Theoretical and Experimental Investigation of the Electronic Structure

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Theoretical and Experimental Investigation of the Electronic Structure and Quantum Confinement of Wet-Chemistry Synthesized AgS Nanocrystals 2

Shu Lin, Yu Feng, Xiaoming Wen, Pengfei Zhang, Sanghun Woo, Santosh Shrestha, Gavin Conibeer, and Shujuan Huang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp511054g • Publication Date (Web): 08 Dec 2014 Downloaded from http://pubs.acs.org on December 18, 2014

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Theoretical and Experimental Investigation of the Electronic Structure and Quantum Confinement of Wet-Chemistry Synthesized Ag2S Nanocrystals Shu.Lin,∗,†,‡ Yu.Feng,∗,†,‡ Xiaoming.Wen,† Pengfei.Zhang,† Sanghun.Woo,† Santosh.Shrestha,† Gavin.Conibeer,† and Shujuan.Huang† School of Photovoltaics and Renewable Energy Engineering, UNSW Australia, Sydney 2052, Australia E-mail: [email protected]; [email protected]

∗ To

whom correspondence should be addressed of Photovoltaics and Renewable Energy Engineering, UNSW Australia, Sydney 2052, Australia ‡ Shu Lin and Yu Feng contributed equally. † School

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Abstract The electronic and excitonic confinement of monoclinic silver sulfide Ag2 S nanocrystals (NCs) has been investigated both theoretically and experimentally. Theoretically, the electronic band gaps and the excitonic ground-state energies of Ag2 S NCs at different sizes are calculated using a hybrid method of density-functional theory (DFT) and effective mass approximation (EMA). The results have shown a good agreement with measured results, including the absorbance and photoluminescence spectra of drop-casted NC thin films. The Ag2 S NCs, synthesized using wet-chemistry methods, have demonstrated a desirable size monodispersion, allowing the measurements to be sufficiently accurate. The results show that both the electronic band gap and the excitonic energy have significant blue shift only when the diameter of monodispersed NCs is reduced below 4 nm, and the excitonic Bohr radius of Ag2 S is determined as being small at around 1 nm.

Keywords: Ag2 S NCs, Electronic structure, Quantum confinement, Wet-chemistry method

Introduction Silver sulfide (Ag2 S) is an interesting and useful material which has been studied during the past few years for applications such as photoconductors, 1 IR detectors 2 and light sensitizer. 3 It has been determined that at room temperature Ag2 S displays electronic properties as a semiconductor, with a bandgap around 1 eV and relatively large absorption coefficients. 4 These properties make Ag2 S a promising material for the next-generation photovoltaic devices. However so far only a few papers have studied the electronic structure of Ag2 S theoretically. Kashida and his group simulated the band structure of Ag2 S using the full-potential LMTO method under the local density approximation (LDA). 5 Their calculated energy gap was 0.63 eV which is much smaller than the experimental results reported. 6 In addition, the crystal structure used for this calculation was not optimized properly, and therefore further affects the accuracy of the calculated electronic structure. In previous studies much attention has been paid to the application of Ag2 S nanocrystals (NCs). 2 ACS Paragon Plus Environment

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However no obvious quantum confinement effect of Ag2 S NCs has been observed, 6–9 indicating a very small Bohr radius for Ag2 S. One of the recent papers published by Qiangbin Wang’s group 10 has demonstrated successful synthesis of high quality Ag2 S NCs with different sizes from 2.4 nm to 7 nm. They have speculated from the photoluminescence (PL) study that the Bohr radius of Ag2 S is around 2.2 nm. However, the speculation is based on the gradual change of the band gap energy with the quantum dot size, and is thus subjective. To illustrate this, it is stated in their paper that the PL emission peak is red shifted with the size of NC increases from 2.4 to 4.4 nm, while kept constant with further size increase. This only implies that the exciton diameter is at somewhere below 4.4 nm, instead of being equal to 4.4 nm. In fact, our numerical results do show a good agreement with their experimental data, while the Bohr radius is calculated to be around 1 nm. In this work we have carried out theoretical calculation of the electronic band structure of the bulk monoclinic Ag2 S using a density functional method with the exchange-correlation functional based on generalized gradient approximation (GGA). The quantum confinement effect of Ag2 S QDs has also been investigated theoretically and experimentally. Our theoretical results on the excitonic confinement of Ag2 S QDs have estimated the Bohr radius of Ag2 S to be as small as around 1 nm. The calculated size-dependent shift on the exciton ground-state energy matches well with the optical characterization results.

Electronic structure of bulk monoclinic Ag2S We have carried out theoretical simulation of the electronic band structure of bulk Ag2 S using a density functional method based on the generalized gradient approximation (GGA). Normconserving pseudo-potentials with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional were used. The computation has been performed with the software package Quantum Espresso. 11 This calculation adopted a plane-wave cutoff energy of 140 Ry, a 5 × 5 × 5 k-grid mesh, a total-energy convergence threshold of 10−8 a.u. and a force convergence threshold of

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10−6 a.u. The choice of these parameters has been justified by convergence tests. The atomic positions in the lattice were obtained by minimizing the ground-state total energy, resulting in the final optimized crystal structure of Ag2 S as shown in Fig. 1. Interesting crosslink structures are found in Ag2 S bulk form. In the primitive Ag2 S cell, sulphur atoms form a deformed bcc lattice and each sulphur atom forms covalent bonds with four silver atoms around. There are two different environment for silver atoms in the primitive cell. As shown in Fig. 1 (b) and (c) for two adjacent primitive cells there is a cross linking type of structure along the c direction comprising alternating S atoms and Ag(type 1) atoms with theses two adjacent zig-zag crosslinking chains joined by Ag(type 2) atoms.These Ag(type 2) atoms, with S atoms linked at each end form a second different crosslink structure along the b direction. Fig. 2 shows the Brillouin zone of Ag2 S. The symmetry points and lines labeled are used to demonstrate the calculated electronic band structure. The detailed crystallographic data calculated for monoclinic Ag2 S is listed in Table. 1 as well as the literature data. It is noted that the primitive cell structure optimized in this work is slightly different from the structure adopted in the reported LDA calculation. 5 In fact, the previous calculation adopted the crystal structure directly from an XRD crystallographic study 12 without performing any computational optimization. This unavoidably affects the accuracy of the following electronic structure calculation, as the crystal structure used in the calculation could yield a total energy well above the ground-state energy. This problem is eliminated here by performing a proper structural optimisation before the electronic structure calculation. The calculated band structure as well as density of states (DOS) of bulk monoclinic Ag2 S is illustrated in Fig. 3. The highest point in the valence band is at the Brillouin zone center while the lowest conduction band edge lies at the Γ−D direction. The calculated electronic structure of bulk Ag2 S displays a direct bandgap of 1.0 eV, along with an indirect bandgap of 0.92 eV. Compared with this result, the experimentally measured band gap of monoclinic Ag2 S is around 1.0 eV. 6 However, it has to be admitted that as a ground-state method DFT Kohn-Sham scheme can not be used to quantitatively predict the electronic gap of a material. 13 The band gap evaluation will be

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c*c* Z C

a* a*

A

B

! Y b*

b* D

E

Figure 2: Brillouin zone of Ag2 S further improved by adopting excited-state methods in future work. While strictly speaking the band structure of Ag2 S demonstrates an indirect bandgap, the conduction-band minimum (CBM) is in fact very close to the zone center. Therefore it exhibits electrical and optical features similar to a direct-bandgap material. The lowest conduction band has two major valleys. The lower one is located at the CBM, lying around the Γ point. The higher valley centes at the zone edge (along the A-B axis). The electronic state energy increases when moving from this centre towards point A and then to Z (or towards B and then to C). On the other hand, the highest valence band has only one valley(local maximum) centered at the Γ point (VBM). At the zone centre both the conduction band and the valence band are not degenerate except for the spin degeneracy. The respective electron density distributions of the CBM and the VBM states are illustrated in Fig. 4. It is noted that the VBM is hybridized from Ag 4d and S 3p atomic orbitals, while the CBM has mixed characters of both Ag s and S s-p orbitals.

Quantum confinement of Ag2S nanocrystals The quantum confinement effect of Ag2 S nanocrystals has attracted much attention as no obvious energy shift has been observed with decreasing size of nanocrystals 14 indicating the very small 6 ACS Paragon Plus Environment

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feasible. By solving the time-independent Schrödinger equation, each energy level corresponds to a particular angular quantum number (s, p, d, f), characterising the orbital angular momentum of carriers rotating in the spherically symmetric potential field. With the decreasing size of nanocrystals, the conduction band shifts up and the valence band down (Fig. 5 (a)). The difference of conduction band 1s and valence band 1s gives the bandgap which hence increases as the nanocrystal decreases in size (Fig. 5 (b)). Table 2: Valley minima and effective masses estimated from the DFT calculated band structure. The valence band maximum is set as the energy reference. Band Lowest conduction band

Valley position Γ A-B (literature work)

Highest valence band

Valley energy in eV (from the valence band edge) 0.914 1.338 0.63 5 (LDA) , 1.0 6,14,18 (experimental)

Γ (literature work)

0

Effective mass (in electron rest mass) 0.42 0.4 0.23 16 , 0.286 17 0.81 1.096 17

0.23 16 ,

The excitonic ground state energies in QDs with different sizes are displayed by the data points in Fig. 5 (b). They are calculated based on the variational principle accounting for the Coulomb interaction between a pair of electron and hole. 19 An empirical expression for the excitonic ground state energy with respect to the QD size has been obtained by fitting the data points:

∆Eex (eV ) = 4.8366 × d (nm) −2.1525 − 0.0959 ,

(1)

where d is the QD diameter and ∆Eex is the deviation of the excitonic ground state energy from the bulk band gap value of Ag2 S. At the bulk extreme (d → ∞), Eq. 1 provides an estimation on the excitonic binding energy (0.096 eV), in consistent with the value calculated from the commonly used Bohr model under EMA (0.104 eV). It is clearly illustrated that there is no obvious blue shift of either excitonic energy or band-toband energy until the diameter of nanocrystals decrease below 2 nm. For instance, the excitonic 8 ACS Paragon Plus Environment

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Ag2 S nanopaticles dispersed in chloroform solution were measured using Perkin-Elmer Lambda spectroscopy.The emission spectra of Ag2 S nanocrystals thin films were studied by a infrared photoluminescence spectroscopy (PL) with an excitation wavelength of 450 nm. The UV-vis-NIR absorbance spectra of the Ag2 S nanocrystal samples are shown in Fig. 7(a). All of the samples exhibit continuous absorbance spectrum from UV wavelengths to NIR wavelengths. The optical bandgap of the synthesized nanocrystals can be estimated by the Bardeen or Tauc equation 22,23

1

(α hυ ) n ∝ (hυ − Eg ).

(3)

where α is the absorption coefficient, hυ refers to the photon energy, and Eg denotes the electronic bandgap. The value n reflects the nature of the involved electronic transition. 24 Based on our calculation, n=1 for spherical nanocrystals with near-direct transitions. The validity of this equation depends on the parabolicity of the bands and their density of states near the band edge. As discussed above, for Ag2 S nanocrystals larger than 4nm in diameter, quantum confinement is negligible and hence the bands remain parabolic and the Tauc equation can be considered appropriate. Fig. 7(b) illustrates the photon energy versus the product of photon energy and the absorbance. Bandgaps of Ag2 S nanocrystals were estimated by extrapolating the linear regions to the horizontal axis. It is found that the as-synthesized nanocrystals of different diameters have bandgaps ranging from 1 eV to 1.25 eV, which confirms the small degree of quantum confinement compared with bulk. Fig. 7(c) shows the NIR PL spectra of the Ag2 S nanocrystal samples from solution. All the samples exhibit NIR spectra with similar peak positions with the main peak centered around 1200 nm. The size-independent peak position of the PL emission of the Ag2 S nanocrystals spectra is due to the heavy carrier effective mass and relatively small exciton Bohr radius, which leads to very little increase of the band-edge energies. Another possible reason is that the surface electronic states induced by the DDT surfactants may be responsible for the lowest emission energies. Based on our previous calculation the exciton binding energy is estimated as 0.1 eV resulting in an emission energy of 0.9 eV. It is clear that a shoulder peak at ∼0.9 eV exists in the the measured PL 11 ACS Paragon Plus Environment

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emission, creating an amorphous tail. This effect is the most significant in small-size nanocrystals, as a result of their poor crystallinity and large surface-to-volume ratio.

Conclusion In summary, we have investigated the electronic structure of bulk monoclinic Ag2 S using a density functional method. The optimized crystal structure of Ag2 S is studied by minimizing the total energy based on the GGA exchange-correlation functional. The quantum confinement effect of Ag2 S nanocrystals is theoretically discussed based on our simulation of the bands energy shift with the deceasing size of nanocrystals. The Bohr radius is found to be 1.15 nm and quantum confinement calculated to be negligible above 4 nm in nanocrystal diameter. Experimentally we successfully synthesized monodispersed Ag2 S nanocrystals with size ranging from 4.4 nm to 6.8 nm. The bandgaps of the fabricated Ag2 S nanocrystals are investigated by absorbance and photoluminescence measurement. The effective mass and Bohr radius we calculated explain the reasons for no obvious quantum confinement effect being observed for Ag2 S experimentally.

Acknowledgement This work is financially supported by the Australia Government through the Australian Renewable Energy Agency (ARENA). We are also thankful to the Mark Wainwright Analytical Centre, University of New South Wales, Australia, for providing characterization facilities for this research.

Supporting Information Available Details on the theoretical methods used for electronic and excitonic state calculation and the experimental methods for nanocrystal synthesis and characterisation. This material is available free of charge via the Internet at http://pubs.acs.org/.

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