Energy band gap and optical properties of nonstoichiometric InN theory and experiment

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Energy band gap and optical properties of
non-stoichiometric InN theory and experiment

• Dimiter Alexandrov 1), Trevor Tansley 2), K.
  Scott A. Butcher 2)
• 1) Department of Electrical Engineering, Lakehead
  University
• Thunder Bay, Ontario P7B5E1, Canada
• 2) Physics Department, Macquarie University
• Sydney, NSW 2109, Australia

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Atomic and bonding electron orbitals belonging to
nearest neighboring atoms
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• Bgt ubA hAgt ubB hBgt
• where
• hAgt 1/2 asA sAgt apA pxAgt apA py Agt
  apA pz Agt
• hBgt 1/2 asB sBgt apB pxBgt apB py Bgt
  apB pz Bgt
• LCAO energy terms
• ?As (asA)2 eAs
• ?Ap (apA)2 eAp
• ?Bs (asB )2 eBs
• ?Bp (apB )2 eBp

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Schrödinger equation for the electron belonging
to bonding orbital
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System of Schrödinger equations
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E n(r) ec n(r) - ?n(r)? ? (r) dv 0

• For s orbital of In atom

0.1 0.2 0.3 0.4
0.5 0.6 0.7 0.8 0.9
1 Å-3
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For p orbital of In atom
0.1 0.2 0.3
0.4 0.5 0.6 0.7
0.8 0.9 1 Å-3
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For s orbital of In atom
0.5
1.0 1.5
Å
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For p orbital of In atom
0.5
1.0 1.5 Å
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Energy Band Gaps

• InSb ? 0.22 0.02 eV
• InAs ? 0.39 0.04 eV
• InP ? 1.38 0.08 eV
• InN ? 1.95 0.04 eV
• GaN ? 3.30 0.10 eV
• AlN ? 6.55 0.2 eV

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Energy band diagram of non-stoishiometric InN
In atom on N site

• Direct energy band gap Eg 0.34 eV ? 0
• Optical absorption edge due to tunneling 0.2 eV

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Energy band diagram of non-stoishiometric InN N
atom on In site