Multiscale Computational Design of Functionalized Photocathodes for

Dec 22, 2017 - We present an integrated computational approach combining first-principles density functional theory (DFT) calculations with wxAMPS, a ...
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Multiscale Computational Design of Functionalized Photocathodes for H2 Generation Kara Kearney, Ashwathi Iyer, Angus Rockett, Aleksandar Staykov, and Elif Ertekin J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.7b10373 • Publication Date (Web): 22 Dec 2017 Downloaded from http://pubs.acs.org on December 22, 2017

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Multiscale Computational Design of Functionalized Photocathodes for H2 Generation Kara Kearney‡,1,2, Ashwathi Iyer‡,2,3, Angus Rockett2,4, Aleksandar Staykov2, Elif Ertekin1,2* 1Department

of Mechanical Science and Engineering, University of Illinois, 1204 West Green Street, Urbana, IL 61801, USA 2International

Institute for Carbon Neutral Energy Research (WPI-I2CNER), Kyushu University, 744 Moto-oka, Nishi-ku, Fukuoka 819-0395, Japan 3Department

of Physics, University of Illinois, 1110 West Green Street, Urbana, IL 61801, USA

4Department

of Metallurgical and Materials Engineering, Colorado School of Mines, 1500 Illinois Street, Golden, CO 80401, USA.

Supporting Information Placeholder ABSTRACT: We present an integrated computational approach combining first-principles density functional theory (DFT) calculations with wxAMPS, a solid-state drift/diffusion device modeling software, to design functionalized photocathodes for high-efficiency H2 generation. As a case study, we have analyzed the performance of p-Si(111) photocathodes functionalized with a set of 20 mixed methyl/aryl monolayers, which have a known synthetic route for attachment to Si(111). DFT is used to screen for high performing monolayers by calculating the surface dipole induced by the functionalization. The trend in the calculated surface dipoles was validated using previously published experimental measurements. We find that the molecular dipole moment is a descriptor of the surface dipole. wxAMPS is used to predict the open-circuit voltage (efficiency) of the photocathode by calculating the photocurrent versus voltage behavior using the DFT surface dipole calculations as inputs to the simulation. We find that the Voc saturates beyond at surface dipole of ~0.3 eV, suggesting an upper limit for achievable device performance. This computational approach provides a possibility for the rational design of functionalized photocathodes for enhanced H2 generation by combining the angstrom-scale results obtained using DFT with the micron-to-nanometer scale capabilities of wxAMPS.

Achieving desirable efficiencies of photoelectrochemical (PEC) H2 production (e.g. 2H+ + 2 e– → H2) depends on precise control of the electronic properties of the semiconductor photocathode.1 Increasing the barrier height at the semiconductorelectrolyte interface can improve performance by enhancing charge separation. One approach for increasing band-bending is via surface functionalization with organic monolayers. Functionalization produces a surface dipole that generates a built-in electric field at the surface, which in turn increases the band-bending and open-circuit voltage of the PEC cell.2

Methylating p-type Si(111) results in stable photocathodes with low surface recombination.3 However, Si-CH3 has a low barrier height and consequently a low open-circuit voltage for H2 generation.4 Rose and co-workers have shown that integrating aryl moieties into the CH3 monolayer is a plausible approach for achieving more positive open-circuit voltages.5 In this work, we integrate DFT with wxAMPS6, a solid-state drift diffusion simulator, to provide a multiscale computational approach for the design of p-type Si(111) photocathodes functionalized with mixed methyl/aryl monolayers for the H2 evolution reaction (HER). DFT is used to calculate the surface dipole upon functionalization while wxAMPS predicts the open-circuit voltage (the experimental metric of efficiency) using the DFT results as input parameters. The electronic structure level analysis and high throughput capability of DFT, when combined with device-scale modeling, provides a computationally inexpensive theoretical analysis ranging from the angstrom to the micron scale.7 First-principles DFT8-9 calculations were performed using VASP10-14 [see SI]. Functionalized silicon was modeled using symmetrically terminated 1×4 periodic supercells with 16 layers of Si atoms and a 12 Å thick vacuum layer. Figure 1 shows a schematic of a Si supercell terminated by methyl/phenyl groups where the dashed line indicates a single unit cell. The surfaces were simulated at 25% coverage of the aryl group and 75% methyl, which was the highest coverage that allowed the molecule with the largest lateral spread considered, anthracene, to fit geometrically on the Si(111) surface. In addition, experimental coverages of a mixed methyl/aryl monolayer on Si(111) have been observed at 1-50% coverage.15 For a few select cases, 50% simulated coverage was considered but the trends reported in this work were unaffected by coverage [see SI]. The surface dipole of the functionalized surface is a combined effect of charge rearrangement at the surface and the intrinsic dipole moment of the covalently attached group.16 An elec-

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tron-withdrawing functional group will result in a positive surface dipole (the dipole moment is defined as a vector pointing from a positive to a negative charge). To calculate the surface dipole (µsurf,z) we follow a rigorous procedure known as “nanosmoothing” [see SI].17-18

capture important trends to enable rational design of functionalized surfaces, the differences between the absolute values do not influence our overall conclusions.

Table 1. Comparison of DFT Results with Published Experimental Mott-Schottky Measurements of the Valence-Band Edge Positions of Functionalized Si(111) Photocathodes. Surface

Valence Band Edge wrt Si-H (eV) (Exp.)5

Termination

(111)

Figure 1. A schematic of a converged Si(111) supercell symmetrically terminated by phenyl groups at quarter coverage with the other sites terminated by methyl groups where blue, brown, and magenta atoms represents Si, C, and H, respectively. The dashed line denotes a single unit cell boundary. As a first step, we compare the surface dipole obtained from DFT with previous experimental work5 on Si(111) functionalized with the following mixed aryl/methyl monolayers: phenyl (Si-Ph), naphthalene (Si-Naph), anthracene (Si-Anth), and 3,5-dimethoxyphenyl (Si-diMeOPh). Experimentally, the valence band edges were measured using Mott-Schottky analysis5, and a shift in the valence band edge or surface potential caused by the surface dipole is given by the Helmholtz equation: ∆ܸ௦௨௥௙ =

ସగఓೞೠೝ೑,೥ ஺

(1)

where µsurf,z is the surface dipole in the direction of the surface normal (111) and A is the surface area of the supercell [see SI]. Table 1 compares the DFT-computed surface dipoles of these systems and the experimentally obtained valence band edges5, both with respect to the Si-H surface at full coverage. The theoretical trends agree with experimental trends, but underestimate the absolute magnitude by approximately 0.5 – 0.6 eV in all cases. Previous work has suggested that ~0.5 eV difference between DFT calculations16 and experimental measurements19 is due to electrolyte screening7. The consistent offset between theory and experiment in Table 1 indicates that such a single systematic effect may be the cause of discrepancy in the absolute values. Since the aim of our work is to demonstrate the utility of a multiscale approach and to

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Surface Dipole wrt Si-H (eV) (DFT)

Methyl

-0.35

-0.84

Phenyl

-0.31

-0.82

Naphthalene

-0.16

-0.77

Anthracene

-0.12

-0.71

DiMeOPh

-0.06

-0.62

All of the functional monolayers considered in Table 1 result in a dipole less positive than Si-H. To gain an understanding of the large surface dipole observed for Si-H, the charges on the surface Si and H were calculated using Bader charge analysis20. The charges, as shown in Figure 2(a), are defined as the difference between the valence charge of the atom and the calculated Bader charge (positive charges indicate electron loss and negative charges indicate electron gain). As expected from the relative electronegativities, there is a larger net electron density, proportional to one electron, around H resulting in a large, positive surface dipole. Figure 2(b) shows the Bader charges on Si-CH3, which is the least positive dipole considered in Table 1. Despite the Si-C bond having a similar partial dipole as Si-H, the overall surface dipole of Si-CH3 is less positive because the C-H bonds have partial dipoles in the opposite direction.

-1.03

a)

b)

1.15

c)

0.05

0.04 -1.12 1.31

d)

-1.60 -1.65 -1.65 -1.60 0.66 0.70 0.71 0.70 0.77 0.80 0.74 0.74 -1.05 1.09 Figure 2. Net charges on (a) Si-H, (b) Si-CH3, (c) Si-diMeOPh and (d) the isolated diMeOPh molecule where the charge is calculated as a difference between the valence charge and the computed Bader charge of each atom. A positive value indicates electron loss, while a negative value indicates electron gain. The blue, brown, magenta, and red atoms correspond to Si, C, H, and O, respectively.

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Figure 3. (a) DFT-computed surface dipoles (eV) with respect to Si-H at full coverage plotted against the molecular dipole moments (Debye) of 20 aryl/methyl mixed monolayers at 25% coverage of the aryl moieties. Inset: Schematic of bromobenzene with the direction of its molecular dipole moment indicated. (b) Photocurrent versus voltage response under AM 1.5 solar spectrum of six representative functionalizations: FMePh (blue), ClPh (red), BrPh (purple), Pyrimidine [attached at the 5 position] (pink), Pyridine (brown), and diNitroPh (green). (c) Open-circuit voltage versus the surface potential shift with respect to Si-H obtained by modulating the electron affinity of Si in wxAMPS. The point at which device performance saturates and the maximum open-circuit voltage is obtained is marked by the red dashed line in both Figure 3a and 3c. Of the aryl/methyl monolayers considered in Table 1, SidiMeOPh has a surface dipole closest to Si-H5. In the case of Si-diMeOPh, the surface dipole includes a contribution from the intrinsic polarity of the molecule in addition to the charge rearrangement between the Si and C forming the surface bond. Figure 2(c) shows the charges on atoms that have a significant amount of net electronic charge for Si-diMeOPh. The greater electronegativity of C compared to Si is reflected in greater electron density on the C atom directly bond to Si. There is also a large relative displacement of charges within diMeOPh that contributes to the overall surface dipole, suggesting that the polarity of the molecule plays a significant role in the total dipole induced at the surface. Figure 2(d) shows the Bader charges of isolated diMeOPh. Because the charges on the isolated diMeOPh and diMeOPh bonded to Si(111) are nearly identical (excluding the carbon directly bonded to silicon), this suggests that the dipole moment of the corresponding isolated molecule is a descriptor of the surface dipole. The correlation between the molecular dipole moment and the corresponding surface dipole is seen in Figure 3a, which shows the surface dipoles with respect to Si-H for 20 aryl/methyl surface functionalizations at 25% aryl coverage (yaxis) plotted against the molecular dipole moment of the cor-

responding isolated aryl moieties (x-axis) [see SI for schematics of the aryl groups considered]. These aryl groups were chosen because they have a known synthetic route for attachment to Si(111); therefore, all of these functionalization are synthetically plausible. The inset in Figure 3a shows the structure of bromobenzene (BrPh), along with the direction of its molecular dipole moment. As the surface dipole becomes more positive, the functionalization is predicted to be more favorable for H2 evolution. As seen from the linear trend (R2 = 0.91) in Figure 3a, the intrinsic polarity of the corresponding isolated molecule is correlated with the induced surface dipole. This is a consequence of the fact that the Si-C bond has nearly identical charge density for all aryl groups considered [see SI]; therefore, the only variation in charge density across different aryl groups when attached to Si arises from the charge density within the functional group (Figure 2(c,d)). The dipole moment of an isolated molecule is computationally inexpensive to calculate, and hence can be used to screen a large number of candidates for functionalization. This is useful because calculating the surface dipoles of functionalized Si surfaces is computationally expensive for organic functional groups with complicated structures. A more extensive analysis including bonding configurations other than Si-C21 shows that this cor-

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relation largely persists across a wide variety of functional groups. Using the calculated surface dipoles as inputs into wxAMPs, we can extend our analysis to the device scale by calculating the open-circuit voltage (Voc) of the photocathode by simulating the photocurrent versus voltage behavior for different organic monolayers [see SI].22 The surface dipole due to functionalization is incorporated into wxAMPS by adjusting the value of the electron affinity of the silicon substrate.22 Figure 3b shows the simulated photocurrent versus voltage behavior for six representative functionalizations whose surface dipoles are shown in Figure 3a – FMePh (blue), ClPh (red), BrPh (purple), Pyrimidine (pink), Pyridine (brown), and diNitroPh (green). Figure 3c shows the calculated Voc plotted against the surface dipole. The x-axis in Figure 3c and y-axis in Figure 3a are identical. As the surface dipole becomes more positive in Figure 3c, the open-circuit voltage initially increases and device performance improves. However, beyond a surface dipole of ~0.3 eV vs Si-H, the Voc does not increase, and hence, device performance saturates. The performance saturates because, beyond this point, the Voc is no longer limited by thermionic emission across the Si|liquid interface [see SI].22 Instead, in the case of higher surface dipoles (> ~0.3 eV), the barrier height at the Si|liquid interface is sufficiently large and the Voc reaches a maximum value limited by bulk recombination processes.22 Hence, all monolayers above the red dashed line (surface dipole > ~0.3 eV) in Figure 3a are predicted to result in a photocathode with the maximum obtainable Voc provided that the density of surface defects upon synthesis is negligible. In closing, we have demonstrated the feasibility of a multiscale approach using first-principles simulations and device modeling to predict the surface dipole and Voc of functionalized p-Si(111) photocathodes. We find that the molecular dipole moment is a descriptor of the surface dipole of the functionalized system and hence can be used to screen for potential functionalizations in a computationally inexpensive manner. Overall, the device modeling illustrates that the Voc saturates beyond a certain value of the surface dipole, indicating that the performance will no longer increase beyond this point, which would not be revealed from first-principles alone. The combined approach provides a set of candidate surface functionalizations for optimal HER with a p-Si(111) photocathode, along with the freedom to proactively select systems that are synthetically accessible. Tutorials of this approach are available online.23

ASSOCIATED CONTENT Supporting Information Computational details; Schematics of aryl groups considered; Additional Bader charge analysis. The Supporting Information is available free of charge on the ACS Publications website.

ACKNOWLEDGMENT This work was supported by the International Institute for Carbon Neutral Energy Research (WPI-I2CNER), sponsored by the Japanese Ministry of Education, Culture, Sports, Science and Technology. This material is also based upon work supported by the National Science Foundation under Grant No. 1545907. The authors would like to thank Professor Michael J Rose and Dylan G Boucher for valuable discussions and comments.

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AUTHOR INFORMATION Corresponding Author *[email protected]

Author Contributions ‡K.K. and A.A.I. contributed equally.

Notes The authors declare no competing financial interests.

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