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