nature energy
Article
https://doi.org/10.1038/s41560-023-01420-7
Charge-carrier-concentration
inhomogeneities in alkali-treated
Cu(In,Ga)Se2 revealed by conductive atomic
force microscopy tomography
Received: 31 August 2022
Accepted: 21 November 2023
Published online: 3 January 2024
Check for updates
Deepanjan Sharma
Dimitrios Hariskos
, Nicoleta Nicoara 1, Philip Jackson3, Wolfram Witte
& Sascha Sadewasser 1
1,2
3
,
3
Photovoltaic power conversion using polycrystalline light-absorbing
semiconductors enables low-cost electricity generation. Cu(In,Ga)Se2
(CIGS) are among the best performing thin-film solar cells with notable
recent improvements upon an alkali-fluoride (AlkF) post-deposition
treatment (PDT). Here we show that the success of this treatment
can be hampered by spatial inhomogeneities in the conductivity. We
apply an emerging conductive atomic force microscopy (C-AFM)
tomography technique and obtain three-dimensional conductivity
maps, enabling imaging of the carrier concentration grain by grain on
the submicrometre scale. We find that a solar cell with KF PDT shows a
stronger inhomogeneity of charge-carrier concentration, while RbF and
CsF lead to narrow distributions at higher charge-carrier concentrations.
The CIGS charge-carrier concentration and its homogeneity influence
directly the open-circuit voltage of solar cells, thereby impacting device
performance. Our insights support the development of higher efficiency
thin-film photovoltaics through optimized AlkF PDTs. Moreover, the C-AFM
tomography method is widely applicable to energy materials.
Photovoltaics (PVs) are widely considered a major component of a
carbon-neutral energy system, which is required to combat climate
change. Current research and development activities are directed
toward lowering the production cost of PVs, improving the performance and widening the possible application range (for example, by
building-integrated PVs). Thin-film solar cells employing polycrystalline absorber layers such as lead–halide perovskites, cadmium
telluride (CdTe) or copper-indium-gallium-diselenide (Cu(In,Ga)Se2,
(CIGS)) permit low-cost manufacturing at high throughput and have
reached record power conversion efficiencies well above 20% in the
past years1. To attain further improvements, substantial research
efforts are directed to understanding the physics of grain boundaries
in these polycrystalline semiconductors and to developing passivation mechanisms to minimize recombination losses at these abundant
structural defects2–11. In the case of CIGS, an alkali-fluoride (AlkF)
post-deposition treatment (PDT) is applied immediately following
the absorber deposition by evaporating alkali-fluoride in a selenium
atmosphere under vacuum12,13. This treatment leads to grain boundary
passivation9,10 and increases the carrier lifetime10,14, thereby reducing
non-radiative bulk recombination. Furthermore, the AlkF PDT also
leads to a higher p-type doping of the CIGS material by means of an
indirect ion-exchange mechanism15,16, where heavy alkali elements
(that is, K, Rb or Cs) diffuse into grain boundaries and displace lighter
Na atoms (typically diffusing from the glass substrate during absorber
deposition) into the adjacent grains17,18. During cool down, Na diffuses
to the surface leaving Cu vacancies behind, which increase the p-type
doping and consequently the open-circuit voltage (Voc) of the solar
cell device15. The preferential presence of heavy alkali elements at the
INL–International Iberian Nanotechnology Laboratory, Braga, Portugal. 2Werkstoffe der Elektrotechnik, Universität Duisburg-Essen, Duisburg, Germany.
Zentrum für Sonnenenergie- und Wasserstoff-Forschung Baden-Württemberg (ZSW), Stuttgart, Germany.
e-mail: Sascha.Sadewasser@inl.int
1
3
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grain boundaries has been directly verified by various imaging methods such as atom probe tomography, nano X-ray fluorescence and
transmission electron microscopy11,19–22. On the other hand, the indirect
doping mechanism has been deduced from macroscopic materials and
device characterization techniques15,16, which assess average values and
ignore possible variations on the scale of grains. A direct observation
of charge-carrier concentrations of individual grains at the nanoscale
has not been reported up to now and requires advanced characterization due to small, micrometre-scale grains and the abundant presence
of grain boundaries.
To understand the electronic properties of polycrystalline semiconductors, scanning probe microscopy methods such as Kelvin probe
force microscopy23 or conductive atomic force microscopy (C-AFM)24
are frequently used as they provide high spatial resolution down to the
nanometre scale. C-AFM images the current between a conductive AFM
tip and the sample, giving insights into the transport properties of the
studied materials. Typically, scanning probe microscopy methods,
including C-AFM, are applied at the surface of the sample under investigation. Very recently, C-AFM has been integrated with a tomography
technique, where the AFM tip is used to physically remove sample
material25, by using high tip forces in the range of several micronewtons in combination with hard, wear-resistant tips (for example,
diamond-coated tips), thereby leading to three-dimensional (3D)
current maps. In few available studies, C-AFM tomography has been
used to image current transport along grain boundaries and stacking
faults in CdTe solar cells26, in halide perovskite semiconductors27 and
along polymer nanowires used in organic electronic applications28.
However, a quantitative understanding of the observed 3D current
maps is still lacking.
Here we demonstrate C-AFM tomography on CIGS solar cell
absorbers exposed to different AlkF PDTs to provide a deeper
understanding of the beneficial effect of the PDT on solar cell performance. Furthermore, we present a quantitative analysis of the
acquired three-dimensional C-AFM current images, yielding maps
of the charge-carrier concentration grain by grain. We find a strongly
inhomogeneous charge-carrier concentration distribution for a
low-efficiency KF-treated CIGS. On the other hand, high-efficiency
RbF- and CsF-treated CIGS absorbers exhibit higher charge-carrier concentrations with narrow distributions. The charge-carrier concentration of the CIGS and its homogeneity have an impact on the open-circuit
voltage and thus the performance of the respective solar cells.
C-AFM tomography on AlkF PDT CIGS
A C-AFM tomography experiment on a CIGS sample without PDT
(non-PDT) is representatively shown in Fig. 1. The tip-induced material removal of the C-AFM tomography measurement mode results in
an increasing depth with increasing scan number (red arrow). For the
selected scans, the relevant information of topography as obtained
in an imaging scan with a larger area (20 × 20 μm2) and the respective C-AFM current map in the tomography area (10 × 10 μm2, taken
in the subsequent scan) are shown. The entire C-AFM tomography
experiment consisted of a total of 197 subsequent scans, reaching
an approximate final depth of 1.84 μm in the tomography area. Similar C-AFM tomography datasets were obtained repeatedly for the
non-PDT sample and several AlkF PDT samples with Alk = K, Rb and Cs
(Supplementary Figs. 1–4). The number of scans of each dataset
and the approximate final depth are summarized in Supplementary
Table 1. From the evolving depth of the tomography area obtained from
the larger imaging scans (Fig. 1a), the experimental removal rate (RR)
can be computed (Supplementary Fig. 5); RR was maintained constant
at about 9 nm per scan by slightly adjusting the applied force (5–6 μN)
during the scans, if required.
A 3D view of the C-AFM current volume (Fig. 2a) impressively
reveals the rich information that is provided by the C-AFM tomography
experiment (see also Supplementary Videos 1 and 2). Individual CIGS
Nature Energy | Volume 9 | February 2024 | 163–171
https://doi.org/10.1038/s41560-023-01420-7
grains show clearly distinct currents and can easily be followed into
the depth, providing a qualitative image of the crystallite structure
in the CIGS film. For each grain (and avoiding the grain boundaries),
a depth profile of the C-AFM current can be obtained (Fig. 2b). The
comparison of these C-AFM current depth profiles from several grains
reveals considerable variation from grain to grain. Nevertheless,
a general trend of increasing current deeper into the CIGS layer is
consistently observed.
Model for quantitative analysis of C-AFM current
To quantitatively understand the obtained depth-dependent C-AFM
current signals, we consider two contributions to the current:
Itotal = I + IO =
V
+ IO ,
R
(1)
where Itotal is a sum of contributions from the C-AFM current through
the CIGS sample (I) upon application of the voltage V and an offset current (IO) that is introduced to account for any offset originating from
the experimental set-up (for example, back contact, tip contact and
so on) and R is the CIGS sample resistance. It is important to note that
at the tip forces used in our experiments, the CIGS material under the
tip does not suffer any phase change (Supplementary Discussion 1),
ensuring that the current I can be fully assigned to the CIGS sample. The
resistance R is considered to depend on the effective sample thickness
at each scan, reflecting that during the C-AFM tomography experiment,
the continuous material removal leads to a continuously changing
sample thickness (D − d) for each obtained depth (d), where D is the
initial thickness of the CIGS sample (Fig. 3a). Thus, the depth-dependent
resistance R(d) can be expressed as:
R(d) =
ρ(D − d)
,
Ac,el
(2)
where Ac,el is the relevant electrical tip–sample contact area and
ρ = σ −1 = (epμ)−1 is the specific resistivity with σ the conductivity, e the
elemental charge, p the charge-carrier (hole) concentration in the
p-type semiconductor and μ the charge-carrier (hole) mobility. Thus,
the total current is:
Itotal =
σAc,el V
epμAc,el V
+ IO =
+ IO .
(D − d)
(D − d)
(3)
To estimate the tip–sample contact area (Fig. 3b), the theory
of contact between elastic bodies is used, which can consider
non-adhesive elastic contact (Hertz model29) and adhesive elastic
contacts (models of Johnson–Kendall–Roberts30 and Derjaguin–
Muller–Toporov (DMT)31). Here we follow the DMT model, which
was confirmed by Celano et al.25 to be suitable to describe the static
indentation of the AFM tip into the surface of the studied material.
The contact radius rc is then given by:
rc = [
2
2
1/3
1 − υsample
1 − υtip
3
× rtip × ((
) + (F + 4πγrtip ) × (
))]
4
Etip
Esample
,
(4)
where rtip is the radius of the tip apex, F is the tip force, γ is the work of
adhesion, Etip and Esample are the Young’s modulus of tip and sample,
respectively, and υtip and υsample are the Poisson ratios of tip and sample,
respectively. Table 1 summarizes typical values from the literature for
the respective material properties of the boron-doped diamond (BDD)
tip and the CIGS sample. No specific value for the work of adhesion γ is
available in the literature; therefore, we estimate γ = 0.75 J m−2, based
on the range of values for ionic solids (0.1–0.5 J m−2) and covalent solids
(1–3 J m−2)32 and the fact that CIGS is a covalent solid with a weak ionic
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Article
Scan 1
a
Scan 33
Scan 63
645
5.65
2 µm
–3.14
Current (nA)
2 µm
0
5.65
Current (nA)
Current
5.65
Current (nA)
–3.14
4 µm
0
5.65
Current (nA)
Current (nA)
2 µm
–3.14
4 µm
0
Depth (nm)
5.65
2 µm
4 µm
0
1,840
Depth (nm)
b
Depth (nm)
4 µm
0
Scan 197
1,340
933
Depth (nm)
4 µm
Scan 91
685
Depth (nm)
Topography
https://doi.org/10.1038/s41560-023-01420-7
2 µm
–3.14
–3.14
2
Fig. 1 | C-AFM tomography on non-PDT CIGS. a, Selected scans of the topography (20 × 20 μm ) at different stages of the tomography experiment (as indicated by the
scan number), showing the evolving hole milled with the AFM tip (darker square in the centre). b, Current maps inside the tomography area taken in the subsequent
scan (10 × 10 μm2).
a
b
2
1
3
5.65
Current (nA)
y
–3.14
4
C-AFM current (nA)
5
3
2
1
0
z
Grain 1
Grain 2
Grain 3
Grain 4
4
0
500
1,000
1,500
Depth (nm)
x
Fig. 2 | Analysing currents from C-AFM tomography on non-PDT CIGS.
a, Three-dimensional representation of the C-AFM current (10 × 10 × 1.8 μm3),
indicating the analysed area for the current depth profiles of 12 grains (in total, 15
grains were analysed; three of them are located in the triangular part that is cut
off in the image). Note that the shown surface corresponds to the current image
at a depth of 415 nm. b, C-AFM current depth profiles (symbols) for four selected
grains and fits (solid lines) with equation (3). Thin lines connecting the individual
data points serve as guides to the eye.
character. From geometrical considerations (Fig. 3b), the indentation
depth di can be expressed as25:
This overlap is accounted for by introducing a contact overlap coefficient α = 2 – Lp/(2rc) (Fig. 3d)25, which then leads to a removal rate of:
di =
rc 2
.
rtip
(5)
Both the di and the rc are given in Table 1, where also a range of values
is considered to account for the uncertainties and variations of the
parameters, namely: tip–sample force F = 5–6 μN, r tip = 100–200 nm
(ref. 33) and γ = 0.5–1 J m−2. Note that despite the mesoscopic tip
radius of 100–200 nm, the indentation depth di is only ~3 nm, leading to an effective rc of 21 nm. Thus, any nano-asperities at the tip
apex are irrelevant, as they will be in full electrical contact with
the sample.
When the indented tip is scanned, plastic deformation of the material occurs, which leads to the material removal25. Therefore, using the
determined indentation depth, the RR of the AFM tomography experiment can be estimated. Here the indentation depth describes the depth
of material removal of a single scan line. However, to obtain the removal
rate of a full scan, the line density needs to be considered (Fig. 3c). Our
typical C-AFM tomography scan is 8 × 8 μm2 to 10 × 10 μm2 with a line
density of 512 lines per scan, leading to a line separation of Lpiezo = 15.6–
19.5 nm per line. This is smaller than the contact diameter (Table 1),
leading to an overlap of the grooves where material is removed.
Nature Energy | Volume 9 | February 2024 | 163–171
RR = 2di α,
(6)
where the factor of 2 accounts for the forward and backward scan. In
the present case, α ≈ 1.54–1.63, which means that there is an overlap
of 50–60%. Table 1 also shows the estimated RR values from the DMT
analysis of our C-AFM tomography experiments. The estimated values
are in excellent agreement with the experimentally observed values
(Supplementary Fig. 5), substantiating that the presented model provides a good description of the C-AFM tomography experiment and
the tip contact radius.
Analysing C-AFM currents grain by grain
To analyse the depth-dependent current profiles according to equation
2
(3), we consider an electrically relevant contact area, Ac,el = π(4rc ) ,
which accounts for the spreading resistance effect of a point-like contact on a flat surface34. The initial thickness was determined for each
sample by X-ray fluorescence measurements (Supplementary Table
2). A fit to the data is performed with two free parameters, the conductivity σ and the current offset IO. Fifteen grains have been analysed for
the non-PDT CIGS sample (marked areas in Fig. 2a). The fact that the
C-AFM currents are constant across many of the grains confirms that
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https://doi.org/10.1038/s41560-023-01420-7
a
b
Resistance
A
D
C-AFM tip
Etip, νtip
F
d
D−d
V
CIGS
c
Trace
rc
Sample
Esample, νsample
Mo
Retrace
d
rtip
Trace
di
Retrace
rc
α
Lpiezo
Scan d
irectio
n
Lpiezo
AlkF PDT CIGS
Fig. 3 | Model for C-AFM tomography. a, Illustration of the depth-dependent
resistance and current throughout the C-AFM tomography experiment, with
the tip and cantilever shown at the sample surface in the beginning of the
tomography experiment and after removing a depth d of sample material
(outlined tip/cantilever). D is the total sample thickness. b, Illustration of the
tip–sample contact area during the C-AFM tomography experiment including
relevant parameters of the DMT model, as given in the text. The tip apex is
approximated by a sphere of radius rtip that pushes with force F onto the surface,
leading to the indentation di. c, Illustration related to estimating the material’s
RR from the di and tip–sample rc. The tip/cantilever scans from left to right (blue
and light blue) in the fast scan direction and from top to bottom (slow scan axis,
illustrated by arrow ‘scan direction’). Scan lines are separated by the piezo step
Lpiezo. Left: expanded illustration of the material removal by the tip. d, Expansion
of the dashed blue area in c, showing the overlap of the tip–sample contact area
from line to line as the tip scans in the slow scan direction (from darker to lighter
blue). The overlap is expressed by the parameter α, as introduced in equation (6)
in the text.
Table 1 | Minimum, maximum and typical values for
parameters used in quantitative analysis of C-AFM currents
analysed by our methodology; in some cases, grains are too small to
extract a reliable depth profile, grains are tilted into the depth of the
film (Supplementary Fig. 6) or grains are not continuous from top to
bottom, for example, in the case of a non-vertical grain boundary or
stacking fault within the grain (Supplementary Fig. 7).
The results of this analysis for individual grains reveal a clear
dependence of the conductivity and the homogeneity of its distribution on the alkali element used for the AlkF PDT (Fig. 4). Non-PDT CIGS
exhibits the lowest conductivity values (indicated by the darker bluish
and greenish colours) and a wider range of conductivities (indicated
by a larger variation of the colours). Following the series of alkali elements from lighter to heavier (K → Rb → Cs), the conductivity increases
(lighter colours) and becomes more homogeneous (less variation in
the colours). These qualitative observations are confirmed by a quantitative statistical analysis of the grain-by-grain conductivities (Fig. 5),
which clearly shows that the average of the conductivity of all analysed
grains increases for heavier alkali elements. From the analysis of the
depth-dependent current profiles averaged across the full tomography
area (Fig. 5b), similar conductivities are extracted (Table 2 and solid
spheres in Fig. 5a). The uncertainty in the fitted values (error bars) and
the variation as a result of the uncertainty in the tip–sample contact
area (up and down triangles) are in a similar range, supporting the high
reliability of the obtained conductivities.
Considering equation (3), also the charge-carrier concentration can be extracted for each individual grain, if the hole mobility is
assumed to be constant. Unfortunately, a reliable measurement of the
mobility is rather difficult for polycrystalline CIGS, where the presence
of grain boundaries can influence the results (especially for transport
Parameter
Typical
Minimum
Maximum
Etip (GPa), BDD
1,220
–
–
υtip, BDD47
0.2
–
–
Esample (GPa), CIGS48
72a
–
–
υsample, CIGS
0.4
–
–
rtip (nm)33
150
100
200
47
48
γ (J m )
0.75
0.5
1
rc (nm)
21.1
17.2
24.8
di (nm)
3.0
2.5
3.5
RR (nm)
9.6
8.3
11.0
−2 32
Values of the parameters used in equations (4)–(6) and the resulting minimum, typical and
maximum values for the extracted values of rc and di. aNote that this value is also in agreement
with a value determined for CIGS by nano-indentation experiments with an AFM49.
current flow proceeds mainly through the individual grains and is not
impacted notably by the grain boundaries, which typically show lower
current signals (meaning that they are less conductive). The fits give
a good description of the experimental C-AFM tomography currents
(Fig. 2b) for all grains. The same analysis was performed for the C-AFM
tomography experiments on the AlkF PDT CIGS samples (Supplementary Figs. 1–4; Supplementary Table 1 provides the number of analysed
grains of all samples). We note that not all grains can be properly
Nature Energy | Volume 9 | February 2024 | 163–171
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a Non-PDT CIGS
b KF PDT CIGS
c RbF PDT CIGS
d CsF PDT CIGS
Charge-carrier
concentration
–3
(cm )
5 × 10
Conductivity
–1
(S m )
17
320
2
10
17
10
1
10
16
10
15
1.9
3 × 10
Current (nA)
5.65
–8.14
Current (nA)
6.94
–7.41
Current (nA)
Conductivity (S m–1)
a
10
2
1
10
0
10
Charge-carrier concentration (cm–3)
Fig. 4 | Mapping conductivities and charge-carrier concentrations on AlkF
PDT CIGS. a–d, Conductivity of individual grains for CIGS samples with
non-PDT (a), KF PDT (b), RbF PDT (c) and CsF PDT (d). The non-PDT CIGS sample
shows lowest values and a wider distribution. For AlkF PDT, it is observed
that the heavier the alkali element, the higher the conductivity and the more
6.71
–7.71
Current (nA)
4.90
homogeneous its distribution. The variations can be attributed to a distribution
in charge-carrier concentration, when a constant mobility is assumed. Note that
not all grains could be analysed; see text for details. The background image is the
current image taken at a depth of 823 nm (a), 725 nm (b), 995 nm (c) and
400 nm (d). The image sizes are 10 × 10 μm2 (a) and 8 × 8 μm2 (b–d).
b
4
17
10
10
16
Individual grains
Total area average
minimum/maximum rc
/
C-AFM current (nA)
–3.14
Non-PDT
KF PDT
RbF PDT
2
Non-PDT
KF PDT
0
CsF PDT
–2
–4
15
10
RbF PDT
–6
CsF PDT
0
500
Sample
1,000
1,500
Depth (nm)
Fig. 5 | Statistical analysis of conductivity and charge-carrier concentrations.
a, Analysis per grain for the CIGS samples with different AlkF PDTs. The box plots
indicate a smaller variation of the conductivity/charge-carrier concentration for
heavier alkali elements. Both y axes apply to all data points shown. b, The solid
circles in a show the conductivity/charge-carrier concentration determined
by fitting (solid lines) the current depth profiles (data points) obtained from
the full C-AFM tomography area using equation (3). For the CsF PDT CIGS
sample, the initial decrease (first two data points) is disregarded (shaded area),
as it is interpreted as a wide-bandgap CsInSe2 surface phase (discussion in
the text). Triangles in a represent the range of conductivities/charge-carrier
concentrations for the minimum and maximum rc as shown in Table 1. The
box plot represents the second and third quartiles (25–75% of samples), the
horizontal line the median and the small open square the mean value. The
whiskers represent the minima and maxima with outliers outside 1.5× the
interquartile range. The error bars on the total-area averages indicate the fit
uncertainty. The sample size for the box plots in a is n = 15 for non-PDT, n = 13 for
KF PDT, n = 24 for RbF PDT and n = 25 for CsF PDT.
measurements). Additionally, the CIGS deposition method, the substrate and a potential PDT might impact the mobility value. In fact,
a wide variety of hole mobilities has been observed (Supplementary
Discussion 2 and Supplementary Table 3), ranging between 0.02 and
268 cm2 Vs−1. The hole mobility for single crystal and epitaxial samples is
typically higher (6–268 cm2 Vs−1) than that obtained on polycrystalline
films. Therefore, considering that our experiments assess the conductivity of individual grains, we use a constant hole mobility of 40 cm2 Vs−1
to estimate the charge-carrier concentration from our conductivity
values (Fig. 5a). Just as for the conductivity, also the charge-carrier
concentration increases from the non-PDT sample to the lighter (K)
and then heavier alkali elements (Rb and Cs), with decreasing variation.
The robustness of the fit results was further confirmed by reducing the
fit range (Supplementary Fig. 9). Note that the average charge-carrier
concentrations for the various AlkF PDTs observed from our analysis
compare well with those obtained by capacitance–voltage (C–V) measurements for relevant sister samples (Supplementary Table 2) and with
results reported in the literature (Supplementary Fig. 10)35–39. We would
Table 2 | Average conductivity σ and charge-carrier
concentration p for the four CIGS samples
Nature Energy | Volume 9 | February 2024 | 163–171
Sample
Non-PDT
σ (S m )
3.4 ± 1.4
14.4 ± 2.4
22.5 ± 3.9
185.6 ± 13.5
p (cm−3)
(5.3 ± 2.2) × 1015
(2.3 ± 0.4) × 1016
(3.5 ± 0.6) × 1016
(2.9 ± 0.2) × 1017
−1
KF PDT
RbF PDT
CsF PDT
Averages obtained by fitting equation (3) to the total-area-averaged experimental C-AFM
tomography currents (Fig. 5b). The ± error of the values corresponds to the uncertainty of the
fitting.
like to point out that the absolute values obtained for the charge-carrier
concentration depend directly on the assumed mobility value
(Supplementary Discussion 2 and Supplementary Table 4). Nevertheless, the variations from grain to grain and from sample to sample can
be considered quantitatively; this is supported by the fact that several
datasets on different samples were obtained with the same tip (that
is, the same tip was used for the experiments on the KF and RbF PDT
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a
b
Simulation:
Present study:
(Refs. 13,43)
15
10 cm
Simulated Voc (V)
Eg/q – Voc ( V)
0.45
0.80
–3
0.40
13
10 cm
–3
0.35
0.75
(Ref. 43)
(Ref. 43)
0.70
Reference samples
Ref. 42
Best Voc
0.65
15
10
10
16
17
10
(Ref. 44)
Non-PDT
Doping concentration NA (cm–3)
KF PDT
RbF PDT
CsF PDT
Sample
Fig. 6 | Impact on solar cell performance. a, Dependence of the open-circuit
voltage deficit (Eg/q − Voc) on the CIGS charge-carrier concentration. Small solid
symbols with purple lines represent the result of simulations with different deep
bulk defect concentrations (from 1013 to 1015 cm−3, indicated by purple arrow). The
solid symbols correspond to relevant sister samples of those studied here (black
square, non-PDT; green circle, KF PDT; red triangle up, RbF PDT; blue triangle
down, CsF PDT; Supplementary Table 2), where the error bar corresponds to
the uncertainty of the full area fit as shown in Table 2. b, Simulated open-circuit
voltage for the charge-carrier concentrations of individual grains of the four
AlkF PDT CIGS samples (small diamonds). The Voc values increase, but the spread
of the Voc values decreases with increasing heavy alkali weight. The solid black
circles are the Voc values of relevant sister samples, measured on full solar cells.
The open orange triangles and cyan squares show experimental values from
refs. 13,42–44 (the numbers at the cyan data points refer to the respective
reference). Error bars to the orange data points reflect the statistical variation
extracted from ref. 42. The box plots represent the second and third quartiles
(25–75% of samples), the horizontal line the median and the small open square
the mean value. The whiskers represent the minima and maxima with outliers
outside 1.5× the interquartile range. The sample size for the box plots is n = 15 for
non-PDT, n = 13 for KF PDT, n = 24 for RbF PDT and n = 25 for CsF PDT.
samples) and by obtaining similar results in experiments with different
tips on the same sample (Supplementary Fig. 11).
Note that the initial decrease of the current observed for the CsF
PDT CIGS sample is not considered for the fit, as it is attributed to a
surface phase. In fact, Lin et al. observed that excess Cs can lead to the
formation of a CsInSe2 layer of ~80 nm thickness on the CIGS surface40.
Such surface layer might additionally be affected by oxidation. Therefore, the initial steep change in the C-AFM current might be related to
the initial removal of a wide-bandgap, poorly conducting surface layer
until a depth of 70–80 nm is reached (grey shaded area in Fig. 5b). As the
above-described current model considers only the effect of a change in
the thickness of a homogeneous semiconductor, the data of the initial
80 nm were disregarded for the fitting.
We would like to point out that IO was fitted for each grain (Supplementary Fig. 12 shows the obtained IO values). The parameter IO reflects
contributions from the contact resistance of the back contact and the
tip–sample contact resistance, which depends on the electronic barrier between the boron-doped diamond tip and the individual grain
surface and its respective electron affinity. The independence of the
two fit parameters IO and p in equation (3) ensures that unique values
are obtained for the conductivities/charge-carrier concentrations
(Supplementary Fig. 12b).
the CIGS samples used in our study show a similar trend, except for
the CsF PDT sample (see discussion below). Furthermore, the SCAPS
simulations were used to evaluate the Voc of every analysed grain in the
four samples, as shown in Fig. 6b. Again, Voc values of the best devices
(retrieved from the literature13,42–44) show a similar trend, except for the
CsF PDT sample. We note here that the simulated Voc values based on our
charge-carrier concentrations should be considered as the maximum
achievable Voc for the p-type CIGS absorber material with the respective
PDT, which might additionally be subject to the influence of the carrier
lifetime10,14. In addition, the interface formation with the buffer layer
and n-type ZnO layers might detrimentally impact the Voc (nevertheless,
reasonable CIGS/buffer layer interface properties are already considered in the SCAPS simulations). The latter might explain the slightly
lower Voc for CsF PDT solar cells, possibly influenced by the interface
quality between the absorber, the highly resistive surface layer (possibly CsInSe2) and the buffer layer. Therefore, we hypothesize here that
the CIGS material after the CsF PDT might actually enable a higher Voc.
Relation to solar cell device performance
The performance improvement resulting from the heavy AlkF PDT on
the CIGS absorber is mostly driven by an increase of the open-circuit
voltage (Voc) of the respective solar cells. This increase can be attributed to reduced non-radiative bulk recombination in the CIGS layer,
facilitated by passivation of grain boundaries9,10 and increase in carrier
lifetime14. Additionally, higher p-type doping is generally reported15,16,
leading to a shift in Fermi level, enabling a larger quasi Fermi-level splitting. To analyse the impact of the changes in charge-carrier concentration extracted from our C-AFM current analysis on the solar cell
performance, we performed solar cell capacitance simulator (SCAPS)41
simulations, which confirm the increase in Voc (and consequently a
decrease in open-circuit voltage deficit, Eg/q – Voc) with increasing
p-type doping (Fig. 6a). The concentration of deep acceptor defects
leads to a slight variation in the (Eg/q – Voc) dependence (purple curves
in Fig. 6a), without affecting the general trend. Reference devices for
Nature Energy | Volume 9 | February 2024 | 163–171
Conclusion
Understanding spatial inhomogeneities in the electronic properties of
polycrystalline absorber materials is key in the quest to achieve better
performing solar cells. We applied careful slice-by-slice, nanoscale
C-AFM tomography experiments to obtain 3D current volumes on polycrystalline thin-film solar cell absorbers and developed a quantitative
analysis that enables extraction of the charge-carrier concentration
for individual grains. We applied this methodology to high-efficiency
CIGS material subject to different alkali-fluoride post-deposition treatments. We found that for samples with lighter alkali elements used
for the PDT, a wide distribution in charge-carrier concentrations is
observed for the grains of the polycrystalline films, while samples with
heavier alkali treatment show narrow distributions and high values of
charge-carrier concentration. Our results reveal that homogeneous
and high values of the charge-carrier concentrations of the CIGS grains
lead to an improved performance potential after the AlkF PDT process
with heavier alkali elements, confirming that a careful optimization
of both CIGS growth and AlkF PDT is required to achieve optimum
performance of respective CIGS solar cells.
The emerging C-AFM tomography technique in combination with
the here-developed quantitative analysis methodology presents an
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Article
invaluable tool for the characterization of semiconductor materials on
the submicrometre scale, enabling deep insights into the function, performance and limitations of a wide range of semiconductor materials
and devices. These insights are expected to guide future progress and
engineering for improved devices. Further studies providing a better
understanding of the electrical and mechanical tip–sample contact
(such as the impact of plastic deformation and cracking under the tip)
would probably improve the reliability of the quantitative analysis.
Future experiments under illumination and the combination with
carrier lifetime measurements could reveal additional insights.
Methods
Samples
CIGS solar cells were fabricated on alkali-aluminosilicate glass with a
sputtered molybdenum (Mo) back contact. The CIGS absorbers were
deposited by similar multi-stage processes with thickness in the range
of 2.6–2.9 μm by co-evaporation of the elements42. During the CIGS
deposition, sodium (Na) and partially potassium (K) diffuse from the
glass into the CIGS at elevated substrate temperatures (heater temperatures were above 650 °C). The integral GGI ([Ga]/([Ga]+[In])) of the
CIGS layers is around 0.3, the integral CGI ([Cu]/([Ga]+[In])) is around
0.9, resulting in bandgap energy values around 1.1 eV (extracted from
external quantum efficiency measurements). The CIGS layers exhibit
a slight double gradient in the GGI profile from top to bottom (Supplementary Fig. 13). The CIGS deposition is followed by an in situ AlkF PDT
(Alk = K, Rb, Cs) applied at elevated temperatures under Se atmosphere
in the same vacuum chamber. The samples with AlkF PDT used in this
study are the same samples used in ref. 9, and the CIGS deposition was
optimized for the RbF PDT. The KF, RbF and CsF PDTs were applied to
CIGS deposited in three consecutive and nominally identical processes.
After the PDT, the samples were annealed and rinsed. In addition, a
sample without any PDT from a later deposition campaign was used as
a reference. The details for all four samples presented in this study, or
relevant sister samples, are listed in Supplementary Table 2.
C-AFM tomography
C-AFM was performed in a Bruker Dimension Icon AFM operated in
ambient environment. We used conductive, highly boron-doped
diamond-coated tips (Nanosensors CDT-NCHR) with a nominal spring
constant of 80 N m−1 and a macroscopic tip radius of curvature of
100 to 200 nm (ref. 33). The wavelength of the AFM detection laser
is 670 nm and the diameter of the light spot on the backside of the
cantilever is 30 μm. Therefore, the laser light is essentially blocked
by the cantilever (width = 30 μm) and the measurements reflect dark
conditions.
A typical C-AFM tomography experiment starts by performing a
20 × 20 μm2 imaging scan using a tip force of 2 to 3 μN. A sample bias
of 8 mV is applied to ensure that the tip–sample current, measured
using the microscope’s Extended Tuna IV-converter with a sensitivity of
1 nA V−1, is in the range of ±5 nA. Subsequently, the C-AFM tomography
area (8 × 8 μm2 or 10 × 10 μm2) is selected and the tip force is increased
to 5 to 6 μN. The high tip force and the mechanically hard diamond
coating lead to a tip-induced material removal as the tip scans across
the scan area. By repeatedly scanning the same area, the sample material is continuously removed and the tip digs deeper and deeper into
the sample. Thus, the surface of the tomography area is continuously
‘refreshed’ by the material’s removal. Furthermore, the tip–sample
current is measured simultaneously at the tip–sample contact, which
has not been exposed to air; thus, the tip is in contact with the bulk
material, and surface oxidation can be excluded. It is one of the essential advantages of the C-AFM tomography method that the bulk of the
material is measured and that surface effects only affect the first few
scans. Every 10–30 scans, a larger imaging scan is acquired at low tip
force, from which the depth of the tomography area is determined
(Supplementary Fig. 5). Dividing the depth by the number of scans,
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https://doi.org/10.1038/s41560-023-01420-7
the RR can be determined (Supplementary Fig. 5). Throughout the
experiments, RR was kept in the range 4–14 nm per scan) by slightly
adjusting the applied force (5–6 μN) during the scans, if required
(Supplementary Fig. 5). Only in the initial part of the C-AFM tomography experiment on the RbF PDT sample, a larger RR = 14 nm per scan
was obtained, which was corrected to RR = 9 nm per scan after 39 scans.
The acquisition of a complete 3D C-AFM tomography experiment
typically requires 24–48 hours.
Device simulations
Solar cell device simulations were performed using SCAPS41. Most
parameters for the simulation were selected based on a model for the
samples used in this study prepared at the Zentrum für Sonnenenergieund Wasserstoff-Forschung Baden-Württemberg (ZSW)45. Other
parameters were taken from ref. 46. These parameters are displayed
in Supplementary Table 5. The shallow acceptor density was varied
between 1015 and 1018 cm−3 and the density of the deep bulk defect 2
between 1013 and 1015 cm−3. The results of these variations are shown by
the multitude of purple lines in Fig. 6a. To convert the charge-carrier
concentrations obtained for all analysed grains into the respective Voc,
the simulated open-circuit voltage dependence for a defect density of
1014 cm−3 was extrapolated, leading to the distributions of Voc values
shown in Fig. 6b.
Reporting summary
Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.
Data availability
Source data are provided with this paper. All other datasets generated
and analysed in the present study are available from the corresponding
author upon reasonable request.
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Acknowledgements
The CIGS samples for this work were prepared as part of the project
Sharc25, funded through the European Union’s Horizon 2020 Research
and Innovation programme under grant agreement number 641004
(N.N., P.J., W.W., D.H., S.S.). E. Bertin is acknowledged for support in
the initial phases of the development of the C-AFM technique on CIGS
samples. We thank I. Khatri, D. Colombara and G. Bacher for helpful
discussions.
Author contributions
S.S. and N.N. conceived the study. D.S., N.N. and S.S. developed the
experimental methodology and data analysis. D.S. performed the
experiments. D.S., N.N. and S.S. performed the data analysis. P.J., W.W.
and D.H. prepared the samples. D.S. and S.S. wrote the paper.
All authors discussed the results and revised the paper.
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Competing interests
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The authors declare no competing interests.
Supplementary information The online version
contains supplementary material available at
https://doi.org/10.1038/s41560-023-01420-7.
Correspondence and requests for materials should be addressed
to Sascha Sadewasser.
Peer review information Nature Energy thanks Bryan Huey and the
other, anonymous, reviewer(s) for their contribution to the peer review
of this work.
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