Effective Masses in ZnGeN2

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Presentation transcript:

Effective Masses in ZnGeN2 James Arnemann Case Western Physics

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

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

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

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/

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

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)

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)

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

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

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

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

Results AlN ZnGeN2 GaN Δ1(meV) -219 65 24 Δ1’(meV) 3.73 A1 -3.82 -4.53 3.73 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

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

The End