| Multiscale Modeling of Quantum Wells in Si and GaN Nanostructures |
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Objectives
To develop a multiscale model for nanowires for calculation of
strains and effect of defects and inclusions in nanowires. The model, based
upon the use of molecular dynamics and lattice Green’s functions, would link
the length scales between the nanoscale diameter of the nanowire and its microscale
length. Background Quantum nanostructures have strong potential for applications in new devices such as ultra low threshold lasers, quantum computers, etc. There is emerging interest in nanowires (nanorods) because of their unusual mechanical, thermal, and electrical properties, and a strong potential for application in devices. According to Access Science: ".. One-dimensional (1D) nanostructures represent the smallest-dimension structure that can efficiently transport electrical carriers, and thus are ideally suited to the critical and ubiquitous task of moving and routing charges, which constitute information in nanoelectronics. ... semiconductor nanowires can be rationally and predictably synthesized in single-crystal form, with all key parameters controlled such as chemical composition, diameter, and length, as well as doping/electronic properties. As a result, semiconductor nanowires represent the best-defined class of nanoscale building blocks." One factor hindering development of devices is a lack of understanding of the role of defects on the electrical, optical, and structural properties of these materials. This is because measurable physical properties do not scale down from macro to nano. Many semiconductor devices now incorporate structures with intentionally-introduced strain, and characterization of this strain and its relationship to device performance and failure is critical to ensure reliable operation. It is generally recognized that multiscale modeling at the quantum as well as semi-classical levels is a powerful new tool which will be critical for industrial development of nanomaterials. Development of successful computer approaches to determining the atomic structure and mechanical strain would represent a significant step towards realizing Virtual Reliability Assessment of nanostructures. |
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Approach Our approach is to integrate lattice Green's functions and molecular dynamics, in order to bridge the gap from the central part of the structure, composed of about one hundred thousand atoms, to broader regions, including millions of atoms. Continuum Green's functions are then used to treat a far-field surface. We have developed a tutorial on the development and use of Green's functions, for these and similar applications. We consider specifically a Si nanowire (diamond structure) and a GaN nanowire (wurtzite structure), although our approach will be generally applicable to all nanowires. For the purpose of illustration we show in Fig 1 the underlying Bravais lattice of the wurtzite structure, which is a rectangular hexagonal close-packed lattice. We model a quantum well in this structure by replacing all atoms in a finite number of basal planes by atoms of a different semiconductor. We first calculate the atomistic structure of the nanowire without defects and then calculate the strain in the wire by introducing a quantum well at the center of the c-axis. The atoms in and around the quantum well are treated by using MD and linked to the host lattice by using the GF. We have shown earlier how to integrate MD and GF methods [Tewary and Read, Computer Modeling in Engineering and Science 6, 359-371 (2004) In this method we write the displacement field u in a lattice containing N atoms with a finite number of defects or discontinuities as u(l)=(1/N) Sk G(k) F(k) exp(ik.l) where l is a lattice site, k is a reciprocal space vector, G(k) is the Green’s function in reciprocal space, and F(k) is the Fourier transform of the Kanzaki force. We calculate F by using MD which includes nonlinear effects. For intermediate magnitudes of l, we use lattice Green’s function. For large l, the above equation reduces asymptotically to macroscopic continuum while the discrete lattice effects are retained in F. Thus, our model is truly multiscale as it seamlessly links the discrete atomistic effects in F to macroscopic scales through the G. |
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Figure 1: Hexagonal Bravais lattice for a nanowire having wurtzite structure. |
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Results Earlier we developed a multiscale model for defects and inclusions in metals and QDs in semiconductors. The model integrates classical molecular dynamics MD and lattice Green’s functions (GF) techniques and is a multiscale model that relates the discrete lattice distortions at the microscopic scale to measurable macroscopic parameters such as strain. We have applied this model to calculate the elastic field due to a Au nanoisland in fcc Cu and a Ge quantum dot in Si containing 2 million atoms. We have also applied this model to polar semiconductor systems to calculate the atomic location in and around an InAs quantum dot in GaAs as shown in Fig 2. We plan to apply our multiscale model to nanowires for which no rigorous multiscale model exists in the literature. |
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Figure 2: InAs quantum dot in GaAs. Red atoms are indium, yellow atoms are arsenic, and brown atoms are gallium. There are two million host atoms in the model.
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Selected Publications B. Yang and V. K. Tewary, "Multiscale modeling of point defects in Si-Ge(001) Quantum Wells," Phys. Rev. (2007), in press. D.T. Read and V.K. Tewary, "Multiscale Model of Near-Spherical Germanium Quantum Dots in Silicon," Nanotechnology, 18, article no. 105402(2007). B. Yang and V.K. Tewary, "Efficient Green’s Function Modeling of Line and Surface Defects in Multilayered Anisotropic Elastic and Piezoelectric Materials," Computer Modeling in Engineering and Science 15, 165-177 (2006). B. Yang and V.K. Tewary, "Green’s Function-Based Multiscale Modeling of Defects in a Semi-Infinite Silicon Substrate," Int. J. Solids & Structures 42, 4722-4737 (2005). V.K. Tewary,"Multiscale Green’s-function method for Modeling Point Defects and Extended Defects in Anisotropic Solids: Application to a Vacancy and Free Surface in Copper," Phys. Rev. B 69, article no. 094109 (2004). V.K. Tewary and D.T. Read, "Integrated Green’s Function Molecular Dynamics Method for Multiscale Modeling of Nanostructures: Application to Au Nanoisland in Cu," Computer Modeling in Engineering and Science 6, 359-371 (2004). B. Yang and V.K. Tewary, "Formation of a Surface Quantum Dot near Laterally and Vertically Neighboring Dots," Phys. Rev. B 68, 035301 (2003). V.K. Tewary, "Change in Low Temperature Thermodynamic Functions of a Semiconductor due to a Quantum Dot," Phys. Rev. B 66, article no. 205321 (2002). |
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Materials Reliability DivisionNIST Materials Science and Engineering Laboratory Last modified on April 02, 2007 The National Institute of
Standards and Technology |
