Dilute nitride semiconductors : band structure, scattering and high field transport

The substitution of a small fraction x of nitrogen atoms, for the group V elements in conventional III-V semiconductors such as GaAs and GaSb strongly perturbs the conduction band of the host semiconductor. In this thesis we investigate the effects of nitrogen states on the band dispersion, carrier scattering and mobility of dilute nitride alloys. In the supercell model we solve the single particle Hamiltonian for a very large supercell containing randomly placed nitrogen. This model predicts a gap in the density of states of GaNxAs1−x, where this gap is filled in the Green’s function model. Therefore we develop a self-consistent Green’s function (SCGF) approach, which provides excellent agreement with supercell calculations and reveals a gap in the DOS, in contrast with the results of previous non-self-consistent Green’s function calculations. However, including the distribution of N states destroys this gap, as seen in experiment. We then examine the high field transport of carriers by solving the steadystate Boltzmann transport equation and find that it is necessary to include the full distribution of N levels in order to account for the small, low-field mobility and the absence of a negative differential velocity regime observed experimentally with increasing x. Overall the results account well for a wide range of experimental data. We also investigate the band structure, scattering and mobility of carriers by finding the poles of the SCGF, which gives lower carrier mobility for GaNxAs1−x, compared to those already calculated, in better agreement with experiments. The calculated optical absorption spectra for InyGa1−yNxAs1−x and GaNxSb1−x using the SCGF agree well with the experimental data, confirming the validity of this approach to study the band structure of these materials.

First-principles calculation of carrier-phonon scattering in n-type Si1−xGex alloys

First-principles electronic structure methods are used to find the rates of inelastic intravalley and intervalley n-type carrier scattering in Si1-xGex alloys. Scattering parameters for all relevant Delta and L intra- and intervalley scattering are calculated. The short-wavelength acoustic and the optical phonon modes in the alloy are computed using the random mass approximation, with interatomic forces calculated in the virtual crystal approximation using density functional perturbation theory. Optical phonon and intervalley scattering matrix elements are calculated from these modes of the disordered alloy. It is found that alloy disorder has only a small effect on the overall inelastic intervalley scattering rate at room temperature. Intravalley acoustic scattering rates are calculated within the deformation potential approximation. The acoustic deformation potentials are found directly and the range of validity of the deformation potential approximation verified in long-wavelength frozen phonon calculations. Details of the calculation of elastic alloy scattering rates presented in an earlier paper are also given. Elastic alloy disorder scattering is found to dominate over inelastic scattering, except for almost pure silicon (x approximate to 0) or almost pure germanium (x approximate to 1), where acoustic phonon scattering is predominant. The n-type carrier mobility, calculated from the total (elastic plus inelastic) scattering rate, using the Boltzmann transport equation in the relaxation time approximation, is in excellent agreement with experiments on bulk, unstrained alloys..

First-principles calculation of P-type alloy scattering in Si1-xGex

The p-type carrier scattering rate due to alloy disorder in Si1-xGex alloys is obtained from first principles. The required alloy scattering matrix elements are calculated from the energy splitting of the valence bands, which arise when one average host atom is replaced by a Ge or Si atom in supercells containing up to 128 atoms. Alloy scattering within the valence bands is found to be characterized by a single scattering parameter. The hole mobility is calculated from the scattering rate using the Boltzmann transport equation in the relaxation time approximation. The results are in good agreement with experiments on bulk, unstrained alloys..

First-principles calculation of alloy scattering in GexSi1-x

First-principles electronic structure methods are used to find the rates of intravalley and intervalley n-type carrier scattering due to alloy disorder in Si1-xGex alloys. The required alloy scattering matrix elements are calculated from the energy splitting of nearly degenerate Bloch states which arises when one average host atom is replaced by a Ge or Si atom in supercells containing up to 128 atoms. Scattering parameters for all relevant Delta and L intravalley and intervalley alloy scattering are calculated. Atomic relaxation is found to have a substantial effect on the scattering parameters. f-type intervalley scattering between Delta valleys is found to be comparable to other scattering channels. The n-type carrier mobility, calculated from the scattering rate using the Boltzmann transport equation in the relaxation time approximation, is in excellent agreement with experiments on bulk, unstrained alloys.

Carrier momentum relaxation in highly doped polar semiconductors and semiconductor heterostructures

Highly doped polar semiconductors are essential components of today’s semiconductor industry. Most strikingly, transistors in modern electronic devices are polar semiconductor heterostructures. It is important to thoroughly understand carrier transport in such structures. In doped polar semiconductors, collective excitations of the carriers (plasmons) and the atoms (polar phonons) couple. These coupled collective excitations affect the electrical conductivity, here quantified through the carrier mobility. In scattering events, the carriers and the coupled collective modes transfer momentum between each other. Carrier momentum transferred to polar phonons can be lost to other phonons through anharmonic decay, resulting in a finite carrier mobility. The plasmons do not have a decay mechanism which transfers carrier momentum irretrievably. Hence, carrier-plasmon scattering results in infinite carrier mobility. Momentum relaxation due to either carrier–plasmon scattering or carrier–polar-phonon scattering alone are well understood. However, only this thesis manages to treat momentum relaxation due to both scattering mechanisms on an equal footing, enabling us to properly calculate the mobility limited by carrier–coupled plasmon–polar phonon scattering. We achieved this by solving the coupled Boltzmann equations for the carriers and the collective excitations, focusing on the “drag” term and on the anharmonic decay process of the collective modes. Our approach uses dielectric functions to describe both the carrier-collective mode scattering and the decay of the collective modes. We applied our method to bulk polar semiconductors and heterostructures where various polar dielectrics surround a semiconducting monolayer of MoS2, where taking plasmons into account can increase the mobility by up to a factor 15 for certain parameters. This screening effect is up to 85% higher than if calculated with previous methods. To conclude, our approach provides insight into the momentum relaxation mechanism for carrier–coupled collective mode scattering, and better tools for calculating the screened polar phonon and interface polar phonon limited mobility.