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://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
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=ħ2ki
2/(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) 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
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
top related