Nanophysics II

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Nanophysics II

• Michael Hietschold
• Solid Surfaces Analysis Group
• Electron Microscopy Laboratory
• Institute of Physics

Portland State University, May 2005
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2nd Lecture3b. Surfaces and Interfaces
Electronic Structure3.3. Electronic Structure
of Surfaces3.4. Structure of Interfaces4.
Semiconductor Heterostructures4.1. Quantum
Wells4.2. Tunnelling Structures
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3b. Surfaces and Interfaces Electronic
Structure
3.3. Electronic Structure of Surfaces 3.4.
Structure of Interfaces
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3.3. Electronic Structure of Surfaces
Projected Energy Band Structure Lattice not
any longer periodic along the sur- face
normal k- not any longer a good quantum
number - Projected bulk bands - Surface state
bands
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Surface States
Two types of electronic states - Truncated
bulk states - Surface states
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Surface states splitting from semiconductor
bulk bands may act as additional donor or
acceptor states
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Interplay with Surface Reconstruction
The appearance and occupation of surface state
bands may ener- getically favour special surface
reconstruc- tions
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3.4. Structure of Interfaces
General Principle µ1 µ2 in thermodynamic
equilibrium
1
2
For electrons this means, there should be a
common Fermi level !
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Metal-Metal Interfaces
Adjustment of Fermi levels Contact
potential ?V12 F2 F1
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Metal Semiconductor Interfaces
Small density of free electrons in the
semiconductor Considerable screening length
(Debye length) Band bending Schottky
barrier at the interface
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Semiconductor-Semiconductor Interfaces
Ec1
Ec2
EF1
EF2
EF
Ev1
Ev2

• Within small distances from the interface (and at
  low
• doping levels)
• band bending may be neglected
• rigid band edges effective square-well
  potentials for the
• electrons and holes.

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Semiconductor Heterostructures4.1. Quantum
Wells4.2. Tunnelling Structures4.3.
Superlattices
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4.1. Quantum Wells
Effective potential structures consisting of well
defined semiconductor-semiconductor interfaces
E
Ideal crystalline interfaces Epitaxy GaAs/AlxG
a1-xAs
Ec
Ev
z
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Preparation by Molecular Beam Epitaxy (MBE)
Allows controlled deposition of atomic
monolayers and complex structures consisting of
them - UHV - slow deposition (close to
equilibrium) - dedicated in-situ analysis
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One-dimensional quantum well from a stupid
exercise inquantum mechanics (calculating the
stationary bound states)for a fictituous system
to real samples and device structures
0
- h2/2m d2/dx2 V(x) f(x) E
f(x) solving by ansatz method A
cos (kx) x lt a f(x) A cos (ka)
e? (a - x) x gt a A cos (ka) e? (a x) x
lt - a, A- sin (kx) x lt a f-(x)
A- sin (ka) e? (a - x) x gt a - A-
sin (ka) e? (a x) x lt - a ? v - 2m E
/ h2, k v 2m E (- V0) / h2 .  
E
- V0
-a 0 a
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From stationary Schroedingers equation
(smoothly matching the ansatz wave functions as
well as their 1st derivatives) cos (ka) / (
ka ) 1 / C tan (ka) gt 0 sin (ka) /
(ka) 1 / C tan (ka) lt 0 C2
2mV0 / h2 a2 . Graphical represenation ? discr
ete stationary solutions
1 / C
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Finite number of stationary bound
states Eigenfunctions and energy level spectrum
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Dependence of the energy spectrum on the
parameter C2 2mV0 / h2 a2
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Quantum Dots Superatoms (spherical symmetry)
Can be prepared e.g. by self-organized island
growth
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4.2. Tunneling Structures
Tunneling through a potential well
V(x)
V0
E
s
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Tunneling probability
Wave function within the wall (classically
forbidden) fin wall exp (- ? s)
? v2m(V0-E)/h2   Transmission
probability T f(s)2 exp (- 2 ? s)
For solid state physics barrier heights of a
few eV there is measurable tunneling for s of a
few nm only.
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Resonance tunneling double-barrier structure
If E corresponds to the energy of a
(quasistationary) state within the
double-barrier T goes to 1 !!! Interference
effect similar to Fabry-Perot interferometer
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I-V characteristics shows negative differential
resistance
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NDR
U