Annalisa FasolinoTheoretische Fysica, Nijmegen

Quantum wellsen

modern electronics

Here you find the slides of the talk given October 24thin Nijmegen. If you wish you can find more information and addresses of many useful internet sites in the slidesof my lectures for the course “Natuurkunde in de praktijk: nanotechnologie”at http://www.sci.kun.nl/tvs/people/fasolino.html/teaching.shtml

Quantum wellsen

modern electronics

• 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

Annalisa Fasolino, Theoretische Fysica, Nijmegen

Wishes for devices

• 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

Which applications

• as small as possible• as fast as possible• low operating costs, small consumption • cheap

Basic function• Switch current on/off• amplification of signals

– small action, big effect

Rr

Vext= 9V

Vmod~100mV

Vout

r varied by external bias = device

With it you can -Switch on/off- Amplify Vmod to Vout

Vout= Vext r/(r+R)

Variable resistanceL=lengthA=surfacen=number of charge carrierse=electron charge=time between collisionsm=mass

2nem

AlR

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

CrystalsRegular periodic arrangement of atoms in a lattice

Simple cubic Face centeredcubic fcc

From http://www.lassp.cornell.edu/sethna/Tweed/Cubic_Crystals.html

From http://www.jwave.vt.edu/crcd/farkas/lectures/structure/tsld001.htm

fcc unit cell

Effects of periodicity (formal)

L cm

a 0.1 nm

Wavefunction must be the same at symmetric positions22 )()( axx ikx

kk exu )( Periodic with period a

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

filled

empty

Energy of electrons

Fermi energy

filled

empty

metalinsulator

empty

filled

semiconductor

GaAs band structure

Conduction band(empty)

Valence band(full)

gap Eg

2*

2

2k

mE k

Metals Insulators

electrons loosely bound to nuclei , “electron gas”

electrons form strong covalent bonds

energy gap between occupied and empty states

NO YES

Cu 4s1 C 2s22p2

Periodic table around semiconductorsIII

s2p1IV

s2p2V

s2p3

B C N

Al Si P

Ga Ge As

In Sn Sb

Valence electrons

DopingThe most important property of semiconductors is represented by thepossibility 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

good and bad of doping

One electron too much (too little). Extra electron does not participate to bonding but remains nearly free

filled

empty

filled filled

dopedDoped + Interactionwith extra proton

+ 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)

First metal-insulator-semiconductorField Effect Transistor (~1960)

1 cm

Present day dimensions 0.4 m (2000 lattice parameters) wide10 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

CB-ed

geE=

eFx

SiO2 p-Si

10nm

Elec

tron

dens

ity

distance

But such short and steepvariations of the potentialrequire a Q.M. description.

H=(p2/2m + eFx) =E

CB-ed

geE=

eFx

SiO2 p-Si10nm

Elec

tron

dens

ity

E1

E2

Classical Quantum Mechanical

= *

distance maximal minimal

Getting rid of impurities: selective doping

Heterostructures: Two layers of different semiconductors with different bandgaps. Separate electrons from ionized impurities !

Unstable: charge transfer ---> band bending

doped layer

undoped sc 2 with smallergap

undoped sc 1

- - - - - - - - - - - - - -

Conductingchannel

Molecular Beam Epitaxy (MBE)

Typical MBE growth chamber Mechanism for RHEED specular spot oscillations

during growth

Atomic layer by layer growth

Mobility

Eveldrift

High -> high speed

*me

optical transitionsAbsorption or emission of photons between full and empty statesNeeds photon energy equal to the energyseparation of electronic levels

absorption emission

hfE ph E

Ehf hf

hchfE

Ehc

6.63 10-34 Js 3 10 8 m/s

E(eV) 1.6 10-19 J/eVE=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 fibersfor 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

xLn

Lx sin2)(

0)()0( L

E

222

2

2

28

Ln

mn

mLhEn

parabolicdependence

22

2k

m

Lnk

2D: electronsare bound along x, free to move perpendicularly

The principle of a semiconductor QWNew artificial material formed by thin layers of semiconductors with different energy gaps

GaAlAs

AlAs GaAs AlAs

AlAsgE AlAs

gEGaAsgE

a QW !

Bound states electron

Bound states holes

new, larger gap

Absorption from 3D to 2D

FromR. DingleFestkoerperprobleme15,21 (1975)

1.53 1.54 1.55 1.56 1.57 1.58 1.65 1.66

Nor

m. P

L in

tens

ity (a

rb. u

nits

) 3 41 2

Photon energy (eV)

well width linewidth1 19.8 nm 0.25 meV2 12.2 nm 0.4 meV3 8.3 nm 1.0 meV4 5.1 nm ~ 5 meV

F. Pulizzi et al., Magnet Lab Nijmegen, 2001

14 nm

21 nm400 nm

10 meV

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

From http://imowww.epfl.ch/Nanoweb/default.htm

Growth on non-planargrooved structures

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

Fromhttp://www.ifm.liu.se/Matephys/AAnew/research/iii_v/qwr.htm#S1.2

Turn a failure into a successWhen the lattice mismatch is too big, layers turn into dots

Self-organized InAs quantum dotsFrom

http://www.ifm.liu.se/Matephys/AAnew/research/iii_v/qwr.htm#S1.2

The dots are formed duringspontaneous 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.