James Arnemann Presentation
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Transcript of James Arnemann Presentation
![Page 1: James Arnemann Presentation](https://reader034.fdocuments.in/reader034/viewer/2022052507/55930c311a28ab15318b4572/html5/thumbnails/1.jpg)
Effective Masses in ZnGeN2
James Arnemann
Case Western Physics
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Outline
Disclaimer Semiconductors and Physics Background ZnGeN2
Calculating Values of the Material Next Step
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Semiconductors
Different energy states Pauli Exclusion Principle Band Gap Metals and Insulators
http://commons.wikimedia.org/wiki/File:Bandgap_in_semiconductor.svg
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Semiconductors (continued) Holes (hydrogen) Photon Emission (<4eV) LEDs (GaN)
http://www.hk-phy.org/energy/alternate/solar_phy/images/hole_theory.gifhttp://64.202.120.86/upload/image/new-news/2009/fabruary/led/led-big.jpg
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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/
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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
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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)
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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)
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Energy
E=P2/(2m) P=ħk Ei=ħ2ki
2/(2mi*)
mi* is the effective mass in the ki direction
If k is close to zero approximately parabolic
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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
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Energy Bands for ZnGeN2 in terms of the Brillion zone (without spin orbit splitting)
E(eV) vs. кx
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Calculations
Effective masses used to calculate constants in the modified Wurtzite Hamiltonian
Mathematica used to calculate E vs. k
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Results
AlN ZnGeN2 GaN
Δ1(meV) -219 65 24
Δ1’(meV) 0 3.73 0
A1 -3.82 -4.53 -6.40
A2 -0.22 -0.47 -0.80
A3 3.54 4.19 5.93
A4 -1.16 -1.93 -1.96
A5 1.33 2.01 2.32
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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
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The End