self-organized InAs quantum dots
From
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

41. 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.