Revisiting the Valence and Conduction Band Size Dependence of

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Revisiting the Valence and Conduction Band Size Dependence of PbS Quantum Dot Thin Films Elisa M. Miller, Daniel M. Kroupa, Jianbing Zhang, Philip Schulz, Ashley R Marshall, Antoine Kahn, Stephan Lany, Joseph M. Luther, Matthew C. Beard, Craig L Perkins, and Jao van de Lagemaat ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.5b06833 • Publication Date (Web): 19 Feb 2016 Downloaded from http://pubs.acs.org on February 21, 2016

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TOC Figure

Revisiting the Valence and Conduction Band Size Dependence of PbS Quantum Dot Thin Films Elisa M. Miller,1> Daniel M. Kroupa,1,2> Jianbing Zhang,1^ Philip Schulz,3* Ashley R. Marshall,1, 2 Antoine Kahn,3 Stephan Lany,1 Joseph M. Luther,1 Matthew C. Beard,1 Craig L. Perkins,1 and Jao van de Lagemaat1# 1

Chemical and Materials Sciences Center, National Renewable Energy Laboratory, Golden, CO 80401, USA 2

3

Department of Chemistry and Biochemistry, University of Colorado, Boulder, CO 80309, USA Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA

#

Corresponding author: [email protected]

^ Current address: School of Optical and Electronic Information, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan, China *Current address: Chemical and Materials Sciences Center, National Renewable Energy Laboratory, Golden, CO 80401, USA >

Equally contributing authors

ABSTRACT: We use a high signal-to-noise X-ray photoelectron spectrum of bulk PbS, GW calculations, and a model assuming parabolic bands to unravel the various X-ray and ultraviolet photoelectron spectral features of bulk PbS as well as determine how to best analyze the valence band region of PbS quantum dot (QD) films. X-ray and ultraviolet photoelectron spectroscopy (XPS and UPS) are commonly used to probe the difference between the Fermi level and valence band maximum (VBM) for crystalline and thin-film semiconductors. However, we find that when the standard XPS/UPS analysis is used for PbS, the results are often unrealistic due to the low density of states at the VBM. Instead, a parabolic band model is used to determine the VBM for the PbS QD films, which is based off of the bulk PbS experimental spectrum and bulk GW calculations. Our analysis highlights the breakdown of the Brillioun zone representation of the

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band diagram for large bandgap, highly quantum confined PbS QDs. We have also determined that in 1,2-ethanedithiol-treated PbS QD films that the Fermi level position is dependent on the QD size; specifically, the smallest bandgap QD films have the Fermi level near the conduction band minimum and the Fermi level moves away from the conduction band for larger bandgap PbS QD films. This change in the Fermi level within the QD bandgap could be due to changes in the Pb:S ratio. In addition, we use inverse photoelectron spectroscopy (IPES) to measure the conduction band region, which has similar challenges in the analysis of PbS QD films due to a low density of states near the conduction band minimum. KEY WORDS: PbS quantum dot films, valence band maximum, photoelectron spectroscopy, energy alignment Characterizing the properties of quantum confined semiconductor nanocrystals is an active area of research due to the ability to control various optoelectronic properties through the manipulation of nanocrystal size, shape, surface chemistry, and composition. Spherical (or 3-D confined) semiconductor nanocrystals are referred to as QDs. Thin films fabricated from QDs retain many of the properties of isolated QDs while gaining advantages typically associated with films (longer range interactions, electronic coupling, increased dielectric screening, etc.). Thus, QD films have unique properties that can be controlled via their synthesis and film fabrication methods.1, 2 Of particular interest for optoelectronic applications is the ability to tune the bandgap and enhance multiple exciton generation.3-5 In addition to these well studied phenomena, QD films also afford the possibility of tuning redox potentials through quantum confinement and surface chemistry.6, 7 As a result, QD thin films are being explored as functional, solutionprocessed films for various applications such as transistors, solar cells, light-emitting diodes (LEDs), water splitting, and photodetectors.8-12 Given their tunable properties, it is essential to quantify and understand how the energetics of QD films are modified depending on their process conditions, different electronic environments, QD-synthesis, size, shape, etc., so as to rationally control their properties and fully utilize their potential. Due to quantum confinement, lead chalcogenide QDs have a highly tunable optical bandgap !"#

(𝐸! ) across the infrared and visible regions of the electromagnetic spectrum depending on their size and shape.13 Quantum confinement is retained even when such particles are coupled in films using short linker molecules, allowing the QDs to preserve their excitonic character and become highly conductive.14-16 In these cases, the states making up the VBM and the conduction band


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minimum (CBM) consist of quantum mechanically coupled first hole and electron levels of individual QDs.17-19 Many approaches for preparing conductive QD films involve exchanging insulating, alkyl ligands that coat the surface of the QDs with shorter, more conductive ligands. Both p- and n-type conductive films can be prepared; the energy levels can be shifted due to ligand-induced surface dipoles and/or other surface chemistries.7, 20-22 Moreover, surface chemistry has been critical in impacting midgap states, blinking/charge trapping, and transport within PbS(e) QD films.16, 23-25 Since knowledge of the precise energetic position of the hole and electron transport levels in QD films is an essential element in the design of energy conversion device architectures, it is necessary to understand how the valence and conduction band (VB and CB, respectively) positions of QD films can be tailored for specific applications. XPS and UPS are regarded as the ‘gold standard’ for determining the filled state energies of bulk semiconductors and these techniques have also been applied to QD films.7, 9, 20, 26-28 In a typical photoelectron spectrum, the onset of photoelectron intensity closest to the Fermi energy generally corresponds to the photoemission of electrons from the VBM or highest occupied state. The position of the VBM is reported with respect to the Fermi energy (EF – EVBM) or to the vacuum level (i.e., the ionization energy, IE). The CBM energy (EF – ECBM) is then indirectly determined by subtracting the optical bandgap and the exciton binding energy from EF – EVBM. In previous photoelectron spectroscopy reports, the analysis was performed in this way for PbS and PbSe QD films, and it was concluded that EF – EVBM and IE do not have a strong dependence on the QD size.7, 26, 27 These results are in disagreement with other techniques such as scanning tunneling spectroscopy (STS) and electric-double-layer-gated transistors combined with advanced ab-initio theory, as well as the effective mass approximation, which conclude that both the EVBM (IE) and ECBM (electron affinity) have a strong dependence on QD size.6, 17, 18, 29-31 In this paper, we show that the XPS/UPS spectra of PbS QD films (and bulk PbS) cannot be analyzed in the standard way for small bandgap PbS QDs because of a low density of states (DOS) near the VBM. Instead, an alternative approach is proposed to analyze the spectra of QD films where the experimental spectral features are fit to a parabolic model. The model is based off of parameters determined from the bulk PbS XPS spectrum. This is motivated by 1) the unrealistic band positions that result from the standard analysis of small bandgap PbS QD spectra and 2) GW calculations are needed to determine the bulk PbS EF – EVBM energy. Therefore, we use this parabolic model to analyze a broad range of PbS QD thin films, where the native ligand has been exchanged with 1,2-ethanedithiol (EDT). The VB region is measured with both UPS


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and XPS, and we also use IPES to analyze unoccupied (i.e., conduction band) states. Similar challenges arise when extracting the EF – ECBM from IPES spectra in that the DOS intensity at the CBM is low and not directly observed. Results A. Absorption Results of PbS QDs and QD Films The XPS/UPS and IPES measurements are performed on films of PbS QDs with diameters ranging from 1.5 nm to 9.0 nm (see Methods section for synthetic details). The QD size is determined from the energy of the first exciton peak in solution absorption measurements and compared to standard sizing curves.32, 33 The conductive QD films are fabricated using a layerby-layer (LbL), dip coating method to exchange native oleate ligands with EDT. These films have not been exposed to ambient air unless specified. Figure 1a displays the absorption spectra of the PbS QDs used for this study. The spectra are normalized at the first exciton peak. The dashed lines represent the spectra of the QDs dispersed in tetrachloroethylene (TCE), while the solid lines correspond to the QD thin film absorption spectra. Note that the QD films were briefly exposed to air (see Methods section for more detail). The first exciton peak is red shifted and broadened in the films relative to the solution measurements. Figure 1b highlights the relationship between the red shift and the QD size. This red shift and slight broadening is expected because the QDs become more coupled as the oleate ligand is exchanged by the shorter EDT ligand, allowing the QD-QD distance to decrease from approximately 2.5 nm to 1.6 nm.34, 35 The first exciton peak of the largest bandgap QD films (𝐸! = 2.45 and 2.50 eV) is not as clearly defined as the other QD sizes. This is likely a result of these large bandgap QDs being in the highly quantum confined regime (portion of the QD sizing curve with the steepest slope) where any slight deviation in QD size within the ensemble would cause a drastic change in the FWHM of the first exciton peak.32 The PbS bandgap (𝐸! ) is defined as the first exciton peak of QD films !"#

(𝐸! ) plus the QD size-dependent exciton binding energy (XBE, which is calculated from Ref. 7, !"#

26 using the solution absorption measurements): 𝐸! = 𝐸!

+ XBE (reported in units of eV). Eg

values for the various QD sizes studied are tabulated in Table 1.


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Figure 1. a) Absorption spectra of different sizes of PbS QDs. In solution (dotted traces), the PbS QDs are capped with oleate. In QD thin films (solid traces), the QDs are ligand exchanged with EDT. b) The relationship between the red-shifted 1st exciton peak in thin films versus solution for various sizes of PbS QDs capped with EDT and oleate, respectively, is shown. The linear fit is also shown.

B. XPS/UPS Results of PbS As mentioned earlier, XPS and UPS are typically used to probe the VB density of states, XPS and UPS energy onset (regularly identified as the VBM) relative to the Fermi energy, atomic core levels, work function (Φ), and IE of the film. In this report, focus is placed on the VB region of the XPS/UPS spectra (XPS VB or UPS VB regions). Note that, for a given sample, the XPS and UPS VB onset values do not differ within the experimental uncertainties of these measurements; therefore, XPS and UPS results are not separated. Figure 2a shows the XPS VB spectra for EDTtreated PbS QD films of varying bandgaps deposited on Au substrates, as well as the spectrum taken from bulk PbS (a natural galena sample that was cleaved in a glovebox filled with nitrogen). The latter spectrum has two prominent peaks centered at 1.5 eV and 3.0 eV below EF (EF = 0 eV), which are consistent with literature reports for bulk PbS and attributed to emission from the S 3p level.36-38 As the PbS QDs become more confined, one would expect to observe a change in the VB density of states. As can be seen in Fig. 2a, the smallest bandgap PbS QD film (𝐸! = 0.66 eV) still retains the 1.5 eV peak; however, it becomes less prominent as the PbS QD bandgap increases and the spectral shape changes. From the UPS/XPS of PbS QD films and bulk PbS, we should also be able to measure the EF – EVBM as a function of quantum confinement.


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Figure 2. a) XPS spectra of various sizes of PbS QD films exchanged with EDT, which are identified by their respective bandgap. For reference, the XPS VB spectrum of single-crystal PbS (cleaved galena) is plotted in black. b) Summary of XPS/UPS VB EF – Eonset (red squares) and EF – EVBM (green circles) values as a function of the PbS bandgap. The x-axis error bars are the corresponding standard deviations calculated using a fit of the first exciton absorbance peak of the QD solution to a Gaussian line shape, and the y-axis error bars are the XPS energy uncertainty. The line between the blue and purple regions corresponds to EF – EVBM = ½Eg (e.g., Fermi level directly between the CBM and VBM). The line between the purple and tan shaded regions corresponds to EF – EVBM = Eg. A value equal to or greater than Eg means that the Fermi level is at or above the CBM, and the film is degenerately n-type. Table 1. Energies (in eV) for a variety of PbS QD sizes and bulk PbS measured via XPS/UPS or IPES. The XPS and UPS VB onset (EF – Eonset) values have uncertainties of +/- 0.05 and +/- 0.025 eV, respectively, and the IPES CB onset values have uncertainties of +/- 0.15 eV. Also included are the results from kp theory for the L – Σ difference and corrections from the parabolic DOS model. QD diameter, nm

Eg

EF -‐ Eonset

L -‐ Σ difference

EF -‐ EVBM from model

EF -‐ EVBM from correction

EF -‐ ECBM from correction

IPES CBonset

Bulk

0.37

0.56

0.40#

0.25^

0.25^

-‐0.12^

-‐

9.1

0.66

0.71

0.36

0.47

0.48

-‐0.18

-‐

9.1*

0.66

0.6

0.36

-‐

0.37

-‐0.29

-‐0.62

8.5

0.66

0.67

0.36

0.46

0.44

-‐0.22

-‐

6.0*

0.82

0.97

0.32

-‐

0.77

-‐0.05

-‐0.4

4.7

0.97

0.9

0.29

0.73

0.74

-‐0.23

-‐

4.5*

0.99

1.00

0.28

-‐

0.84

-‐0.15

-‐0.49

2.9*

1.43

0.86

0.17

-‐

0.80

-‐0.63

-‐0.58

2.9

1.45

0.85

0.17

0.8

0.80

-‐0.65

-‐

2.9

1.45

0.81

0.17

0.75

0.76

-‐0.69

-‐

2.9

1.45

0.71

0.17

0.69

0.66

-‐0.79

-‐

2.9

1.45

0.83

0.17

0.78

0.78

-‐0.67

-‐

2.8

1.48

0.89

0.15

0.84

0.84

-‐0.64

-‐

2.7

1.56

0.95

0.14

0.89

0.92

-‐0.64

-‐

+

+

-‐

+

-‐

1.7 1.5

2.24 2.50

0.98 1.00

-‐ -‐

-‐ -‐

0.98 +

1.00


-‐1.26 -‐1.50

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*Measurements with UPS and IPES only ^VBM value used from fitting shown in Fig. 3 + Value from standard analysis, see text for more detail # Ref 39, 40 To determine the EVBM position, the rise in intensity is often fit to a line, where the point that intersects the baseline is determined and usually assigned as the EF – EVBM value. The results for this standard analysis for the different QD films and bulk PbS are shown in Fig. 2b (red squares) and Table 1; however, given the magnitude of the values, we do not assign them as EF – EVBM but as EF – Eonset. Note that the y-axis error bars in Fig. 2b are determined by the XPS energy uncertainty and the x-axis error bars represent the corresponding standard deviation of a fit of the QD solution first exciton absorbance peak to a Gaussian line shape. The shaded regions in Fig 2b represent different Fermi level positions. When the EF – EVBM value falls within the blue (purple) region, the Fermi level lies closer to the EVBM (ECBM). If the Fermi level is between the VBM and CBM, then the EF – EVBM value resides on the EF – EVBM = ½Eg line. If the Fermi level of a film is at or above the CBM (degenerately n-type), then the EF – EVBM value would fall on the EF – EVBM = Eg line or in the tan region. For a degenerately n-type film, we would expect to detect intensity in

the photoelectron spectrum at 0 eV, similar to a metal. However, we do not observe any spectral features at 0 eV for the films studied (Fig. 2a); furthermore, we have not found any indication from other experimental techniques that these films are degenerately n-type. Therefore, we conclude that the Eonset does not equal the EVBM, except for the largest bandgap PbS QD films (which will be explained below). Instead, additional analyses must be applied to determine the EF – EVBM for the smaller bandgap PbS films. Additional measurements, not shown, were conducted to check for spurious effects such as charging and photovoltages. To check for possible contributions from the substrate, such as a Schottky contact between Au and the PbS QDs, we measured X-ray excited secondary electron cut-offs with widely varying excitation intensities: ambient light from the experimental setup (white light, UHV windows uncovered, ion gauges on, and 350 W X-ray power) and ambient light minimized (lights off, UHV windows covered, ion gauges off, and 25 W X-ray power). Irradiation of a Schottky junction during the XPS experiments could cause a source-induced photovoltage to be present, violating the tacit assumption that the Fermi levels of the spectrometer and that of the sample surface are equilibrated.41 Also, the measurements were repeated on various substrates, such as Pt and MoOx, as well as for varying QD film thicknesses (10’s to 100’s nm thick). No significant dependence of the secondary electron cut-offs on the


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choice of substrates or illumination intensity was observed. Thus, we concluded that neither photovoltage nor band bending in the QD layer significantly influenced our measured band edge positions. C. XPS Analysis of Bulk PbS The XPS spectrum of bulk PbS reveals that Eonset lies as much as 0.6 eV below the Fermi energy, an energy difference considerably larger than the PbS bulk bandgap of ~0.4 eV.42 Thus, the inconsistency between Eonset and realistic bounds for EVBM of a known semiconductor motivated us to better understand the X-ray excited VB spectrum of bulk PbS. To this end, we first compare the measured spectral shape with the DOS obtained from ab initio band-structure calculations. For this analysis, the results of GW calculations from the NREL Materials Database (see also methods section below) are used.43 Excluding spin-orbit coupling (SOC), the GW bandgap is 0.78 eV. The effect of SOC is estimated from a separate calculation using standard density functional theory, showing that the Pb-p/S-s like CBM is lowered by 0.41 eV, while the Pb-s/S-p like VBM remains practically unchanged. Thus, the GW+SOC bandgap is found to be 0.37 eV, which is in good agreement with previous GW calculations by Svane et al.44 Figure 3 compares the calculated DOS with the experimental XPS spectrum. We note that the dwell time/data point for this experimental spectrum was extremely long, 254 s. This was in order to increase the signal-to-noise ratio of the measurement in hopes of detecting the VBM. Overall, there is good agreement between the calculated DOS structure and the XPS spectral features. In order to align the energy scales, we broaden the DOS with a ~350 meV FWHM Gaussian line shape, which is the instrument response of the spectrometer. Because the DOS calculation does not account for the XPS cross-section, we only fit the broadened DOS to the rising edge (Electron Binding Energy = 0 − 1 eV) of the experimental spectrum. From this procedure, similar to that used by Kraut et al. and Chambers et al., 45, 46 45, 46 45, 46 we determine EF − EVBM = 0.25 eV +/− 0.05 eV.44, 45 See methods section for determining the instrument response and energy uncertainty. Indirectly, this places the CBM at EF − ECBM = -0.12 eV. The large difference between EF − Eonset and EF − EVBM results from the fact that the (unbroadened) DOS has a tail with low intensity that extends several tenths of an eV beyond the rising edge. In fact, at energies close to the VBM, i.e., Electron Binding Energies = 0.25 – 0.45 eV, the VB DOS remains below 1% of the maximum DOS peak intensity. These observations encourage us to analyze the low signal-intensity region of the bulk PbS spectrum. However, when we do this, there is no clear


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feature that is due to the VBM. Therefore, we do not use the low signal-intensity region to determine the VBM but instead rely on the DOS fitting procedure described above.

Figure 3. Comparison of the XPS of bulk PbS experimental data with the GW calculated DOS. The DOS spectrum is shifted by 0.25 eV to overlap with the XPS spectral features. The broadened GW DOS is fit to the leading edge of the experimental data to determine the VBM value, EF – EVBM = 0.25 +/- 0.05 eV.

We also use our GW calculations to unravel the contributions of the PbS VB region critical points to the XPS spectral features. Figure 4 shows the GW calculated band diagram of bulk PbS along with the corresponding DOS. We observe that the strong increase of the VB DOS at about 0.5 eV below the VBM originates mostly from the Σ point, whereas the L point only contributes a relatively low DOS close to the VBM. Thus, the prominent shoulder (Fig. 3 – Electron Binding Energies = 0.5 – 1.0 eV) in the bulk PbS XPS spectrum should be associated with the Σ point energies rather than the VBM. Instead, the L-point energies give rise to the low intensity tail of the XPS spectrum (Fig. 3 – Electron Binding Energies = 0.25 – 0.45 eV). This analysis further supports our argument that the standard analysis of the XPS VB region does not extract the correct EF – EVBM of bulk PbS. Note further that the high intensity spectral features at binding energies between 2 and 4 eV below the VBM (Fig. 3 and 4) are caused by less dispersive VBs, particularly around the Γ point. As PbS becomes quantum confined, different parts of the band diagram (and associated DOS) will be affected differently. This understanding will be key to interpreting the PbS QD film spectra and will be discussed below.


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Figure 4. The GW band structure of bulk PbS and the corresponding total and atomic site projected DOS. The band energies are given with respect to the VBM. The initial rise of the VB DOS originates primarily from the Σ point and not from the VBM at the L point.

A simple DOS model is used to fit the PbS bulk XPS spectrum and obtain fit parameters, which are used to model the PbS QD film spectra. The DOS model assumes a parabolic shape using the effective mass approximation for the L point (upper VBM) and Σ point (lower VBM), which is ∝ 2𝑚!∗

!

!

𝐸 − 𝐸!"#

!

!.

In the model, 𝑚!∗ is the effective mass at the L point (0.10) or

Σ point (0.45, estimated from the PbSe Σ value)47, 48 and 𝐸!"# is the energy of the L or Σ point maximum with respect to the Fermi energy. For this model, we pin the L point to 0.25 eV and use a value of 0.65 eV for the Σ point (L – Σ difference is 0.40 eV).39, 40 The DOS for both the L and Σ points are convoluted with a ~350 meV FWHM Gaussian, which is the instrument response of the spectrometer. Because we do not know the exact 𝑚!∗ for the Σ point or the shape of the Σ DOS (Σ is a saddle point), a ratio parameter between the L and Σ DOS is included, which comes out to be 2.5 in the PbS bulk modeling. The DOS model is a first approximation of the bulk spectrum (Fig. S1). Therefore, this model is applied to the PbS QD film spectra as a first approximation to determine the VBM position. See SI for more details. D. XPS Analysis of PbS QD Films Before the DOS model can be applied to the PbS QD XPS spectra, the QD size-dependent L – Σ difference must be determined. This splitting between the L and Σ VBM energy levels can be approximated using kp theory as described by Kang and Wise where the parameters used are detailed in the Methods section.48 Similar to previous reports,29, 49 we apply a constant correction factor to the QD diameter in the calculations to better model the physical boundary conditions of the QD core. In this way, we relax the infinite potential boundary conditions imposed by the k•p calculations and allow the QD electron and hole wavefunctions to delocalize into the ligand shell/surrounding environment. We find good agreement between the derived kp L and Σ transitions with their respective experimental size-dependent optical transitions (Fig. 5a), which gives us confidence that the k•p theory results are reasonable for QD sizes in the range of 2.5 – 10 nm (Eg = 1.6 – 0.6 eV). The calculated k•p L point VBM and Σ point VBM (Fig. 5b, red and blue traces, respectively) are offset at a QD diameter of 22 nm (outside of the quantum confined regime for PbS, which has a Bohr radius of 18 nm) to match the reported L – Σ difference for bulk PbS (0.4 eV). 39, 40 Then, the QD size-dependent L – Σ difference can be determined (Fig 5b.


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black trace and Table 1). It is known that kp theory breaks down for strongly quantum confined QDs;48 furthermore, the L and Σ points (and ultimately the Brillouin zone description) are not good descriptors of the band diagram at larger bandgaps (Eg > 1.9 eV, diameters < 2 nm). Therefore, we argue that for our two largest bandgap samples (Eg = 2.24 and 2.50 eV), Eonset equals EVBM.

Figure 5. The kp theory calculations of PbS QDs at the L and Σ points for different QD diameters. a) The L point (red line) and Σ point (blue line) kp transition energies agree nicely with experimental values from absorption data (markers) taken by our group at NREL and Geiregat et al.50 b) The kp energy levels for the L point VBM (red) and Σ point VBM (blue) are offset by 0.4 eV at a QD diameter of 22 nm, which is in line with experimental data of bulk PbS. 39, 40 The QD size-dependent L – Σ difference used in the DOS model is displayed in black.

To determine EF – EVBM of the PbS QD films, we apply the DOS model to the XPS VB spectra. This model is parameterized using the kp derived L – Σ differences, the DOS ratio determined from the bulk model (2.5), and the FWHM from the instrument response of the spectrometer (350 meV). See Fig. S1 for more details. The results from the DOS model are tabulated in Table 1 under the header “EF – EVBM from model”. We only apply this model to the XPS spectra of PbS QD films because the DOS model is parameterized by XPS and not UPS, which has a different photoemission cross section. A correction to all of the spectra can be generalized and applied to the UPS spectra. To do this, the differences between the “EF – Eonset” and “EF – EVBM from model” vs Eg are plotted and follow a linear trend: correction = 0.382 - 0.226Eg. Figure S2 shows the correction fit, which highlights the robustness and validity of this correction. The largest correction will occur for the spectra of small bandgap PbS films where the calculated L – Σ difference is greatest. We use this correction formula at each QD bandgap to convert the EF –


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Eonset to EF – EVBM. The corrected EF – EVBM values are listed in Table 1 as “EF – EVBM from correction” and are plotted in Fig. 2b as the green circles. The EF – EVBM from correction values are then used to determine the EF – ECBM, which are listed in Table 1 as “EF – ECBM from correction”. In general, this correction can be applied to the standard EF – Eonset value of any PbS QD film for bandgaps smaller than 1.9 eV. The low-DOS tail occurs only in small bandgap PbS QDs and is most strongly pronounced in the bulk PbS film. For large bandgap, highly quantum confined QDs, the low-DOS tail vanishes where the L – Σ difference is essentially zero, and the conventional XPS analysis yields the correct EF – EVBM value. Therefore, the correction for the largest bandgap PbS QD films is 0 eV. For clarification, let us briefly discuss the origin of this behavior. The large dispersion and low effective mass of the VB around the L point arises from the delocalized nature of the topmost Pbs/S-p VB. Note that the localization in k-space around the L point implies delocalization in real space. Hence, light effective mass bands will generally be more affected by quantum confinement than heavy mass bands. Thus, decreasing QD size will effectively reduce the dispersion of the L-derived VB so that for larger bandgap PbS QDs this L-derived band no longer forms a tail. For bands with larger effective masses, such as the Σ band, this quantum confinement-induced effect is less pronounced. This effect is illustrated by our kp calculations that show the energy at the L point decreasing faster than that at the Σ point with decreasing QD diameter (Fig. 5b). Thus, for large bandgap QDs, the VBM is formed by states derived from the flat, high mass bulk bands, and the extrapolation of the DOS will consequently coincide with the VBM. E. IPES Results of PbS QD Films To further probe the band energetics of PbS QD films, IPES is used to probe the unoccupied electronic states (CB states) for a subset of the QD sizes and compared with UPS (Fig. 6 and Table 1). The first observation to note from Fig. 6 is that the energy difference between the UPS and IPES onsets does not agree with the 𝐸! for all QD films. For example, the 𝐸! = 0.99 eV PbS QD thin film has a UPS to IPES onset difference of 1.49 eV. The 0.5 eV discrepancy exceeds the uncertainty of our measurements and supports our previous argument that an alternative analysis is needed. Similar to the UPS VB spectra, it is likely that this discrepancy is due to very low DOS at the CBM. Indeed, the calculated DOS (Fig. 3) shows that the onset of intensity near the CBM is very gentle - similar to what was observed for the VBM. Therefore, we suggest that a


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similar correction is needed for the IPES CBonset values for the smaller bandgap QD films, which will be a focus of future studies.

Figure 6. UPS (thin traces) and IPES (bold traces) band onsets for films of PbS QDs with four different sizes.

Discussion The “EF – EVBM from correction” values (solid green circles) and the corresponding “EF – ECBM from correction” values (open green circles) are shown in Fig. 7 along with the measured Pb:S ratio for the QD films (black crosses). The experimentally derived QD band energies highlight that the Fermi level with respect to the VBM/CBM changes with QD size. The smaller bandgap QD films have the Fermi level closer to the CBM, and the larger bandgap QD films have the Fermi level near the middle of the bandgap. A compelling reason for the observed Fermi level shift in the QD samples is that the Pb:S ratio changes as a function of QD bandgap (black crosses in Fig. 7). According to calculations by Kim et al., the transport characteristics of PbS QDs become more n- or p-type (Fermi level closer to CBM or VBM, respectively) by increasing the amount of Pb or S, respectively.51 Additionally, Oh et al. found that by manipulating the Pb:chalcogen stoichiometric ratio of PbSe and PbS QD films through post synthetic colloidal


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atomic layer deposition (PC-cALD), they were able to control the carrier type, concentration, and Fermi level of the QD films. They showed that excess Pb (chalcogen) resulted in a Fermi level closer to the CBM (VBM), and were able to fabricate field effect transistors (FETs) from small bandgap QDs (less than Eg = 0.7 eV) that showed n-type (p-type) transport characteristics.52, 53

Figure 7. The EF – EVBM and EF – ECBM for different sizes of PbS QD films. The solid green circles are the “EF – EVBM from correction” which utilizes the DOS model. Open green circles are the respective “EF – ECBM from correction” values. The black crosses are the Pb:S ratios measured via XPS for the various sizes of PbS QD films.

Indeed, our XPS results indicate that the Pb rich, small bandgap QD films have a Fermi energy closer to the CBM than the S rich, large bandgap QD films. FETs made using our EDTexchanged PbS QD films further support these results (Fig. S3). Specifically, for FETs made from PbS QDs (Eg = 0.71 – 0.98 eV), we see n-type behavior with electron mobilities ranging from 0.04 – 0.22

!"! !∙!

. FETs are all fabricated and measured in a nitrogen-filled glovebox.

Additionally, we perform Seebeck coefficient measurements on air exposed EDT-exchanged PbS QD films with bandgaps of 0.66 eV. However, we measure a Seebeck coefficient of 365.45 +/6.32

!" !

for the 0.66 eV QD film, which signifies a p-type film (Fig. S4). This contradiction in

film type between the FET and Seebeck measurements on small bandgap films lead us to further analyze these films with additional XPS measurements. Also, we are unable to make meaningful measurements for the 1.45 eV QD films with either FET or Seebeck measurements, which suggests that the carrier concentration of these films is very low. The film properties are further investigated with XPS measurements before and after air exposure to explain the FET and Seebeck measurements.


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Upon air exposure, lead chalcogenide QDs are known to readily oxidize,35, 52, 54 which likely impacts QD band energetics by shifting the Fermi level closer to the VBM. To test this theory, we conduct XPS measurements on 0.66 eV and 1.45 eV EDT-exchanged PbS QD films before and after air exposure. For both films, the Fermi level shifts towards the VBM after air exposure (Fig. S5). For the 0.66 eV QD film, this shift is close to the bandgap magnitude such that the conductivity type of the film changes from n-type to p-type, which explains the positive Seebeck coefficient for the film exposed to air during the measurement. The shift in the 1.45 eV QD film is similar in magnitude. However the shift towards the VBM may not be great enough to generate sufficient carriers to make a meaningful Seebeck coefficient measurement since the Fermi level moves from ~1/2Eg to ~1/3Eg with air exposure (Fig. S5). Overall, we find that these additional measurements support our XPS/UPS “EF – EVBM from correction” values, which show the Fermi level of EDT-exchanged PbS QDs shifting towards the VBM as the PbS QD bandgap increases (Fig. 7). Conclusions For EDT-exchanged PbS QD films, we have shown that the standard way for analyzing the VBM using XPS/UPS is not correct for all QD sizes. This is demonstrated by obtaining very high signal-to-noise spectra of the VB region of bulk PbS with XPS. The bulk PbS EF – EVBM is determined from the energetic shift of a broadened DOS calculation that is offset to match the rising edge of the experimental data. Because we do not have DOS calculations for PbS QDs, we develop a different approach to determine the EF – EVBM values for these QD films. The spectra of the PbS QD films are fit to a parabolic shape using the effective mass approximation for both the L and Σ bands, where the parameters are set from bulk PbS data. This parabolic DOS model uses calculated L – Σ differences from kp theory. Due to changes in the DOS from quantum confinement, it is argued that the largest bandgap (Eg > 1.9 eV) spectra can be analyzed in the standard way to determine EF – EVBM values since the VBM is no longer in the “tail” of the VB spectrum. We find that the Fermi level of EDT-exchanged PbS QDs shifts towards the VBM with increasing QD bandgap, which can be explained by a decreasing Pb:S stoichiometric ratio of the ligand-QD complex – an observation that emphasizes the importance of surface chemistry and stoichiometry on QD band energetics. Finally, we used IPES to measure the CB region for four PbS QD films. The CBonset is not the CBM at all QD sizes due to a low DOS, similar to what was found in the UPS and XPS spectra. Given the similarities between the electronic structures of lead


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chalcogenide QDs, we anticipate that the XPS/UPS measurements of PbSe and PbTe QD films will require a similar analysis, which will be explored in future work. Methods Materials Lead (II) oxide (PbO, 99.999% trace metals basis), bis(trimethylsilyl) sulfide (TMS2S, synthesis grade), oleic acid (OAH, technical grade, 90%), 1-octadecene (ODE, technical grade, 90%), 1,2ethanedithiol (EDT, ≥98.0%), acetonitrile (anhydrous, 99.8%), tetrachloroethylene (TCE, ≥99.9%), hexane (anhydrous, ≥95%), and ethanol (EtOH, anhydrous, ≥99.5%) were purchased from Sigma Aldrich. All chemicals were used as received. The bulk sample came from a galena crystal purchased from Eggers Lapidary, Golden, CO. The galena was cleaved in a glove box and transported under ultra-high vacuum to the XPS experimental setup for measurements. PbS QD Synthesis All syntheses were performed using standard air-free techniques unless otherwise stated. The larger sizes of PbS QDs were synthesized using a size-control technique described in Zhang et al., which follows Hines’ method.55, 56 In a typical synthesis, 0.45 g PbO, 10.5 g OAH, and 10 g ODE were loaded in a 100 mL flask and heated to 100 oC under vacuum with multiple nitrogen purge cycles to degas the solution. The temperature was then raised to 120 oC, and the solution was stirred under nitrogen for 1 h to obtain a clear solution. Subsequently, the temperature was raised to 150 oC followed by a fast injection of 120 µL TMS2S, diluted in 5 mL ODE. Right before the injection, the heating mantle was removed, and the solution was allowed to cool naturally after the injection. Smaller PbS QDs were prepared using the synthetic procedure described above followed by an immediate ice water bath after the S precursor injection. The PbS QDs were purified twice by precipitation and centrifugation using ethanol as the anti-solvent, followed by re-dissolution in hexane. Purified QDs were suspended in TCE for absorption measurements or hexane for film formation. QD Film Preparation Thin films of PbS QDs were prepared by LbL from sequential dipping of a substrate in a 20 mg/mL PbS QD hexane solution followed by dipping in a 1 mM EDT acetonitrile solution. For photoelectron spectroscopy samples, this LbL sequence was repeated a total of 10 to 30 times to build up a QD film sufficiently thick (10’s – 100’s nm thick) that photoelectron spectroscopy measurements probed outside of the band-bending region of the substrate/QD interface. Thin


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films of Au (100 nm) on glass were used as substrates for XPS/UPS/IPES measurements. For absorption and Seebeck coefficient measurements, QD films were prepared on glass microscope slides, and films for Seebeck coefficient measurements were contacted with indium wire. FET substrates consisted of doped silicon that were coated with a 200 nm thick thermal SiO2 gate oxide and patterned with source/drain electrodes (5 nm Ti/35 nm Au, 10 µm channel length, 1000 µm width). QD films were deposited via five to ten LbL cycles, and unwanted areas of each film were removed with a swab. FET Measurements FET measurements were performed in a nitrogen filled glovebox with a homemade probe station using a Keithley 2636A dual-channel SourceMeter driven by LabVIEW software. Seebeck Coefficient (Thermopower) Measurements Seebeck measurements were performed on a home-built Seebeck system, described in detail elsewhere,57 that uses copper blocks for temperature control and making electrical contact to the film. Indium pads are first pressed onto the EDT-exchanged PbS QD films to ensure good Ohmic and thermal contact to the copper blocks. The spacing between the copper blocks is 4 mm, so the minimum possible spacing between the indium pads is ~6 mm. For this study, the spacing was closer to 10 mm. Resistive heaters connected to each of the blocks produce the temperature gradient, which is measured by a differential thermocouple. At least four different temperature gradients (between –3 and +3 K) are measured for each sample, with the slope of the best-fit line for these points being used for the reported Seebeck coefficient. These values are corrected for the contributions from all other components of the electrical circuit (i.e., the Seebeck voltage due to the copper/indium contacts). Based on the physical dimensions of our system, the estimated error in the Seebeck values reported by our system are

Revisiting the Valence and Conduction Band Size Dependence of

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