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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
PV Doping 2
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?
PV Doping 5
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
PV Doping 164
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
PV Doping 6
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
∆
PV Doping 7
This is unusual: most defects do not pair-up
∴ Defect-pair formation energies in binaries are still positive and very large
PV Doping 8
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
PV Doping 10
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
PV Doping 15
The stability of 2VCu + InCuleads to “off-stoichiometric”
ordered structures
++–
Cu:In:Se ratios can be 1:5:81:3:53:7:12
PV Doping 16
Comparison between the Expected (Cu(n-3m)In(n+m)Se2n) and theObserved OVC Components
(theory)
PV Doping 17
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
PV Doping 22
“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.
PV Doping 23
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
PV Doping 28
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
PV Doping 30
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
+++
PV Doping 31
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.
_
+ + _
PV Doping 32
• 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
PV Doping 33
(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:
PV Doping 34
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– – –
PV Doping 35
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
PV Doping 36
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
PV Doping 39
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°
PV Doping 40
(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
PV Doping 42
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).
PV Doping 44
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.
PV Doping 45
−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
PV Doping 48
−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
PV Doping 49
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
PV Doping 52
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
+++
PV Doping 57
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.
PV Doping 60
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.
PV Doping 61
Understanding Doping Bottlenecks
Alex Zunger
National Renewable Energy Laboratory (NREL) Golden, Colorado 80401
PV Doping 64
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?
PV Doping 66
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 …
PV Doping 67
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.
PV Doping 68
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
PV Doping 69
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!
PV Doping 70
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
PV Doping 72
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
PV Doping 74
First: Determine position of Fermi energy corresponding to the maximal doping in each material
PV Doping 75
How Do We Know at which Value of EF “Killer Acceptors” Form to Limit
n-Type Doping?
(n)
Input Output
PV Doping 76
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
PV Doping 78
• 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)
PV Doping 82
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)
PV Doping 83
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
PV Doping 84
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?
PV Doping 91
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)
PV Doping 92
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
PV Doping 93
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
PV Doping 94
How can one guess if hydrogenmakes a given oxide conductive
or not?
H in GaAs: amphoteric
H in ZnO: conductive
PV Doping 139