Session P28: Dopants and Defects in Semiconductors VII

Defects and Small Polarons on Oxide Surfaces

The presence and behavior of defects on the surface of oxides are central in many research areas, including catalysis, photochemistry, solar cells, and surface science in general. Experimental characterization of individual defects and their activities are challenging and often requires special preparations of the surface. First-principles calculations based on density functional theory are a powerful tool to study surfaces and defects, often providing information on properties that are difficult to access experimentally. Here we discuss the behavior of defects on oxide surfaces from the perspective on first-principles calculations. We use the oxygen vacancy on TiO$_{\mathrm{2}}$ surface as example, a system that has been extensively reported in the literature. Using DFT with a hybrid function, we discuss surface states induced by the defect and localization of the excess charge in the form of small polarons [1,2]. We then discuss the effects of hydrogen and compare the behavior of these defects on the surface with that in the bulk [3]. We also compare our recent results with previous theoretical studies and experiments. Finally, we generalize the findings on TiO$_{\mathrm{2}}$ to the surfaces of other oxides. [1] M. Setvin, C. Franchini, X. Hao, M. Schmid, A. Janotti, M. Kaltak, C. G. Van de Walle, G. Kresse, and U. Diebold, Phys. Rev. Lett. \textbf{113}, 086402 (2014). [2] P. G. Moses, , A. Janotti, C. Franchini, G. Kresse, and C. G. Van de Walle, J. Appl. Phys. \textbf{119}, 181503 (2016). [3] A. Janotti, C. Franchini, J. B. Varley, G. Kresse, and C. G. Van de Walle, Phys. Status Solidi RRL \textbf{7}, 199 (2013).   

Quantum Monte Carlo study of the oxygen vacancy in vanadium dioxide

Transition metal oxides (TMO's) have presented fundamental challenges for accurate fully ab initio calculations. Vanadium dioxide, in particular, has remained difficult to describe in a consistent and predictive manner for leading theoretical approaches, such as density functional theory (DFT). Quantum Monte Carlo (QMC) methods present an attractive alternative to DFT as they have been shown to be accurate for a range of TMO's, including bulk phases of VO$_2$. In this work we expand the application of QMC to inquire into the behavior of isolated oxygen vacancies in VO$_2$, carefully controlling for known sources of systematic error. We compare our preliminary results with broadly used DFT approximations including hybrid functionals and Hubbard-U type approaches.   

A linear scaling ab initio study of impurities and the metal-insulator transition in doped silicon

Impurities in silicon are responsible for the states in the band gap, and they play a key role in modulating the conductivity of semiconductor devices. In this presentation, we discuss our computational efforts to investigate the metal-insulator transition of these states, particularly, in Titanium- and Sulfur- doped silicon. Both are potential highly efficient photovoltaic materials and are also targeted materials for the study of Mott and Anderson localization. We introduce a supercell scaling ansatz to identify the transition and validate it on the single-band Anderson model. We then apply the locally-self consistent multiple scattering (LSMS) method to the calculation and characterization of these mid-gap states. The LSMS method is a linear scaling ab initio method based on real space multiple scattering theory and Green function technique, and is one of the few scientific application codes capable of demonstrating performance beyond the petascale. To accurately describe the single impurity states, we employ large unit cells with more than 10,000 atomic sites.   

Comparing deep level transient spectroscopy with first-principles calculations

Deep level transient spectroscopy (DLTS) has been used extensively to determine the ionization energy and capture cross sections of defects in semiconductors. We examine the standard formulation used to analyze DLTS measurements, and perform first-principles calculations of ionization energies and nonradiative capture coefficients using density functional theory with a hybrid functional. A critical evaluation highlights discrepancies that can arise in the analysis of DLTS measurements. We apply our analysis to gallium vacancy complexes and impurities in GaN. The ionization energy extracted from a DLTS measurement includes a barrier for nonradiative capture. Our calculations show this barrier is unique to each defect and can be as large as 0.6 eV. The barrier can also have a strong temperature dependence. We comment on the consequences of failing to account for this barrier when interpreting activation energies extracted from DLTS measurements.   

Combining DFT, Cluster Expansions, and KMC to Model Point Defects in Alloys

In an alloy, defect energies are sensitive to the occupations of nearby atomic sites, which leads to a distribution of defect properties. When radiation-induced defects diffuse from their initially non-equilibrium locations, this distribution becomes time-dependent. The defects can become trapped in energetically favorable regions of the alloy leading to a diffusion rate that slows dramatically with time. Density Functional Theory (DFT) allows the accurate determination of ground state and transition state energies for a defect in a particular alloy environment but requires thousands of processing hours for each such calculation. Kinetic Monte-Carlo (KMC) can be used to model defect diffusion and the changing distribution of defect properties but requires energy evaluations for millions of local environments. We have used the Cluster Expansion (CE) formalism to ``glue'' together these seemingly incompatible methods. The occupation of each alloy site is represented by an Ising-like variable, and products of these variables are used to expand quantities of interest. Once a CE is fit to a training set of DFT energies, it allows very rapid evaluation of the energy for an arbitrary configuration, while maintaining the accuracy of the underlying DFT calculations. These energy evaluations are then used to drive our KMC simulations. We will demonstrate the application of our DFT/MC/KMC approach to model thermal and carrier-induced diffusion of intrinsic point defects in III-V alloys.   

Many-Body Theory for Point-Defect Effects on Electron-Energy-Loss and Optical Absorption Spectra in Layered Semiconductors

For a layered and doped semiconductor system, in the presence of point defects by proton radiation, the changes of both electron-energy–loss and optical absorption spectra can theoretically be related to the Coulomb renormalized polarization and optical-response functions, respectively. The ladder approximation has been employed first for calculating the point-defect induced vertex correction to the Feynman’s bubble diagram for the polarization function of non-interacting subband electrons in layered semiconductors. Based on the random-phase approximation, the intralayer screening from both intrasubband and intersubband electronic excitations in the system, as well as the interlayer Coulomb coupling of electrons, are also taken into account by computing the inverse dielectric-function matrix and solving the self-consistent Dyson equations at the same time.   

Charge Carrier Scattering with Defects from First-Principles Calculations

Phonons and defects are the main sources of charge carrier scattering in materials. While first-principles electron-phonon calculations are being actively studied, electron-defect scattering has not been explored extensively from first principles. Scattering due to defects is important both because defects are naturally present in materials and because it limits carrier mobility at low temperature, and at room temperature in highly doped samples. We discuss the formalism to compute electron-defect scattering from first principles. The main quantities in the calculation are the matrix elements of the defect perturbation potential in a Kohn-Sham basis. Both the local perturbation potential due to electrons and ions and the non-local contribution from the pseudopotential are considered. We interpolate these matrix elements on fine girds to calculate the carrier relaxation time and low temperature mobility in silicon due to elastic scattering with neutral defects, such as vacancies and Frenkel pairs, using Fermi’s golden rule and the Born approximation. The development of efficient parallel algorithms for electron-defect calculations is also discussed.   

Origin of the distinct diffusion behaviors of Cu and Ag in covalent and ionic semiconductors

Group IB elements Cu and Ag are important contact materials in semiconductor devices due to their low resistivity. However, they have shown puzzling diffusion behaviors in semiconductors: Cu diffuses much faster than Ag in covalent semiconductors like Si and GaAs, but Ag diffuses faster than Cu in more ionic II-VI semiconductors such as CdS and CdTe despite Ag has larger size than Cu. In this work, we reveal the underlying mechanisms of these different diffusion behavior by combining the first-principles calculations and group theory analysis. We identified the important roles of the crystal symmetry enforced s-d coupling as well as the Coulomb energy and strain energy in determining the diffusion behaviors of Cu and Ag in the covalent and ionic semiconductors. We show that the s-d coupling is absent in pure covalent semiconductors but increases with the ionicity of the zinc-blende semiconductors, and the coupling strength of Cu, owing to its higher d orbital energy, is much larger than Ag. In conjunction with the Coulomb interaction and strain energy, the s-d coupling is able to explain all the diffusion behaviors of Cu and Ag in covalent to ionic semiconductors. H.-X. Deng, J.-W. Luo, S.-S. Li, S.-H. Wei, Phys. Rev. Lett. 117, 165901 (2016).   

Ab initio calculations of surface effects on Raman spectra of BP-codoped Si nanocrystals

We use a real-space pseudopotential method implemented within density functional theory to calculate Raman spectra for B-doped, P-doped, and (B,P)-co-doped Si nanocrystals. We consider the role of dopant location, bonding structure, and nanocrystal size on these spectra. We find that features of the Raman spectra can be correlated with the dopant structure.   

Improvisation of photocurrent of bismuth vanadate (BiVO$_{\mathrm{4}})$ photo catalyst by Nb doping

Bismuth vanadate (BiVO$_{\mathrm{4}})$ is a good candidate as a photo catalyst for hydrogen evolution via water splitting and environmental remediation by degrading chemical pollutants. The conduction band minima of BiVO$_{\mathrm{4}}$ is mostly composed of V -- 3d bands which are very localized. Due to this localization nature of the V -- 3d band, the charge carriers transport is not easy within BiVO$_{\mathrm{4}}$. In this present study, density functional theory (DFT) has been used to study the Nb incorporation on both cation site of bismuth vanadate with and without oxygen vacancy. It shows that Nb incorporation on both cationic site replaces the V -- 3d localized band by the less localized Nb -- 4d bands. Nb doping in BiVO$_{\mathrm{4}}$ creates a shallow donor level which is beneficial for charge carrier transport. The solubility of Nb in BiVO$_{\mathrm{4\thinspace }}$has also been studied and it shows high solubility of Nb in BiVO$_{\mathrm{4}}$ with both oxygen rich and poor growth condition. Finally, the single phase stability of BiVO$_{\mathrm{4\thinspace }}$via the chemical potential landscape analysis will be presented.   

Pseudomorphic growth of Ge$_{\mathrm{1-}}_{y}$Sn$_{y}$ (y $=$ 0.06 - 0.17) films and devices on Ge/Si(100) \textit{via} chemical precursors

Epitaxial films of Ge$_{\mathrm{1-}}_{y}$Sn$_{y}$~have been grown pseudomorphically on Ge-buffered Si(100) using gas-source molecular epitaxy. Ultra-low temperatures (150-200~$^{\circ}$ C) and low pressures in conjunction with specialized precursors such as Ge$_{\mathrm{4}}$H$_{\mathrm{10}}$~and SnD$_{\mathrm{4}}$~resulted in films with compositions (y $=$ 0.06-0.17). Thorough characterization illustrates that the thin films possess excellent crystal quality and low defectivites with thicknesses 39-370 nm; these thicknesses match or exceed those previously reported for pseudomorphic films attained~\textit{via}~traditional growth methods. The introduction of P(GeH$_{\mathrm{3}})_{\mathrm{3}}$~during growth was used to achieve~\textit{in}~\textit{situ}~$n$-type doping, SIMS analysis indicates uniform distributions of carriers with concentrations up to 1.7x10$^{\mathrm{19}}$~cm$^{\mathrm{-3}}$. Prototype GeSn~\textit{pn}~diodes were fabricated and demonstrate the typical tunneling diode IV characteristics associated with this type of device structure. In contrast to typical MBE methods, pseudomorphic growth using this technique allows for scale-up and \textit{in situ} doping as needed for commercial realization.   

Using Scanning Microwave Impedance Microscopy (sMIM) to characterize defects in dopants and dielectrics in semiconductor devices

As semiconductor technologies adopt advanced designs and materials, it becomes critical to be able to characterize, at the nanoscale, dopant distributions, dielectric properties and interface and thin-film quality. Scanning Microwave Impedance Microscopy (sMIM) is an atomic force microscope (AFM) based electrical measurement technique that measures local permittivity and conductivity at nanoscale dimensions. It can also measure the capacitance of the tip-sample junction or nanostructures. Non-linear properties of samples and nano-structures can be probed by applying a bias to the sMIM tip and recording capacitance-voltage curves. This talk will present results of characterizing and imaging a number of materials and structures from advanced semiconductor technologies. Examples will include (1) quantifying the doping level and imaging the doping distributions of both Si and III-V devices, and (2) quantifying dielectric properties including the use of capacitance-voltage curves to characterize defects in buried gate oxides.