Surfaces, Interfaces, and Layered Devices

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Surfaces, Interfaces, and Layered Devices
Building blocks for nanodevices!
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Schematic representation of the potential
landscape in a finite crystal, which gets
modified close to the surface.
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To find energies and wave functions one should
solve the Schrödinger equation in a realistic
potential, which often has to be found in a
self-consistent way generally difficult!
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Energy of surface states in the one-dimensional
Shockley model, shown as a function of the
lattice constant a. After Shockley1939.
Maue-Shockley states no modification of the
potential Tamm-Goodwin states due to
modification of the potential In general more
complicated than simple models
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For those who likes theory
1D model with weak periodic potential
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Perturbation theory (update)
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where are unknown coefficients. To find
them we substitute the above expression into
second equation from the previous slide to get
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What happens if the spectrum is degenerate, Em
Ek ?
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At
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The previous consideration is valid for an
infinite crystal. What will happen in a
semi-infinite one?
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• Surface states in real systems are much more
  complicated.
• In particular, one has to allow for
• So-called surface reconstruction (change of
  symmetry)
• Changes in the surface potential to preserve
  electrical neutrality
• Possibilities for surface states to serve as
  donors and acceptors

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Band bending and Fermi level pinning
What happens to the surface states if the
material is doped? Usually both donor-like and
acceptor-like surface states will appear, and
that leads to important complications. Let us
consider an example of a n-doped
semiconductor. Then the donor electrons in the
conduction band will reduce their energy by
occupying the acceptor-like surface states. In
this way a negative surface charge will be
generated, counterbalanced by a positive charge
from ionized donors in the depletion layer near
the surface.
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Before equilibration
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How to find the thickness of the depleted
layer? If the donors are fully ionized then the
charge density is . Then, the
Poisson equation gives the z-dependence of the
potential
Then
The total surface density,
, is still small comparing to the
integrated density of surface states, so the
chemical potential is almost independent of the
doping concentration.
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Semiconductor-metal interfaces

• Schottky barriers
• Ohmic contacts

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Band alignment and Schottky barrier
Typical energy band alignment between a metal
(left) and a semiconductor (right) before charge
transfer across the interface is allowed.
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Density of interface states
Interface states can be both donor-like and
acceptor-like
How the bands will align near the interface?
Interface Al - GaAs
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Donor electrons will occupy IGS as well,
generating a depletion level and additional band
bending
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Schottky model
Interface states are ignored
Positions of the Fermi levels of a metal and a
n-doped semiconductor in equilibrium as obtained
within the Schottky model.
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Schottky diode
Band diagram at positive (a) and negative (b)
voltage
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Ohmic contacts
Ohmic contacts can take place when conduction
band of both sides overlap
Without Schottky barrier
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Semiconductor heterointerfaces
n
p
Before charge transfer
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Types of alignment in heterostructures
Type I, center
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Field effect transistors and quantum wells

• Si-MOSFET
• GaAs-HEMT
• Other devices

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Si-MOSFET
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Vg 0
Ambipolar device
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Size quantization discrete modes!
Quasi-two-dimensional electron gas
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GaAs-HEMT
Typical choice interface Al0.3Ga0.7As -
GaAs, Type I alignment, conduction band of
Al0.3Ga0.7As is 300 meV higher than that one of
GaAs. The top of the Al0.3Ga0.7As is 160 meV
below that one of GaAs.
Al0.3Ga0.7As
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(b) schematic structure of a GaAs HEMT with the
gate electrode grounded. (c) For gate
voltages below -400 mV, Ec at the interface moves
above the chemical potential, and the electron
gas is depleted
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• Advantages of GaAs-based systems
• Crystalline structure, low interface scattering
• Doped layer is rather remote from the
  two-dimensional electron gas
• Very high mobility the present record is 1440
  m2/Vs, that corresponds to the mean free path of
  120 µm.
• Possibility to engineer band offsets by varying
  content of Al. In this way one can make quantum
  wells.

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Other types of layered devices
The materials cannot be combined arbitrarily
because of interface strains
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Organic FET

• Plastic transistors
• Less expensive
• Mechanically soft

At present time such systems are just in the
beginning of the way
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Summary

• FETs and quantum well, and other layered devices
  are widely used. They are also promising for
  future.
• Interfaces strongly influence the band
  structure, in particular, dispersion laws,
  effective masses, etc. Many issues are already
  understood, but many things have to be done.
• Organic transistors are in the beginning of
  their way.