We propose investigation of optical spectra of small co-doped (doped simultaneously by group V element (Phosphorus) and group III element (Boron)) silicon nanocrystals using explicitly correlated Quantum Monte Carlo (QMC) methods. The accurate QMC spectra calculated for various silicon nanocrystal systems will be compared with spectra simultaneously calculated with computationally much cheaper TDDFT (Time Dependent Density Functional Theory) method with the quest to determine parameters for TDDFT calculations able to accurately describe much larger systems, closer to the sizes explored experimentally. The calculated spectra will be made available to the related NaMSeN project. 

Condensed Matter Physics
Vedecká časť: 

The desire of miniaturizing modern electronic devices has lead to the need of using silicon building blocks having only a few nanometers in size. However, due to the indirect nature of the electronic band-gap in pristine silicon crystal, the device optical performance is strongly limited with decreasing dimensions. In order to overcome these limitations and enhance optical properties of silicon nanocrystals (SNC), we propose to tune the optical spectra by dopants. In particular, we will examine the co-doped SNC (doped simultaneously with phosphorus and boron). 

Current experiments deal with 5 to 3 nm SNC. The desire is achieving the size of 2 nm.  However, calculation of such sizes of SNCs (even 2 nm)  are realistically still not feasible with the accurate QMC calculations [1]. Hence,  we propose to focus on smaller SNCs with up to ~400 explicitly correlated electrons which, based on our experience, are feasible. In addition to electronic properties, also the geometries and dopant positions pose a problem [2]. This part of the problem will be solved at the DFT level. Using the DFT structures, we will compute several excited states for various spin multiplicities. We plan to study also the so-called “dark states”, states not visible in laboratory optical experiments. Given that QMC is the most accurate method available at system sizes of interest here, excitation spectra included [3], we propose to utilize the QMC results for tuning the DFT xc-functional, so as to provide reasonably accurate TDDFT results. Such a reparametrized TDDFT treatment will subsequently be used for calculations on systems of sizes of interest to real device application.

As outlined above, theoretical modeling will be done at both mean-field single-particle (DFT) and explicitly correlated many-body (QMC) level. At variance with QMC methods, depending on the application and xc-functional used, the accuracy of the DFT methods varies wildly and frequently the DFT results are incorrect even qualitatively [4]. QMC methods are projection methods which project out ground-state of a trial many-body wavefunction. The projection is done using stochastic sampling methods. Both VMC (Variational Monte Carlo) and DMC (Diffusion Monte Carlo), are strictly variational. QMC is exact for Bosonic states and suffers from the Fermionic sign problem for a Fermionic state. The Fermionic sign problem is normally counteracted by application of the so-called fixed-node/fixed-phase approximation, which is the only fundamental approximation. In practice, the fixed-node approximation is imposed by choice of a trial wave function typically constractued from a cheaper method, such as, for instance, DFT or cheaper quantum chemistry method, typically post-Hartree-Fock. Next VMC plus optimization of the trial wavefunction are performed, followed by DMC to determine the final energies (accounting for significantly more correlation energy than the VMC). In principle the QMC methods aim at chemical accuracy (0.04eV, 1kcal/mol, 1 mHa). While both DFT and QMC approaches have the same O(N3) asymptotic scaling with system size, the QMC has a significantly larger (≈1000) prefactor. Hence, QMC methods will be used to push the accuracy limits, and the DFT methods to push the system size limits. Three actions are foreseen:

1) Ground state electronic structure of the Si-based nanoparticle systems with the primary aim of benchmarking performance of the DFT methods and identifying the most appropriate xc-functionals. This will be done on smaller model systems. Such a study will be useful also for determining the “best” nodal hypersurfaces for pure QMC (DMC) calculations. In addition, a series of real calculations will be performed on selected systems identified experimentally.

2) Similar exercise will be repeated for low-energy excited electronic states, where DFT deficiencies similar to those found in ground-states are expected [4], followed again by real calculations for selected systems identified experimentally. We note that both triplet and singlet states, or indeed any spin-state, can be determined and that the ordering of the excited states is very likely to be affected by electronic correlations [4].

3) QMC study of interaction of closely packed Si-based nanoparticles and study of the linker molecules and conductance mechanism between linked Si-based nanoparticles [5].

[1] W. M. C. Foulkes, L. Mitas, R. J. Needs, and G. Rajagopal, Rev. Mod. Phys. 73, 33 (2001).

[2] R. Guerra, S. Ossicini, J. Am. Chem. Soc. 136, 4404 (2014).

[3] M. Dubecký, R. Derian, M. Allan, and I. Štich, Phys. Chem. Chem. Phys. 13, 20939 (2011).

[4] L. Horváthová, M. Dubecký,L. Mitas, and I. Štich, Phys. Rev. Lett. 109, 053001 (2012).

[5] M. Zemanová Diešková, I. Štich, and P. Bokes, Phys. Rev. B 87, 245418 (2013).

Socioekonomický a technologický dopad: 

Light-emitting devices play a fundamental role in todays society since  they  are the key compontents of modern technologies (i.e LED screens, LED light sources, ...) . Silicon-based light-emitting devices have been extensively studied in the last two decades with the hope of realizing the “Si-based integrated opto-electronics” (i.e. electronic and optical components integrated in one structure and made by the same technology). However, this aim was not fully achieved yet. The main obstacles are the low absorption cross section and emission rate (due to the indirect band-gap transitions still dominating optical transitions in Si nanocrystals down to ~2 nm ) on the single object level and poor conductance of nanocrystal ensembles on the device level. 

Another interesting application of Si nanocrystals is in medicine and biology.  Since Si nanocrystals are biodegradable, non-toxic and biocompatible, they can used, for example, as luminscent probes.  Nonetheless, the same problem of low optical activity arises.

Effect of heavy codoping of Si nanocrystal by P and B could solve or alleviate the problem of pristine Si devices.  Thus the study of optical properties of co-doped systems  is essential  for the future applicability of Silicon nanocrystal.

Technická časť: 

For most of the calculations we will use the QWalk ( and/or CASINO ( computer codes, written in C++ and Fortran, respectively. Both codes use MPI implementations of communications. The communications overheads are negligible, especially in comparison to other electronic structure methods. They are capable of optimization of the many-body wavefunction via Variational Monte Carlo (VMC) and of Diffusion Monte Carlo (DMC) calculation for determining the final energies within the statistical error bars. The codes compile using almost any MPI environment and their performance has been tested on a range several different platforms, standard x86, IBM Power architecture, CRAYs etc. In principle QMC codes can be compiled without any external libraries, but BLAS or EINSPLINE libraries can help to improve the performance. For DFT calculations we will use standard well established gaussian basis set codes like GAMESS ( etc., or when needed plane wave basis set codes like Quatum Espresso ( etc.

QMC method provides a very favourable polynomial scaling with the system size (number of electrons), compared to correlated quantum chemistry methods; e.g. Coupled Cluster method, CCSD(T), which scales as O(N7) compared to DMC, which has an O(N3-4) scaling, see [1]. From the computational points of view scaling of QMC calculations with number of cores are unprecedend, reaching practically linear dependence up to hundreds of thousands, see e.g.

Requested core-hours was obtained based on the above scaling chart with respect to the expected number of electrons and Jastrow type, contained 12 computation tasks: three different surface reconstractions and three different doped situations for two different geometries of silicon nanocrystals, (3 + 3) * 2 = 12

[1] M. Dubecký, R. Derian, P. Jurečka, P. Hobza, L. Mitas and M. Otyepka, Quantum Monte Carlo for noncovalent interactions: an efficient protocol attaining benchmark accuracy, Phys. Chem. Chem. Phys. 16, 20915 (2014).

Prepojenie s grantovými úlohami: 
VEGA 2/0162/15; NaMSeN Visegrad Group (V4)-Japan Joint Research Program on Advanced Materials application ID 49
19 200.00
New project, hence no scientific publications or results as yet. For previous publications achieved using SIVVP infrastructure, see other projects.