THEORY OF ELECTRONIC AND STRUCTURAL PROPERTIES OF MATERIALS: NOVEL GROUP-IV MATERIALS AND REAL SPACE METHODS
Open Access
- Author:
- Zhang, Peihong
- Graduate Program:
- Physics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- April 26, 2001
- Committee Members:
- Vincent Henry Crespi, Committee Chair/Co-Chair
Thomas E Mallouk, Committee Member
Nitin Samarth, Committee Member
Renee Denise Diehl, Committee Member
James Bernhard Anderson, Committee Member - Keywords:
- multigrid
finite element methods
Electronic structure
real-space methods
carbon nanotubes
ab initio
band structure
semiconductor
planewave
pseudopotential - Abstract:
- This dissertation consists of two parts. The first part employs existing computational techniques to study the electronic and structural properties of novel group-IV and related materials, namely, carbon nanotubes, boron nitride nanotubes, and crystalline group-IV alloys. In the second part, we develop a new electronic structure calculation technique based on finite element methods with multigrid acceleration. The computation time of our new technique scales quadratically with the number of atoms in the system i.e., O(N^2), as opposed to the unfavorable cubic scaling (O(N^3)) for most existing <i> ab initio </i> methods. Chapter 1 gives an overview of theoretical methods involved in this dissertation. Topics covered in this chapter are orthogonal and nonorthogonal tight-binding total energy models, density functional theory, pesudopotential planewave methods of electronic structure, and the GW approximation for calculating accurate bandgaps in semiconductors. Chapter 2 focuses on the structural properties of carbon and boron nitride nanotubes. First, a new nucleation model for carbon nanotubes is proposed. Detailed atomistic simulations indicate that this model agrees in several aspects with experimental observations. The new model does not resort to the formation of energetically unfavorable pentagonal rings, as other nucleation models do, to produce the required curvature for a nanotube nucleus. Second, plastic deformation of carbon nanotube under high tensile stress is studied using a tight-binding total energy model. The elastic limits of carbon nanotubes are found to be higher than any other known materials and very sensitive to the so-called wrapping angle of nanotubes. Elastic limits of boron nitride nanotubes are also studied and compared against those of carbon nanotubes. Chapter 3 is devoted to the electronic and structural properties of novel group-IV alloys formed from CVD precursor. Group-IV alloys have attracted considerable research interest recently. Using the newly developed UltraHigh Vacuum Chemical Vapor Deposition (UHV CVD) technique, group-IV alloys such as Si_4C and Ge_4C, which contain 20 atomic % carbon, have been realized. In this chapter, <i> ab initio </i> results on the electronic and structural properties of these high carbon concentration group-IV materials are presented. General trends of the effects of substitutional carbon are understood. More importantly, two molecular precursors are proposed for synthesizing the group-IV alloys Si_2Sn_2C and Ge_3SnC, which have direct energy band gaps and lattice match silicon to better than 1%. This result might open a new way of integrating silicon-based microelectronics with optoelectronics. Finally, a new class of molecular precursors, X_6C_2H_18 (X=Si, Ge), is proposed for group-IV alloys containg 25 atomic % carbon. The computational time of traditional <i> ab initio </i> techniques such as pseudopotential planewave methods scales at least as O(N^3), where N is the number of atoms in the system. This unfavorable scaling limits the number of atoms one can study using these methods to several hundreds, even with the most powerful supercomputers available today. In chapter 4, we develop an O(N^2) <i> ab initio </i> electronic structure calculation technique based on the finite element methods with multigrid acceleration. O(N^2) scaling is achieved by avoiding explicit re-orthogonalization between eigenvectors, which is made possible by a multigrid algorithm. With these new techniques, we can perform <i> ab initio </i> calculations for systems containing more than 32 atoms on a single workstation (Compaq alpha DS10).