1.021 , 3.021, 10.333, 22.00 : Introduction to Modeling and Simulation : Spring 2012 Part II – Quantum Mechanical Methods : Lecture 1 1

A Bit More Solar P V , Some V&V and a Few Concluding Thoughts

Jeffrey C. Grossman

Department of Materials Science and Engineering Massac husetts Institute of T ec hnology

1

Par t II T opics

1. It ’ s a Quantum W orld: The Theor y of Quantum Mechanics

2. Quantum Mechanics: Practice Mak es P erf ect

3. Fr om Man y-Body to Single-Par ticle; Quantum Modeling of Molecules

4. Application of Quantum Modeling of Molecules: Solar Thermal Fuels

5. Application of Quantum Modeling of Molecules: Hydr ogen Storage

6. Fr om Atoms to Solids

7. Quantum Modeling of Solids: Basic Pr oper ties

8. Advanced Pr op . of Materials: What else can w e do?

10. Application of Quantum Modeling of Solids: Solar Cells Par t II S ome P V , S ome V&V and S ome C oncluding Thought s

9. Application of Quantum Modeling of Solids: Solar Cells Par t I

2

Outline

• Some mor e PV

• V erification and V alidation

• A f e w mor e thoughts

3

Comparison of PV Technologies

W e are here, e.g.,

• amorphous silicon

• polymers

• all-carbon

• quantum dots

This image is in the public domain. Source: Wikimedia Commons .

4

Fundamental P r ocesses In v olv ed in Solar Photo v oltaics: Elect r on ’ s Vie w

Photo-excitation Relaxation

CBM

E f Extraction

T ransport

Extraction

E f

T ransport

Recombination

VBM

External Load

5

Cr ystalline Silicon Solar PV

(80% of cur r ent mar k et)

• Light Absorption

• Band Ga p

• Band Structur e

• Electr on/Hole T ranspor t

© Helmut Föll. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/fairuse .

• Electr on/Hole Mobilities

4 π 3 ∂E

σ = e 2 τ

∫ d k

� − ∂ f � v ( k ) v ( k )

6

Amorphous Silicon Solar PV (3% of cur r ent mar k et)

• Light Absorption (is actuall y pr etty g ood)

• Electr on-Hole Separation (also not a pr oblem)

• Electr on/Hole T ranspor t (Holes ar e Slo w!)

• Hole Mobilities

• Hole T ra ps: fr om total energ y diff er ences (E neutral -E charged )

7

Organic Solar PV

• Light Absorption (need to ca ptur e mor e of the solar spectrum)

• Band ga p

• Electr on-Hole Separation

• Orbital energies

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P ol y(3-hexylthiophene) (P3HT): E g,exp = 2.1 eV

Lo w-energ y

R

p hotons ar e not absorbed!

R

8 Ega p = Eo Ega p = 0.55Eo Ega p = 1.1Eo

Dy e Sensitized Solar PV

Gratzel and O’Regan (Natur e , 1991)

Made up of 3 activ e materials:

• Dy e absorbs light.

• TiO 2 nanopar ticles with v er y

large surface ar ea tak e electr on.

• Liquid electr ol yte deliv ers ne w electr on fr om cathode to dy e .

Image in the public domain. Via M. R. Jones on Wikimedia Commons .

ww w .energ y e r .com 9

Dy e Sensitized Solar PV

• Biggest pr oblem is a

liquid electr ol yte .

• Relativ e energ y le v els

of TiO2 and dy e also k e y .

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10

Going High Efficiency: Fundamental Limits

Excess energy above E g heat

n

Conductio n band

E g

= max. V OC

V alence band

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As ba nd g a p in c re a ses , the m ax imum open c ir c uit v olt a ge in c re a ses , b ut the fr ac tion of the sol a r spe c trum ab sor b ed de c re a ses .

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Multi-J unction Solar PV

Figures removed due to copyright restrictions. See http://www.nexpw.com/technology _tm.html .

• Light Absorption

• Band ga ps

• Conductivity Acr oss Interfaces

• Band ga ps, Band structur es

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K e y Mechanism in Organic Solar PV: Charge Separation at the Interface

Charge separation at this interface is highl y efficient*:

- - Wh y?

* N. S. Sariciftci et al., Science, 1992, 258 , 1474

What is the detailed

mechanism f or this pictur e?

B. Kraabel et al., JC P , 1996, 104, 4268

C. J. Brabec. et al, CPL , 2001, 340, 232

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Excited State

Charge separated

state: essentially degenerate with bridge state.

0.02 eV

1.3 eV

Bridge state forms: hybridization of P3HT

* state and C60 t 1u

state.

P3HT

C 60

Y . Kanai and JCG, NanoLett 2007

14

C N T / P 3 H T : M e t allic C N T

Carbon nanotubes instead of C60? V ery little success thus fa r .*

E f near P3HT • Large charge transfer to the

* state metallic CNT (~0.3 electron)

• Fermi level just above P3HT HOMO state

Figures removed due to copyright restrictions. See • No interface states are formed,

f

Figures 4 and 5 in N ano L etters 8, no. 3 (2008). so no E

pinning

• Small built-in potential (0.06 eV), junction-induced exciton dissociation highly unlikely

CNT/Polymer solar cells unlikely to work well with mixed CNT distribution.

*e.g. Kymakis, E. et al. Rev . Adv . Mater . Sci. 2005, 10, 300

Y . Kanai and JCG, NanoLett (2008).

15

Using Computational Quantum Mechanics to Design Ne w Mechanisms

Straight Wire

What could this mean for a solar cell?

VBM

CBM

T apered Wire

VBM

CBM

Electron/hole charge separation through thermalization?

Axial charge redistribution due to quantum confinement

Majo po ential ad an age : no doping needed �

Z. W u, J. B. Neaton, and JCG, PRL 100, 246804 (2008); Nanoletters (2009)

16

Amorphous Silicon P V : The Slow Holes

No dangling bonds Dangling bond

0.8

Hole trap depth (eV)

0.6

0.4

0.2

0

-0.2

-6

-4 -2 0 2

Total energy (eV)

© APS Publishing. All rights reserved. See: Wagner, L .K., and J. C. Grossman. Physical Review Letters 101, no. 265501 (2008). This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use / .

This type of bond switch can be as bad for hole mobility as dangling bonds.

17

Hole T raps: Dangling Bond vs. Strain

Dangling bond hole trap

Strain-only hole trap (stronger)

© APS Publishing. All rights reserved. See: Wagner, L .K., and J. C. Grossman. Physical Review Letters 101, no. 265501 (2008). This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use .

Wager and JCG, Phys. Rev. Lett. 101, 265501 (2008) .

18

L.K.

New Microscopic Picture of Holes in a-Si

Computational quantum mechanics shows

© APS Publishing. All rights reserved. See: Wagner, L .K., and J. C. Grossman. Physical Review Letters 101, no. 265501 (2008). This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use .

that pressure can mitigate these traps!

Wager and JCG, Phys. Rev. Lett. 101, 265501 (2008) .

19

L.K.

Another Thin-Film PV Example: Hype r -Doped Silicon

• Silicon doped with chalcogen atoms (sulfu r , selenium, tellurium) to non-equilibrium concentrations.

• Strong optical response at photon energies where silicon is typically transparent.

• Promise as a photovoltaic material?

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20

Ev olution of Density of States

SiSe Si 53 Se 1

21

Si 431 Se 1 pure Silicon

Needing to Kno w Structur e and

Chemistr y

Image of quantum vials in public domain. Figure © source unknown. Data adapted from Physical Review B 60, no. 2704 (1999). All rights

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Needing to Kno w Structur e and Chemistr y

Clean Surface Oxygenated Cluster

Emits blue light

Emits red light

A. Puzder et al. Physical Review Letters, 88 097401 (2002)

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23

V alidation

Ho w do w e kno w when a sim ulation is right?

24

Example: R a yleigh- T a ylor Instabilit y

Fr om Leo P . Kadanoff, “The Good, the Bad, and the A wful [ Scientific Sim ulation and Pr ediction”

25

Example: R a yleigh- Ta y lor Instabilit y

• Idea: occurs an ytime a dense , he a vy fluid is accelerated into a light fluid or lesser density

• Slight per turbations to plane parallel interfaces ar e unstable …fingers gr o w into sets of inte r ­ penetrating fingers

• Obser v ed in w eather in v ersions, salt domes, star

nebulae

• Ho w to model this pr ocess? Requir es solving h ydr odynamics equations.

26

Example: R a yleigh- Ta y lor Instabilit y

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Example: R a yleigh-

Ta y lor Instabilit y

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28

V alidation and V erification

V erification and validation (V&V) ar e pr ocesses that help to ensur e that models and sim ulations ar e cor r ect and r eliable .

V erification: “Did I build the thing right?”

H a v e the model and sim ulation been built so that the y full y satisfy the de v eloper ’ s intent?

V alidation: “Did I build the right thing?”

Will the model or sim ulation be able to adequatel y suppor t its intended use? Is its fidelity a ppr opriate

f or that?

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after Dale Pace

W e’ve learned a lot!

30

Some of the key r emaining challenges

The electron correlation problem . Only seriously affects a fraction of materials, but that fraction tends to contain interesting physics and technological potential. At this point there is no logical follow-up on LDA/GGA

31

Some of the key r emaining challenges

The time-scale problem . Short (MD) and long (thermo) is not a problem.

Intermediate is a problem. e.g. phase transformations.

32

Some of the key r emaining challenges

The knowledge problem . T o study an engineering property/behavior with atomistic­ scale modeling, one needs to understand somewhat what controls that property (in order to include the relevant boundary conditions).

e.g. If a property is controlled by impurities then intrinsic calculations will be irrelevant (Si conductivity).

33

Some of the key r emaining challenges

The structure problem . Even though the structure-property relation is a key tenet of Materials Science, we have only very limited ability to predict structure (crystal structure, amorphous, microstructure,

.)

34

Theory of Properties:

The Multi-Scale Materials V iew

Continuum

Microstructure

Atoms

Electrons

Properties

35

Theory of Properties:

The Multi-Scale Materials V iew

Continuum

Microstructure

Electrons

Atoms

Properties

Courtesy of Patrick J. Lynch . License: CC-BY.

36

Co mp u t a tio n s sh o u l d n o t substitute for lack of knowledge

Computational modeling is very powerful, but be smart!

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