Theoretical Study of the Band Gap Anomaly of InN PowerPoint PPT Presentation

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Title: Theoretical Study of the Band Gap Anomaly of InN


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Theoretical Study of the Band Gap Anomaly of InN
Su-Huai Wei National Renewable Energy Laboratory
Work was done with P. Carrier and G. M. Dalpian
and supported by U.S. DOE, Basic Energy Science
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Theoretical Challenge
  • Experimentally measured band gaps of nominal
    InN show a wide range of variation from 0.6 eV
    to 2.0 eV.
  • What is the true band gap of pure InN?
  • What is the origin of the variation of the
    measured band gap?

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  • Theoretical Approach
  • The systematic band-structure calculations
    are performed using the FLAPW method within the
    local density approximation (LDA).
  • The LDA band gap error is corrected by adding
    to the LDA potential a d-like external potential
    inside spheres centered at each atomic site a.
  • The parameters of the external potential are
    fitted first to experimental energy levels only
    for AlP, GaP, InP and GaN. The same parameters
    are then used to predict the band gaps of all the
    other III-V compounds.

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Predicted Band Gaps
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Why InN Has a Small Band Gap than InP?
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Chemical Effects
Due to the large electronegativity, N atom has
much lower s orbital energy than other group V
elements. Due to chemical effect alone
Eg(MN) lt Eg(MP)
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Volume Deformation Effects
Due to the large electronegativity of N and
relatively large In-N bond lengths, InN has the
smallest deformation potential in III-V
semiconductors Due to deformation potential
effect alone Eg(MN) gt Eg(MP)
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Why InN Has a Smaller Band Gap than InP
  • For most III-V semiconductors, the deformation
    potentials are
  • large, so compound with small atom (GaN) has
    larger band gap
  • than compound with large atom (GaP).
  • InN has a very small deformation potential,
    therefore,
  • Eg(InN) lt Eg(InP)

Wei et al., PRB 67, 165209 (2003)
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Origin of the Measured Large Band Gap of InN
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Band Structure of InN and GaN
  • The conduction band of InN is strongly
    non-parabolic!

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Effects of Non-parabolicity of Bands
  • The conduction band effective mass of InN is
    a strong function
  • of Fermi energy or electron carrier
    density

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Effects of Non-parabolicity of Bands
  • The a2 is not a linear function of E. The
    measured band gap
  • depends on where the straight lines are
    drawn

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Moss-Burstein Effects
  • The absorption edge increases significantly
    with the carrier
  • density, in agreement with recent
    experiment J. Wu et al.
  • PRB66, 201403 (2002)

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Moss-Burstein Effects
  • When InN is highly n-type doped, absorption
    within the
  • conduction band is also possible, that
    can even lead to a
  • negative M-B effects

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Effects of Oxygen
  • The formation of InNxO1-x alloy lowers the
    conduction band edge
  • However, the conduction band of InNxO1-x is
    partially occupied,
  • therefore, the absorption edge increases
    significantly due to M-B
  • effect at x0.03 or n1x1021 cm-3, the
    reduction of Eg(0) is
  • 0.06 eV, but the absorption edge Eg(n)
    increased by 1.7 eV

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Effects of Oxygen
  • Formation of ON can induce the formation of
    VIn. The band gap
  • is reduced because ON create a shallow
    donor level and VIn
  • creates a deep acceptor level inside the
    gap

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Effects of Oxygen
  • Formation of In2O3 film on InN surface can
    lead to a significant
  • change in the DOS or XPS spectrum.
  • Formation of (InN)n/(In2O3)m superlattices
    can also increase the
  • band gap. But the effect is not large.

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  • Summary
  • Using a corrected LDAC method, we show that
    the band gap of wurtzite InN is about 0.8 0.1
    eV, in good agreement with recent experiments.
  • The small band gap of InN (smaller than InP) is
    due to its very small band gap deformation
    potential, which is partly due to the high
    ionicity of InN.
  • The possible origin of the measured large band
    gap is analyzed in terms of the non-parabolicity
    of the bands, the effects of oxygen and the
    Moss-Burstein shift. The doping induced M-B shift
    has the largest effect on the measured band gap.
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