nano_calc

Ab initio electronic structure calculations All the material science problems are solved ! ----- Schrodinger, 1930’s
1 2 1 Z {−∑ ∇ i + ∑ +∑ }Ψ (r1 ,..rN ) = EΨ (r1 ,..rN ) i 2 i , j | ri − r j | i , R | ri − R |
One of the highest priorities in nanotechnology, by various government reports
Large scale computation •supercomputers •new methodologies
Contact: linwang wang, lwwang@
Contact: linwang wang, lwwang@
Theoretical Challenge
atom molecules
nanostructures
bulk No analytical solutions, and expansions (Feynman diagrams, k-space)
•Mechanical properties, surface effects and no dislocations
Contact: linwang wang, lwwang@
New physics in nanostructure New phenomena appear •Not the same as in molecules •Not the same as in bulk •Not a simple continuous interpolation between them Many physical effects are amplified here (due to the different scaling among them). It is a nanolab for many physical phenomena •Single electron effect •Enhanced many body interactions (exchange) •New carrier dynamics •Mechanics without dislocation Need both fundamental experimental and theoretical researches.
V (r )
Contact: linwang wang, lwwang@
Planewave expansion of the wavefunction
ψ ( r ) = ∑ C ( q )e
q
iqr
Fast Fourier Transformation between real space ψ(r) and Fourier space C(q).
Contact: linwang wang, lwwang@
EPM potential
Contact: linwang wang, lwwang@
Folded Spectrum Method
Hψ i = ε iψ i
( H − ε ref ) 2ψ i = (ε i − ε ref ) 2ψ i
--------Nanotechnology Science, Engineering and Technology Research Directions, Edited by D.H. Lowndes, at ORNL.
Numerical modeling tools •synthesis •properties Nanotechnology +
Large scale atomistic electronic structure calculations of nanostructures
Lin-Wang Wang
NERSC Lawrence Berkeley National Lab
US Department of Energy Office of Science
Linear equation, but extremely large dimension:
Ψ (r1 ,..r2 )
Many approximated approaches to solve the above equation Density functional theory and local density approximation ----- W. Kohn’s 1997 Nobel prize
Selfconsistent calculations
1 2 {− ∇ + V (r )}ψ i (r ) = Eiψ i (r ) 2
Selfconsistency
{ψ i }i =1,.., N
ρ ( r ) = ∑ | ψ i ( r ) |2
i N
N electron N wave functions
Contact: linwang wang, lwwang@
Non-selfconsistent calculations for nanostructures Generate potential directly from atomic positions {R}
V (r ) = ∑ vα (r − R)
method
Ab initio method
? new methods
Why we need atomistic calculations ? •To get the correct symmetry •To describe surface •To include the whole band structure ( e.g, Γ-X coupling) •To achieve quantitative predictions •To make connections to ab initio calculations.
Time for one FFT (sec)
size
Contact: linwang wang, lwwang@
Examples of new properties
•Band gap increase
CdSe quantum dot
•Single electron effects on transport (Coulomb blockade).
Contact: linwang wang, lwwang@
Overcome the challenges “One immediate hurdle is to develop theoretical tools to describe accurately the electronic structure of large QD (10^4-10^6 atoms)”
1 2 1 {− ∇ + V (r , [ ρ (r )]) + ∑ }ψ i (r ) = Eiψ i (r ) 2 R |r−R| ρ ( r ) = ∑ | ψ i ( r ) |2 ψ i (r ) : single electron wave function
i
Contact: linwang wang, lwwang@
Contact: linwamark of civilization Bronze age
Stone age
Semiconductor information age
Nanostructure age
Contact: linwang wang, lwwang@
Contact: linwang wang, lwwang@
A parallel Fast Fourier Transformation code •Specially designed for PW elec. structure calculation. •Work load balance •Memory balance •Minimum communication
Nanostructure as a new material Definition: Nanostructure is an assembly of nanometer scale “building blocks”.
Why nanometer scale: That is the scale when the properties of these “building blocks” become different from their bulk counterparts. We are engineering the properties of the materials by changing the sizes. We have added a new dimension into periodic table.
•New O(N) methods: still a research topic, cannot be applied to a million atom system.
Need new computational approaches •Not ab initio, but equally reliable •Hybrid methods •New algorithms, for problems unique to million atom calc.
Contact: linwang wang, lwwang@
Atomistic calculations of nanostructures Cannot use the current ab initio method (e.g, LDA). •Ab initio method: need only to input atomic numbers ! •Memory O(N^2) •Computation O(N^3) up to a few hundred atoms
Old methods
No statistical mechanics
New approaches
Numerical simulation will play a major role.
Contact: linwang wang, lwwang@
Computational challenge atom molecules size 1-100 atoms nanostructures 1000-10^6 atoms bulk Infinite (1-10 atoms In a unit cell) •Ab initio method •Effective mass method
R
vα (r )
V (r )
Empirical pseudopotential method (EPM) Fit
vα (r )
from experimental band structures
and ab initio V(r). EPM provides one of the best band structures for semiconductors
Making new solid state materials
•New crystal compounds
A3 B1
•Alloys
A1− x Bx
•Impurity and doping •Modifying the size and shape of the material
Contact: linwang wang, lwwang@