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://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

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=ħ2
ki
2
/(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
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

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