Last update: 6 August 2012.

PhD Scholarship: Project "ORGAnic Solar Cell VOLTage by Numerical Calculation" (ORGAVOLT)

Département de Chimie Moléculaire (DCM) de l'Université de Grenoble

and the Rhône-Alpes (NanoSTAR) Node of the European Theoretical Spectroscopy Facility (ETSF)

Position and Starting date

I am looking for a student with a solid background in physics, chemistry, or a related field and who is comfortable with mathematics and scientific programming for a 3 year scholarship for doctoral studies leading to a PhD in (Theoretical) Chemistry at the University of Grenoble beginning January 2013 (though an earlier date may be possible for an outstanding candidate!)

This opening has no citizenship restrictions and the PhD thesis may be written in French or English. See the Section entitled "The Ideal Candidate" for additional information about how to apply.

Keywords

• Theoretical physical chemistry/chemical physics.
• Organic solar cells; polymer bulk heterojunction (BHJ) solar cells.
• Photochemistry; electrochemistry.
• Electronic structure theory; excited states; excitons.
• Density-functional theory (DFT); time-dependent density-functional theory (TD-DFT).
• Many-body perturbation theory (MBPT); Green's functions; Hedin's equations; GW; Bethe-Salpeter equation (BSE).
• Software development; high-perfomance computing (HPC).

Background

The modern global economy is heavily dependent upon energy for lighting, heating, transportation, communication, and computing, to name just a few of many needs. Most of our global energy needs are supplied by fossil fuels which are in limited supply, polluting, and have an availability which is subject to changing diplomatic relations. The nuclear alternative (which furnishes 80% of the electricity generated in France) has both the problem of nuclear disposal and the risk of nuclear accidents such as the well-known cases of Three Mile Island (1979), Chernobyl (1986), and the Fukushima Daiichi nuclear disaster (2011). Hence the interest to diversify energy resources by considering alternatives, one of which is solar energy. This thesis project is oriented towards an improved ability to model organic photovoltaics ("plastic solar cells").

A wide variety of different types of solar cells have emerged in recent years. (See also Ref. [W05] for a good introduction to the physics and jargon of photovoltaics.) Which technology is best depends upon the application. Although photoefficiency may be the main criterion for solar cell selection for some needs ((e.g., satellites in outer space), the most important criterion for most applications is the cost per kilowatt-hour of electricity generated. Silicon solar cells have dominated this niche ever since reasonably pure silicon became readily available as a relatively inexpensive biproduct of the computer industry. Organic solar cells fill yet another niche characterized by their light weight and ease of manufacture in a variety of forms. An important objective is improve to their materials properties and cost per kilowatt-hour.

Organic electronics is a diverse field characterized by a diversity of applications of organic conductors and semiconductors (often, but not always polymers). The review of Spanggaard and Krebs gives an overview of the field of organic solar cells up to the year 2007 [KG07]. The conventional mechanism usually used to describe such solar cells involves four steps:

1. An initially-absorbed photon forms a "localized" electron-hole pair called an exciton.
2. This exciton diffuses to an interface.
3. Exciton dissociation occurs at the interface to liberate a free electron and/or a free hole.
4. One or both of these must then diffuse to the electrodes in order to generate electricity in the external circuit.

Important insight into Step 2 was obtained by Tang in 1986 [T86]. He studied the photovoltaic properties of a layer of copper phtalocyanine with a layer of a perylene tetracarboxylic derivative as a function of layer thickness and was able to demonstrate that the diffusion length of the excitons formed is only about 10 nm. This lead to the development of electron donnor-acceptor polymer bulk heterojunction (BHJ) solar cells made by deliberately inducing fine scale phase separation of polymers thereby significantly reducing the distance over which excitons need to diffuse to reach the interface between the two polymers. Although polymer BHJ solar cells have reached the stage of commercialization, there is much active research into obtaining a more detailed understanding of their underlying working mechanism and of how to optimize their photovoltaic properties. The development of predictive models and modeling software has a key role to play in this research. Note that quantitative models are most likely necessary to obtain even qualitatively correct results.

A key problem when constructing models is the need for a more detailed understanding of Step 3 of the above mechanism. Naïvely the exciton is simply pulled apart at the interface made up of the union of electron-donating and electron-accepting polymers to form parallel layers of opposing charges (Step 3a). However there must then also be an additional mechanism responsable for freeing the charges from the charged double layer (Step 3b) so that they may then diffuse to the electrodes in Step 4. This may be regarded as a photochemical mechanism whereby very fast nuclear motion is responsable for excited-state potential-energy-surface hopping from a localized charge neutral state, to a localized charge transfer state, to a delocalized (free particle) excited state. Most likely nuclear relaxation will form an excitonic intermediate (meaning chemical subunits are more tightly bound in the excited than in the ground state). As there are both localized and delocalized states, this problem has aspects reminiscent of both isolated molecular states and delocalized bands in a solid. Thus part of the excitement is to find better ways to model what happens at this "nanointerface" between quantum chemistry and condensed matter physics.

Research Project

This ORGAVOLT project focuses on deriving, implementing, applying, and dissiminating better methods and software for modeling organic solar cells and BHJs in particular. This is an international collaboration involving research groups in France, Spain, and Singapore. In my group in Grenoble, we will focus on developing an efficient implementation of the Bethe-Salpeter equation (BSE) suitable for BHJ applications, on testing this implementation, and on applying it to obtain a better understanding of what goes on in Step 3 of the above mechanism. Although it is quite natural for those of us in chemical physics to think of excitons at BHJs, as would photochemists, in terms of nuclear motion on potential energy surfaces in molecules, we cannot escape from the fact that our "molecules" are connected to delocalized bands in a solid. Thus an important aspect of this work is thinking at the interface between molecular and solid-state theories.

The ideal theoretical method should be one which is appropriate for both molecules and solids. Finding such a method is actually a nontrivial problem, but using density-functional theory (DFT) to describe the ground state and solving the Bethe-Salpeter equation (BSE) to obtain information about excited states represents the state-of-the-art in this area. Since polymere BHJ solar cells are significantly more complex than systems to which the BSE method is usually applied, we will focus on improving the numerical method and implementation of the BSE method for such systems.

Although the Kohn-Sham molecular orbital equation is now well-known among chemists, this is not yet the case for the BSE. The BSE comes from Hedin's exact formulation [H65] of many-body perturbation theory (MBPT) which involves five coupled equations for the one-particle Green's function G, the vertex correction Γ, the (4-point) susceptibility χ, the screened interaction W, and the self-energy Σ:

1. G=G₀+G₀ΣG ,
2. Γ = 1 + (δΣ/δG)GGΓ ,
3. χ=-iGGΓ ,
4. W=v+vχW ,
5. Σ=iGWΓ .

See also Ref. [ORR02].

Molecular ionization and electron attachment spectra and solid-state band structure may be calculated from Eq. (1) which may be reformulated as a quasi-particle equation which resembles the familiar Hartree-Fock equation except that (i) Koopmans' theorem is exact and (ii) all the complicated many-body effects are hidden in the self-energy. The state-of-the-art for solids is to solve the coupled equations in GW approximation in which the vertex Γ=1 and hence the self-energy, Σ=GW. We are already experienced with this in that Refs. [CC89,CC91] appear to be the earliest applications to molecules. GW calculations are now increasingly common for molecules [ORG+95,HCC97,SFZO01,GRM_01,HSB05,BAO11,FKS11], and the method appears to work quite well if the molecules are not too small.

The BSE is the two-particle analogue of Eq. (1), namely L=L₀+L₀ΞL. Ref. [HC10] explains the relationship between the BSE and the polarization propagator (PP) method which is more common in quantum chemistry. In most cases, both the BSE and PP methods are reduced to equations similar to our formulation of time-dependent DFT (TD-DFT) for molecular calculations [C95]. As TD-DFT is a normal first step along the path towards programming the BSE and as we have a well-developed expertise in TD-DFT in Grenoble (see e.g., Refs. [C95,C09,CND11,CH12]), we expect to be especially well positionned for development of BSE code.

Code development will be carried out in a post self-consistent field (SCF) stand-alone FORTRAN code. An important accent will be on computational efficiency and good software engineering practices.

Initial tests will be carried out on a layer of anthracene or pentacene on a layer of C₆₀ as such systems are conceptually simpler than those of BHJs while still sharing many characteristics of BHJs (e.g., organic molecules, bands, localized states, charge transfer ...). They are also systems which have been investigated experimentally in the lab of X.Y. Zhu [KJWZ11] and whose experimentally measured values will provide a valuable reality check as we develop our programs and ideas. We will then go on to look at systems which more closely resemble real BHJs from the experimental group of Georges HADZIIOANNOU at Bordeaux and for which spectroscopic data is expected to be forthcoming.

References

[CH12] M.E. Casida and M. Huix-Rotllant, "Progress in Time-Dependent Density-Functional Theory," Annu. Rev. Phys. Chem. 63, 287 (2012).

[BAO11] X. Blase, C. Attaccalite, V. Olevano, "First-principles GW calculations for fullerenes,porphyrins, phtalocyanine, and other molecules of interest for organic photovoltaic applications," Phys. Rev. B 83, 115103 (2011)

[CND11] M.E. Casida, B. Natarajan, and T. Deutsch, "Non-Born-Oppenheimer dynamics and conical intersections," in Fundamentals of Time-Dependent Density-Functional Theory, edited by M. Marques, N. Maitra, F. Noguiera, E.K.U. Gross, and A. Rubio, Lecture Notes in Physics, Vol. 837 (Springer Verlag: 2011), p. 279. Preprint at http://arxiv.org/abs/1102.1849.

[HC10] M. Huix-Rotllant and M.E. Casida, "Formal Foundations of Dressed Time-Dependent Density-Functional Theory for Many-Electron Excitations," arXiv:1008.1478v1 [cond-mat.mes-hall] 9 Aug 2010.

[C09] M.E. Casida, "Review: Time-Dependent Density-Functional Theory for Molecules and Molecular Solids," J. Mol. Struct. (Theochem) 914, 3 (2009).

[KG07] H. Spanggaard and F.C. Krebs, "A brief history of the development of organic and polymeric photovoltaics," Solar Energy Materials and Solar Cells 83, 125 (2007).

[HSB05] P.H. Hahn, W.G. Schmidt, and F. Bechstedt, "Molecular electronic excitations from a solid-state approach," Phys. Rev. B 72, 245425 (2005).

[W05] P. Würfel, Physics of Solar Cells: from Principles to New Concepts (Wiley-VCH: Weinheim, Germany, 2005).

[ORR02] Onida, L. Reining, A. Rubio, "Electronic excitations: density-functional versus many-body Green's-function approaches," Rev. Mod. Phys. 74, 601(2002).

[GRM+01] J. C. Grossman, M. Rohlfing, L. Mitas, S. G. Louie, and M. L. Cohen, "High Accuracy Many-Body Calculational Approaches for Excitations in Molecules," Phys. Rev. Lett. 86, 472 (2001).

[SFZO01] Y. Shigeta, A.M. Ferreira, V.G. Zakrzewski, and J.V. Ortiz, "Electron propagator calculations with Kohn-Sham reference states," Int. J. Quant. Chem. 85, 411 (2001).

[HCC97] C.-H. Hu, D.P. Chong, and M.E. Casida, "The parameterized second-order Green function times screened interaction (pGW2) approximation for calculation of outer valence ionization potentials," J. Electron Spectr. 85, 39 (1997).

[ORG+95] G. Onida, L. Reining, R.W. Godby, R. Del Sol, and W. Andreoni, "Ab initio calculations of the quasiparticle and absorption spectra of clusters: the sodium tetramer," Phys. Rev. Lett. 75, 818 (1995).

[C95] M.E. Casida, "Time-dependent density-functional response theory for molecules," in Recent Advances in Density Functional Methods, Part I, edited by D.P. Chong (World Scientific: Singapore, 1995), p. 155.

[CC91] M.E. Casida and D.P. Chong, "Simplified Green-function approximations: Further assessment of a polarization model for second-order calculation of outer-valence ionization potentials in molecules," Phys. Rev. A 44, 5773 (1991).

[CC89] M.E. Casida and D.P. Chong, "Physical interpretation and assessment of of the Coulombhole and screened-exchange approximation for molecules," Phys. Rev. A 40, 4837 (1989); Erratum, ibid 44, 6151 (1991).

[T86] C.W. Tang, "Two-layer organic photovoltaic cell," Applied Physics Letters 48, 183 (1986).

[H65] L. Hedin, "New method for calculating the one-particle Green's function with application to the electron gas problem," Phys. Rev. 139, A796 (1965).

The Ideal Candidate

The ideal candidate should have the equivalent of a French Masters degree in either chemistry, physics, materials science, computer science, or a related field. Much more important than the specific area of training is that the student have a talent for scientific programming and mathematics and be motivated, energetic, and interested in learning new skills, and in applying them to doing cutting-edge research within a team working on a Grand Challenge problem. For this reason, motivated candidates with Masters degrees in other areas will also be considered.

The position is open to all candidates, regardless of nationality. To demonstate equivalence to a French Masters degree, it suffices to have either done your Masters in France or in another country which has signed the Bologna accord. Candidates from outside Europe should demonstrate adequate research experience.

Non-francophones may write their thesis in English and Grenoble is a remarkably international city in many ways. However access to French courses will be arranged for non-francophones to obtain at least a working knowledge of the language, in order that such students will be more comfortable living here.

To apply, please contact:

Mark E. CASIDA

Département de Chimie Moléculaire (DCM)

Université Joseph-Fourier

38041 Grenoble

FRANCE

Tel : 04 76 63 56 28

Mark.Casida@ujf-grenoble.fr

https://sites.google.com/site/markcasida/home

Applications by e-mail are preferred. As I receive very large amounts of e-mail and am sometimes incommunicado when traveling, please make sure that the subject line is clear and please retransmit if you have not heard back with a week or so. (I will endeavor to answer all e-mails.)

The application should include the following:

1. Motivational cover letter describing previous experience.
2. Curriculum vitae (CV).
3. Copies of undergraduate and Masters transcripts.
4. Names and addresses of 3 people who know you well as a student and/or researcher.

For full consideration, applications should be received by 1 November 2012. However earlier applications are encouraged and applications received by 1 October 2012 are preferred. (Outstanding applications received later than 1 November 2012 may still be considered, especially if a suitable candidate has not yet been found.)

About the Co-Laboratory

The ORGAVOLT project is a collaborative effort involving

• At the Département de Chimie Moléculaire (DCM), Université Joseph Fourier (Grenoble I):
  • Mark E. CASIDA
• At the Laboratoire d'Ondes et Matières d'Aquitaine (LOMA), Université de Bordeaux, Bordeaux, France:
  • Dietrich FOERSTER
  • Rémi AVRILLER
• At the Centro de Fisica de Materiales (CFM) and the Donostia International Physics Center (DIPC), University of Basque Country (UPV/EHU), San Sebastian, Spain:
  • Daniel SANCHEZ-PORTAL
  • Peter KOVAL

In addition, the ORGAVOLT team has a close contact with the experimental group of Georges HADZIIOANNOU at Bordeaux which works on organic photovoltaics, and Mark E. CASIDA is also collaborating with the group of Haibin SU in Singapore on topics closely related to ORGAVOLT.

See also: http://dietrich.foerster.free.fr/orgavolt_job_details.pdf