First-Principles Calculation of Charge Transfer at the Silicon–Organic

Jun 28, 2017 - Hybrid inorganic–organic (HIO) materials are attractive in many fields such as field-effect transistors (FETs),(1-3) solar cells,(4-6...
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First-Principles Calculation of Charge Transfer at the Silicon−Organic Interface Xiaoming Wang,† Keivan Esfarjani,†,‡ and Mona Zebarjadi*,†,§,∥ †

Institute for Advanced Materials, Devices and Nanotechnology, Rutgers University, Piscataway, New Jersey 08854, United States Department of Mechanical and Aerospace Engineering, §Electrical and Computer Engineering Department, and ∥Department of Materials Science, University of Virginia, Charlottesville, Virginia 22904, United States

‡

S Supporting Information *

ABSTRACT: Organic dopants are frequently used to surface dope inorganic semiconductors to increase their functionality. In this paper, we introduce a methodology to screen out materials for optimal surface doping and predict accurately band offsets and charge transfer using the GW method. To illustrate the approach, we study charge transfer at hybrid silicon−molecule interfaces. The goal is to find the best molecular acceptors to surface dope silicon with hole densities as high as 1013 cm−2. We use the chemical hardness method for quick screening, followed by first-principles density functional theory (DFT) and more accurate GW calculations for a handful of the most optimistic candidates. The chemical hardness method is derived from the thermodynamic analysis of the energy levels of the two subsystems in contact. This method is simple, fast, and relatively accurate. Therefore, as our first step, we use it to narrow our search for molecular dopants. Then, for the most optimistic candidates, we perform first-principles DFT calculations and discuss the necessity of GW corrections. Consistent with experimental observations, we find 3,5-difluoro2,5,7,7,8,8-hexacyanoquinodimethane and 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane to be good p-dopants with charge transfer densities larger than 1013 cm−2 when placed in the nitrogen-terminated orientation on the silicon substrate. This screening approach is quite general and applicable to other hybrid interfaces. an over 80% share.14 In addition, nanostructured silicon is promising for efficient thermoelectrics. Bulk silicon has a large power factor of ∼4 mW/(m K2)15 at room temperature. Using nanostructuring16−18 or adding holes,19 the thermal conductivity could be reduced to as low as 2−3 W/(m K), which allows silicon to have a ZT of 0.4 at room temperature and ZT values as high as 0.95 at 900 °C.16,19 The basic operating principles of HIO devices are based on charge transfer between an inorganic body and an organic compound at the interface. After contact, chemical potentials should align, resulting in bending of the bands and charge accumulation near the interface and surface doping of the inorganic material.11,12,20 Charges are confined normal to the interface but free to move in the parallel direction. One can extend such a 2D geometry to a 3D geometry and use a nanowire forest surface-doped with molecules or periodic holey structures with surface-doped holes. In that case, if the distance between the dopants is less than the screening length, then it is possible to have free carriers which are not tightly bound to the interface and could travel within the bulk of the matrix to lower surface scattering. The high mobility as a result of surface

1. INTRODUCTION Hybrid inorganic−organic (HIO) materials are attractive in many fields such as field-effect transistors (FETs),1−3 solar cells,4−6 and thermoelectrics7−9 owing to their low cost, easy processing, and material abundance. Self-assembled monolayers (SAMs) of molecules are usually used in FETs as highcapacitance dielectrics due to their insulating properties.1,2 The molecular SAMs are also found to be potential dopants to tune the carrier densities of semiconductor devices.10−13 Recently, HIO materials have been introduced in the thermoelectric field. In the thermoelectric field, the figure of merit, ZT, is a parameter measuring the performance quality of thermoelectric materials. The thermoelectric figure of merit ZT = σS2T/κ, where σ is the electrical conductivity, S is the Seebeck coefficient, κ is the thermal conductivity, and T is the temperature. Thermoelectric device efficiency is an increasing function of ZT. In the case of HIOs, for example, by intercalation of molecules, layered transition-metal dichalcogenide TiS2 demonstrates a promising ZT of 0.28 at 373 K due to enhancement of the thermoelectric power factor (σS2) and reduction of the thermal conductivity.9 Silicon is advantageous as the inorganic part in HIO devices due to its high performance in integrated circuit electronics and mature fabrication technology. Within the current photovoltaic technology, silicon-based solar cells dominate the market with © 2017 American Chemical Society

Received: April 6, 2017 Revised: June 6, 2017 Published: June 28, 2017 15529

DOI: 10.1021/acs.jpcc.7b03275 J. Phys. Chem. C 2017, 121, 15529−15537

Article

The Journal of Physical Chemistry C

2.1. Chemical Hardness Method. For silicon−molecule HIO materials, we employ a thermodynamic model called the chemical hardness method to predict the charge transfer. In this model, the total energy of a system is expanded in powers of the net charge (δn) to the second order as follows:

transfer doping, free of ionized impurity scattering, could improve the performance of the electronic devices and was also found able to enhance the performance of bulk thermoelectric materials.21,22 It is crucial to maximize the charge transfer to achieve good performance of the HIO devices. The propensity of charge transfer at the interface requires proper band alignments of the participating organic and inorganic materials. Take p-doped silicon with molecular dopants as an example. The charge transfer energy for hole doping of Si, Δ, is defined as Δ = EA − IP (VBM, valence band maximum), where EA is the electron affinity of the molecule and IP is the ionization potential of the silicon surface in contact (or VBM). Charge transfer occurs spontaneously in the ground state whenever Δ is negative, whereas positive values of Δ indicate charge transfer excitations. To optimize the charge transfer of silicon−molecule interfaces, one needs to screen the molecules to find the smallest Δ. To apply surface transfer doping, the silicon surface should be passivated to prevent charge confinement by the surface states. Although there are significantly less molecule donors than acceptors to dope silicon by surface transfer doping, an experimental study13 has seen efficient n-type doping of silicon by cobaltocene with transferred electron density as high as 2 × 1013 cm−2. Several other studies23−27 show that strong acceptors such as tetracyanoquinodimethane (TCNQ) and 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane (F4TCNQ) could withdraw electrons from silicon, resulting in p-type doping. Despite experimental advances, questions such as how many charges per molecule are transferred in these HIO systems or which molecule is the best to efficiently inject carriers to silicon have not been addressed systematically. Herein, we study the charge transfer between silicon and a diversity of molecule acceptors by using a combination of approaches ranging from the chemical hardness method to the first-principles density functional theory (DFT) and many-body Green function GW formalism. In thermoelectric devices, both n-doped and p-doped legs are needed, and indeed, both types of HIO materials exist. p-type doping needs molecules with larger electron affinity, while n-type doping prefers a lower ionization potential. Since silicon has an EA of 4.05 eV and an IP of 5.17 eV,28 molecules with an EA near 5.17 eV or larger and an IP near 4.05 eV or smaller have great potential to dope silicon with holes and electrons, respectively. While for p-type doping there are many dopant candidates, for n-type doping there is only one in the literature which results in a surprisingly high doping concentration.13 Thus, we focus only on p-type doping in this paper. We screen out the best candidates for charge transfer using the simple and approximate models, and then perform the state-of-the-art first-principles DFT and many-body GW calculations to accurately address the band alignments and charge transfer of the screened candidates. We find that both F4TCNQ and 3,5-difluoro-2,5,7,7,8,8-hexacyanoquinodimethane (F2HCNQ) with strong electron-withdrawing ability can effectively dope silicon with hole densities as high as 1013 cm−2.

E(δn) = E0 +

1 ∂ 2E ∂E (δn)2 δn + 2 ∂(δn)2 ∂(δn)

= E0 + μ δn +

1 η(δn)2 2

(1)

where E0 is the total energy of the neutral system. By definition, the first derivative of the total energy is the chemical potential (μ), and the second derivative is called the chemical hardness (η).29 As its name indicates, materials with large chemical hardness do not easily allow charge transfer when put in contact with other materials. We assume that, after contact, the chemical hardnesses of the two materials are, to leading order, not modified due to deformations or charge transfer. Clearly, in the case of chemisorption, where hybridization takes place, this might not be a good approximation. However, in the physisorbed case, such an assumption is realistic. Note that, in the case of chemisorption, the question of how much charge is transferred is not a well-defined question as there are shared electrons at the surface bonds. Therefore, this study is only focused on the physisorbed cases. Assume that, after contact, charge δq = −e δn (e > 0) is transferred from A to B as a result of the chemical potential difference between A and B. Then the total energy of the A/B system could be written as the sum of the total energies of the isolated charged systems (A and B) and the charging energy of the resulting capacitor (or dipole layer) formed between A and B: E = EA ( −δn) + E B(δn) +

(δn)2 2CAB

(2)

After the two systems are put in contact with each other, the charge transfer is determined by minimization of the total energy with respect to δn: δn =

μA − μB ηA + ηB + 1/CAB

(3)

where the coefficient CAB is the mutual capacitance of the two subsystems, which can be approximately evaluated using the following formula: |ci|2 |cj|2 1 = e2 ∑ 4πε0|ri − rj| CAB i∈A ,j∈B

(4)

where ε0 is the vacuum permittivity and ri and rj are the positions of atoms belonging to the A and B subsystems, respectively. In the linear combination of atomic orbitals (LCAO) framework, ci is the coefficient of the atomic orbital (ϕi) centered on atom i in the decomposition of the highest occupied molecular orbital (HOMO) of A or lowest unoccupied molecular orbital (LUMO) of B:

2. METHODOLOGY A quick and approximate scan of different molecules for charge transfer in silicon−organic systems is performed by using the chemical hardness method. Then, through first-principles DFT and GW calculations, we provide a more accurate description of the band alignment and charge transfer in the filtered top candidates. 15530

DOI: 10.1021/acs.jpcc.7b03275 J. Phys. Chem. C 2017, 121, 15529−15537

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The Journal of Physical Chemistry C n ⎧ ⎪ ΨHOMO | LUMO = ∑ ciϕi ⎪ i=1 ⎨ n ⎪ ∑ |ci 2| = 1 ⎪ ⎩ i=1

(5)

In case A is a semi-infinite system, the dielectric screening by A can be incorporated by adding the effect of induced image charges30 in eq 4. However, since, compared to the chemical hardness term, the modification is quite small, we neglect these interactions. The chemical hardness method was once used to calculate the charge transfer in heteroatomic molecules and heteromolecular dimers and later extended to solid interfaces.31,32 In solid materials, when a gap exists, the chemical hardness is equivalent to the band gap. The capacitance term 1/ CAB in eq 3 is usually small compared to typical band gaps and can be calculated as the Coulomb interaction between the LUMO of the acceptor and the HOMO of the donor in the presence of the bulk surfaces. The merit of this method is that it uses the chemical properties of individual parts and does not require a calculation of the system A + B put together. The results are simple in form, transparent, and easy to understand. Therefore, if EA and IP of the molecule candidates are tabulated in advance, a quick back of an envelope calculation can provide a reasonable estimate of the charge transfer, allowing us to eliminate “bad” candidates. 2.2. First-Principles DFT and GW Calculations. Though the chemical hardness method gives a qualitative and intuitive estimation of the charge transfer within some simplifications and approximations, the main drawback of the method is neglecting the physics and chemistry or deformations and hybridizations at real interfaces. DFT-based first-principles calculations can take into account the interface structure relaxations which are believed to be important for charge transfer. However, the dynamic polarization effects which have a great impact on the electronic levels of molecules and semiconductors are not captured by normal DFT or even hybrid functional calculations.33,34 To this end, we resort to many-body perturbation theory (MBPT) in its GW approximation35−37 for a more accurate description of the band alignments and charge transfer at silicon−organic interfaces. All the GW calculations in the present study are single-shot G0W0 calculations which use normal DFT (PBE (Perdew−Burke− Ernzerhof) in this work) single-particle states as input. The wave functions are not updated during the GW calculations, and only the orbital energies are corrected perturbatively. We perform DFT and GW calculations on F2HCNQ−, F4TCNQ−, and TCNQ−silicon HIO systems. The slab model is adopted to represent the interface structure. To perform the DFT calculations, we employ the Quantum ESPRESSO package.38 The generalized gradient approximation (GGA)-based PBE39 functional is used for the exchangecorrelation energy. The ion−electron interactions are treated using the SG15 optimized norm-conserving Vanderbilt (ONCV)40,41 pseudopotentials. The cutoff energy of the plane wave basis set is 60 Ry. Monkhorst−Pack42 k meshes of 3 × 3 × 1 and 8 × 4 × 1 are used to sample the Brillouin zone for the unit cell of the parallel orientation (PO) and nitrogen-terminated orientation (NO) configurations, respectively; see Figure 1. A vacuum thickness of 12 Å is used to eliminate the periodic image interactions. To correctly deal with the van der Waals interactions, we employ the nonlocal

Figure 1. Schematic configurations of the Si(100):H−TCNQ interface. (a) Top and (b) side views of the parallel orientation (PO). (c) Top and (d) side views of the nitrogen-terminated orientation (NO). For PO, we perform both PBE and GW calculations on the unit cell shown in (a), while (c) shows the supercell in GW calculation for NO; the shaded area displays the unit cell in PBE calculation. The yellow, gray, white, and blue balls denote the Si, C, H, and N atoms, respectively.

DFT functional vdW-DF-cx43 to relax the structure (see Table S1 in the Supporting Information). The top silicon layers, the interface hydrogen atoms, and the molecules are allowed to relax, while the bottom silicon and hydrogen atoms in the silicon slab are fixed to the prerelaxed positions. The force convergence criterion is set to 1e−4 Ry/bohr. GW calculations are performed only at the Γ-point using the WEST code,44 based on the DFT-optimized structure. In the spectral decomposition of the dielectric matrix, we include NPDEP = 1024 eigenvectors. Supercells of 11.541 × 11.541 × 21.88 Å3 and 15.388 × 15.388 × 28.16 Å3 are constructed for the PO and NO configurations, respectively; see Figure 1. Details of the convergence study of the slab thickness and GW parameters can be found in the Supporting Information.

3. RESULTS AND DISCUSSION First, we compare the charge transfer calculated by the chemical hardness (CH) method with those of different charge analysis methods, namely, the Mulliken,45 Hirshfeld,46 Voronoi,47 and Bader48 charges, as shown in Table 1. In addition, the charge transfer can be obtained by calculating the difference in the electron densities of the system before and after contact: Δρ = ρAB − ρA − ρB. ρAB, ρA, and ρB are the electron densities of the Table 1. Charge Transfer at the Si(100):H−F4TCNQ Interface with the PO Configuration, Obtained by Different Methodsa Mulliken charge (e) charge (e)

Hirshfeld

0.14 Bader

0.13 CDD

DOSI

0.20

0.18

0.22

Voronoi 0.16 CH 0.22

a

CDD = charge density difference, DOSI = density of states integral, and CH = chemical hardness. 15531

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Figure 2. Net charge transfer δn between the Si(100):H slab and 23 molecular acceptors calculated by the chemical hardness method. Δ is the charge transfer energy.

Figure 3. Band decomposition of Si(100):H−TCNQ in the Wannier function basis for (a) PO and (b) NO configurations. The color bar shows the relative weights of Si(100):H (red) and TCNQ (blue). In the right panel of each figure, the high-symmetry k points of the corresponding first Brillouin zone are displayed.

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Table 2. Band Gap (or HOMO−LUMO Gap) Eg and Charge Transfer Energy Δ of TCNQ, F4TCNQ, and F2HCNQ on the Si(100):H Surface with PO and NO Configurationsa gas phase

on Si(100):H/PO

on Si(100):H/NO Δn

molecule TCNQ F4TCNQ F2HCNQ

method PBE GW PBE GW PBE GW

IP (eV) 7.02 8.86 7.31 9.14 7.67 9.42

EA (eV) 5.60 3.99 5.98 4.42 6.36 4.89

Eg (eV) 1.42 4.87 1.33 4.72 1.31 4.53

dPO (Å) 2.32

Eg (eV) 1.41 2.17 1.31 1.46 1.23 1.37

2.07 1.27

Δ (eV) 0.05 0.77 0.04 0.67 0.03 0.64

dNO (Å) 0.84 0.90 1.32

Eg (eV)

Δ (eV)

cm−2

1.11 1.54 1.19 1.37 0.90 1.13

−0.01 0.34 −0.01 0.17 −0.06 0.12

× × × × × ×

4.0 2.0 5.7 1.3 5.4 2.5

e 13

10 1012 1013 1013 1013 1013

0.24 0.01 0.34 0.08 0.32 0.15

a d is the smallest distance between the molecule and Si(100):H surface. δn is the charge transfer in units of cm−2 or e/molecule, evaluated according to eq 6. The gas-phase IP and EA of the molecules are shown for comparison. Both the PBE and GW results are presented. We do not show the charge transfer for the PO configuration as it is too small due to the large charge transfer energy.

Figure 4. Band spectrum of Si(100):H−TCNQ calculated by PBE and GW. The HOMO and LUMO are the corresponding TCNQ frontier orbital states. VBM is the Si(100):H valence band maximum.

to the band gaps of 2.0 and 4.0 eV for Si(100):H and F4TCNQ, respectively. Therefore, we neglect the capacitance term in eq 3 for the charge transfer in silicon−molecule systems. By doing this, we neglect the effect of molecular orientations, which is included in the capacitance term, on the charge transfer. Since the capacitance term is neglected, we end up with an upper bound estimate of the charge transfer with the chemical hardness method. In Table 1 and Figure 3, IP = 5.82 eV and EA = 3.86 eV are used for the Si(100):H slab. Figure 2 summarizes the charge transfer between the Si(100):H slab and some well-known molecular acceptors calculated by eq 3. A complete list of the molecular acceptors is shown in the Supporting Information. From Figure 3, the general trend is that the smaller the charge transfer energy, the larger the charge transfer. However, the charge transfer is not a monotonic function of the charge transfer energy and is affected by the chemical hardness values. The driving force of the charge transfer is the chemical potential difference (i.e., electrons transfer from higher chemical potentials to the lower ones), while the resisting force of the charge transfer is the chemical hardness. It is hard to withdraw electrons from chemically hard materials. For example, the charge transferred from F2HCNQ (with a chemical hardness of 4.53 eV) is much larger than that of benzonitrile (with a chemical hardness of 9.44 eV); see Table S2 in the Supporting Information. Among all acceptors, F2HCNQ and F4TCNQ stand out to hold more potential as surface dopants. Note that we are using the GW data for F2HCNQ and F4TCNQ in Figure 3, since the experimental data are not available. The GW method is the most reliable way to calculate the IP and EA of molecules. It

hybrid system and isolated A and B subsystems, respectively. The net charge transfer is δn = ∫ Δρ(z)z dz, where z is the spatial coordinate perpendicular to the interface and Δρ(z) is the planar averaged charge density difference in the corresponding direction. The nodal point of Δρ(z) is considered as the interface for the purpose of integration. We denote this method as the charge density difference (CDD) method. For the hybrid systems with physisorption, one can also calculate the charge transfer by integrating the local density of states (LDOS) of either subsystem: ⎧ ⎪ ⎪ δn = ⎨ ⎪ ⎪ ⎩

VBM

∫−∞

f (E) LDOS(E) dE

electron

+∞

∫CBM [1 − f (E)] LDOS(E) dE

hole

(6)

where f is the Fermi−Dirac distribution function. This method is denoted as DOSI in Table 1. To compare the different methods at the same level, we employ the SIESTA49 code, which is capable of employing all the methods discussed above. As a test, we calculate the charge transfer at the Si(100):H− F4TCNQ interface with the PO configuration. As can be seen from Table 1, all methods give similar results. Note that this is only true for the physisorption case. In the chemical hardness method, the chemical potential and chemical hardness are obtained by the EA and IP as μ = −(EA + IP)/2 and η = IP − EA. The IP and EA of the molecules are calculated using the ΔSCF method, which is also extended to solids.50 For the Si(100):H−F4TCNQ interface, the capacitance term 1/CAB in eq 3 is calculated to be 0.4 eV, which is much smaller compared 15533

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The Journal of Physical Chemistry C can however occasionally overestimate the EA by almost 0.5 eV. In the case of F2HCNQ and F4TCNQ, however, even a lower value of the EA would still be larger than that of other considered molecules, and that would not change our conclusions. More accurate results refer to first-principles calculations. In the next step, we perform first-principles DFT and GW calculations on the top molecule candidates, namely, F4TCNQ and F2HCNQ. TCNQ is also included for comparison. The main results of the DFT and GW calculations are summarized in Table 2. In what follows, we take TCNQ as an example to present the GW calculations. The hydrogenterminated silicon (100) surface with 1 × 1 reconstruction51 (Si(100):H) is used in all the calculations. Parts a and b of Figure 1 show the structure of TCNQ on the Si(100):H surface in the parallel orientation (PO), which is found to be the most stable configuration of the TCNQ molecule or SAM on the silicon surface.25,27 The smallest distance dPO between TCNQ and the Si(100):H surface is 2.32 Å, and chemical bonds do not form at the interface. We construct the band decomposition, as shown in Figure 3a, of the hybrid structure in terms of maximally localized Wannier functions (MLWFs).52,53 As the Wannier functions near the interface are well localized (Figure S3 in the Supporting Information), the band structures of each part of the hybrid system are clearly identified. The HOMO and LUMO levels of TCNQ can be classified as the blue curves in Figure 3a, from which the PBE HOMO−LUMO gap of TCNQ in the PO configuration is extracted to be 1.41 eV, which is nearly the same as the gas-phase value of 1.42 eV; see Table 2. Figure 4 shows the comparison of PBE and GW eigenvalues of the supercell calculation. The GW gap of TCNQ decreases from 4.87 to 2.17 eV when it approaches the silicon surface, indicating a large polarization-induced screening due to interfacial charge transfer.33,34 The GW corrections shift the LUMO of TCNQ and the VBM of silicon up and down, respectively, increasing the charge transfer energy from 0.05 to 0.77 eV, which is too high for effective charge transfer at room temperature, since the thermal excitation energy is around 0.025 eV. The large differences in the eigenvalues between DFT and GW calculations are consistent with previous studies54−57 on dielectric−molecule systems, indicating the necessity of GW calculations for these hybrid systems. Putting molecules in crystal form, the gap renormalizes due to electronic polarization effects.58−60 Within the nonlocal vdW-DF-cx functional, the relaxed lattice parameters of the TCNQ crystal are a = 8.86 Å, b = 7.19 Å, and c = 15.95 Å, which agree well with experiment;61 see Table S1 in the Supporting Information. Figure 5 shows the TCNQ HOMO and LUMO energies in the gas phase and in crystal form. Bulk gaps are aligned to the middle of the gas-phase gap. The relatively large discrepancy between the GW-calculated HOMO and LUMO levels and those measured experimentally for the gas phase is due to neglecting the atomic relaxation in response to electronic excitation and can be partly improved by using hybrid functionals as the starting point for GW calculations. The results of GW calculations are much closer to the experimental data in the crystal form. The bulk band gap decreases to 2.92 eV compared to 4.87 eV for the gas phase. The HOMO and LUMO levels of the crystal phase are shifted up and down, respectively. The resulting larger electron affinity is favored for hole injection. To this end, we construct the hybrid structure with a compact stack of TCNQ including strong intermolecular interactions, as shown in Figure 1c,d. The

Figure 5. HOMO and LUMO energies of TCNQ in the gas and crystal phases. The experimental data are taken from refs 62−64.

distance dNO between the nitrogen atoms and silicon surface is as small as 0.84 Å. However, the N atoms are right on top of the vacuum surrounded by the four H atoms. The Wannier functions are still well localized, and there is no chemical bond formed at the interface, as seen in Figure S3b (Supporting Information). We denote this configuration as the nitrogenterminated orientation (NO). The idea is to increase the dynamical screening effect in the TCNQ environment and lower the LUMO level. We note that the goal can also be achieved by stacking more TCNQ molecules in the PO configuration on top of the silicon surface. However, this will increase the computational burden substantially. Moreover, the initial guess of the TCNQ configuration is motivated by the lamella structure of its crystal phase; see Figure S4 (Supporting Information). We extracted one layer of TCNQ from its crystal form and put it on the silicon surface. We tried different molecular orientations. After relaxation, the most stable configuration, as shown in Figure 1c,d, was used for further band structure calculations. Therefore, the result of this configuration can serve as a good reference to TCNQ thin films. Though the interface structure in experiment may be complicated or even not in the crystal form but disordered, we believe the actual structure highly depends on the fabrication method. We are not claiming that they are systematically formed on the interface, but propose that these metastable structures, if made, would have a favorable charge transfer to the silicon substrate. Figure 3b shows the band decomposition in terms of MLWFs. The dispersion of TCNQ bands along the ΓX direction indicates strong intermolecular coupling which is due to the wave function overlap between the TCNQ molecules, as shown in Figure S5 (Supporting Information). The band gap of TCNQ in the NO configuration is corrected from 1.11 eV for PBE to 1.54 eV by GW calculations. The LUMO of TCNQ touches the VBM of silicon at the Y point within PBE, as shown in Figure 3b. The charge transfer energy is increased to 0.34 eV within GW; see Table 2. The charge carrier density can be calculated according to eq 6. The GW DOS is approximated as a rigid shift of the DFT DOS by the corrected charge transfer energy, since the GW corrections on the bands near the frontier orbitals which dominate the charge transfer are quite similar, as shown in Figure 4. The Fermi level in the GW DOS is set to be at the point where the number of holes in silicon equals that of 15534

DOI: 10.1021/acs.jpcc.7b03275 J. Phys. Chem. C 2017, 121, 15529−15537

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4. CONCLUSION In summary, we investigated charge transfer at silicon−organic interfaces by a combination of approaches ranging from a thermodynamic method to first-principles DFT and GW calculations. A variety of molecular acceptors are screened by using the approximate but simple chemical hardness method. We validated this thermodynamic method by comparing its results to those of several other standard charge transfer calculation methods. The top candidates filtered by the chemical harness method are further studied by more accurate first-principles GW calculations, capturing the dynamic polarization effects which are significant for HIO systems. The GW method can predict a more accurate band gap and band alignment than normal DFT calculations. We find that both F4TCNQ and F2HCNQ SAMs can efficiently dope silicon, achieving hole concentrations as high as 1013 cm−2 when placed in the NO configuration, and are physically absorbed on the silicon surface without forming chemical bonds. The approach used in the present work is quite general and could be applied to other HIO systems, and the results provide important guidance for high-performance HIO device design. Charge transfer being exponentially dependent on band alignment, very accurate electronic structure methods such as GW are required to produce a reliable prediction of the charge transfer, as can be seen for instance in Table 2.

electrons in TCNQ. Parts a and b of Figure 6 display the local density of states (LDOS) by PBE and GW, respectively. As

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b03275. Complete list of the molecular acceptors, lattice parameters compared with different vdW-DF functionals, and convergence tests of GW calculations (PDF)

Figure 6. Local density of states (LDOS) of Si(100):H−TCNQ in the NO configuration for (a) PBE and (b) GW calculations. The GW LDOS is obtained by rigidly shifting the PBE LDOS with the corrected band offset. The shaded areas indicate hole accumulation.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

seen, consistent with Figure 4, the GW corrections push the LUMO of the molecule higher while lowering the VBM of the silicon slab. Therefore, the GW correction removes the overlap of the LDOS in PBE calculations. The hole concentrations of silicon are calculated to be 4.0 × 1013 and 2.0 × 1012 cm−2 by PBE and GW, respectively. The calculation details of F4TCNQ and F2HCNQ are quite similar to that of TCNQ, since all three molecules share a similar structure; see Table S2 in the Supporting Information. The EA increases in the order of TCNQ < F4TCNQ < F2HCNQ, consistent with the electron-withdrawing ability, H < F < CN. The charge transfer energy decreases as the EA increases, for both PO and NO configurations. Even for the strongest acceptor, F2HCNQ, the charge transfer energy in the PO configuration is as large as 0.64 eV, still too high for effective charge transfer. For the NO configuration, both F4TCNQ and F2HCNQ can dope silicon effectively with hole concentrations of 1.3 × 1013 and 2.5 × 1013 cm−2, respectively. Therefore, the F2HCNQ or F4TCNQ SAMs with lower coverage will not be able to dope silicon effectively. Instead, one would expect to use higher surface coverage or thin films to achieve good performance in the silicon−organic devices.

Xiaoming Wang: 0000-0002-5438-1334 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the SOE HPC cluster of Rutgers, the Rivanna cluster of the University of Virginia, and XSEDE, which is supported by National Science Foundation Grant ACI1053575, for providing the computational resources. This work is supported by National Science Foundation Grants 1403089 (K.E.) and 1400246. (M.Z.). We also thank Dr. Junxi Duan for useful discussions.

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REFERENCES

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