An Inversion Domain Superlattice of 4H-SiC for Room-Temperature

Sep 14, 2018 - An inversion domain superlattice of 4H-SiC is designed theoretically for generating room-temperature and tunable terahertz (THz) radiat...
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An Inversion Domain Superlattice of 4H-SiC for Room-Temperature and Tunable Terahertz Generation Run Yang,†,‡,§ Kang Yan,†,‡,§ Yao Huang,†,‡,§ Xiaoxu Liu,†,‡,§ Jian Chen,‡,∥ Zhiyong Zhang,*,†,‡,§ and Xinglong Wu*,†,‡,§ Collaborative Innovation Center of Advanced Microstructures, ‡National Laboratory of Solid State Microstructures, §Key Laboratory of Modern Acoustics, MOE, Institute of Acoustics, and ∥Research Institute of Superconductor Electronics, Nanjing University, Nanjing 210093, P. R. China

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ABSTRACT: An inversion domain superlattice of 4H-SiC is designed theoretically for generating room-temperature and tunable terahertz (THz) radiation via the combination of the density functional theory and classic coupled-wave equations. For such symmetric structures, our calculations indicate that only the Raman and infrared active E′ modes contribute to the THz parametric generation in the frequency range of 0.2−3.3 THz. The lowest E′ modes correspond to the relative shearing movement of the C−C and Si− Si double layers, and its energy can be adjusted to the sub-THz region by increasing length of the superlattice unit cell. With a pump source operating at 1.064 μm, the maximal THz gain in the process of stimulated polariton scattering was obtained to be 1.26 cm−1 at room temperature for a y-plate superlattice, which is slightly lower than that in the commonly used LiNbO3 under the same pump power. Such inversion domain superlattices of 4H-SiC with different unit lengths can be prepared experimentally via the atomic layer epitaxy method.

T

Because of its superior material qualities such as high breakdown field, high thermal conductivity, poly types of SiC is a promising material for high-temperature, and high-power THz emitting devices.19 In this respect, a lot of proposals were presented such as electrically driven nitrogen-doped 4H-SiC THz emitting devices,20 THz electroluminescence (EL) induced by current injection through 4H-SiC p−n junctions21 and THz EL from 6H- and 4H-SiC structures with natural superlattice, which is attributed to steady-state Bloch oscillations of electrons,22 transient-photocurrent radiation from large-aperture 6H- and 4H-SiC photoconductive antennas,23 THz generator via optical rectification24 or via surface phonon polaritons,25 and difference frequency generation of coherent THz wave via phase matching condition.26 Some of them have been realized in experiments. Here we construct an inversion domain superlattice of 4H-SiC along the hexagonal axis via the DFT calculation.27 In the neighboring inversion domains, the sequence of the atoms is reversed, which leads to the superlattice units [(SiC)4m(CSi)4n] with m and n being the numbers of unit cells of 4H-SiC contained in the two domains. The two inversion domain boundaries (IDBs) in one superlattice unit are constructed by the Si−Si and C−C double layers, respectively. Such a polarization superlattice can be prepared experimentally via atomic layer epitaxy at a low substrate temperature of 1000 °C with properly chosen cycle sequence of source gases of Si2H6 and C2H2, as reported previously.28 In 4H-SiC and also in

erahertz wave, with frequency ranging from 0.1 to 10 THz, has significant scientific research values and wide applications in the field of imaging,1 astrophysics and atmospheric science,2 biological and medical sciences,3 security screening and illicit material detection,4 nondestructive evaluation,5 and communications technology.6 One of the main topics of the community is the preparation of highperformance THz sources, which should be able to work at room temperature,7 be tuned in a wide spectral range conveniently8,9 and have a power and conversion efficiency as high as possible.10 A lot of THz radiation sources with different mechanisms have been developed, including the backward-wave oscillator,11 high-frequency transistors,12 Josephson junctions in superconductors,13 the quantum cascade laser,14 terahertz parametric oscillator,15 THz emission from self-assembled ZnO mesocrystal microspheres,16 and tunable terahertz sources based on difference frequency generation via organic crystals.17,18 Until now, THz wave is still in one of the fastest developing spectral regions14 and new mechanisms and novel materials working in THz wave emitters are introduced continually. Widely tunable THz wave can be generated at room temperature by optical parametric processes via laser light scattering from the polariton mode of nonlinear crystals LiNbO3 or MgO:LiNbO3.15 When pumped by a nanosecond Q-switched Nd:YAG laser, coherent THz-wave sources have been realized in the range between 0.7 and 3 THz with a line width of about 100 MHz. Surprisingly, as a promising mechanism, after the realization in LiNbO3 and MgO:LiNbO3, stimulated polariton scattering has little been applied to artificially engineered materials to find better THz emitters, e.g., high strength and device miniaturization. © XXXX American Chemical Society

Received: June 11, 2018 Revised: September 10, 2018 Published: September 14, 2018 A

DOI: 10.1021/acs.cgd.8b00890 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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other hexagonal polytypes of SiC, the Si−C double layers are nonequivalent, which leads to spontaneous polarization. Furthermore, in the inversion domain superlattice of 4H-SiC, a transfer of Mulliken charge ΔQ = 0.22e takes place from the C−C double layer to the Si−Si one. As a result, the electrostatic potential for electrons is negative at the C−C and positive at the Si−Si layers. The relative movement between the C−C and Si−Si double layers gives rise to three infrared (IR) active collective vibration modes, one stretching and two shearing with respect to the c-axis. The three modes can be artificially tailored via adjusting m and/or n so that their frequencies can be located into a lower THz region. If some of the three IR active collective modes are also Raman active, coherent THz radiation can be generated via stimulated polariton scattering.29 The THz source based on an inversion domain superlattice of 4H-SiC has not been studied previously. In this work, such a source is studied via the combination of the DFT and classic coupled-wave equations and the results are compared with those of LiNbO3 and MgO:LiNbO3. For such symmetric structures with m = n, the inversion domain superlattice of 4H-SiC has D3h symmetry (6̅m2). According to group theory analysis, there are four types of phonon modes: A1′, A2″, E′, and E″, where modes A2″ and E′ are IR active and the other two are inactive. In Figure 1, we illustrate the lowest A″2 mode for the structure with m = n = 2, where the arrows represent the relative movement of atoms in one superlattice unit. In this collective vibration mode, the C− C and Si−Si double layers move as a whole, respectively. As we can see, this mode is caused by the relative stretching movement between the C−C and Si−Si double layers, and the atoms far away from the C−C and Si−Si double layers are almost immobile. The lowest doubly degenerate E′ modes correspond to the relative shearing movement of the C−C and Si−Si double layers. The lowest IR inactive A′1 and E″ modes are caused by the relative movement, stretching and shearing, respectively, of the two inverse domains of 4H-SiC in one superlattice unit, and the C−C and Si−Si double layers are almost immobile. Hence, there are two types of inversion domains. One corresponds to the arrangement of Si−C double layers and the other to the relative movement. They are in the same phase for the lowest A1′ and E″ modes, whereas there is a π/2 phase difference between the two types of inversion domains for the lowest A″2 and E′ modes. The wave numbers of the former are lower than the latter, and the differences decrease with increasing domain size (m = n). From the density functional perturbation theory (DFPT) calculation, the wavenumber of the lowest A″2 mode is 108 cm−1, whereas the lowest doubly degenerate E′ modes have a wavenumber of 57 cm−1. The frequency difference caused by the lattice anisotropy is large in the inversion domain superlattice of 4H-SiC. As a comparison, the wave numbers of the corresponding modes of the structure with m = n = 1 are 213 and 110 cm−1, respectively. With increasing domain size, the gradual reversing of the relative movement between the two nearest double layers becomes even slower so that the wavenumbers of the lowest A″2 and E′ modes can be further decreased. To be applied in the THz parametric generation, the working phonon modes have to be both IR and Raman active. For our system, the four types of phonon modes are all Raman active except the A2″ modes. As a result, only the E′ modes contribute to the THz parametric generation. In Figure 2a,b, we illustrate the Raman intensities for the superlattices with m

Figure 1. Lowest A2″ (left) and A1′ (right) modes for m = n = 2. The yellow (gray) balls represent the Si (C) atoms. In our DFT calculation, the Si−Si double layers are located at the middle of the superlattice unit, whereas the C−C layers are at the end.

Figure 2. Raman intensity versus Raman shift at different temperatures for the structures with m = n = 1 in (a) and 2 in (b). In our calculation, the incident light is set as 514.5 nm and the Lorentzian smearing as 10 cm−1.

= n = 1 and 2, respectively. For m = n = 1, the lowest E′ and E″ modes correspond to the two peaks with the Raman shift 110 and 92 cm−1. When m and n increase to 2, the wavenumbers of the two modes reduce to 57 and 52 cm−1, and the two peaks B

DOI: 10.1021/acs.cgd.8b00890 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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merge into a single one due to the Lorentzian smearing of 10 cm−1. Their intensities are enhanced about 1 order of magnitude compared to the double peaks for m = n = 1 under the same temperature because the excitation of the lowest E′ and E″ modes becomes easy with the domain size increased. The Raman intensity is ∝ n0 + 1, with n0 the Bose distribution. As a result, the lowest E′ and E″ peaks are greatly enhanced when the temperature is increased from 10 to 500 K, whereas those peaks with Raman shifts larger than 500 cm−1 are almost unchanged even if the temperature is increased to 500 K. Here, one should remember that when CASTEP calculates the Raman intensity, the anharmonic forces in the crystal lattice is not taken into account, so the blue-shifting and broadening of the Stokes peaks with temperature is beyond the capability of CASTEP. In the latter calculation, the line-width Γ at room temperature is set as 4 cm−1 since most of first-order Raman peaks take this value. The optical phonon modes and Raman spectrum are obtained from the density functional perturbation theory in local density approximation (LDA), using the CASTEP package code with norm-conserved pseudopotential.30 The plane-wave energy cutoff of 750 eV is used to expand the Kohn−Sham wave functions and geometry optimization is carried out until convergence tolerances of 5 × 10−6 eV for energy, 0.01 eV/Å for force, 0.02 GPa for stress, and 5 × 10−4 Å for maximum displacement are reached. The Monkhorst− Pack k-point meshes are 8 × 8 × 2, which has been tested to converge. Although LDA calculation usually underestimates the band gap, the relative position of the highest occupied (lowest unoccupied) state with respect to the valence (conductance) band edge shows agreement between the results obtained from pure LDA, GW, and hybrid functional calculations. Thus, we obtain the dielectric function from LDA, then the result is shifted up by the difference between the experimental and LDA-calculated indirect gap of bulk 4H-SiC, as done in ref 27. How should one use those optical-phonon modes to generate THz radiation? For the IR-active transversal A″2 and E′ modes, they are coupled with the electromagnetic field to form polaritons. The energy flux of this type of quasi-particle, corresponding to the heat radiation of the TO phonons, is ∝ ℏωTn0vg with ℏωT being the polariton eigen-energy and vg the group velocity. This blackbody radiation, however, is incoherent and is not our interest. To generate coherent THz radiation, a kind of particle-number conversion is needed. The stimulated polariton scattering provides such a mechanism, where the pump, Stokes, THz, and vibration waves are coupled together. When the stimulated Stokes Raman scattering takes place, the THz radiation is coherent. In this stimulated light scattering, the energy conservation ωP = ωS + ωT (P: pump, S: Stokes, and T: THz) and the momentum conservation, or the phase-matching condition: kP⃗ = kS⃗ + kT⃗ should be satisfied simultaneously. In this process, only the IR and Raman active E′ modes contribute to the THz radiation. We suppose an experimental setup with a y-plate of the superlattice (Figure 3). The pump wave is incident from the surface at z = 0, and kP⃗ is located in the xz plane. The pump, Stokes, and THz waves are all polarized in the y direction. The interaction of the three waves and vibration (the lowest doubly degenerate E′ modes) waves is described by the classical coupled-wave equation,15,29 which can be solved via the plane wave approach and assuming negligible depletion of the pump

Figure 3. Experimental setup assumed in our calculation. The lightyellow block represents an inversion domain superlattice of 4H-SiC. M1 and M2 are two mirrors coated with high reflection films.

wave. The obtained parametric gain of the Stokes and THz waves is É | l 2 Ñ1/2 o oÄÅÅÅ o ij g0 yz ÑÑÑÑ o o αT o ÅÅ o o j z Å Ñ 1 16 cos 1 gT = + ϕ − m } j z Å Ñ j z o o Å Ñ j z o Å Ñ 2 o α oÅÅÇ o k T { ÑÑÖ o o (1) n ~ where ϕ is the angle between kP⃗ and kS⃗ . It is determined by the energy conservation and the phase-matching condition so that ωT is tunable by varying ϕ. g0 is the parametric gain in the lowloss limit and αT is the absorption coefficient. They are ij πω ω I yz g0 = jjj 3 To So Po zzz j 2c n n n z T S P{ k and

1/2

χP

(2)

y 2ωT ijj ω⊥2 ϵ⊥0 − ωT2 ϵ∞ ⊥ z zz Imjj 2 2 j ω − ω − ιω Γ zz c T T { k ⊥

1/2

αT = 2|Imk T | =

(3)

Here, ω⊥ is the frequency of the lowest E′ modes. noP, noS, and o nT are the refractive coefficients (o: ordinary). noPand noS can be derived directly from the relative dielectric function obtained from the DFT calculation, but due to the influence of polariton, noT is set as Re

(

ω⊥2 ϵ⊥0 − ωT2 ϵ∞ ⊥ ω⊥2

−

ωT2

− ιωT Γ

1/2

)

. The effective

second-order nonlinear coefficient χP is calculated to be χP = dE +

2 (ϵ⊥0 − ϵ∞ ⊥ )ω⊥

ω⊥2 − ωT2

dQ

(4)

According to our experimental setup, the coefficient dE, stemming from electronic polarization, is 16πd22. For 4H-SiC (6 mm), there are three nonvanishing second-order nonlinear optical coefficient,31 and their experimental values are d31 = 6.5 pm/V, d15 = 6.7 pm/V, and d33=−11.7 pm/V. For our system (6̅m2), group-theory analysis shows that the nonvanishing second-order nonlinear optical coefficients are d22 = −d21 = −d16. Calculating these nonlinear coefficients directly from the self-consistent energy levels and wave functions is beyond the CASTEP’s capabilities. The bond model32 assumes that the induced polarization on a crystal is the vector sum of the polarizations on all bonds. However, the contributions of the corresponding bonds are different from those in 4H-SiC due to the charge redistribution in the formation of inversion domains. So, d22 cannot be derived from the bond model simply by using the nonlinear coefficients of 4H-SiC; otherwise, it should be zero. The Miller’s rule tells that the Miller’s coefficient, that is, the ratio between the second-order C

DOI: 10.1021/acs.cgd.8b00890 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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susceptibility and the multiplication of the three related linear susceptibilities, is weakly dispersive and almost a constant for a wide range of crystals.32 According to this empirical rule, setting d22 in the range from −6 to −12 pm/V looks acceptable for a crude estimate. In the latter calculation, we compare the results with d22 = −6, −8, and −10 pm/V. The nonlinear coefficient dQ, stemming from the ionic polarization, satisfies dQ e/4π = ey⃗ ·9(y) · ey⃗ with e being the electronic charge and 9(y) the Raman tensor of the lowest E′ mode vibrating along the y direction. Group-theory analysis shows that for a 6̅m2 system, the Raman tensors of the Raman and infrared active E′ modes have two nonzero forms: 9(x) and 9(y),33 which guarantees that our experimental setup can work. Especially, the nonzero 9(y) has the form −dd . Generally, the Raman tensor of an E′ mode obtained from CASTEP is not in this form. The effective d coming from the y component of the mode is obtained by subtracting the mean value of 9 xx and 9 yy . The total contribution of the two lowest degenerate E′ modes to 9 yy(y) is 0.1606e Å/V, and we accept it as a satisfactory datum although several detailed factors in Raman scattering are not included in CASTEP as we have said. If the pump wave is supplied by a nanosecond Q-switched Nd:YAG laser operating at 1.064 μm wavelength, the THz gain can be considerably enhanced, since this pump source can supply output power reaching 300 MW/cm−2. At room temperature, the obtained maximal THz gain is about 1.26 cm−1 in our system (the black solid line Figure 4a), which is comparable to that in LiNbO3 under the same pump power.34 In LiNbO3 the working A1 mode is 248 cm−1 (∼7.4 THz), whereas in our system the lowest E′ modes are 57 cm−1 (∼1.7 THz), about four times lower than LiNbO3. In the vicinity of

(

the absorption peak, gT ∝

g02 αT

and is small, whereas in the

lower ωT side far away from that peak, gT ∼ g0. As eq 2 shows, 1/2 g0 ∝ ω1/2 T χP . So, in the latter situation, g T ∝ ωT χP . Although the lowering of ωT inevitably decreases the parametric gain, the merit of our system is that it can work in the sub-THz region. At room temperature, for LiNbO3, the maximal gain is reached at about 2 THz, and the THz wave can be tuned in the range from 0.7 to 3 THz, whereas for our system, the maximal gain appears at 0.56 THz, and from 0.2 to 1 THz, gT is larger than 1 cm−1. Even at 0.1 THz, gT is still larger than 0.5 cm−1. As a THz wave emitter, our system can by tuned in the sub-THz range from 0.2 to 1 THz via the phase-matching condition by varying ϕ. Although the Raman peak with the lowest shift in Figure 2b looks high, it is the result of the cocontribution of the lowest E′ and the lowest E″ modes. The effective component of the Raman tensor, 9 yy(y), is not strong enough to offset the effect of lowering of ωT to sub-THz by increasing the value of χP. The maximal gain our system can reach is lower than that of LiNbO3. This result gives a clue how to design phonon modes as THz sources; that is, the modes should have strong Raman scattering to enhance the effective second-order nonlinear coefficient. This result is obtained with Γ = 4 cm−1 and d22 = −10 pm/ V. Here, Γ = 4 cm−1 is an empirical parameter representing room temperature. As a comparison, the result with Γ = 3 cm−1 is presented, which corresponds to a lower temperature. In this situation, the absorption peak is decreased, and consequently, gT is increased, but it still follows ωT1/2 χP with ωT approaching zero. In Figure 4b, we compare the results with different second-order nonlinear optical coefficients d22. With d22 decreased from −10 to −6 pm/V, the maximal gain is changed from about 1.26 cm−1 to about 1.03 cm−1. αT does not vary with d22, which influences gain only through g0 ∼ χP. Generally, this effect is weak. Decreasing 9 yy(y) has similar effect as d22. With m = n increased, the induced polarization diminishes the effective gap to Eg−2ΔV. Here, ΔV/d = 0.013 eV/Å, with d being the length of one domain.27 For m = n = 1, d = 10.05 Å, which can be used in a rough estimate. On the other hand, due to strong direct transitions between the interface states localized in the C−C and Si−Si bilayers, the maximal range for tuning the gap is decreased to about 2.5 eV to avoid the lowest unoccupied interface state falling below the highest occupied one.27 Since the 1.064 μm (∼1.2 eV) laser is used as the pump source, the threshold is m = n = 5. Above and at this threshold, the pump wave is strongly absorbed and the mechanism of stimulated polariton scattering fails. An inversion domain superlattice of 4H-SiC with unit length smaller than 81 Å can be prepared via the atomic layer epitaxy method.28 In the epitaxy process, the surface reconstruction mechanism plays an important role.27,28 On the other hand, with m = n increased from 2 to 4, the tunable range is red-shifted, but the gain is lowered too. So, m = n = 2 is the best scheme as a THz wave emitter. In conclusion, our numerical calculation shows that an inversion domain superlattice of 4H-SiC can be used as a room-temperature and widely tunable THz source as expected. Compared with commonly used LiNbO3, such a system has a slightly weak maximal gain, but the merit is that the working frequency can be adjusted in the range of 0.2−3.3 THz and lowered to between 0.2 and 1 THz. In view of the fixed

)

Figure 4. Gain and absorption coefficients for the parametric THzwave generation using the structure with m = n = 2, pumped at 1.064 μm with pumping power of 300 MW/cm2. (a) Γ = 4 (black solid) and 3 cm−1 (red dashed) with d22 = −10 pm/V. (b) d22 = −10 (black solid) − 8 (green dashed) and −6 pm/V (magenta dotted) with Γ = 4 ∞ cm−1. The other parameters are ϵ0∥ = 10.88, ϵ0⊥ = 10.30, ϵ∞ ∥ = 7.40, ϵ⊥ = 7.14, and 9 yy(y) = 0.1606eÅ/V . D

DOI: 10.1021/acs.cgd.8b00890 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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(13) Ozyuzer, L.; Koshelev, A. E.; Kurter, C.; Gopalsami, N.; Li, Q.; Tachiki, M.; Kadowaki, K.; Yamamoto, T.; Minami, H.; Yamaguchi, H.; Tachiki, T.; Gray, K. E.; Kwok, W.-K.; Welp, U. Emission of Coherent THz Radiation from Superconductors. Science 2007, 318, 1291−1293. (14) Williams, B. S. Terahertz Quantum-Cascade Lasers. Nat. Photonics 2007, 1, 517−525. (15) Henry, C. H.; Garrett, C. G. B. Theory of Parametric Gain near a Lattice Resonance. Phys. Rev. 1968, 171, 1058−1064. (16) Wu, X. L.; Xiong, S. J.; Liu, Z.; Chen, J.; Shen, J. C.; Li, T. H.; Wu, P. H.; Chu, P. K. Green Light Stimulates Terahertz Emission from Mesocrystal Microspheres. Nat. Nanotechnol. 2011, 6, 103−106. (17) Uchida, H.; Tripathi, S. R.; Suizu, K.; Shibuya, T.; Osumi, T.; Kawase, K. Widely Tunable Broadband Terahertz Radiation Generation Using a Configurationally Locked Polyene 2-[3-(4hydroxystyryl)-5,5-dimethylcyclohex-2-enylidene] Malononitrile Crystal via Difference Frequency Generation. Appl. Phys. B: Lasers Opt. 2013, 111, 489−493. (18) Liu, P. X.; Xu, D. G.; Li, Y.; Zhang, X. Y.; Wang, Y. Y.; Yao, J. Q.; Wu, Y. C. Widely Tunable and Monochromatic Terahertz Difference Frequency Generation with Organic Crystal DSTMS. Europhys. Lett. 2014, 106, 60001. (19) Xuan, G.; Lv, P.-C.; Zhang, X.; Kolodzey, J.; Desalvo, G.; Powell, A. Silicon Carbide Terahertz Emitting Devices. J. Electron. Mater. 2008, 37, 726−729. (20) Lv, P.-C.; Zhang, X.; Kolodzey, J.; Powell, A. Compact Electrically Pumped Nitrogen-Doped 4H-SiC Terahertz Emitters Operating Up to 150 K. Appl. Phys. Lett. 2005, 87, 241114. (21) Andrianov, A. V.; Gupta, J. P.; Kolodzey, J.; Sankin, V. I.; Zakhar’in, A. O.; Vasilyev, Yu. B. Current Injection Induced Terahertz Emission from 4H-SiC p-n Junctions. Appl. Phys. Lett. 2013, 103, 221101. (22) Sankin, V. I.; Andrianov, A. V.; Zakhar’in, A. O.; Petrov, A. G. Terahertz Electroluminescence from 6H-SiC Structures with Natural Superlattice. Appl. Phys. Lett. 2012, 100, 111109. (23) Ropagnol, X.; Bouvier, M.; Reid, M.; Ozaki, T. Improvement in Thermal Barriers to Intense Terahertz Generation from Photoconductive Antennas. J. Appl. Phys. 2014, 116, 043107. (24) Zhao, Z. Y.; Song, Z. Q.; Shi, W. Z.; Zhang, J. T. Feasibility of Terahertz Generation and Detection in 3C-SiC Single Crystal. Jpn. J. Appl. Phys. 2015, 54, 082601. (25) Caldwell, J. D.; Lindsay, L.; Giannini, V.; Vurgaftman, I.; Reinecke, T. L.; Maier, S. A.; Glembocki, O. J. Low-Loss, Infrared and Terahertz Nanophotonics Using Surface Phonon Polaritons. Nanophotonics 2015, 4, 44−68. (26) Fischer, M. P.; Buhler, J.; Fitzky, G.; Kurihara, T.; Eggert, S.; Leitenstorfer, A.; Brida, D. Coherent Field Transients below 15 THz from Phase-Matched Difference Frequency Generation in 4H-SiC. Opt. Lett. 2017, 42, 2687−2690. (27) Deak, P.; Buruzs, A.; Gali, A.; Frauenheim, T. Strain-Free Polarization Superlattice in Silicon Carbide: A Theoretical Investigation. Phys. Rev. Lett. 2006, 96, 236803. (28) Fuyuki, T.; Yoshinobu, T.; Matsunami, H. Atomic Layer Epitaxy Controlled by Surface Superstructures in SiC. Thin Solid Films 1993, 225, 225−229. (29) Shen, Y. R. The Principle of Nonlinear Optics; Wiley: New York, 1984; pp 169−172. (30) Refson, K.; Clark, S. J.; Tulip, P. R. Variational DensityFunctional Perturbation Theory for Dielectrics and Lattice Dynamics. Phys. Rev. B: Condens. Matter Mater. Phys. 2006, 73, 155114. (31) Sato, H.; Abe, M.; Shoji, I.; Suda, J.; Kondo, T. Accurate Measurements of Second-Order Nonlinear Optical Coefficients of 6H and 4H Silicon Carbide. J. Opt. Soc. Am. B 2009, 26, 1892−1896. (32) Shen, Y. R. The Principle of Nonlinear Optics; Wiley: New York, 1984; pp 29−38. (33) Loudon, R. The Raman Effect in Crystals. Adv. Phys. 1964, 13, 423−482. (34) Kawase, K.; Shikata, J.; Ito, H. Terahertz Wave Parametric Source. J. Phys. D: Appl. Phys. 2002, 35, R1−R14.

working mode in LiNbO3, another merit of our system is its radiation frequency is related with the lowest E′ mode and can be adjusted to the sub-THz region by changing the length of the superlattice unit cell. Artificial tailoring of the working phonon mode is different from tuning frequency via phasematching condition and, combined with the latter, can provide more flexibility. A clue from our calculation is the possibility of designing a similar structure with some special materials which can perform better in the wide THz region.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (Z.Y.Z). Fax: 86-25-83595535. Tel: 86-83686303. *E-mail: [email protected] (X.L.W.). ORCID

Xinglong Wu: 0000-0002-2787-3069 Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by National Basic Research Programs of China (2014CB339800), National Key R & D Program of China (2017YFA0303200), and National Natural Science Foundation (61521001 and 11674163).

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REFERENCES

(1) Chan, W. L.; Deibel, J.; Mittleman, D. M. Imaging with Terahertz Radiation. Rep. Prog. Phys. 2007, 70, 1325−1379. (2) Siegel, P. H. Terahertz Technology. IEEE Trans. Microwave Theory Tech. 2002, 50, 910−928. (3) Siegel, P. H. Terahertz Technology in Biology and Medicine. IEEE Trans. Microwave Theory Tech. 2004, 52, 2438−2447. (4) Federici, J. F.; Schulkin, B.; Huang, F.; Gary, D.; Barat, R.; Oliveira, F.; Zimdars, D. THz Imaging and Sensing for Security Applications-Explosives, Weapons and Drugs. Semicond. Sci. Technol. 2005, 20, 266−280. (5) Hor, Y. L.; Federici, J. F.; Wample, R. L. Nondestructive Evaluation of Cork Enclosures Using Terahertz/Millimeter Wave Spectroscopy and Imaging. Appl. Opt. 2008, 47, 72−78. (6) Federici, J.; Moeller, L. Review of Terahertz and Subterahertz Wireless Communications. J. Appl. Phys. 2010, 107, 111101. (7) Jepsen, P. U. Nanomechanics: Terahertz Radiation Gets Shaken Up. Nat. Nanotechnol. 2011, 6, 79−80. (8) Kumar, S.; Hu, Q.; Reno, J. L. 86 K Operation of Terahertz Quantum-Cascade Lasers Based on a Diagonal Design. Appl. Phys. Lett. 2009, 94, 131105. (9) Betz, A. L.; Boreiko, R. T.; Williams, B. S.; Kumar, S.; Hu, Q.; Reno, J. L. Frequency and Phase-Lock Control of a 3 THz Quantum Cascade Laser. Opt. Lett. 2005, 30, 1837−1839. (10) Vodopyanov, K. L. Optical THz-Wave Generation with Periodically-Inverted GaAs. Laser Photonics Rev. 2008, 2, 11−25. (11) He, W.; Donaldson, C. R.; Zhang, L.; Ronald, K.; McElhinney, P.; Cross, A. W. High Power Wideband Gyrotron Backward Wave Oscillator Operating Towards the Terahertz Region. Phys. Rev. Lett. 2013, 110, 165101. (12) Knap, W.; Lusakowski, J.; Parenty, T.; Bollaert, S.; Cappy, A.; Popov, V. V.; Shur, M. S. Terahertz Emission by Plasma Waves in 60 nm Gate High Electron Mobility Transistors. Appl. Phys. Lett. 2004, 84, 2331−2333. E

DOI: 10.1021/acs.cgd.8b00890 Cryst. Growth Des. XXXX, XXX, XXX−XXX