Tunable Semiconductors: Control over Carrier States and Excitations in Layered Hybrid Organic-Inorganic Perovskites

TL;DR

This paper predicts how changing organic and inorganic parts in layered hybrid organic-inorganic perovskites can systematically control carrier states, energy levels, and excitations, enabling tunable optoelectronic properties.

Contribution

It introduces a first-principles approach to predict and control carrier states and energy level alignments in layered hybrid perovskites through organic-inorganic component variation.

Findings

Carrier states can be tuned via organic-inorganic component variation.

Energy level alignments can be systematically controlled.

Transport and recombination properties are adjustable.

Abstract

For a class of 2D hybrid organic-inorganic perovskite semiconductors based on $\pi$-conjugated organic cations, we predict quantitatively how varying the organic and inorganic component allows control over the nature, energy and localization of carrier states in a quantum-well-like fashion. Our first-principles predictions, based on large-scale hybrid density-functional theory with spin-orbit coupling, show that the interface between the organic and inorganic parts within a single hybrid can be modulated systematically, enabling us to select between different type-I and type-II energy level alignments. Energy levels, recombination properties and transport behavior of electrons and holes thus become tunable by choosing specific organic functionalizations and juxtaposing them with suitable inorganic components.

Figures

Tables

Table 1. Table S1: The PBE+TS total energy difference (E(2 × \times 2) - E(1 × \times 2)) of the PBE+TS predicted structure using the (1 × \times 2) and (2 × \times 2) unit cells for the syn-anti-syn AE4T \ce PbX4 (X = Cl, Br, I) and the all-anti AEnT \ce PbBr4 (n = 2, 3, 4, 5). K-point grids settings of 1 × \times 4 × \times 2 were used for the (1 × \times 2) calculation, whereas 1 × \times 2 × \times 2 k-point grids were used for the (2 × \times 2) calculation. The FHI-aims “tight” numerical defaults (Table S2 ) were used for both calculations. The total energy of the syn-anti-syn AE4T \ce PbBr4 is 2.44 eV/cell lower than that of the all-anti AE4T \ce PbBr4 compound (both in a (2x2) configuration).

Compounds	Energy Difference (eV)
AE4T\cePbCl4	-2.49
AE4T\cePbBr4	-2.70
AE4T\cePbI4	-2.73
AE2T\cePbBr4	-3.76
AE3T\cePbBr4	-0.79
all-anti-AE4T\cePbBr4	-1.50
AE5T\cePbBr4	-0.83

Table 2. Table S2: Basis functions (radial functions) in the “tight” computational settings used for the DFT-PBE+TS relaxation for H, C, N, O, S, Cl, Br, I and Pb elements.

	H	C	N	S
minimal	1s	[He]+2s2p	[He]+2s2p	[Ne]+3s3p
tier 1	H(2s,2.1)	H(2p,1.7)	H(2p,1.8)	S2+(3d)
	H(2p,3.5)	H(3d,6.0)	H(3d,6.8)	H(2p,1.8)
		H(2s,4.9)	H(3s,5.8)	H(4f,7)
				S2+(3s)
tier 2	H(1s,0.85)	H(4f,9.8)	H(4f,10.8)	H(4d,6.2)
	H(2p,3.7)	H(3p,5.2)	H(3p,5.8)	H(5g,10.8)
	H(2s,1.2)	H(3s,4.3)	H(1s,0.8)
	H(3d,7.0)	H(5g,14.4)	H(5g,16)
		H(3d,6.2)	H(3d,4.9)

Table 3. Table S3: DFT-PBE total energy convergence with different k-grid settings for reciprocal-space integrals of AE4T \ce PbBr4.

K-grid	$\Delta E$(eV)	$\Delta E$(meV/atom)
1$\times$2$\times$2	0*	0*
2$\times$4$\times$4	-0.066	-0.16

Table 4. Table S4: Basis functions (radial functions) in the “intermediate” computational settings used for the DFT-HSE06+SOC calculation for H, C, N, O, S, Cl, Br, I and Pb elements.

	H	C	N	S
minimal	1s	[He]+2s2p	[He]+2s2p	[Ne]+3s3p
tier 1	H(2s,2.1)	H(2p,1.7)	H(2p,1.8)	S2+(3d)
	H(2p,3.5)	H(3d,6.0)	H(3d,6.8)	H(2p,1.8)
		H(2s,4.9)	H(3s,5.8)	H(4f,7)
				S2+(3s)
tier 2	H(1s,0.85)	H(4f ,9.8)	H(4f,10.8)	H(5g,10.8)aux
	H(3d,7.0)aux	H(5g,14.4)aux	H(5g,16)aux

Table 5. Table S5: Computationally predicted unit cell parameters of AE4T \ce PbX4(X = Cl, Br, I) relaxed by DFT-PBE+TS. The experimental structure refinements for AE4T \ce PbBr4 Mitzi  et al. ( 1999 ) and AE4T \ce PbI4(this work) are shown for comparison.

HOIPs	a(Å)	b(Å)	c(Å)	$\alpha$	$\beta$	$\gamma$	V(Å3)
AE4T\cePbCl4
PBE+TS	40.85	11.29	10.95	90.0∘	91.8∘	90.0∘	5049
AE4T\cePbBr4
Exp.Mitzi et al. (1999)	39.74	11.68	11.57	90.0∘	92.4∘	90.0∘	5369
PBE+TS	40.01	11.60	11.47	90.0∘	91.3∘	90.0∘	5322
$\Delta$(%)	0.67	-0.74	-0.87	0.02	-1.17	0.04	-0.88
AE4T\cePbI4
Exp.∗	38.79	12.18	12.33	90.0∘	92.3∘	90.0∘	5818
PBE+TS	39.02	12.10	12.22	90.0∘	91.1∘	90.0∘	5771
$\Delta$(%)	0.59	-0.65	-0.86	0.04	-1.31	0.04	-0.81

Table 6. Table S6: Here and in Table S7 , we provide anisotropic band curvatures (in effective mass units, m e subscript 𝑚 𝑒 m_{e} ) at the Γ Γ \Gamma point, derived from the HSE06+SOC computed energy band structures for all compounds addressed in this work. For each material, separate band curvatures are given for the HOMO and the LUMO of the organic and the inorganic component. The absolute VBM and CBM of each material are marked with ∗ symbols in the table. Corresponding band structure diagrams can be found in Figure 2 (main paper) and in Figure S12 of this supporting information. The curvature parameters were determined by parabolic fits to individual bands at the Γ Γ \Gamma points, in the directions parallel to the coordinate axes [see Figure 2(a) in the main paper], with small spacings of the fitted points of 0.01 a 0 − 1 superscript subscript 𝑎 0 1 a_{0}^{-1} or 0.02 a 0 − 1 superscript subscript 𝑎 0 1 a_{0}^{-1} , where a 0 subscript 𝑎 0 a_{0} is the Bohr radius. The curvature parameters thus correspond to the diagonal elements of the effective mass tensor in this coordinate system, without a diagonalization of the effective mass tensor. Nevertheless, the diagonal elements give a clear qualitative indication of the band curvatures in the organic and inorganic components of each material considered. Large effective mass values correspond to essentially flat bands at the Γ Γ \Gamma point and are unlikely to be meaningful in the context of band-like transport; values above 20  m e subscript 𝑚 𝑒 m_{e} are therefore not further detailed in the table.

Material	Direction	HOMO (inorg.)	HOMO (org.)	LUMO (inorg.)	LUMO (org.)
AE4TPbCl4	$\Gamma$-X	$>$20	$>$20∗	$>$20∗	$>$20
	$\Gamma$-Y	0.42	$>$20∗	0.32∗	1.38
	$\Gamma$-Z	0.46	2.66∗	0.43∗	6.8
AE4TPbBr4	$\Gamma$-X	$>$20	$>$20∗	$>$20∗	$>$20
	$\Gamma$-Y	0.31	$>$20∗	0.26∗	1.57
	$\Gamma$-Z	0.33	2.23∗	0.31∗	15.9
AE4TPbI4	$\Gamma$-X	17.3	$>$20∗	$>$20∗	$>$20
	$\Gamma$-Y	0.27	$>$20∗	0.22∗	7.6
	$\Gamma$-Z	0.27	11.4∗	0.22∗	9.0

Table 7. Table S7: Here and in Table S6 , we provide anisotropic band curvatures (in effective mass units, m e subscript 𝑚 𝑒 m_{e} ) at the Γ Γ \Gamma point, derived from the HSE06+SOC computed energy band structures for all compounds addressed in this work. See caption of Table S6 for details.

Material	Direction	HOMO (inorg.)	HOMO (org.)	LUMO (inorg.)	LUMO (org.)
AE1TPbBr4	$\Gamma$-X	11.1∗	5.1	$>$20∗	$>$20
	$\Gamma$-Y	0.37∗	4.6	0.23∗	0.97
	$\Gamma$-Z	0.38∗	1.7	0.44∗	1.08
AE2TPbBr4	$\Gamma$-X	$>$20	$>$20∗	$>$20∗	6.9
	$\Gamma$-Y	0.33	7.5∗	0.23∗	16.9
	$\Gamma$-Z	0.37	1.2∗	0.36∗	2.9
AE3TPbBr4	$\Gamma$-X	$>$20	$>$20∗	$>$20∗	$>$20
	$\Gamma$-Y	0.38	$>$20∗	0.24∗	2.8
	$\Gamma$-Z	0.39	1.9∗	0.55∗	$>$20
AE4TPbBr4 (all-anti)	$\Gamma$-X	16.3	$>$20∗	$>$20∗	$>$20
	$\Gamma$-Y	0.40	5.6∗	0.24∗	2.3
	$\Gamma$-Z	0.39	1.1∗	0.35∗	$>$20
AE5TPbBr4	$\Gamma$-X	$>$20	$>$20∗	$>$20∗	$>$20
	$\Gamma$-Y	0.55	7.3∗	0.24∗	5.5
	$\Gamma$-Z	0.54	1.2∗	0.55∗	2.8

Full text

Supporting Material

Tunable Semiconductors: Control over Carrier States and Excitations in Layered Hybrid Organic-Inorganic Perovskites

Chi Liu

Department of Chemistry, Duke University, Durham, North Carolina 27708, USA

  

William Huhn

  

Ke-Zhao Du

Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708, USA

  

Alvaro Vazquez-Mayagoitia

Argonne Leadership Computing Facility, 9700 S. Cass Avenue, Lemont IL 60439, USA

  

David Dirkes

Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599, USA

  

Wei You

Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599, USA

  

Yosuke Kanai

Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599, USA

  

David B. Mitzi

Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708, USA

Department of Chemistry, Duke University, Durham, North Carolina 27708, USA

david.mitzi@duke.edu

  

Volker Blum

Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708, USA

Department of Chemistry, Duke University, Durham, North Carolina 27708, USA

volker.blum@duke.edu

Short Description

This Supplemental Material includes: structural details of the perovskites in our simulations; energetic impact of the supercell choice; impact of spin-orbit coupling in the reported energy band structures; computational details (basis sets and k-space grid convergence); validation of computational protocols by comparing to experimental results for MAPbI3, for AE4TPbBr4 and for AE4TPbI4; experimental details for the synthesis and characterization of a new AE4TPbI4 crystal; and additional computed orbitals, energy band structures, band curvature parameters, full and partial densities of states supporting the general findings demonstrated in the actual paper. Computational validation for MAPbI3 also includes comparison to a more sophisticated many-body dispersion treatment.Ambrosetti et al. (2014) Synthesis details include Refs. Muguruma et al. (1996a, b, 1998). All computational input and output files (raw data) are available at the NOMAD repository.NOM

I (2$\times$2) supercell of AE4TPbBr4

II Comparison of (2$\times$2) and (1$\times$2) structure models relaxed by DFT-PBE+TS

II.1 Nomenclature of Pb-X-Pb bond angles (X = Cl, Br, I)

II.2 PBE+TS total energy

III Effect of spin orbit coupling

IV Computational basis settings: tight

V K-grid convergence test

VI Computational basis settings: intermediate

VII Validation of the computational approach

VIII Optimized structures of AE4TPbX4 (X = Cl, Br, I)

IX Construction of the computational structure models of the HOIP compounds assessed in this work

We perform full relaxation of both unit cell parameters and cell-internal atomic coordinates on the initial input structure for all the HOIPs investigated. Initial models for the structure optimization were constructed as follows:

• •

AE4T\cePbBr4: Taken as the experimental structure in Ref. Mitzi et al. (1999).

• •

AE4T\cePbX4 (X = Cl, I): Obtained by taking the experimental structure of AE4T\cePbBr4 and replacing the Br atoms with Cl and I. The lattice parameters and the atomic coordinates of non-halogen atoms were kept the same among the three hybrid compounds for the input structure. The initial configuration of AE4T molecules was kept to be syn-anti-syn as in the experimental structure of AE4T\cePbBr4.

• •

all-anti-AE4T\cePbBr4: Obtained by taking the experimental structure of AE4T\cePbBr4 and changing the configuration of AE4T to all-anti. The inner two thiophene rings of the syn-anti-syn AE4T were rotated by 180∘ around the two C atoms labeled by red “+” as the rotation axis (Fig. S7). This rotation was performed for all the 8 AE4T molecules in the unit cell.

• •

AEnT\cePbBr4 (n = 1, 2, 3, 5): Obtained by taking the experimental structure of AE4T\cePbBr4 and replacing the AE4T organic part by all-anti AEnT molecules. Using AE3T-\cePbBr4 as an example, we start from the experimental structure of AE4T\cePbBr4 with syn-anti-syn AE4T molecules. The oligothiophene part (4T) is removed while the inorganic Pb-Br framework together with the \ceEtNH3 tails are kept–i.e., the configuration of the Pb-Br framework together with the \ceEtNH3 tails is not changed during the construction. The adjacent inorganic layers are then pushed towards each other to reduce the distance between them to the extent that it is suitable for the insertion of the 3T molecules (all-anti). We then place the optimized 3T molecules into those positions where the 4T molecules originally existed (for AE4T\cePbBr4). This construction process preserves the configuration between the inorganic Pb-Br framework and the \ceEtNH3 tails (Fig. S1) and keeps the two inorganic layers in each unit cell identical.

X Experimental details for AE4T\cePbI4

Chemical. \cePbI2 (99.999% trace metal basis), HI (57 wt. % in \ceH2O, with hypophosphorous acid as stabilizer, assay 99.95%) and N,N-Dimethylformamide (anhydrous, 99.8%) were purchased from Sigma-Aldrich company. AE4T$\cdot$HI was synthesized in the lab.Muguruma et al. (1996a, b, 1998) 2-butanol (99.5%) was purchased from VWR International.

Synthesis. 2 mg \cePbI2 and 3 mg AE4T$\cdot$HI were dissolved in 0.7 ml DMF with a drop of HI. Then, 2 ml 2-butanol was layered on the top of the solution (Figure S8a). The target crystals came out after several days (Figure S8b).

Characterization. Single crystal X-ray diffraction data were collected in a Bruker D8 ADVANCE Series II at room temperature. The unit cell parameters determined from this data are a = 38.779(3) Å, b = 6.0863(5) Å, c = 12.3306(10) Å, $\beta$ = 92.271(4), V = 2908.0(4) Å3, C2/c.

XI DFT-HSE06+SOC frontier orbitals for AE4TPbX4 (X=Cl, Br, I)

XII DFT-HSE06+SOC band structures of AEnTPbBr4 (n = 1, 2, 3, 4, 5)

XIII HOMO-LUMO Gaps of isolated oligothiophene molecules

XIV Effective Mass Parameters Derived from the Band Structures Computed in This Work

XV Total and Partial Densities of States