Electron properties of 13-atom nanoparticle superlattices

Journal Pre-proofs Electron properties of 13-atom nanoparticle superlattices U.N. Kurelchuk, P.V. Borisyuk, O.S. Vasilyev PII: DOI: Reference:

S0167-577X(19)31732-X https://doi.org/10.1016/j.matlet.2019.127100 MLBLUE 127100

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Materials Letters

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1 December 2019

Please cite this article as: U.N. Kurelchuk, P.V. Borisyuk, O.S. Vasilyev, Electron properties of 13-atom nanoparticle superlattices, Materials Letters (2019), doi: https://doi.org/10.1016/j.matlet.2019.127100

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Electron properties of 13-atom nanoparticle superlattices U.N. Kurelchuka,∗, P.V. Borisyuka, O.S. Vasilyeva a National

Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow, Russia

Abstract A density functional theory (DFT) study of electronic properties and Seebeck coefficient S of d-metal (Au, Ag, Pt, Pd, Ta) 13-atom nanoparticle superlattices is presented. The geometry optimization, calculations of electronic structure and density of electron states (DOS) was performed in DFT generalized gradient approximation in Perdiew-Burke-Ernzerhoff form (GGA-PBE) with full relativistic pseudopotentials. From the band structure S values are calculated using semi-classical Boltzmann equation in τ approximation. A size-dependent appearance of features in DOS near Fermi level is shown. The influence of these features on S is discussed. Potential usage of such model materials with strong DOS features near Fermi level as a source of varied energy monochromatic photons in metal insulator semiconductor structures for resonant excitation of long-lived forbidden states, including nuclear ones is discussed. Keywords: d-metals; nanoparticle superlattice, density functional theory, electronic properties, Seebeck coefficient. 1. Introduction The task of photoelectric, thermoelectric materials (PEM and TEM) efficiency enhancement is one of actual challenges of current energetics, ecology and nanotechnology. Properties of PEM and TEM defines the efficiency of thermal energy or photon energy conversion into electricity. Now the state-ofthe-art TEM, for example, is predicted to have thermoelectric figure of merit 2 T (where σ is electrical conductivity, S is the Seebeck coefficient, T ZT = κσS e +κl is temperature, κe , κl are electronic and lattice thermal conductivity) up to the value 3, but for the most of commercially produced materials the value ZT < 2 [1]. In fact, TEM must have conflicting properties, namely high S and σ values along with low κe and κl values. In order to optimize charge and transport properties a number of approaches are now under study while modeling new efficient ∗ Corresponding

author Email address: [email protected] (U.N. Kurelchuk)

Preprint submitted to Materials Letters

November 29, 2019

TEM [1, 2]. The difficulty of the problem is caused by complex dependence of charge and transport properties on carrier quantum properties in material such as concentration, velocity and density of electron states in the vicinity of the Fermi level Ef , effective masses, mobility. At the same time, nanomaterials are known to show dependence of quantum properties on size of nanomaterial (e.g. nanoparticle (NP), nanotube). That fact is widely used to optimize TEM properties by doping semiconductor nanomaterials into bulk ones [3, 4]. The reason is that S is dependent not only on DOS value at Ef , ρ(EF ), but on the d ln ρ its behavior S ∼ dE . Thus the electron band structure size-dependent E=Ef

change in nanomaterials may lead to formation of local density electron peak near Ef that would enhance S. Unfortunately, size dependent quantum properties changes mostly in the size range of several nanometers that is in the size range when semiconductors might become dielectric due to bandgap broadening and electron density decrease. At the same time metal NPs shows metallic properties down to 2 nm in diameter and lower [5] that opens the possibility of porous materials formation made of nanometer sized d-metal NPs (as soon as d-metals already have DOS features near Ef ) and study its electron properties. In this work electron properties of model porous material, namely superlattice made of d-metal 13-atom NPs (Au, Ag, Pt, Pd, Ta) placed in a sites of cubic/hexagonal lattice was studied by computation method. The geometry of model material was optimized, it’s electronic structure was calculated using density functional theory. Using the obtained data the S value was calculated. The use of such material is discussed in the context of their application in photovoltaic and thermoelectric devices. From the TEM point of view the studied thermoelectric materials are considered as standard thermocouples with different sign of S, and from the photovoltaic devices point of view, the use of such films in metal-insulator-semiconductor junction (MISJ) and metal-insulatormetal junction (MIMJ) is discussed. 2. Methods and calculations Geometry of NPs was defined taking into account that the most energetically preferable and stable form of 1-2 nm sized d-metall NPs is icosahedron with 13 atoms [6, 7]. This initial geometry was then optimized by Broyden, Fletcher, Goldfarb, Shanno method taking into account electron-electron interaction in the GGA-DFT framework. The parameters of model superlattices with defined symmetry (cubic, hexagonal) was determined by a structure relaxation procedure using interatomic potential of the embedded atom model [8] in order to avoid disordering by interatomic forces and save individual NPs. Further structure optimization is made for elementary cell at each step using self-consistent potential, calculated by DFT method considering valence and subvalence electrons. Ground state and band structure is calculated for optimized cell. All the DFT calculations are made using generalized gradient approximation with exchange energy Exc functional parameterization in PBE form considering spinorbital interaction and non-collinear magnetization with full relativistic ultrasoft 2

DOS, arb. nits

b lk hexagonal c bic −8

−7

−6

−5

−4 −3 E-E , eV

−2

−1

0

1

f

Figure 1: (Left) The calculated DOS for Au-13 NP superlattices: cubic hexagonal and the calculated bulk Au DOS for comparison; (Right) A schematic representation of cubic 13-atom NP superlattice

pseudopotentials [9] in the basis of plane waves in Quantum Espresso program [10]. Self-consistent ground state calculations were performed on a 4 × 4 × 4 inverse space k-grid with a plane wave cutoff energy of 540 eV. For the obtained ground state, the band structure of Ei,k and DOS was calculated on the Monkhorst-Pack k-grid 48 × 48 × 48. Seebeck coefficient S calculated from the solution of semi-classical Boltzmann transport equation in the constant relaxation time τ approximation via the numeric band structure Ei,k : " #   R P ) ′ vi,k × vi,k δ(E − Ei,k ) (E − µ) − ∂f (E,µ,T dE ∂E i=1..N,k∈BZ 1 " # S=   eT R P ) ′ vi,k × vi,k δ(E − Ei,k ) − ∂f (E,µ,T dE ∂E i=1..N,k∈BZ

where: i = 1..N is the indexes of the bands, k is the wave vectors in the 1st Brillouin zone marked as BZ, µ is the chemical potential, f (E, µ, T ) is the Fermi distribution) was calculated by the BoltzTrap method [11]. Seebeck coefficient was calculated for temperature range 300-500 K. 3. Results The results of DOS and S calculations of the most energetically favorable lattices (cubic and hexagonal) of the most stable small NPs is shown in Fig. 1. The calculations have shown that for superlattices with a cubic symmetry made of 13-atom NPs the quantum size effect is observed clearer, resulting in the electron population at Ef increase ρ(Ef ) and the steepening of DOS ρ(E)|E=Ef near Ef . In Fig. 1 one can see that density of the valence and subvalent states of superlattices compared to the bulk one migrates to Ef . The cubic superlattice has a steeper DOS near Ef , which is an indirect sign of an increase in the direction-averaged group velocity. A schematic representation of cubic 13-atom 3

100

Pd-13 Ta-13 Au-13

90

|S|, μV/K

DOS, arb.units

80 70

Au Ag Pd Ta Pt

60 50 40 30

−8

−7

−6

−5

−4 −3 E-E , eV

−2

−1

0

1

300

f

325

350

375

400 T, K

425

450

475

500

Figure 2: (Left) DOS calculated for cubic Au-13, Pd-13, Ta-13 superlattices; (Right) Absolute values of S calculated for Me-13 superlattices, Me=Au, Ag, Pt, Pd, Ta for temperature range T = 300 − 500 K

NP superlattice is presented in Fig. 1 (Right). Figure 2 (Left) shows the DOS of model Au-13, Pd-13, Ta-13 superlattices. The calculated values of S at T=300500 K for superlattices of various d-metal 13-atom NPs (Au, Ag, Pt, Pd, Ta) are shown in Fig. 2 (Right). In Fig. 2 (Right) one can see that the calculated absolute values of S of the model nanostructured materials made of Au, Ag, Pt, Pd, Ta at temperature range 300-500 K are significantly higher than the one for the corresponding bulk metals (1.94 µV /K, 1.5 µV /K, −2.2 µV /K, −10.0 µV /K, −1.9 µV /K for bulk Au, Ag, Pt, Pd, Ta correspondingly [12]). For all model NP superlattices, a significant increase in S(T ) can be seen, as well as an increase in its temperature derivative (with the exception of Pt). The values reached at T = 500 K for Au, Ag, Pt, Pd, Ta 13-atom NP superlattices are 93 µV /K, 81 µV /K, -30 µV /K, -61 µV /K, 45 µV /K correspondingly. 4. Discussion Considering the obtained results it seems reasonable to use such NP films/ tracks/ electrodes with different S as thermocouples or Peltier elements. It is important to note that the conductivity of NP systems is close to metal (for example, for nickel NPs one can reach values close to the conductivity of bulk metal[13]). This means the possibility of using these structures in MISJ or MIMJ structures instead of metal films [14]. Then conductivity of metal NP films allows to generate uniform the potential difference at the interface semiconductor/insulator/NP film. Additionally, possessing strong quantum features in connection with the size effects for metals with unfilled d-orbitals, NP film will increase the efficiency of electron tunneling from states near Ef . Indeed, numerical estimations of the product of the probability of tunneling through a dielectric barrier (SiO2 ) with a thickness of 2 nm and the applied 5 V bias between Pd NP metal film (superlattice) and a semiconductor (Si++ ), show that the probability of tunneling electrons near Ef at room temperature (the product of DOS and the probability of tunneling [15] into empty Si states from the filled states of the palladium superlattice) is 3 times greater than for 4

Intensity, arb. units

Au Pd

0.0

0.2

0.4

E-E , eV

0.6

0.8

1.0

f

Figure 3: The spectrum of tunneling electrons from NP film (Au, Pd) into Si through a dielectric barrier (SiO2 ) with 2 nm thickness

a Au NP metal film (see Fig. 3). The width of the tunnel electron spectrum for a superlattice of NPs with an unfilled d-shell (palladium) is FWHM=0.13 eV, which is substantially smaller than the width of the tunnel electron spectrum for d-shell filled NPs (gold), where FWHM=0.20 eV. In fact, the observed in Fig. 3 shape of tunneling electrons spectrum indicates that the studied structures allow to form a flow of electrons with a narrow, almost monochromatic energy distribution. In this case, the kinetic energy of tunneling electrons is associated with the bias applied to the semiconductor and a metal in MISJ structures. This circumstance is very attractive for using such structures for spectroscopy of defects in the band gap of thin-film dielectrics. Thus by changing the bias it is possible to fill discrete states in the bandgap with electrons. One can expect the appearance of features in tunneling IV-curves measurements that will be observed in case of resonant combination of tunneling electrons energy with individual levels localized in a band gap. In this case, the kinetic energy of tunnel electrons should not exceed the energy difference between Ef and insulator vacuum level. With increasing electron energy, tunneling will pass through a continuous part of the spectrum (above the vacuum level), that will lead to the impossibility of resonant tunneling through vacancy and impurity levels. However, another interesting possibility opens up to carry out resonant excitation of long-lived forbidden states, including nuclear ones [16]. That is the capture of electrons from the continuous spectrum by ion traps followed by radiative recombination and emission of monochromatic radiation. The condition for this process, followed by the emission of a photon with energy hν, is determined by the equality between electron kinetic energy and bound state binding energy, measured from the vacuum level. By varying the tunneling electron energy, it is possible to scan with photons of different energies. If a separate optical spectral line appears during scanning for some electron energy, then the excitation of this bound state occurs. In fact, that is the formation of an internal source of monochromatic photons with reconfigurable energy. The key feature

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here is that tunneling electrons current can be very large up to several amperes [17], which means that even the long-lived, forbidden states used today in quantum metrology for systems with embedded ions in the matrix of a wide-band dielectric crystal can be excited. Thus, the use of NP superlattices considered in the work has considerable practical interest and can help in solving both fundamental and modern engineering problems. Acknowledgements This work was financially supported by Grant of the Russian Science Foundation (project No. 19-72-30014). References [1] T. Zhu, Y. Liu, C. Fu, J. P. Heremans, J. G. Snyder, X. Zhao, Compromise and Synergy in High-Efficiency Thermoelectric Materials, Advanced Materials 29 (14) (2017). [2] J. He, T. M. Tritt, Advances in thermoelectric materials research: Looking back and moving forward, Science 357 (6358) (2017). [3] H. Alam, S. Ramakrishna, A review on the enhancement of figure of merit from bulk to nano-thermoelectric materials, Nano Energy 2 (2) (2013) 190– 212. [4] C. H. Lee, G. C. Yi, Y. M. Zuev, P. Kim, Thermoelectric power measurements of wide band gap semiconducting nanowires, Applied Physics Letters 94 (2) (2009) 2007–2010. [5] V. Borman, P. Borisyuk, O. Vasiliev, M. Pushkin, V. Tronin, I. Tronin, V. Troyan, N. Skorodumova, B. Johansson, Observation of electron localization in rough gold nanoclusters on the graphite surface, JETP Letters 86 (6) (2007). [6] M. Zhou, M. Y. Sfeir, Y. Chen, Y. Song, R. Jin, R. Jin, Electron localization in rod-shaped triicosahedral gold nanocluster, Proceedings of the National Academy of Sciences of the United States of America 114 (24) (2017) E4697–E4705. [7] B. Narayanan, A. Kinaci, F. G. Sen, M. J. Davis, S. K. Gray, M. K. Chan, S. K. Sankaranarayanan, Describing the Diverse Geometries of Gold from Nanoclusters to Bulk - A First-Principles-Based Hybrid Bond-Order Potential, Journal of Physical Chemistry C 120 (25) (2016) 13787–13800. [8] P. A. Olsson, Transverse resonant properties of strained gold nanowires, Journal of Applied Physics 108 (3) (2010).

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