Thesis and publications

 

 

 

 

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Thesis summary

The topic of this thesis is the limitations imposed on the electron mobility in dilute nitride materials due to the processes of alloy and phonon scattering. To this end, we derive an ‘n-band’ model Hamiltonian via a Green’s function approach encapsulating the interaction of extended conduction band states with n – 1 localised nitrogen states. A feature of this approach is that it implies that the energy eigenvalues of the system are complex, with the imaginary parts being interpreted as energy broadenings.

From the derived Hamiltonian, we can extract analytical formulae describing the dispersion relations required for transport calculations. Analytical expressions for the 2D and 3D densities of states are derived from the imaginary part of the Green’s function. Using the results of the n-band Hamiltonian in conjunction with S-matrix theory, an alloy scattering rate for dilute nitrogen concentrations is obtained.

The ladder method for solving Boltzmann’s transport equation in the case of inelastic scattering via polar optical phonons is developed to deal with non-parabolic energy bands. General expressions for the ladder coefficients in 2D and 3D are derived. Scattering rates for acoustic phonon scattering in a non-parabolic for both 2D and 3D are also found in a form that can be used in the ladder method.

Finally, we calculate the Hall mobility in bulk GaNxAs1-x limited by alloy and phonon scattering and compare to observed values. Whilst there is residual resistivity left to be accounted for, the agreement is reasonable for highly degenerate material.

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Publications on dilute nitrides

PhD work

    Alloy and Phonon Scattering (book),
    M Vaughan,
    VDM Verlag (2009)
    ISBN-13: 9783639130867; ISBN-10: 3639130863

    The Hall Mobility in Dilute Nitrides (book chapter),
    MP Vaughan and BK Ridley,
    Dilute III-V Nitride Semiconductors and Material Systems, 255 (2008),
    doi: 10.1007/978-3-540-74529-7_10

    Electron-nitrogen scattering in dilute nitrides,
    MP Vaughan and BK Ridley,
    Physical Review B 75, 195205 (2007)
    doi: 10.1103/PhysRevB.75.195205

    Inhibition of negative differential resistance in modulation-doped n-type Gax In1- xNy As1- y/ GaAs quantum wells
    Y Sun, MP Vaughan, A Agarwal, M Yilmaz, B Ulug, A Ulug, N Balkan, et al,
    Physical Review B 75, 205316 (2007)
    doi: 10.1103/PhysRevB.75.205316

    Effect of non-parabolicity on the density of states for high-field mobility calculations in dilute nitrides,
    MP Vaughan and BK Ridley,
    physica status solidi (c) 4, 686 (2007)
    doi: 10.1002/pssc.200673342

    Alloy and phonon scattering-limited electron mobility in dilute nitrides (PhD thesis),
    MP Vaughan,
    Dissertation Abstracts International 68 (04) (2007)

    Solution of the Boltzmann equation for calculating the Hall mobility in bulk GaN(x)As(1 - x),
    MP Vaughan and BK Ridley,
    Physical Review B 72, 075211 (2005)
    doi: 10.1103/PhysRevB.72.075211

    Solution of the Boltzmann equation for the electron Hall mobility in GaNAs,
    MP Vaughan and BK Ridley,
    Proceedings of SPIE 5840, 790 (2005)
    doi: 10.1117/12.608323

Subsequent publications on dilute nitrides

    Modelling and direct measurement of the density of states in GaAsN,
    MP Vaughan, S Fahy, EP O'Reilly, L Ivanova, H Eisele and M Dähne,
    physica status solidi (b) 248, 1167 (2011)
    doi: 10.1002/pssb.201000700

    Direct measurement and analysis of the conduction band density of states in diluted GaAs1- x Nx alloys,
    L Ivanova, H Eisele, MP Vaughan, P Ebert, A Lenz, R Timm, O Schumann, et al
    Physical Review B 82, 161201 (2010)
    doi: 10.1103/PhysRevB.82.161201

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M.P. Vaughan (2007)