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Calculation of Effective Masses in ZnGeN2: Implications for Semiconductor Technology

This document explores the fundamental aspects of the semiconductor ZnGeN2, focusing on calculating effective masses and its implications in electronic applications. It discusses the crystal structure of ZnGeN2, comparing it to other materials, analyzes energy states through the Pauli Exclusion Principle, and explains the significance of the band gap. The results shed light on properties such as exciton binding energy and defect energy levels, offering insights into potential future applications in semiconductors and LED technology.

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Calculation of Effective Masses in ZnGeN2: Implications for Semiconductor Technology

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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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