How Could Cheap SemiconductorsAct as Good Electronic Materials?

(the physics of defect tolerance and carrier-separation at grain boundaries)

Alex Zunger

National Renewable Energy Laboratory (NREL) Golden, Colorado 80401

In honor of my friend and colleague,Prof. Yoram Shapira

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Some Historical Facts …

• Polycrystalline Si and GaAs cells are less efficient than their crystalline counterpart.

“official explanation”:

• Impurities and defects accumulate at GB’s causing strong e-h recombination there.

• Problem can be partially cured by (sophisticated) passivation.

• Surprisingly, polycrystalline CIGS cell outperform their crystalline counterparts!

• The hope: Can one

(1) understand what makes certainpolycrystalline solids good devices and

(2) use this understanding to make other solids behave this way?

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Bulk CIGS

GIIn Se

Cu

112

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Defect formation energy:

Energyof defect

Energyof host

µelem = chemical potential of a in elemental phase

na = +1; atom type a is removed (host)

na = -1; atom type a is added (dopant)

q = charge state of defect

EV = valence band energy

EF = Fermi energy

Chemical potentials

Fermienergy

α

How to Optimize Growth and Doping Conditions for n-type CIGS

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What are the leading point defects in CIS?What are their positions in the gap?

Phys. Rev. B 57, 9642 (1998)PV Doping 98

The first episode:Impurities are bad, but in CIGS

they combine to give a good defect

The story of

(a) VCu

(b) InCu anti-site

(c) Their combination

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Forming isolated defects in crystals costs energy but, can a defect-pair be spontaneously

stable?

Stability of pair depends on:

(a)How costly is the formation of the isolated defects

(b)How much energy is gained by combining two defects

∆

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This is unusual: most defects do not pair-up

∴ Defect-pair formation energies in binaries are still positive and very large

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Positive ∆H!

But, 2V– and In++ Combine Exothermically

Negative ∆H!

Cu Cu

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Formation energy of charged non-interacting pair 3.40 eVInteraction energy of InCu with 2VCu -2.60 eVArray energy of (InCu + 2VCu)n -0.80 eVTotal formation energy of array of pairs ~0 eV

Once they order, energy is lowered further

Spontaneous formation of defect array!

∆Hf eV eV eV eV

Mechanism of Stabilization of Defect Arrays in CIGS

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Single Pair of (InCu + 2VCu) in CIS(Se not shown)

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VCu and InCu have deep gap levels, but they pair-up

Because the defect that creates the off-stoichiometry

2V– and In2+

is both stable, and electrically inactiveCu Cu

Phys. Rev. Lett. 78, 4059 (1997) PV Doping 14

• Formation of vacancies; anti-sites normally cost energy.

• The defect complex (2V– + In++ ) forms spontaneously in CIS (Cu-poor condition).

• The defect-pair formation eliminates deep InCu donor.

• These defects are further stabilized via their spatial ordering ⇒ Ordered Vacancy Structures.

Certain defect pairs form spontaneously in CIS

Cu Cu

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The stability of 2VCu + InCuleads to “off-stoichiometric”

ordered structures

++–

Cu:In:Se ratios can be 1:5:81:3:53:7:12

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Comparison between the Expected (Cu(n-3m)In(n+m)Se2n) and theObserved OVC Components

(theory)

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The 3 Puzzles of Chalcopyrite

Relative to II-VI’s, CuInSe2:

(a) Tolerates a large range of off-stoichiometry;

(b) This off stoichiometry does not lead to deep NR traps

(c) Forms peculiar phases: CuIn5 Se8, CuIn3Se5, Cu3In7Se12

The Answers

(a) The stability of off-stoichiometry compounds is a consequence of stability of the units in CuInSe2

(b) Pairing of with eliminates the deep levels

(c) These phases are formed by a repetition of m units of ( + ) with n units of CuInSe2

−Cu2V ++

CuIn

−Cu2V ++

CuIn

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“Self-passivation by spontaneous pairing of individually harmful defects” explains many things,

What do grain boundaries do?

but not why poly-CIGS outperforms crystalline CIGS.

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The second episode:How can certain grain-boundaries

be good?

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Grain Boundary

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Actually, satellite view of the Grand Canyon

Grain Boundary

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pn junction

window layer

absorber layer

Mo

CdS n–

ZnO

CIGS p+CIGS

(220

)

Cross section SEM image

1mm

K. Ramanathan, et al. Prog. Photovolt. Res. Appl. 11, 225 (2003).

Solar cell

buffer layer

back contact Mo

h+e–

In this talk:

How come GBs are good in Cu(In,Ga)Se2 solar cells, but not in Si and GaAs devices??

Grain boundaries (GB) in thin-film Cu(In,Ga)Se2

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The Prevailing “Folkfore” about Grain-Boundaries in

Chalcopyrites

• In some sense, they are not so bad (as in Si, GaAs) as evidenced by the fact that the devices work so well.

• Some kind of charged-defects, impurities or growth conditions facilitate this.

Acknowledgement for discussion on above:Noufi, Cahen, Contreras, Kaydanof, Stanbery, Sites

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Classical Model of GB Effect onTransport: Charged Defects

J.Y.W. Seto, JAP 46, 5247 (1975)

But, charge defects enhance recombinations ⇒ slow down the mobility

GB repels electrons (majority), attracts holes

(minority)

GB repels holes (majority), attracts electrons (minority)

–

n-type caseNegatively charged ions

Acceptors, e.g. VCu

p-type casePositively charged ions

Donors, e.g. VSe++

e-

h+

GB GIGI

EVB

ECB----

h+

e-

ECBEVB

GI GB GI

+++

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Opinions in the Literature on Charged-defects that cause GB

Band-bending

• S. Schuler, S. Siebentritt, et al.[29th IEEE PV Conf. p. 504 (2002)]

• GB have some charged donors.

• Niemegeers, et al.[Prog. Photovolt. Res. Appl. 6, 407 (2002)]

• ODC has high concentration of charged acceptors.

• Romero, et al.

• Excess acceptors VCu at GB on surface.

• Herberholt, et al. [Eur. Phys. J. AP 6, 131 (1999]

• VSe drives Cu out forming Vse – Vcu complex.

_

+ + _

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• Defects unknown; identity is speculativeoften unlikely.

• Charge will slow down mobility; not animprovement on cell performance.

• Beneficial effect of GB should not depend on specific defects, as it’s a generalphenomenon, existing under manygrowth scenarios!

• Mechanism keeps Eg constant; noimprovement in Voc.

Problems with Electrostatic Explanations

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(1) Model the GBs

(2) Calculate the electronic properties of theGB, focusing on localization of electronsand holes near and away from the GB

In this work, we:

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Quick Review of Pertinent Surface Physics

• In ‘conventional’ semiconductors, non-polarsurface is the most stable.

• Reasons: polar surfaces require forming vacancy-arrays for their electrostatic stability. In III-Vs this is energetically costly.

• Two types of surfaces:

Non-polarPolar

(220)(112)Se; (112)CuChalcopyrites

(110)(001); (111)III-V’s– – –

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Why do polar surfaces normally have higher energy?

Macroscopic dipolecauses divergence of surface energy…

Unless cancelled byreduction of surface charge by atomic or electronic defects; costs energy!

+8-8+8-8+8-8+8-8

+6-6+8-8+8-8+8-6

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11

10

9

8

7

6

5

4

3-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0

µ(As)-Etot(As)

Sur

face

ene

rgy

of s

uper

cell

(eV

)

Equivalent area of unfaceted (110)

As ad-trimer (111)

VGa (111) + Ga adatom (111)

VGa (111)

Defect-free (111)

GaAs (2x2) Supercell

Non-polarmoststable

In III-Vs the Non-polar (110) Surface is the Most Stable Surface

GaAs (110) much lower in energy than (111) facets for any reconstruction

(after Moll et al. 1996)PV Doping 38

• Which crystal surface is the most stable?– Non-polar (110)– polar (112)cation

– polar (112)anion

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Quick Review of Pertinent Surface Physics

• In chalcopyrites, the polar surface is the most stable since it is energetically ‘cheap’ to create VCu.

• Two types of surfaces:

Non-polarPolar

(220)(112)Se; (112)CuChalcopyrites

(110)(001); (111)III-V’s– – –

(112) Cation facet

(112) Anionfacet, equivalent

to (112)

(110) surface

35.4°35.4°

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(110) → (112)cation + (112)anion occurs spontaneously

0

2

4

6

8

10

-1.6 -1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 1.6

CuInSe2 Surface Energy Comparison

Sur

face

ene

rgy

ofsu

perc

ell (

eV)

µ(Cu) – µ(In)

Equivalent area of unfaceted (110)

2VCu (112) CuIn(112)

Defect-free (112)

Reconstructed (112) facets of chalcopyrites are lower energy

than (110) at almost all chemical potential values!

Jaffe and Zunger, PRB, 64, 241304 (2001)PV Doping 41

Unlike all binaries, in chalcopyrites the polar surfaces are more stable than

the non-polar surfaces

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2VCu

InCu

Se

• Polar (112) surface is thestablest surface in CIS Jaffe and Zunger, PRB 64, 241304 (2001)

(112) CIGS

(110

)

The (112)-Surface

Liao and Rocket, 29th IEEE Conf. p. 515 (2002).

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So,

• What’s special about GB in CIGS: theyhave polar-like atomic structure, i.e.,

Rows of Cu atoms are missing

• What’s the electron/transport consequence of that?

• Let’s calculate the electronic structure ofmodel GBI with polar surfaces/interfaces.

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2VCu

GB

GI

(112)-surface Two (112)-surfaces

112

Model CIS GB/surface

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−6 −4 −2 0 2−4

−2

0

2

4

6

8

−6 −4 −2 0 2−4

−2

0

2

4

6

8

−6 −4 −2 0 2−4

−2

0

2

4

6

8

GI

DO

S [1

/laye

reV

]

p

Crystalline CISHas strong d-DOSat and below VBM.

GB

GI

GIGB

GI

DO

S [1

/laye

reV

] d

p

The GB lacks d-DOSstates.Near VBM!

DO

S [1

/laye

reV

]

p

p

Energy [eV]

VBM

d

p

Layer- and Angular-projected Density-of-States

d

GI

GI

GB

GI

GB

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−2 −1.5 −1 −0.5 0 0.5−3

−2

−1

0

1

2

3

GI

GB

GI

GIGB

GI

DO

S [1

/laye

reV

]

d

p

p GI

GB

−2 −1.5 −1 −0.5 0 0.5−3

−2

−1

0

1

2

3

DO

S [1

/laye

reV

]

p

p

Energy [eV]

GI

GB

d

−2 −1.5 −1 −0.5 0 0.5−3

−2

−1

0

1

2

3

DO

S [1

/laye

reV

]p

d

GI

VBM

Layer- and Angular-projected Density-of-States: Zoom

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Meaning of Fact that Hole Wavefunction Avoids the GB

• GB is hole-poor.

• Weak e-h recombination at GB, even if many defects there.

• GI is relatively chemically pure (most defects segregated to GB).

• Mechanism does not require charge.

h+

EC

EV

GI GB GI

EV–1eV

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The Advantage with Charge-neutral GB/surface Defects

Charge-neutral defects do not slow down the mobility of minority carriers

in p-type CIGS

h+

e-

ECB

EVB

GI GB GI

Charged defects at GB:Both carrier types are affected by the GB potential. Band gapunchanged.

Neutral defects at GB:Only one carrier type is affected by the GB potential.No recombination in GB.

h+

e-

ECBEVB

GI GB GI

+++

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Conclusions

• Polar (112) surface is the most stable GB/surface in CIGS. It requires VCu.Jaffe and Zunger, PRB 64, 241304 (2001)

• GB/surface with VCu or NaCu creates a hole barrier due to reduced Cu,d–Se,prepulsion.

• Since there are no holes at the GB, there is no recombination, despite many defects.

• Grain interior is chemically rather pure.

This explains the puzzle why polycrystalline CIGS

outperforms the crystalline counterparts.

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A New Model for Polycrystalline CIGS: Features

• Do not need to assume charged ions at the GB or interface.

• Accept that the most basic property of a GB is that it is “surface like”.

• Show that in CIGS the GB creates a natural reflector for holes, due to:

• having Cu-poor surface reconstruction

• having Na

• The “hole reflector” means that electrons in the GB have no partner to recombine with ⇒ No band-to-band recombination.

• At the same time, grain-interior in poly material may be purer than in single crystal.

• “Secret of success”: design a barrier for one carrier type at GB or surface.

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Understanding Doping Bottlenecks

Alex Zunger

National Renewable Energy Laboratory (NREL) Golden, Colorado 80401

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Some Observations and Questions

• Most electronic devices require doping.

• Why are certain solids difficult to dope?

– p-ZnO; n-diamond; n-CuGaSe2

– n, p-MgO; p-nitrides

• Are the reasons for “failure to dope”circumstantial and temporary, or do they reflect a fundamental limitation?

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Technologies that Could Fail Due to Doping Limitations

1. High-efficiency multi-junction thin-filmsolar cells: CuGaSe2 based

2. Solid-state lighting via AIN/GaN junctions

3. Diamond based electronics

In all cases, WIDE-GAP materialcannot be doped …

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1. Dopants cannot be introduced: (solubility limit)

2. Dopants can be introduced, but the energy levels are too deep —poor conductivity. e.g., ZnS:Cu is deep

3. Free charge carrier cannot be stably introduced regardless of the type of dopants:spontaneous formation of “killer defects.”

Three Types of Failures to Conduct

Note:(3) is the ultimate limiting factor, as (1) and (2)can be overcome by changing dopant or by co-doping.

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Basic Thermodynamics ofDefect Formation of Solids

• Defect formation enthalpy is not a number: it’s a function (µ, EF)

• Theory vs experiments for defects in CIS

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Defect Formation Enthalpy Depends on the Fermi Energy

e.g., donors:

• A donor produces electrons• The electrons are released into the Fermi sea:

E (A+) = E(A0) - E(0/+) + EF

• Thus, E(A+) goes up as EF goes up!

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E(A0) = E(A0)

E(A+) = E(A0) - E(0/+) + EF

E(A-) = E(A0) + E(-/0) - EF

• Donors are difficult (easy) to form in n-type(p-type) materials.

• Acceptors are difficult (easy) to form in p-type (n-type) materials.

Thermodynamics of Doping

EV EF EC

A+

-/0A00/+

A-

• Donor• Produces

electrons

• Acceptor• Produces

holes• Easier to

form in n-type

∆Hf

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Defect Formation Energies vs Chemical Potentials in CuInSe2

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Dope intentionally n-type. EF goes up

Energy to form acceptors (Vc) goes down

At a critical EF = such native acceptors will form spontaneously

This will destroy intentional n-doping!

Q: What is the position of in the gap?

(energy where compensating defectis created)

)(npinE

The catch with EF-dependenceof formation energies

)(npinE

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First: Determine position of Fermi energy corresponding to the maximal doping in each material

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How Do We Know at which Value of EF “Killer Acceptors” Form to Limit

n-Type Doping?

(n)

Input Output

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Maximum Carriers Densities Measured

Note diverse ranges of experimental doping limitsin II-VI binaries and I-III-VI ternaries

(a) n-Type

(b) p-Type

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• We took Nmax from experiment and decided εF for each material.

• How can we compare εF for different materials?

• Check 1984 “Vacuum-Pinning Rule.”

Plot with respect to absolute band edge!

Procedural Question

(n)

(n)

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Doping Rules

If εCBM >> εpin Cannot dope n-type

If εVBM << εpin Cannot dope p-type

(n)

(p)

CuInSe2 CuAlSe2 CuIn5Se2

ZnO ZnS ZnSe ZnTe CdS CdSeCdTe CuInS2 CuInTe2 CuGaSe2

-1.00

0.00

0.53

1.26

0.18

0.60

1.170.95

1.23

1.73

0.97

0.97

0.81

2.20

3.74

0.531.26

0.180.60

1.170.95 1.23

1.73

0.97

0.97

0.81

TCOII-VI Binaries I-III-VI2Ternaries

εpin(n)

εpin(p)

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Doping Limit Rule(phenomenological)

1. A material with εCBM > εpin

cannot be doped n-type.

2. A material with εVBM < εpin

cannot be doped p-type.

(n)

(p)

PV Doping 89

• Good n-type: ZnO, ZnSe, CdS, CdSe, CdTe,CuInSe2, InAs, InP, InSb

• Poor n-type: ZnS, CuGaSe2, CuAlSe2

• Good p-type: ZnTe, CdTe, GaSb, InSb

• Poor p-type: ZnO, ZnS, Zn, Se, CdS, CdSe

Doping Trends

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Establish Some Basic Design Principles for Doping

To help us navigate rationally through the Periodic Table

• “Strategic Principles”

• Pauling-esque rules

• Find chemical regularities

PV Doping 90

Large χ : Yes, n Small χ : No, n(InAs, ZnO) (Diamond, AlN, CuAlSe2)

Large Φ: No, p Small Φ: Yes, p(CdS, ZnO) (Tellurides, antimonides)

Vacuum

CBM

VBM

VBM

CBM

Φεpin

(n)

εpin(p)

χχ

Φ

Example: Two materials, same band gap. Which dopes better?

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N-type doping requires a material with large electron-affinity χ (low CBM).

e.g., large alloy bowing can lower CBM:

Rule I

GaAs

cbmGaAs(N)

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p-doping requires a material withsmall work function Φ.

How can we reduce Φ?: Use active d-band

ZnO

Ev

CuAlO2

Cu, 3d

Zn, 3d

Rule II

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Once the “killer defect” is identified, find growth conditions that destabilize/eliminate it.

(a) p-type doping is killed by Vanion

(b) n-type doping is killed by Vcation; DX

“Kill the Killer”

e.g., for n-doping, use cation dopants,to fill Vcation (AlN:Si). Cation-rich conditions.

e.g., for p-doping, prefer anion dopants, to fill Vanion (ZnO:N). Anion-rich conditions.

Rule III

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Hydrogen: a Common Impurity in Semiconductors

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How can one guess if hydrogenmakes a given oxide conductive

or not?

H in GaAs: amphoteric

H in ZnO: conductive

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Will H make all oxides conductive?

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H-derived Electrical Level in Oxides

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H(+/–) Level in CIS and CGS

H dopes CIS but not CGS

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Conclusions

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References

http://www.sst.nrel.gov

Publications (sort)

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