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Ab Initio Study of Electronic Excitation Effects on SrTiO Shijun Zhao, Yanwen Zhang, and William J. Weber

J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b08185 • Publication Date (Web): 14 Nov 2017 Downloaded from http://pubs.acs.org on November 19, 2017

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The Journal of Physical Chemistry

Ab Initio Study of Electronic Excitation Effects on SrTiO3

Shijun Zhao,† Yanwen Zhang†,‡ and William J. Weber‡,†,*

†

Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA ‡

Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37996, USA

*

[email protected]

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Abstract

Interaction of energetic ions or lasers with solids often induces electronic excitations that may modify material properties significantly. In this study, effects of electronic excitations on strontium titanate SrTiO3 (STO) are investigated based on first-principles calculations. The lattice structure, electronic properties, lattice vibrational frequencies and dynamical stabilities are studied in detail. The results suggest that electronic excitation induces charge redistribution that mainly observed in Ti-O bonds. The electronic band gap increases with increasing electronic excitation, as excitation mainly induces depopulation of Ti 3d states. Phonon analysis indicates that there is a large phonon band gap induced by electronic excitation because of the changes in vibrational properties of Ti and O atoms. In addition, a new peak appears in the phonon density of states with imaginary frequencies, an indication of lattice instability. Further dynamics simulations confirm that STO undergoes transition to an amorphous structure under strong electronic excitations. The optical properties of STO under electronic excitation are consistent with the evolution of atomic and electronic structures, which suggests a possibility to probe the properties of STO in non-equilibrium state using optical measurement.


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1. Introduction

Understanding ion-solid interactions is fundamental to applications of ion beam techniques in synthesizing, analyzing and modifying materials. In such applications, energy is transferred from energetic ions to both electrons and atomic nuclei in target materials, which leads to defect production and property changes. It is well established that the energy transfer to atomic nuclei is through elastic collisions (nuclear energy loss), resulting in ballistic collision cascades. However, inelastic energy loss to electrons is more complicated and its effects on defect behavior are less understood.1 It has been shown that electronic energy loss, as well as the coupling between electronic and atomic processes, play a significant role in governing defect dynamics under ion irradiation.1–4

Intense energy deposition into electrons in target materials induces strong electron excitations and ionization. It is expected that the effect of such electronic energy loss on defect production and evolution is more pronounced in ceramics than in metals because of their relatively low thermal conductivities, in which electron excitations are highly localized.5 Indeed, substantial recrystallization is observed in electron beam irradiated strontium titanate SrTiO3 (STO), which is ascribed to localized electronic excitations.6 Irradiation of STO single crystals with swift heavy ions leads to remarkable modifications of the surface due to strong electronic excitation.7,8 Studies also demonstrate an extraordinary synergy between electronic energy loss and pre-existing defects STO.9,10 As a typical perovskite oxide, STO possess an exceptional variety of properties, such as blue light emission11,12 and ferroelectricity,13 and it is also considered for nuclear waste immobilization.14 Given its simple cubic lattice symmetry and technological importance, STO is an ideal model system to study the effects of electronic excitations on lattice stabilities.

Experimentally, strong electronic excitations and ionization often occur during swift heavy ion and laser irradiations. Both methods can create extreme non-equilibrium conditions in materials, thus providing 3 ACS Paragon Plus Environment


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viable ways to manipulate electrons and modify material properties.15 In these processes, the electrons are excited in a very short time (a few tens of femtoseconds). Through electron-electron collisions, these excited electrons quickly re-populate according to a Fermi-Dirac distribution. The high electronic energy subsequently dissipates into the lattice via electron-phonon coupling and leads to local heating of the lattice.16–19 In the widely used two-temperature model20 to describe the energy transport between the electronic and atomic subsystem, it is generally assumed that the excited electrons can achieve an equilibrated state rapidly so that an electronic temperature Te can be defined. This temperature is much higher than lattice temperature Ti initially, and evolution of the system is governed by heat diffusion equations. However, this two-temperature model requires many thermodynamic parameters, such as electronic heat capacities, electron-phonon coupling constant and thermal conductivities, which necessitate further approximations in order to obtain these quantities. On the other hand, first-principles calculations based on the finite-temperature density functional theory (FT-DFT)21–24 can be directly employed to study time evolution of the two-temperature system by defining a finite electronic temperature. Previous FT-DFT simulations have been successfully used to understand the properties of metals and semiconductors due to the presence of excited electrons induced by laser irradiation.15,25–28

In this work, the effect of electronic excitation on the lattice stability of STO is studied using the FT-DFT method. The lattice structures, electronic properties, phonon frequencies and dynamic evolutions of STO under strongly electronic excitations are investigated. It is found that excitation mainly induces instability in the Ti-O bonds, consistent with dynamic simulations. In accordance with the changes of Ti-O bonds, there is a large phonon band gap observed upon excitations. Initiated by the breaking of Ti-O bonds, a transition to an amorphous structure is observed at Te=3 eV. The influence of electronic excitation on optical properties of STO is also discussed.

2. Calculation details 4 ACS Paragon Plus Environment

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FT-DFT calculations were performed using the Vienna ab initio simulation package (VASP).29 Interactions between nuclei and core electrons were treated within the projector-augmented-wave (PAW) method.30 A gradient corrected functional in the Perdew-Burke-Ernzerhof (PBE) form was used to describe the exchange and correlation interactions.31 Spin-polarized calculations were carried out with an energy cutoff of 500 eV and a 10×10×10 k-point mesh. The energy and force convergence criteria were set to be 10-4 eV and 0.01 eV/Å, respectively. The total energies at different volumes were calculated, and the equilibrium lattice parameters were determined by fitting the energy-volume curve to the third-order Birch-Murnaghan equation of state.32,33 The optimal lattice structure of STO was then subjected to electronic excitations by increasing Te. The electronic densities of states (DOS) were computed using a denser k-point mesh of 20×20×20 with the tetrahedron method by performing a non-self-consistent calculation using the pre-calculated charge density from a self-consistent run. Phonon calculations were performed using the finite differences method34 with a displacement of 0.01Å. A 2×2×2 supercell and a 5×5×5 k-point mesh were applied to calculate the force constants. The code PHONONPY35 was used to calculate phonon frequencies based on the obtained force constants. Note that previous calculations suggest that the supercell size used here is adequate to give accurate phonon frequencies for a simple cubic lattice.36

Ab initio molecular dynamics (AIMD) simulations at finite temperature were also performed to study the influence of electron excitation on the STO structure. These simulations were carried out in a 2×2×2 supercell with a reduced 3×3×3 k-point mesh. Here a lower k-point sampling was used because of the high computational cost of MD simulations. This method is frequently used in AIMD simulations to provide an efficient but still accurate enough sampling of the configuration space. The microcanonical ensemble (constant NVE) was adopted, and the electrons were initially populated according to a FermiDirac distribution with different electronic temperatures to model the electronic excitations. A timestep of 0.5 fs was used and the total simulation time was around 2 ps.



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To calculate optical properties of STO under electronic excitation, the ABINIT package37 was used with PAW pseupotentials and the PBE functional. The cutoff energies for plane-waves and the fine FFT grid were 450 eV and 1200 eV, respectively. The accuracy of PAW atomic data was tested regarding the lattice parameters and electronic properties at ambient conditions. The Ionic configurations used for optical calculations were extracted from the last 2500 steps of previous AIMD simulations. A total of 5 structures were simulated with an interval of 500 steps, and the final results are averaged. The optical properties were calculated from the Kubo-Greenwood formalism.38 In this calculation, a 6×6×6 k-point mesh was used, and considerable electronic states were included to take into account the high electronic temperatures.

3. Result

3.1 Electronic properties

Excitation of electrons may lead to significant changes in the lattice structure and electronic properties. To describe this effect, the variation of the lattice constant for STO at different Te is first studied by calculating the electronic free energy at different lattice constants. The results are shown in Figure 1(a). The optimal lattice constant can be obtained by fitting the energy-volume data to the third-order BirchMurnaghan equations of state.32,33 At ambient conditions, the lattice constant of STO is determined to be 3.94 Å, in good agreement with previous results based on the PBE functional.36,39 Compared to the experimental value of 3.90 Å,40 the calculated value is slightly overestimated (1%), which is typical of the used PBE functional. With increasing Te, the free energy of the system decreases because of increased contribution from the entropy TeS. This is also found in previous calculations for other materials.41 Moreover, the minimum in the free energy curve shifts to larger lattice constants with increasing Te. At a high Te of 4 eV, no minimum is identified in the considered region. Therefore, electronic excitation will lead to lattice expansion. This effect can be understood by weakened interatomic forces because more 6 ACS Paragon Plus Environment

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valence electrons are excited to mid-gap state or conduction bands at high Te. Taking into the consideration that instantaneous energy deposition leads to hot electrons within a short time before the lattice is influenced, we calculate the DOS and phonon frequencies at different Te using the lattice parameters at normal conditions.42

Figure 1 Te-dependent electronic free energy (a) and DOS (b) of STO. In (a), the dotted line represents the optimal lattice constant of STO at ambient conditions (3.94 Å) calculated by fitting the energy-volume curve. In (b), the DOS calculated at 10-3 eV is denoted by shaded area. The Fermi-Dirac distributions of electrons are also given with dashed lines. The Fermi level is set to be 0 eV.

The changes of DOS with increasing Te are shown in Figure 1(b). The energy band gap of STO at ambient conditions is calculated to be 1.83 eV at the PBE level. This value is comparable to a previous 7 ACS Paragon Plus Environment


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value of 1.81 eV39 based on the PBE functional, as well as values of 1.8043 and 1.61 eV44 based on the local density approximation (LDA). All these values are smaller than the experimental value of 3.25 eV45 because standard DFT functionals, such as PBE and LDA, always underestimate gap energies. To solve this problem, methods beyond standard DFT can be used, such as the DFT+U method,46,47 hybrid functionals, such as PBE048 and HSE,49 or many-body perturbation approaches.50 For STO, it has been demonstrated that these methods can give an electronic band gap close to experimental values.36,43,44,51–54 In this study, we focus on the effects of electronic temperature, and the discussion regarding the trend of electronic properties induced by electronic excitation is not likely to be affected by this underestimation, although the exact transition electronic temperature that leads to changes of electronic properties of STO would be influenced. Figure 1(b) shows that the energy gap increases with increasing Te. At Te=4 eV, the band gap is 6.39 eV, much higher than the value at normal conditions. In the DOS plot, the valence band maximum is set to zero in order to make comparisons. The valence band from -5 to 0 eV shrinks gradually, since electronic excitation leads to electron depopulation in valence band. For conduction band, the band minimum increases with increasing Te. The change of DOS is attributed to the change of electron populations, as shown by dashed lines in Figure 1(b). Here the increase of band gap is obtained by increasing Te but keeping the lattice structure unperturbed. This state can only exist in a short time when electronic subsystem is highly excited. The subsequent energy exchange between electronic and ionic systems will lead to lattice heating, as demonstrated by molecular dynamics in the following sections, which will further affect the band gap of STO.

Further insight into the changes of electronic structure can be gained from charge redistribution plot and the projected densities of states (PDOS) provided in Figure 2. The charge density difference between Te=0 eV and Te=2 eV is given. The PDOS demonstrates that the top of the valence band is composed of 2p states from O. The bottom of the conduction band is mainly from hybridization between 3d states from Ti and 2p states from O,39 as evidenced from the enlarged inset in Figure 2(a). Upon electronic excitations, Figure 2(b) shows that there is electron buildup around O atoms; whereas electron depletion occurs 8 ACS Paragon Plus Environment

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around Ti atoms. The electrons transfer from Ti to O atoms, while the electrons around Sr are not influenced much. This is understandable since the valence band top and conduction band bottom mainly involve states from Ti and O. Under excitation, parts of electrons from valence bands are excited to band gap region or conduction band, as indicated by population distribution in Figure 1(b). The charge density difference analysis suggests that there is electron gain in O atoms and depletion in Ti atoms, suggesting that Ti atoms are more prone to excitations. To confirm this observation, we have calculated the electron number in O 2p states by integration of PDOS to the Fermi level. The results show that the occupied electrons in O 2p states increases by 0.42 e/atom from Te=0 to Te=4 eV, whereas those in Ti 3d states decreases by 0.84 e/atom. Therefore, excitation mainly induces depopulation of Ti 3d states and population of O 2p states.

Figure 2 The projected density of states (PDOS) of STO at ambient conditions (a) and the charge difference isosurface between Te=0 eV and Te=2eV (b). In (a), an enlarged inset about the details near the band gap region is also provided. In (b), charge accumulation is denoted by purple color while charge depletion is denoted by yellow. The isovalue is set to be 0.005 e/Bohr3. Sr, Ti and O atoms are represented by green, blue and red balls, respectively.

3.2 Lattice stabilities 9 ACS Paragon Plus Environment


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The electronic properties under electronic excitations suggest that the Ti-O bonds are strongly affected, which may change the mechanical stability of STO lattice. To evaluate the lattice stabilities upon excitations, the phonon frequencies at different Te are calculated. At normal conditions, the frequencies at the Γ and R points are provided in Table I, together with previous calculations36,55 and experiment values.56,57 Owing to the cubic symmetry, there are four t1u modes and one t2u mode at the Γ point. Among them, three t1u modes are infrared active and the t2u mode is neither infrared nor Raman active. At the R point, there are six modes. Our calculated frequencies are in good agreement with literature values based on the PBE functional. Specifically, the TO1 mode is soft with an imaginary frequency of 128 cm-1. Also, the R4+ mode is soft, in line with previous results. These two soft modes at the Γ and R points are responsible for the ferroelectric58 and anti-ferrodistortive57 properties of STO, respectively. Note that STO is an incipient ferroelectric material,13 which is characterized by the saturation of dielectric constant with decreasing temperature.59 Previous studies also suggest that phonon frequencies of STO from ab initio calculations are dependent on the functional used, as well as the harmonic approximations.36 At the PBE level, our results are in line with previous reports, which yield imaginary frequencies at both Γ and R points.

Table I Phonon frequencies (in cm−1) of STO calculated at the Γ and R points compared to previous theoretical (Theo.) and experimental (Expt.) values.

Γ (0,0,0)

R (0.5, 0.5, 0.5)

Present

Theo.36

Theo.55

Expt.56,57

t1u (TO1)

130i

133i

115i

91

t1u (TO2)

145

146

147

170

t2u (silent)

233

226

234

265

t1u (TO3)

509

508

512

547

R4+

68i

86i

~90i

52

R5+

125

128


145

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R4-

414

413

446

R5+

423

419

450

R3+

431

433

474

R1+

797

798

~800

Upon electronic excitation, phonon frequencies may be changed due to the modification of the potential energy surface in the system. Previous studies have demonstrated that when Te is increased, metals tend to become more stable due to increased Debye temperature, elastic constants and melting temperature.42 On the other hand, semiconductors, such as Si, become unstable because of transverse acoustic phonon instability. For STO, the variation of phonon frequencies at the Γ and R points under different Te are provided in Figure 3, together with the total phonon DOS. These phonon frequencies are calculated based on the optimized lattice at normal conditions, but at different Te. This corresponds to the first step of instantaneous energy deposition prior to any significant energy transfer from the hot electronic subsystem to the cold lattice.



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Figure 3 Te-dependent phonon frequencies at the Γ (a) and R (b) points and phonon DOS (c). In (a), there are four t1u modes and one t2u mode at the Γ point. In (b), six modes are shown at the R point. The shaded curve in (c) denotes phonon DOS at ambient conditions.

Figure 3 shows that the phonon frequencies at the Γ and R points show different variations with increasing Te. At the Γ point, the frequencies of all modes first increase when Te increases to 1 eV.


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Afterwards, all frequencies decrease with increasing Te, except the TO3 mode that continuously increases at higher Te. The frequencies at the R point exhibit different variations for different modes, indicating that bond softening and hardening are both induced by excited electrons. At high Te, frequencies at both points start to split and form a gap at ~500 cm-1. Note that the degeneracies of the phonon modes are not affected by electronic excitations, since the lattice symmetry is not changed in the calculations. Here, the two soft modes at the Γ and R points show strong temperature dependencies. The total phonon DOS in Figure 3(c) suggests that there is a phonon band gap produced ranging from 400-600 cm-1 because of electronic excitation, which is also visible from frequencies at the Γ and R points as shown in Figure 3(a) and 3(b). The phonon band gap is ascribed to perturbed Ti-O bonding in STO due to electronic excitation, since the intermediate and high frequency states are contributed by Ti and O vibrations. Another feature is that there are sharp peaks developed at imaginary frequencies starting from Te= 2 eV, leading to another band gap around 100i-0 cm-1. The appearance of this peak indicates that the STO lattice may be strongly perturbed starting at Te=2 eV.

The frequencies reported above are calculated within the harmonic approximation. Upon instantaneous energy deposition, the electrons become hot quickly whereas the lattice is still not affected. The energy exchange between electrons and ions will lead to strong anharmonicities. It is suggested that anharmonicity starts to dominate and cannot be ignored for times greater than ~100 fs.15 In this case, anharmonicities and phonon-phonon interactions should be considered. To this end, ab initio molecular dynamical simulations are performed, as described in the next section.

3.3 Dynamical properties

The response of STO to electronic excitations is further examined by performing AIMD simulations at different Te. The evolution of ionic temperature (Ti) as a function of simulation time is shown in Figure 4(a). It is suggested that Ti is not much influenced when Te=1 eV. Further increase of Te induces a 13 ACS Paragon Plus Environment


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significant increase of Ti as the ions in STO start to acquire kinetic energy from the interaction with excited electrons. Figure 4(a) shows that the increase of Ti is very fast (~ 0.1 ps), then it stabilizes around a constant value. At Te=2 eV, the equilibrium Ti is about 500 K, whereas it increases to 1000 K and 1700 K at Te values of 3 eV and 4 eV, respectively.

Figure 4 The evolution of ionic temperature (Ti) (a) and radial pair distribution function g(r) (b) at different electronic temperatures. The shaded curve in (b) denotes g(r) at normal conditions (Te=Ti=300K).

The structure changes can be better understood by the radial pair distribution function g(r), as provide in Figure 4(b). Here the g(r) of STO at normal conditions (Te=Ti=300K) is represented by the shaded curve. It is seen that the first peak is located at approximately 1.94 Å, which represents the averaged Ti-O first nearest neighbor distance. When electrons are excited, the position of the first peak starts to shift towards larger distances, suggesting an elongation of the Ti-O bonds. At Te=3 eV, only one sharp peak is found at 14 ACS Paragon Plus Environment

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~2.5 Å, and the long-range order disappears, suggesting an amorphous transition. In this case, Figure 4(a) shows that the equilibrium Ti is 1000 K. Note that this lattice temperature is far below the melting temperature of STO (2300 K). An additional AIMD simulation was performed at Te=Ti=1000 K and 2000 K to check the g(r), and it is found that all the peaks are still well preserved. Therefore, the amorphization observed under electron excitation is not a thermal melting process.

The dynamic simulations suggest that excitation-induced melting of STO starts from Te=3eV. At this state, the results shown in Figure 3 indicate that there is a sharp peak at imaginary frequencies developed in phonon DOS. Therefore, the lattice becomes unstable due to the excitation, which further facilitates the melting of the lattice. Experimentally, it is reported that irradiation of STO by swift heavy ions can lead to discontinuous chains of nanosized hillocks on the surface under grazing incidence,7,8 discontinuous or continuous amorphous tracks in defect-free or defective STO,10 or amorphous surface layer8 under normal incidence. These observations may not be fully explained by a thermal melting process within the twotemperature model. Our ab initio results provide evidence that amorphization induced by high electronic excitation may not entirely a thermal process. Instead, it may be initiated by excitation-induced lattice instability, followed by nonthermal melting. In reality, a combination of these processes may be involved.

The time evolution of the total electronic free energy and mean squared displacements (MSD) at Te=4 eV are shown in Figure 5. The results indicate that, upon electronic excitation, the total electronic free energy first decreases through energy transfer between the electronic and ionic subsystems and then achieves a stable state. The decrease of electronic free energy is ~ 1 eV per formula unit. The MSD suggests that the system becomes diffusive, with O diffusing the fastest. The Ti atoms also have a larger diffusivity than Sr, as determined by the slope of MSD, suggesting a larger displacement of the Ti-O bonds, which contributes more to the amorphization of STO, consistent with previous electronic analysis.



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Figure 5 Time evolution of the total electronic free energy at Te=4 eV (a) and the corresponding mean squared displacements (MSD) of STO (b). In (a), the initial energy is set to be 0 eV.

The optical and thermal properties under electronic excitations are of particular interest because these parameters characterize the energy absorption ability of materials. The evolution of the dielectric function ε=ε1+iε2 and optical index ݊෤ =n+ik at different Te is shown in Figure 6. The experimental dielectric function at ambient conditions60 is also provided. Compared to experimental data, the present calculations underestimate the peak positions, which can be traced back to the underestimation of the band gap for STO. As a result, the peaks, representing interband and intraband transitions, appear at lower energies. Nevertheless, the general features of the spectra are correctly reproduced. Thus, the general trend of the spectra, which is of interest here, is not affected.


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Figure 6 The calculated real (ε1) and imaginary (ε2) parts of the complex dielectric function, as well as the refractive index (n) and extinction coefficient (k) of STO under different electronic temperatures. The crosses denote experimental dielectric function at ambient conditions.60

At normal conditions, our calculated ε1(0) and n(0) are 6.5 and 2.6 respectively, which are comparable with values of 6.2 and 2.5 from a previous caclulation.61 As STO is an incipient ferroelectric material, the dielectric constant of STO is extremely high (order of 104) at low temperature.59 In our calculations, the static dielectric constant, which is given directly by its real part ε1(0), is orders of magnitude lower than the experimental measurement. The discrepancy originates from the role played by phonons, especially the low frequency soft mode phonons. Previous studies based on a simplified classical oscillator dispersion model indicate that by adding phonon contributions, the static dielectric constant of STO increases significantly (1245 at 85 K).62 The results suggest that soft phonon modes and their temperature dependence have a dominant effect on the static dielectric properties. Quantitatively understanding of this effect would require knowledge of temperature-dependent phonon frequencies and phonon mode 17 ACS Paragon Plus Environment


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strengths. Nevertheless, our calculated dielectric function is in reasonable agreement with previous calculations and experimental measurement at ambient condition, which helps to validate our results.

Electronic excitation induces electronic and lattice structure changes to STO, which further leads to changes of optical properties. With increasing Te, both ε1(0) and n(0) decrease. The decrease of static dielectric constant ε1(0) is also found when lattice temperature increases.59 The imaginary part ε2 is obtained directly from electronic structure calculations, and the onset for absorption reflects the interband gap value. At Te=0, the first peak corresponds to the transition from O (2p) upper valence band to Ti (3d) lower conduction band, as can be seen from PDOS in Figure 2. The optical gap, as determined by the absorption edge, increases first and then decreases with increasing Te. There is an additional small peak developed at Te=4 eV, which is induced by highly overlapped bands near the gap region. In general, the smeared, flat DOS leads to flat peaks in the optical responses. Note that for the static lattice, excitation induces increase of band gap continuously as shown in Figure 1. Thus the results here indicate that both electronic and structural changes contribute to the band gap change of STO. In particular, the non-thermal structural changes, rather than electronic effects, are responsible for the decrease of band gap. This can also be inferred from the significant changes in optical parameters starting from Te=3 eV, which is in accordance with the amorphization observed in this case. Therefore, optical properties can be used to diagnose the electronic and structural state of STO under electronic excitations.

4. Conclusion

The effects of electronic excitation on STO are studied through first-principles calculations. The scenario investigated here corresponds to transient energy deposition into the electronic system by irradiation of highly-ionizing ions or laser beams. It is found that under strong electronic excitations, the Ti-O bonds are the most influenced in STO, which is inferred from electronic structure calculations. Increasing Te mainly induces depopulation of Ti 3d states and further leads to increasing electronic band gap of STO. An 18 ACS Paragon Plus Environment

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analysis of the phonon properties suggests that there is a phonon band gap formed due to changed Ti and O vibrations under electronic excitation. Direct dynamic simulations reveal an amorphous transition of STO starting at Te=3 eV. The transition is initiated by lattice instability that is induced by soft phonon modes. The evolution of optical properties along with increasing Te suggests that the changes in optical properties can be used to diagnose structural and electronic changes under electronic excitations.

Acknowledgment

This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Science and Engineering Division.

Reference

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Table of Contents


Page 26 of 33

Free energy (eV/unit cell)

(a) PageThe 27 of Journal 33 of Physical Chemistry −40

8

DOS (States/eV/atom)

1 2 −60 3 4 −80 0 eV 5 1 eV 6 −100 2 eV 7 3 eV 4 eV 8 9 −120 3 4 5 6 7 10 Lattice constant (Å) 11 (b) 12 4 13 0.5 eV 14 1.0 eV 2.0 eV 15 3 3.0 eV 16 4.0 eV 17 2 18 19 20 1 21 22 ACS Paragon Plus Environment 0 23 −6 −4 −2 0 2 4 6 8 24 25 Energy (eV)

10

DOS (States/eV/atom)

(a) 1 2 3 4 5 6 7 8 9 10 11

(b)


2

0.1

0 1

0

−6

−4

−2 0 2 4

−2

Sr(s) Sr(p) Ti(s) Ti(p) Ti(d) O(s) O(p)

ACS Paragon Plus Environment 0 2 4 6 8 10 Energy (eV)

Page 28 of 33

(a) PageThe 29 of Journal 33 of Physical Chemistry Frequency (cm−1)

900 600 300 0

300i 0

1

2 Te (eV)

3

4

0

1

2 Te (eV)

3

4

800

Frequency (cm−1)

1 2 3 4 5 6 7 8 9 10 (b) 11 12 13 14 15 16 17 18 19 20 21 22 (c) 23 24 25 26 27 28 29 30 31 32 33 34 35

600 400 200 0

Phonon DOS (States/unit cell)

200i

6 5 4

Te=1 eV Te=2 eV Te=3 eV Te=4 eV

3 2 1 0 Paragon Plus Environment ACS 200i 0 200 400 600 800 Frequency (cm−1)

(a)

The Journal of Physical Chemistry Page 30 of 33 2500 2000

1 eV 2 eV 3 eV 4 eV

Ti (K)

1 2 1500 3 4 1000 5 6 500 7 8 0 9 0 0.5 1 1.5 10 Time (ps) 11 (b) 12 13 1 eV 5 14 2 eV 15 3 eV 4 4 eV 16 17 3 18 19 2 20 21 1 22 ACS 0 Paragon Plus Environment 23 0 1 2 3 4 5 24 25 r (Å) g(r)

2

6

Page 31 of 33

Energy (eV/formula unit)

(a)

0 Electronic free energy

−0.5

−1

−1.5

(b) 12

MSD (Å2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Tot O Ti Sr

9 6 3 0 0

0.5

1 Time (ps)

1.5

ACS Paragon Plus Environment

2

(c) The Journal of Physical4Chemistry 0 eV 1 eV 2 eV 3 eV 4 eV

9 6

Page 32 of 33

3 2

0 eV 1 eV 2 eV 3 eV 4 eV

3 1 0 0

(d)

8 0 eV 1 eV 2 eV 3 eV 4 eV

6 4

2

k

ε2

ε1

1 2 3 4 5 6 7 8(b) 9 10 11 12 13 14 15 16 17 18 19 20

n

(a) 12

0 eV 1 eV 2 eV 3 eV 4 eV

1

2 0 0

5

ACS Paragon Plus Environment 0 10 15 20 0 5 10 15 Energy (eV) Energy (eV)

20

Excitation induced electronic density redistribution Page 33 TheofJournal 33 of Physical Chemistry DOS (States/eV/atom)

4

1 2 3 4 5 6 7

0.5 eV 1.0 eV 2.0 eV 3.0 eV 4.0 eV

3 2 1 0

ACS Paragon Plus Environment −6

−4

−2

0 2 4 Energy (eV)

6

8

10

Ab Initio Study of Electronic Excitation Effects on SrTiO3 - American

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