Biaxial Strain-modified Acceptor Activation Energy of Wurtzite GaN Analyzed by k∙p Method

1. Biaxial Strain-modified Acceptor Activation Energy of Wurtzite GaN Analyzed by k∙p Method Presented by: Ning Su John Simon Lili Ji Instructor: Dr. Debdeep Jena 12/13/2004 EE698D Advanced semiconductor physics

2. Outline • Introduction • Background • Motivation • Band structure calculation • Conduction and valence band Hamiltonian • Band structure modification by biaxial strain • Acceptor activation energy and conductivity • Density of States (DOS) calculation • Effective mass calculation • Conclusion EE698D: Advanced Semiconductor Physics

3. Introduction • Role of strain on electronic and optical properties of semiconductors has been carefully studied for several decades device applications: HBTs Lasers • To better understand the effect of strain on semiconductor properties, fundamentalstudies of band structure is of great importance e.g. 1)tight-binding method 2) K∙P method--- used in this work EE698D: Advanced Semiconductor Physics

4. Introduction-cont’d • Biaxial strain in Wurtzite Gallium Nitride (GaN) • Large biaxial strain in bulk wurtzite GaN large lattice mismatch between GaN & substrate, post-cooling • Less well understood compared to zinc-blend GaN • Acceptor activation energy in GaN • Large Ea of Mg-doped GaN (120~260meV) limits room temperature p-GaN conductivity • Strained modified Ea, a potential way to improve electrical property Motivation of this work !! EE698D: Advanced Semiconductor Physics

5. Simulation Model k∙P method Hamiltonian derivation Band Structure under strain m* tensor DOS Hole distribution mobility Fermi-Direc conductance life time Critical thickness EE698D: Advanced Semiconductor Physics

6. Band Structure under Strain • Conduction and valence bands Hamiltonian • Conduction band ( parabolic band model) • Valence band (ref. a) where and • Band structure can be obtained by finding eigenvalues of the Hamiltonians defined above ref. a: S. L. Chuang and C. S. Chang, Phys. Rev. B, 54, 2491 (1996) EE698D: Advanced Semiconductor Physics

7. Band structure-cont’d • Energy values for band edge as a function of strain ( -2%~2%) • At the tensile strain of 0.107%, the LH band rises above the HH band edge • Band gap for compressive strain for tensile EE698D: Advanced Semiconductor Physics

8. Band structure-cont’d • Valence band dispersions 1% compressive unstrained • kx and kz are transverse and longitudinal axes along [0001] direction 1% tensile EE698D: Advanced Semiconductor Physics

9. Acceptor Activation Energy • Assumption: Acceptor energy level is fixed with respect to vacuum level • Typical value of EA =160 meV is chosen for Mg-doped GaN • EA decreases faster with tensile strain EE698D: Advanced Semiconductor Physics

10. Effective Mass effective mass as a function of strain derived from band structure EE698D: Advanced Semiconductor Physics

11. DOS and Hole Distribution DOS Hole distribution Fermi-Dirac function EE698D: Advanced Semiconductor Physics

12. Hole Concentration NA=1018cm-3 Hole concentration as a function a strain EE698D: Advanced Semiconductor Physics

13. Mobility and Conductivity Mobility and conductivity along transverse and longitudinal directions under strain (Assume life time =0.1ns ) EE698D: Advanced Semiconductor Physics

14. Conductance Critical thickness is used for the layer thickness EE698D: Advanced Semiconductor Physics

15. Conclusion • Strain modified Band structure was calculated using k∙p method • Acceptor activation energy was found to decrease with strain • Hole concentration increases rapidly with tensile strain • µ & σ was enhanced in the [0001] direction EE698D: Advanced Semiconductor Physics

16. Acknowledgement We acknowledge Prof. Debdeep Jena for his directions and helpful discussions. EE698D: Advanced Semiconductor Physics