Energy Bands and IIIV Alloys

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Energy Bands and III-V Alloys

• EP 4E03 September 19, 2006
• Streetman Section 3.1, with emphasis on 3.1.5

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Goals

• Review, in a qualitative manner, the underlying
  principles of energy bands in solids
• Discuss the importance of III-V materials
• Introduction to various alloys,
• Main applications,
• Design considerations.

Note This presentation does not strictly follow
Streetmans treatment, but instead introduces the
topics in a different manner. Moreover, a wider
coverage of the important III-V materials is
provided.
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Review of Energy Bands (1)
In crystalline solids, the atoms are assembled
in a periodical arrangement, in such a way as to
minimize the energy of the system
Example NaCl crystal (ionic bound)
Kasap, S.O., Principles of electrical engineering
materials and devices, McGraw-Hill, 1997
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Review of Energy Bands (2)
Holden A., The nature of solids, Dover
Publications, 1965
The permitted energies that an electron can
occupy in the isolated atoms are split into
energy bands as the atoms get closer to each
other. This can also be visualized in terms of an
overlap of the electron wave functions (Streetman
section 3.1.2).
Outer shell
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Review of Energy Bands (3)
Mathematically, it means solving the
time-independent Schrödingers equation
where U(r) is the periodic effective potential
energy that describes the arrangement of atoms in
the crystal.
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Review of Energy Bands (4)
The solution to the equation is usually given in
the form of a band diagram E vs k.
Yu, P.Y., Cardona, M., Fundamentals of
semiconductors, Springer, 2005
e.g. GaAs crystal
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Review of Energy Bands (5)
Direct band gap semiconductors (e.g. GaAs, InP,
InAs, GaSb)
The minimum of the conduction band occurs at the
same k value as the valence band maximum.
Eg 1.4 eV
Cohen M.L., Chelikowski, J.R., Electronic
Structure and Optical Properties of
semiconductors, Springer, 1989
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Review of Energy Bands (6)
Indirect band gap semiconductors (e.g. Si, Ge,
AlAs, GaP, AlSb)
The minimum of the conduction band does not occur
at the same k value as the valence band
maximum. An electron promoted to the conduction
band requires a change of its momentum to make
the transition to the valence band (typ. occurs
via lattice vibrations).
Eg 2.3 eV
Cohen M.L., Chelikowski, J.R., Electronic
Structure and Optical Properties of
semiconductors, Springer, 1989
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III-V Materials
Binary Compounds
III
V
IV

• Arsenides GaAs, AlAs, InAs
• Phosphides GaP, AlP, InP
• Antimonides GaSb, AlSb, InSb
• Nitrides GaN, AlN, InN

Tu, K-N, Mayer, J.W, Feldman, L.C., Electronic
thin film science for electrical engineers and
materials scientists, McMillan, 1992
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Why III-Vs for devices?

• Very low effective mass compared to Si (e.g.
  mnl,Si 0.98mo, mn,GaAs 0.067mo, mn,InSb
  0.014mo)
• This translates into very high electron
  mobilities for high-speed electronic applications.

• A wide variety of these materials have a direct
  band gap
• Photon emission is most efficient during
  recombination processes, so very suitable for
  light sources (lasers, LEDs), but also detectors.

• Possibility to create alloys consisting of the
  different elements
• The properties of the device (e.g. emission
  wavelength of a light source) can be tailored to
  suit the needs (band gap engineering).

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Ternary III-V Alloys (1)
The group III lattice sites are occupied by a
fraction x of atoms III1 and a fraction (1-x) of
atoms III2.
Arsenides e.g. InGaAs (used in the active
regions of high-speed electronic devices, IR
lasers, and long-wavelength quantum cascade
lasers)
Phosphides e.g. InGaP (GaAs-based quantum well
devices such as red diode lasers)
Antimonides e.g. AlGaSb (employed in high-speed
electronic and infrared optoelectronic devices)
Nitrides e.g. InGaN (key constituent in the
active regions of blue diode lasers and LEDs)
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Ternary III-V Alloys (2)
The group V lattice sites are occupied by a
fraction y of atoms V1 and a fraction (1-y) of
atoms V2.
Arsenides Antimonides e.g. InAsSb (smallest band
gap of all III-Vs, very important material for
mid-infrared optoelectronic devices)
Arsenides Phosphides e.g. GaAsP (often used for
red LEDs)
Phosphides Antimonides e.g. GaPSb
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Ternary III-V Alloys (4)
Band Gap Engineering Arsenides, Phosphides,
Antimonides
http//www.rpi.edu/schubert/Light-Emitting-Diodes
-dot-org/chap07/F07-06-R.jpg
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Ternary III-V Alloys (3)
Band Gap Engineering Nitrides
l
207 nm
248 nm
http//www.onr.navy.mil/sci_tech/31/312/ncsr/mater
ials/gan.asp
310 nm
413 nm
620 nm
1.24 mm
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Quaternary III-V Alloys (1)
Why?
Provide even greater flexibility in device design
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Quaternary III-V Alloys (2)
The case of GaxIn1-xAsyP1-y
Wide variety of compositions (hence various
emission wavelengths) are lattice matched to
either GaAs or InP
Panish, M.B., Temkin, H., Gas source Molecular
Beam Epitaxy, Springer, 1993
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Design Considerations
Most practical devices consists in
heterostructures, i.e. layered thin film
structures made of dissimilar materials deposited
on top of each other (e.g. quantum well). Based
on the device requirements, the designer will
select the proper alloy, while keeping in mind
that typical substrates consist in binary
compound (such as GaAs, InP, InP, GaSb) in order
to minimize the effects of lattice mismatch.
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Lattice-matched structure
By definition, f 0, i.e. both the substrate
material and the film material have the same
lattice constant. A misfit f lt 5 10-4 is
generally considered very good, and for practical
purposes is assumed lattice-matched (e.g.
AlGaAs/GaAs structures)
Ohring, M., The Materials Science of Thin Films,
Academic Press, 1992
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Strained Structures
f ? 0 (i.e. as ? af)
f lt 0 compressive strain f gt 0 tensile strain
For relatively thin film thicknesses, cubic
crystals will distort (strain develops within the
layer) to achieve the same in-plane lattice
constant. Such a layer is referred to as
pseudomorphic.
Ohring, M., The Materials Science of Thin Films,
Academic Press, 1992
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Relaxed Structure
Beyond a certain critical thickness hc, it is
energetically more favourable for the film to
relax, i.e. achieve a state where its lattice
constant tends towards its unstrained value.
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Critical Thickness (1)
hc is obtained by minimizing Etot with respect to
the strain. This results in a transcendent
equation
where n is the Poissons ratio of the film
material.
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Critical Thickness (2)