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

4. Semiconductors (continued)
Holes (hydrogen)
Photon Emission (<4eV)
LEDs (GaN)

5. Crystal Structure
Different materials have different crystal structures
Symmetry (Unit Cell and Brillouin Zone)
Cubic, Hexagonal (NaCl, GaN)

6. ZnGeN2 II-IV-N2 as opposed to III-N Broken Hexagonal Symmetry
Still Approximately Hexagonal

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 (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 (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 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

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