Theoretical Investigation on Band Structure of the BAlGaInN Semiconductor Materials

1
Theoretical Investigation on Band Structure of
the BAlGaInN Semiconductor Materials

• Speaker Sheng Horng Yen 2003/5/26

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Outline

• Crystal structure
• CASTEP theory introduction
• Wurtzite and zinc-blende AlGaInN energy-band
  property
• Zinc-blende BAlGaInN energy-band property

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Crystal coordinate

• In order to describe crystal structure, we choose
  some symmetric coordinate systems.
• Three axes of these coordinates are represented
  by (a, b, c).
• Angles between any two axes are represented by
  (?, ?, ?).

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Lattice types in three dimensions
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Common structures of semiconductor

• (a) Cubic zinc-blende structure
• (b) Hexagonal wurtzite structure

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Crystal band diagram

• Wurtzite structure of GaN band diagram

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CASTEP theory introduction

• The calculating method is based on First
  Principle. (Physical fundamental principle )
• What is First Principle

Physical principle calculation
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Density Functional Theory

• First principle method is according to DFT.
  (Density Functional Theory)
• It is difficult to deal with a many-electron
  system because each electron does not interact
  only with nearest electrons.
• Kohn and Sham use mean-field theory to deal with
  such system.
• In Kohn-Sham method, the electron density plays a
  crucial role. So this function is so-called DFT.

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Local Density Approximation

• For purposes of practical calculation, Kohn-Sham
  theory function must be supplemented by an
  approximation.
• But LDA will underestimate band-gap energy of
  semiconductor.
• Now, some alter methods for LDA like
  electron-density gradient and electron
  self-energy can make band-gap energy approach
  experimental results.

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Wurtzite AlGaInN energy-band property

• InGaN energy-band property
• 1.strain-free
• 2.with strain
• AlGaN energy-band property
• 1.strain-free
• 2.with strain
• AlInN energy-band property
• 1.strain-free
• 2.with strain

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InxGa1-xN parameter

• Lattice constant
• a(x)3.501x3.162(1-x)
• b(x)3.501x3.162(1-x)
• c(x)5.669x5.142(1-x)
• Band-gap energy
• Eg(x) x Eg,InN (1-x) Eg,GaN - b x
  (1-x)

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Eg versus Indium composition

• Band-Gap Energy decreases with Indium composition
  increases. (b1.210 eV)

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Band-gap energy curves in different strain

• Tensile strain makes the bowing parameter smaller.

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AlxGa1-xN parameter

• Lattice constant
• a(x)3.082x3.162(1-x)
• b(x)3.082x3.162(1-x)
• c(x)4.948x5.142(1-x)
• Band-gap energy
• Eg(x) x Eg,AlN (1-x) Eg,GaN - b x
  (1-x)

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Eg versus Aluminum composition

• Band-Gap Energy increases with Aluminum
  composition increases. (b0.353 eV)

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Band-gap energy curves in different strain

• When tensile strain is about 2, the bowing
  parameter has a minimum value.

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AlxIn1-xN parameter

• Lattice constant
• a(x)3.082x3.501(1-x)
• b(x)3.082x3.501(1-x)
• c(x)4.948x5.669(1-x)
• Band-gap energy
• Eg(x) x Eg,AlN (1-x) Eg,InN - b x
  (1-x)

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Result 1

• Band-gap energy curves of AlGaInN.

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Result 2
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Result 3

• Tensile strain makes the bowing parameter of
  AlxIn1-xN smaller.

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Zinc-blende AlGaInN energy-band property

• InGaN energy-band property
• 1.strain-free
• 2.with strain
• AlGaN energy-band property
• 1.strain-free
• 2.with strain
• AlInN energy-band property
• 1.strain-free
• 2.with strain

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InxGa1-xN parameter

• Lattice constant
• a(x)b(x)c(x)4.932x4.537(1-x)
• Band-gap energy
• Eg(x) x Eg,InN (1-x) Eg,GaN - b x
  (1-x)

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Eg versus Indium composition

• Direct bowing parameter is 1.379 eV.
• Indirect bowing parameter is 1.672 eV.

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Band-gap energy curves in different strain

• Under different strain, the direct bowing
  parameters always smaller than indirect.

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AlxGa1-xN parameter

• Lattice constant
• a(x)b(x)c(x)4.376x4.537(1-x)
• Band-gap energy
• Eg(x) x Eg,AlN (1-x) Eg,GaN - b x
  (1-x)

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Eg versus Aluminum composition

• Direct bowing parameter is 0.755 eV.
• Indirect bowing parameter is 0.296 eV.

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Band-gap energy curves in different strain

• Under different strain, the direct bowing
  parameters always larger than indirect.

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AlxIn1-xN parameter

• Lattice constant
• a(x)b(x)c(x)4.376x4.932(1-x)
• Band-gap energy
• Eg(x) x Eg,AlN (1-x) Eg,InN - b x
  (1-x)

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Eg versus Aluminum composition

• Direct bowing parameter is 2.729 eV.
• Indirect bowing parameter is 3.624 eV.

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Band-gap energy curves in different strain

• When strain is about 2.7, direct and indirect
  bowing parameters have a point of intersection.

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Result

• Band-gap energy and lattice constant curves of
  zinc-blende Nitride-compounds.

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Zinc-blende BAlGaInN energy-band property

• BAlN energy-band property
• 1.strain-free
• 2.with strain
• BGaN energy-band property
• 1.strain-free
• 2.with strain
• BInN energy-band property
• 1.strain-free
• 2.with strain

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BxAl1-xN parameter

• Lattice constant
• a(x)b(x)c(x)3.596x4.376(1-x)
• Band-gap energy
• Eg(x) x Eg,BN (1-x) Eg,AlN - b x
  (1-x)

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Eg versus Boron composition

• Direct bowing parameter is large.
• Indirect bowing parameter is 0.576 eV.

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Band-gap energy curves in different strain

• Under different strain, direct bowing parameter
  is much larger than indirect.

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BxGa1-xN parameter

• Lattice constant
• a(x)b(x)c(x)3.596x4.537(1-x)
• Band-gap energy
• Eg(x) x Eg,BN (1-x) Eg,GaN - b x
  (1-x)

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Eg versus Boron composition

• Direct bowing parameter is 9.158 eV.
• Indirect bowing parameter is 2.084 eV.

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Band-gap energy curves in different strain

• Under different strain, direct bowing parameter
  is much larger than indirect.

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BxIn1-xN parameter

• Lattice constant
• a(x)b(x)c(x)3.596x4.932(1-x)
• Band-gap energy
• Eg(x) x Eg,BN (1-x) Eg,InN - b x
  (1-x)

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Eg versus Boron composition

• Direct bowing parameter is 11.180 eV.
• Indirect bowing parameter is 6.736 eV.

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Band-gap energy curves in different strain

• Under different strain, direct bowing parameter
  is much larger than indirect.

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Summary

• ?-? Nitride compounds still have many unknown
  physical properties.
• There are two reasons for larger bowing
  parameter.
• 1.Nitride compounds have Indium atom.
• 2.Large lattice constant difference between
  atoms of column ? will result large bowing
  parameter.