First principles calculation of electron-phonon and alloy scattering in strained SiGe

First-principles electronic structure methods are used to predict the mobility of n-type carrier scattering in strained SiGe. We consider the effects of strain on the electron-phonon deformation potentials and the alloy scattering parameters. We calculate the electron-phonon matrix elements and fit them up to second order in strain. We find, as expected, that the main effect of strain on mobility comes from the breaking of the degeneracy of the six Δ and L valleys, and the choice of transport direction. The non-linear effects on the electron-phonon coupling of the Δ valley due to shear strain are found to reduce the mobility of Si-like SiGe by 50% per % strain. We find increases in mobility between 2 and 11 times that of unstrained SiGe for certain fixed Ge compositions, which should enhance the thermoelectric figure of merit in the same order, and could be important for piezoresistive applications.

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..

Fabrication and characterization of doped and porous silicon nanowires as anodes for lithium ion batteries

By using Si(100) with different dopant type (n++-type (As) or p-type (B)), it is shown how metal-assisted chemically (MAC) etched silicon nanowires (Si NWs) can form with rough outer surfaces around a solid NW core for p-type NWs, and a unique, defined mesoporous structure for highly doped n-type NWs. High resolution electron microscopy techniques were used to define the characteristic roughening and mesoporous structure within the NWs and how such structures can form due to a judicious choice of carrier concentration and dopant type. Control of roughness and internal mesoporosity is demonstrated during the formation of Si NWs from highly doped n-type Si(100) during electroless etching through a systematic investigation of etching parameters (etching time, AgNO3 concentration, %HF and temperature). Raman scattering measurements of the transverse optical phonon confirm quantum size effects and phonon scattering in mesoporous wires associated with the etching condition, including quantum confinement effects for the nanocrystallites of Si comprising the internal structure of the mesoporous NWs. Laser power heating of NWs confirms phonon confinement and scattering from internal mesoporosity causing reduced thermal conductivity. The Li+ insertion and extraction characteristics at n-type and p-type Si(100) electrodes with different carrier density and doping type are investigated by cyclic voltammetry and constant current measurements. The insertion and extraction potentials are demonstrated to vary with cycling and the occurrence of an activation effect is shown in n-type electrodes where the charge capacity and voltammetric currents are found to be much higher than p-type electrodes. X-ray photo-electron spectroscopy (XPS) and Raman scattering demonstrate that highly doped n-type Si(100) retains Li as a silicide and converts to an amorphous phase as a two-step phase conversion process. The findings show the succinct dependence of Li insertion and extraction processes for uniformly doped Si(100) single crystals and how the doping type and its effect on the semiconductor-solution interface dominate Li insertion and extraction, composition, crystallinity changes and charge capacity. The effect of dopant, doping density and porosity of MAC etched Si NWs are investigated. The CV response is shown to change in area (current density) with increasing NW length and in profile shape with a changing porosity of the Si NWs. The CV response also changes with scan rate indicative of a transition from intercalation or alloying reactions, to pseudocapactive charge storage at higher scan rates and for p-type NWs. SEM and TEM show a change in structure of the NWs after Li insertion and extraction due to expansion and contraction of the Si NWs. Galvanostatic measurements show the cycling behavior and the Coulombic efficiency of the Si NWs in comparison to their bulk counterparts.

Giant enhancement of n-type carrier mobility in highly strained germanium nanostructures

First-principles electronic structure methods are used to predict the rate of n-type carrier scattering due to phonons in highly-strained Ge. We show that strains achievable in nanoscale structures, where Ge becomes a direct bandgap semiconductor, cause the phonon-limited mobility to be enhanced by hundreds of times that of unstrained Ge, and over a thousand times that of Si. This makes highly tensile strained Ge a most promising material for the construction of channels in CMOS devices, as well as for Si-based photonic applications. Biaxial (001) strain achieves mobility enhancements of 100 to 1000 with strains over 2%. Low temperature mobility can be increased by even larger factors. Second order terms in the deformation potential of the Gamma valley are found to be important in this mobility enhancement. Although they are modified by shifts in the conduction band valleys, which are caused by carrier quantum confinement, these mobility enhancements persist in strained nanostructures down to sizes of 20 nm.

Fingerprints of a size-dependent crossover in the dimensionality of electronic conduction in Au-seeded Ge nanowires

We studied the electrical transport properties of Au-seeded germanium nanowires with radii ranging from 11 to 80 nm at ambient conditions. We found a non-trivial dependence of the electrical conductivity, mobility and carrier density on the radius size. In particular, two regimes were identified for large (lightly doped) and small (stronger doped) nanowires in which the charge-carrier drift is dominated by electron-phonon and ionized-impurity scattering, respectively. This goes in hand with the finding that the electrostatic properties for radii below ca. 37 nm have quasi one-dimensional character as reflected by the extracted screening lengths.

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.