Download Surfaces, Interfaces, and Layered Devices

Surfaces, Interfaces, and Layered Devices
Building blocks for nanodevices!
W. Pauli: “God made solids, but surfaces were the work of Devil.”
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Interface between a crystal and vacuum
Schematic representation of the potential landscape in a
finite crystal, which gets modified close to the surface.
Surface states (S) may result, with typical energies
inside the gap between the valence band (VB) and the
conduction band (CB)
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Surface states emerge from the conduction and valence band since the
total number of states is conserved.
Surface states are usually partly filled, so the chemical potential is
located within the surface band.
Hence, the energy bands get bended and the Fermi level gets pinned –
utmost important for semiconductor heterostructures.
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!
1D chain of 10 atoms.
The surface states are split from
other N-2 states, their energies
turn out to be larger than those
of bulk states
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Energy of surface states in the
one-dimensional Shockley model,
shown as a function of the
lattice constant a.
After [ShockleyI939].
At e.g. a2, both a donor-like
and an acceptor-like surface
states are
present.
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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Surface states in real systems are 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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Depleted layer
Illustration:
Zdep
Before equilibration
After equilibration: the surface gets
charged, an upward band bending
results, the Fermi level gets pinned
keeping neutrality
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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
compared to the integrated density of surface states, so
the chemical potential is almost independent of the doping
concentration.
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In a p-type material the bands bend downwards creating a
well for electrons rather than a barrier.
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Semiconductor-metal interfaces
Schottky barriers
Ohmic contacts
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Interfaces are like surfaces; it is semi-extended functions that
have to match at the interface.
Most interesting are the situations where the states are located in
the conduction band of one component, but in the gap of other one.
Most important example – the states in the gap of a
semiconductor, but in a conduction band of a metal.
The extended wave functions in a metal induce evanescent waves
in a semiconductor – the so-called induced gap states (IGS).
These states are similar to
the decaying wave function
in vacuum.
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Band alignment and Schottky barrier
Work function
Electron affinity
Typical energy band alignment
between a metal (left) and a
semiconductor (right) before charge
transfer across the interface is
allowed.
New feature - induced gap
interface states (IGS) due to
matching of the wave functions.
Interface states can be both
donor-like and acceptor-like
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Before charge transfer
After charge transfer
from donors
After charge transfer
from metal
Schottky
barrier
Since depletion layer is very
thin, the step is drawn as sharp
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Schottky model
Schottky barrier
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
(semiconductor is grounded)
Band diagram at positive (a)
and negative (b) voltage
(semiconductor is grounded)
Current-voltage curve
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Variety of Applications.
The Schottky diode is used in a wide variety of applications. It can naturally be
used as a general-purpose rectifier. However, in terms of RF applications, it is
particularly useful because of its high switching speed and high-frequency
capability.
Schottky diodes are similarly very good as RF detectors as their low capacitance
and forward-voltage drop enable them to detect signals which an ordinary PN
junction would not see.
It has already been mentioned that the Schottky diode has a high-current density
and low forward-voltage drop. As a result, Schottky diodes are widely used in
power supplies. By using these diodes, less power is wasted, making the supply
more efficient.
The Schottky diode is used in logic circuits as well as a fundamental building block
in a number of other devices
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Ohmic contacts
Ohmic contacts can take place when conduction band of
both sides overlap
InAs - metal
Without Schottky barrier
With narrow Schottky
barrier (heavily doped)
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Conventional semiconductor interface: p-n junction
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Semiconductor heterointerfaces
Alignment of surface chemical potentials
n
p
IGS
“Quantum charge”
is neglected
IGS
Before charge transfer
Equilibration of bulk chemical potentials
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Types of alignment in heterostructures
Type I,
center
Type II,
staggered
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Type II,
misaligned
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There are many theoretical models for the interface band alignment.
However, the agreement between theory and experiments is often
hampered by surface defects and imperfections, interface strains, etc.
Still, the state-of-art technology can provide close-to-perfect interfaces,
which can be considered by modern analytical and numerical models.
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Field effect transistors and quantum wells
Si-MOSFET
GaAs-HEMT
Other devices
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Si-MOSFET
p-doped Si
Ohmic contacts
Metallic
gate
Oxide, SiO2
Band alignment along the dashed line at Vg=
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Vg = 0
Vg > 0
Vg < 0
Inversion (acc. of electr.)
Accumulation of holes
Ambipolar device
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Wave functions and eigenenergies: Simple model
Splitting of
variables
Triangular potential
approximation
Schrödinger
equation
Dimensionless variable
Localization length
Airy function
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Energy quantization is given by the roots
Quasi 2DEG
2DEG
Fermi
level
Each level generates a sub-band in the energy spectrum
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Transverse wave functions in a triangle well
Normalized
electron
densities
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and
Size quantization – discrete modes!
Quantized levels of transverse motion
Electron density profile
Quasi-two-dimensional
electron gas
Ions and electrons are separated and
Coulomb scattering is relatively weak
However, oxide is amorphous and the interface scattering is noticeable
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Usage of Si-MOSFETs for digital electronics according to CMOStechnology, as well as most important circuits for realizing logical
operations are briefly discussed in the Sec. 3.4.1.1 of the textbook.
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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 valence
band is 160 meV below that of GaAs.
In contrast to Si, GaAs remains undoped, and the
electrons are provided by the doping layer (Si)
inside the Al0.3Ga0.7As. This is called the
modulation doping.
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Why δ-doping is advantageous?
Doping
layer
Scattering potential
2DEG
Matrix element
Backscattering is exponentially suppressed
large mobility
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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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Quantum confined vs. bulk carriers
Evolution of electron
mobility over time, after
modulation doping was
introduced
After L. Pfeiffer et al., 1989.
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Significance of various
scattering mechanisms in
Ga[Al]As HEMT
Dots – experimental results for
the structure with
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Many technological problems: lattice matching, interface
states, possibilities for modulation doping, etc.
doping of a heterostructure implemented in such way that the resulting
free electrons are spatially separated from the positive donor ions; as a
result scattering of moving electrons on the dopant atoms is avoided; aslo,
due to the separation, electrons remain free and mobile even at the very low
temperatures
The band gap engineer’s map
It is shown which compounds can
tolerate
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Other types of layered devices
Quantum wells
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Organic FET
pentacene
“Plastic” transistors
• Less expensive
• Mechanically soft
polythiophene
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.
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