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Effective Masses in ZnGeN 2

Effective Masses in ZnGeN 2. James Arnemann Case Western Physics. Outline. Disclaimer Semiconductors and Physics Background ZnGeN 2 Calculating Values of the Material Next Step. Semiconductors. Different energy states Pauli Exclusion Principle Band Gap Metals and Insulators.

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Effective Masses in ZnGeN 2

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  1. Effective Masses in ZnGeN2 James Arnemann Case Western Physics

  2. Outline • Disclaimer • Semiconductors and Physics Background • ZnGeN2 • Calculating Values of the Material • Next Step

  3. Semiconductors • Different energy states • Pauli Exclusion Principle • Band Gap • Metals and Insulators http://commons.wikimedia.org/wiki/File:Bandgap_in_semiconductor.svg

  4. Semiconductors (continued) • Holes (hydrogen) • Photon Emission (<4eV) • LEDs (GaN) http://64.202.120.86/upload/image/new-news/2009/fabruary/led/led-big.jpg http://www.hk-phy.org/energy/alternate/solar_phy/images/hole_theory.gif

  5. Crystal Structure • Different materials have different crystal structures • Symmetry (Unit Cell and Brillouin Zone) • Cubic, Hexagonal (NaCl, GaN) http://geosphere.gsapubs.org/content/1/1/32/F5.small.gif http://www.tf.uni-kiel.de/matwis/amat/def_en/kap_2/basics/b2_1_6.html http://www.fuw.edu.pl/~kkorona/

  6. ZnGeN2 • II-IV-N2 as opposed to III-N • Broken Hexagonal Symmetry • Still Approximately Hexagonal http://www.bpc.edu/mathscience/chemistry/images/periodic_table_of_elements.jpg

  7. Hamiltonian (Energy) • Symmetry gives Structure • Breaking Symmetry gives more terms • Hamiltonian depends on L,σ, and k • Cubic Hamiltonian (Constants Δ0,A,B, and C) Taken from Physical Review B Volume 56, Number 12 pg. 7364 (15 September 1997-II)

  8. Wurtzite Hamiltonian • Hexagonal (Think GaN) • │mi,si>for p like orbital • Represented by 6x6 matrix Taken from Physical Review B Volume 58, Number 7 pg. 3881 (15 August 1998-I)

  9. Energy • E=P2/(2m) • P=ħk • Ei=ħ2ki2/(2mi*) • mi* is the effective mass in the ki direction • If k is close to zero approximately parabolic

  10. Calculating Effective Mass • Use Full Potential LMTO to calculate Energy as a function of the Brillouin zone • Look at values close to zero and fit parabolas

  11. Energy Bands for ZnGeN2 in terms of the Brillion zone (without spin orbit splitting) E(eV) vs. кx

  12. Calculations • Effective masses used to calculate constants in the modified Wurtzite Hamiltonian • Mathematica used to calculate E vs. k

  13. Results

  14. Conclusions • These calculations can be used to deduce properties of the material, e.g. exciton binding energy, acceptor defect energy levels • Possible Future uses in electronics

  15. The End

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