Traditional inorganic semiconductors can be electronically doped with high precision. Conversely, there is still conjecture regarding the assessment of the electronic doping density in metal-halide perovskites, not to mention of a control thereof. This paper presents a multifaceted approach to determine the electronic doping density for a range of different lead-halide perovskite systems. Optical and electrical characterization techniques, comprising intensity-dependent and transient photoluminescence, AC Hall effect, transfer-length-methods, and charge extraction measurements were instrumental in quantifying an upper limit for the doping density. The obtained values are subsequently compared to the electrode charge per cell volume under short-circuit conditions (), which amounts to roughly 1016 cm−3. This figure of merit represents the critical limit below which doping-induced charges do not influence the device performance. The experimental results consistently demonstrate that the doping density is below this critical threshold (∼1012 cm−3, which means ≪ ) for all common lead-based metal-halide perovskites. Nevertheless, although the density of doping-induced charges is too low to redistribute the built-in voltage in the perovskite active layer, mobile ions are present in sufficient quantities to create space-charge-regions in the active layer, reminiscent of doped pn-junctions. These results are well supported by drift–diffusion simulations, which confirm that the device performance is not affected by such low doping densities.
References
1.
C. R.
Abernathy
, S. J.
Pearton
, R.
Caruso
, F.
Ren
, and J.
Kovalchik
, “Ultrahigh doping of GaAs by carbon during metalorganic molecular beam epitaxy
,” Appl. Phys. Lett.
55
, 1750
–1752
(1989
).2.
H. J.
Queisser
and E. E.
Haller
, “Defects in semiconductors: Some fatal, some vital
,” Science
281
, 945
–950
(1998
).3.
R. A.
Street
, “Doping and the Fermi energy in amorphous silicon
,” Phys. Rev.
49
, 1187
–1190
(1982
).4.
C. K.
Chiang
et al, “Electrical conductivity in doped polyacetylene
,” Phys. Rev. Lett.
39
, 1098
–1101
(1977
).5.
I. E.
Jacobs
and A. J.
Moulé
, “Controlling molecular doping in organic semiconductors
,” Adv. Mater.
29
, 1703063
(2017
).6.
P.
Pingel
, R.
Schwarzl
, and D.
Neher
, “Effect of molecular p-doping on hole density and mobility in poly(3-hexylthiophene)
,” Appl. Phys. Lett.
100
, 143303
(2012
).7.
P.
Pingel
and D.
Neher
, “Comprehensive picture of p-type doping of P3HT with the molecular acceptor F4TCNQ
,” Phys. Rev. B
87
, 115209
(2013
).8.
I. E.
Jacobs
et al, “Comparison of solution-mixed and sequentially processed P3HT:F4TCNQ films: Effect of doping-induced aggregation on film morphology
,” J. Mater. Chem. C
4
, 3454
–3466
(2016
).9.
A.
Musiienko
et al, “Photo-Hall-effect spectroscopy with enhanced illumination in p-Cd1−xMnxTe showing negative differential photoconductivity
,” Phys. Rev. Appl.
10
, 014019
(2018
).10.
R.
Sandheep
, U.
Thomas
, and K.
Thomas
, “Comment on ‘Resolving spatial energetic distributions trap states metal halide perovskite solar cells
,’” Science
371
, eabd8014
(2021
).11.
J.
Siekmann
, S.
Ravishankar
, and T.
Kirchartz
, “Apparent defect densities in halide perovskite thin films and single crystals
,” ACS Energy Lett.
6
, 3244
–3251
(2021
).12.
J.
Euvrard
, Y.
Yan
, and D. B.
Mitzi
, “Electrical doping in halide perovskites
,” Nat. Rev. Mater.
6
, 531
–549
(2021
).13.
L.
Huang
et al, “Schottky/p-n cascade heterojunction constructed by intentional n-type doping perovskite toward efficient electron layer-free perovskite solar cells
,” Sol. RRL
3
, 1800274
(2019
).14.
L.
Huang
and Y.
Zhu
, “p-n heterojunction perovskite solar cell with bilateral Ohmic contacts
,” Appl. Phys. Lett.
118
, 052105
(2021
).15.
W.-J.
Yin
, T.
Shi
, and Y.
Yan
, “Unusual defect physics in CH3NH3PbI3 perovskite solar cell absorber
,” Appl. Phys. Lett.
104
, 063903
(2014
).16.
J. M.
Ball
and A.
Petrozza
, “Defects in perovskite-halides and their effects in solar cells
,” Nat. Energy
1
, 16149
(2016
).17.
Q.
Wang
et al, “Qualifying composition dependent p and n self-doping in CH3NH3PbI3
,” Appl. Phys. Lett.
105
, 163508
(2014
).18.
P.
Cui
et al, “Planar p-n homojunction perovskite solar cells with efficiency exceeding 21.3
%,” Nat. Energy
4
, 150
–159
(2019
).19.
A.
Musiienko
et al, “Defects in hybrid perovskites: The secret of efficient charge transport
,” Adv. Funct. Mater.
31
, 2104467
(2021
).20.
J.
Kim
, S.-H.
Lee
, J. H.
Lee
, and K.-H.
Hong
, “The role of intrinsic defects in methylammonium lead iodide perovskite
,” J. Phys. Chem. Lett.
5
, 1312
–1317
(2014
).21.
J.
Euvrard
, O.
Gunawan
, and D. B.
Mitzi
, “Impact of PbI2 passivation and grain size engineering in CH3NH3PbI3 solar absorbers as revealed by carrier-resolved photo-Hall technique
,” Adv. Energy Mater.
9
, 1902706
(2019
).22.
A.
Zohar
et al, “What is the mechanism of MAPbI3 p-doping by I2? Insights from optoelectronic properties
,” ACS Energy Lett.
2
, 2408
–2414
(2017
).23.
P.
Schulz
et al, “Electronic level alignment in inverted organometal perovskite solar cells
,” Adv. Mater. Interfaces
2
, 1400532
(2015
).24.
D.
Shin
et al, “Mechanism and timescales of reversible p-doping of methylammonium lead triiodide by oxygen
,” Adv. Mater.
33
, 2100211
(2021
).25.
M.
Stolterfoht
et al, “The impact of energy alignment and interfacial recombination on the internal and external open-circuit voltage of perovskite solar cells
,” Energy Environ. Sci.
12
, 2778
–2788
(2019
).26.
P.
Caprioglio
et al, “High open circuit voltages in pin-type perovskite solar cells through strontium addition
,” Sustainable Energy Fuels
3
, 550
–563
(2019
).27.
F.
Zu
et al, “Unraveling the electronic properties of lead halide perovskites with surface photovoltage in photoemission studies
,” ACS Appl. Mater. Interfaces
11
, 21578
–21583
(2019
).28.
T.
Hellmann
et al, “The electronic structure of MAPI-based perovskite solar cells: Detailed band diagram determination by photoemission spectroscopy comparing classical and inverted device stacks
,” Adv. Energy Mater.
10
, 2002129
(2020
).29.
A.
Walsh
, D. O.
Scanlon
, S.
Chen
, X. G.
Gong
, and S. H.
Wei
, “Self-regulation mechanism for charged point defects in hybrid halide perovskites
,” Angew. Chem., Int. Ed.
54
, 1791
–1794
(2015
).30.
S.
Reichert
et al, “Ionic-defect distribution revealed by improved evaluation of deep-level transient spectroscopy on perovskite solar cells
,” Phys. Rev. Appl.
13
, 034018
(2020
).31.
Y.
Cheng
et al, “The detrimental effect of excess mobile ions in planar CH3NH3PbI3 perovskite solar cells
,” J. Mater. Chem. A
4
, 12748
–12755
(2016
).32.
L.
Bertoluzzi
et al, “Mobile ion concentration measurement and open-access band diagram simulation platform for halide perovskite solar cells
,” Joule
4
, 109
–127
(2020
).33.
M. H.
Futscher
et al, “Quantification of ion migration in CH3NH3PbI3 perovskite solar cells by transient capacitance measurements
,” Mater. Horiz.
6
, 1497
–1503
(2019
).34.
T.
Kirchartz
et al, “Sensitivity of the Mott–Schottky analysis in organic solar cells
,” J. Phys. Chem. C
116
, 7672
–7680
(2012
).35.
O. J.
Sandberg
, M.
Nyman
, and R.
Österbacka
, “Direct determination of doping concentration and built-in voltage from extraction current transients
,” Org. Electron.
15
, 3413
–3420
(2014
).36.
O.
Almora
, C.
Aranda
, E.
Mas-Marzá
, and G.
Garcia-Belmonte
, “On Mott-Schottky analysis interpretation of capacitance measurements in organometal perovskite solar cells
,” Appl. Phys. Lett.
109
, 173903
(2016
).37.
J.
Diekmann
et al, “Pathways toward 30% efficient single-junction perovskite solar cells and the role of mobile ions
,” Sol. RRL
5
, 2100219
(2021
).38.
L. B.
Valdes
, “Resistivity measurements on germanium for transistors
,” Proc. IRE
42
, 420
–427
(1954
).39.
G. K.
Reeves
and H. B.
Harrison
, “Obtaining the specific contact resistance from transmission line model measurements
,” IEEE Electron Device Lett.
3
, 111
–113
(1982
).40.
L. J.
van der Pauw
, “A method of measuring specific resistivity and Hall effect of discs of arbitrary shape
,” Philips Res. Rep.
13
, 1
–9
(1958
).41.
D. K.
Schroder
, Semiconductor Material and Device Characterization
(John Wiley & Sons
, 2006
).42.
S.
Ravishankar
, Z.
Liu
, and T.
Kirchartz
, “Multilayer capacitances: How selective contacts affect capacitance measurements of perovskite solar cells
,” (2021
).43.
O.
Gunawan
et al, “Carrier-resolved photo-Hall effect
,” Nature
575
, 151
–155
(2019
).44.
S.
Feldmann
et al, “Photodoping through local charge carrier accumulation in alloyed hybrid perovskites for highly efficient luminescence
,” Nat. Photonics
14
, 123
–128
(2020
).45.
F.
Staub
et al, “Beyond bulk lifetimes: Insights into lead halide perovskite films from time-resolved photoluminescence
,” Phys. Rev. Appl.
6
, 044017
(2016
).46.
T. J.
Savenije
, D.
Guo
, V. M.
Caselli
, and E. M.
Hutter
, “Quantifying charge-carrier mobilities and recombination rates in metal halide perovskites from time-resolved microwave photoconductivity measurements
,” Adv. Energy Mater.
10
, 1903788
(2020
).47.
J.
Kniepert
, I.
Lange
, N. J.
van der Kaap
, L. J. A.
Koster
, and D.
Neher
, “A conclusive view on charge generation, recombination, and extraction in as-prepared and annealed P3HT:PCBM blends: Combined experimental and simulation work
,” Adv. Energy Mater.
4
, 1301401
(2014
).48.
V. M.
Le Corre
et al, “Revealing charge carrier mobility and defect densities in metal halide perovskites via space-charge-limited current measurements
,” ACS Energy Lett.
6
, 1087
–1094
(2021
).49.
G.
Juška
, K.
Arlauskas
, M.
Viliūnas
, and J.
Kočka
, “Extraction current transients: New method of study of charge transport in microcrystalline silicon
,” Phys. Rev. Lett.
84
, 4946
–4949
(2000
).50.
J.
Thiesbrummel
et al, “Universal current losses in perovskite solar cells due to mobile ions
,” Adv. Energy Mater.
11
, 2101447
(2021
).51.
T.
Kirchartz
and D.
Cahen
, “Minimum doping densities for p-n junctions
,” Nat. Energy
5
, 973
–975
(2020
).52.
J.
Hüpkes
, U.
Rau
, and T.
Kirchartz
, “Dielectric junction: Electrostatic design for charge carrier collection in solar cells
,” Sol. RRL
6
, 2100720
(2021
).53.
B.
Das
, I.
Aguilera
, U.
Rau
, and T.
Kirchartz
, “Effect of doping, photodoping and bandgap variation on the performance of perovskite solar cells
,” arXiv:2112.03445 (2021
).54.
M.
Burgelman
, J.
Verschraegen
, S.
Degrave
, and P.
Nollet
, “Modeling thin-film PV devices
,” Prog. Photovoltaics
12
, 143
–153
(2004
).55.
M.
Burgelman
, P.
Nollet
, and S.
Degrave
, “Modelling polycrystalline semiconductor solar cells
,” Thin Solid Films
361–362
, 527
–532
(2000
).56.
A.
Musiienko
et al, “Deep levels, charge transport and mixed conductivity in organometallic halide perovskites
,” Energy Environ. Sci.
12
, 1413
–1425
(2019
).57.
E. A.
Duijnstee
et al, “Toward understanding space-charge limited current measurements on metal halide perovskites
,” ACS Energy Lett.
5
, 376
–384
(2020
).58.
W.
Peng
et al, “Quantification of ionic diffusion in lead halide perovskite single crystals
,” ACS Energy Lett.
3
, 1477
–1481
(2018
).59.
J. W.
Orton
and M. J.
Powell
, “The Hall effect in polycrystalline and powdered semiconductors
,” Rep. Prog. Phys.
43
, 1263
–1307
(1980
).60.
T.
Kirchartz
, J. A.
Márquez
, M.
Stolterfoht
, and T.
Unold
, “Photoluminescence-based characterization of halide perovskites for photovoltaics
,” Adv. Energy Mater.
10
, 1904134
(2020
).61.
S.
Feldmann
et al, “Tailored local bandgap modulation as a strategy to maximize luminescence yields in mixed-halide perovskites
,” Adv. Opt. Mater.
9
, 2100635
(2021
).62.
C. M.
Wolff
et al, “Orders of recombination in complete perovskite solar cells: Linking time-resolved and steady-state measurements
,” Adv. Energy Mater.
11
, 2101823
(2021
).63.
T.
Kirchartz
, L.
Krückemeier
, and E. L.
Unger
, “Research update: Recombination and open-circuit voltage in lead-halide perovskites
,” APL Mater.
6
, 100702
(2018
).64.
J. M.
Richter
et al, “Enhancing photoluminescence yields in lead halide perovskites by photon recycling and light out-coupling
,” Nat. Commun.
7
, 13941
(2016
).65.
E.
Gutierrez-Partida
et al, “Large-grain double cation perovskites with 18
μs lifetime and high luminescence yield for efficient inverted perovskite solar cells
,” ACS Energy Lett.
6
, 1045
–1054
(2021
).66.
G.
Juška
, N.
Nekrašas
, V.
Valentinavičius
, P.
Meredith
, and A.
Pivrikas
, “Extraction of photogenerated charge carriers by linearly increasing voltage in the case of Langevin recombination
,” Phys. Rev. B
84
, 155202
(2011
).67.
G.
Juška
et al, “Charge transport in pi-conjugated polymers from extraction current transients
,” Phys. Rev. B
62
, R16235
–R16238
(2000
).68.
M.
Stolterfoht
et al, “Approaching the fill factor Shockley–Queisser limit in stable, dopant-free triple cation perovskite solar cells
,” Energy Environ. Sci.
10
, 1530
–1539
(2017
).69.
D.
Kiermasch
et al, “Unravelling steady-state bulk recombination dynamics in thick efficient vacuum-deposited perovskite solar cells by transient methods
,” J. Mater. Chem. A
7
, 14712
–14722
(2019
).70.
M.
Fischer
, K.
Tvingstedt
, A.
Baumann
, and V.
Dyakonov
, “Doping profile in planar hybrid perovskite solar cells identifying mobile ions
,” ACS Appl. Energy Mater.
1
, 5129
–5134
(2018
).71.
N.
Wu
, D.
Walter
, A.
Fell
, Y.
Wu
, and K.
Weber
, “The impact of mobile ions on the steady-state performance of perovskite solar cells
,” J. Phys. Chem. C
124
, 219
–229
(2020
).72.
O.
Almora
et al, “Capacitive dark currents, hysteresis, and electrode polarization in lead halide perovskite solar cells
,” J. Phys. Chem. Lett.
6
, 1645
–1652
(2015
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
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