Synthesis of second-order nonlinearities in dielectric-semiconductor-dielectric metamaterials

Optical materials possessing second-order nonlinear susceptibility, χ⁽²⁾, are essential for the realization of high-speed photonic devices that need to be integrated into photonic integrated circuits (PICs) for achieving such functionalities as ultrafast modulation, switching, and nonlinear wave mixing of optical fields on a chip. However, existing materials that exhibit large χ⁽²⁾ (e.g., lithium niobate (LiNbO₃) and potassium dihydrogen phosphate (KDP) crystals) are not compatible with CMOS technology.^1–3 Single-crystalline silicon is prohibited to exhibit non-zero electrical dipole- induced χ⁽²⁾ due to the nature of its centrosymmetrical lattice.⁴ Still, second-harmonic responses can be generated if quadrupolar and magnetic dipoles are considered.^5,6 However, the demonstrated conversion efficiencies are relatively small compared to bulk effects of commonly used nonlinear crystals. Strain engineering on silicon waveguides has been proven as a way to introduce non-zero χ⁽²⁾ in silicon;^7–9 however, strain induced χ⁽²⁾ in Si has been reported recently to be much lower than that reported in the past.^10–13 Additionally, CMOS-compatible dielectric materials such as aluminum oxide (Al₂O₃), silicon dioxide (SiO₂), and silicon nitride (SiN_x) are reported to have extremely low χ⁽²⁾ because of their amorphous nature.^14–16 Therefore, the need for CMOS-compatible materials exhibiting prominent χ⁽²⁾ that can be easily integrated with modern silicon photonic material platforms is highly desirable.

Metamaterials have attracted significant attention because their physical properties can be synthesized with the selection of materials and their spatial distributions.^17,18 Metal-dielectric multilayers exhibit plasmonic-enhanced χ⁽²⁾ values resulting from the interface between metal and dielectric layers,¹⁹ and the effective χ⁽²⁾ can be further increased via charging the density of electrons at the surface of metals by applying an external DC electric field.²⁰ However, the use of metals leads to high optical insertion loss in the fabricated device. To overcome the loss issue, Alloatti et al. demonstrated an all-dielectric ABC metamaterial that exhibits χ⁽²⁾ and consists of three different dielectric layers deposited by atomic layer deposition (ALD)¹⁶ where the symmetry is broken via introducing asymmetry of surface density states on their interfaces, and the value of the reported highest component of the χ⁽²⁾ tensor, χ⁽²⁾_zzz, is 0.26 pm and Clemmen et al. modified the calculations and claimed that the value of χ⁽²⁾_zzz based on the concept of all-dielectric metamaterials can be as high as 5 pm/V.²¹ A larger value of χ⁽²⁾ is also claimed to be achievable in this type of metamaterial via choosing the dielectric materials that exhibit high asymmetries in the density of their surface interfaces; however, these surface states existing in high density of interfaces also act as trapping centers, resulting in higher optical losses.²² 

The electric field induced second-harmonic (EFISH) effect offers an alternative way to engineer effective χ⁽²⁾ in materials by exploiting their χ⁽³⁾.²³ The induced effective χ⁽²⁾ through this effect has been demonstrated theoretically and experimentally, in both metal-semiconductor (MS) and metal-oxide-semiconductor (MOS) structures.^23–25 However, in our previous work, we have shown that the induced effective χ⁽²⁾ only exists at tens of nanometers depth of the bulk from the semiconductor surface, where a high electric field is localized.¹⁰ In order to utilize this effect more effectively, in this manuscript, we propose and demonstrate a dielectric-semiconductor-dielectric (DSD) metamaterial consisting of a semiconductor thin film (i.e., a-Si) cladded with two different dielectric layers (i.e., SiO₂ and Al₂O₃). We exploit the creation of fixed charges (Q_f) of opposite signs on the surfaces of the semiconductor in the DSD multilayer structure to engineer and maximize a non-zero built-in electric field within the a-Si layer, which in turn interacts with χ⁽³⁾ of the semiconductor, resulting in an enhanced, effective χ⁽²⁾ in the bulk of the metamaterial.

When a dielectric layer is deposited on a semiconductor, the semiconductor's valence and conduction band energies may locally deviate from their bulk values due to the existence of surface charges in the dielectric layer, leading to perturbations away from the material's bulk carrier distributions.²⁶ At the dielectric/semiconductor interfaces, the neutral atoms in the dielectric layer tend to donate mobile electrons or holes into the semiconductor, leaving fixed charges at the dielectric side, which then create a space charge region within the semiconductor, resulting in a depletion region. Different dielectrics exhibit dissimilar polarities and densities of Q_f at their interfaces with the same semiconductor, causing different electrical properties in the induced depletion regions. Intuitively, when a thin film of the semiconductor is cladded with different dielectrics with opposite polarities at either sides, the larger asymmetry of Q_f results in a higher built-in electric field and a more prominent effective χ⁽²⁾ in the semiconductor. Therefore, we propose to exploit different polarities of these fixed charges on semiconductor interfaces to maximize the nonlinear optical properties of the metamaterial structures consisting of multiple periods of asymmetrical DSD thin film stacks as shown in Fig. 1(a), where an a-Si thin layer is cladded with SiO₂ and Al₂O₃. The thin thickness of the a-Si layer is fundamentally important to create a constant high static induced electric field within the semiconductor layer, enhancing the average effective χ⁽²⁾ in the bulk of the DSD stack. To characterize the Q_f presented at the two semiconductor-dielectric interfaces, the most common technique is to analyze the capacitance-voltage (C-V) behavior of a MOS structure consisting of the dielectric materials of interest. Two test samples were fabricated for characterizing Q_f at SiO₂/a-Si and Al₂O₃/a-Si interfaces (supplementary material: C-V measurement). The experimental results showing C-V curves performed at 10 kHz are displayed in Fig. 1(b). The calculated Q_f densities are determined to be +1 × 10¹² cm⁻² and −2 × 10¹² cm⁻² for SiO₂ and Al₂O₃, respectively. The measured different signs and quantities of Q_f from these two dielectrics are expected to cause a large non-zero gradient of field distribution within the a-Si thin film, supporting the fundamental concept of nonlinear DSD metamaterials.

Using the measured surface charges, we simulate both the symmetrical SiO₂/a-Si/SiO₂ and asymmetrical Al₂O₃/a-Si/SiO₂ stacks using the TCAD SILVACO tool to obtain the electric field distributions in these two cases as shown in Fig. 2. The thicknesses of a-Si and dielectrics are assigned to be 25 nm and 10 nm, respectively, and the thickness of a-Si is determined from the simulations to achieve a high internal electric field close to that of the Si's breakdown electric field. For the symmetrical case (black solid line), as expected, the Q_f creates a narrow depletion region and the induced electric field drops dramatically away from the surface. Due to the symmetry in the polarity of Q_f, the electric fields from left and right depletion regions exhibit the same magnitude but in opposite directions, resulting in a zero net field (blue dashed line) within the a-Si layer. On the other hand, for the asymmetrical case (red solid line), different Q_f polarities on each side create a depletion region that extends into the entire a-Si layer, resulting in a constant non-zero statistic electric field (∼1 × 10⁵ V/cm) inside the a-Si. This high field is expected to interact with a-Si's inherent χ⁽³⁾, which ranges from 2.3 × 10⁻¹⁹ to 9.2 × 10⁻¹⁹ m²/V² at a wavelength of 800 nm^27–29 to induce a prominent effective χ⁽²⁾ (i.e., 3.8 to 15.3 pm/V) through the EFISH effect in the asymmetrical DSD stack.

To validate this approach experimentally, we fabricated four samples, with one and two periods of asymmetrical (Al₂O₃ (10 nm)/a-Si (25 nm)/SiO₂ (10 nm)) and symmetrical (SiO₂ (10 nm)/a-Si (25 nm)/SiO₂ (10 nm)) stacks on fused silica substrates (supplementary material: sample preparation). The characterization of second-order nonlinearities of these DSD metamaterials is performed using the Maker fringe setup, the details of which are mentioned in our previous work,³⁰ wherein a fs Ti-Sapphire laser at 800 nm was used as a pump with a fixed incident angle of 45 degrees. Figure 3(a) shows the measured second-harmonic optical power with mixed polarizations (combination of p- and s-polarized waves) generated from one and two periods of the asymmetrical nonlinear metamaterial as a function of pump power. The detected signals, as expected, scale quadratically with the pump power, verifying the fact that the detected signal comes only from the SHG effect of the thin film stacks. Figure 3(b) shows the generated p- and s-polarized SHG signals from one and two periods of the asymmetrical metamaterial as a function of the polarization angle of the pump field, where 0° stands for the s-polarized and 90° represents for the p-polarized fundamental beam. The result for the p-polarized SHG from two periods of the symmetrical DSD composite metamaterial is also shown for comparison (i.e., red). The curves corresponding to the symmetrical metamaterial show a relatively low signal, which is close to the background noise of our setup, indicating that no observable SHG effect occurs. This experimental result is consistent with our theoretical prediction that EFISH is negligible for the case when a-Si is cladded with the same dielectric on both interfaces. In contrast, both the p- and s-polarized SHG signals generated from asymmetrical samples are prominent. The bare fused silica substrate and single layers of a-Si, Al₂O₃, and SiO₂ separately grown on silica are all measured under the same experimental conditions as those used for the characterization of DSD metamaterials, and no observable signals were detected. These results confirm the fact that the contribution of quadrupolar and magnetic dipoles and interfacial effects to the observed SHG signal is negligible in our case, and the prominent SHG in the asymmetrical DSD metamaterial originates from bulk a-Si layers though the EFISH effect. By fitting these data and using the Maker fringe analysis,³¹ we calculate all the three independent components of the χ⁽²⁾ tensor: χ⁽²⁾_zzz, χ⁽²⁾_xxz, and χ⁽²⁾_zxx as represented in Table I, and the coordinate system is shown in Fig. 1(a). The value of the dominant diagonal component, χ⁽²⁾_zzz, is ∼ 2 pm/V and has the same direction as the induced built-in electric field within the a-Si layer, proving that the effective χ⁽²⁾ in the asymmetric metamaterial originates mostly from the EFISH effect. The small discrepancy between the expected and the measured value originates from the considered χ⁽³⁾ value for a-Si.²⁷ Also, the calculated χ⁽²⁾ tensors from samples with one and two periods of the stack match each other, indicating that the medium composed of more cycles of the asymmetric DSD stack exhibits the same nonlinear properties, enabling potential applications of devices in a waveguide configuration for on-chip realization of nonlinear optical devices. The generated second-harmonic signals from the two periods of the DSD stack are only twice as large as the one generated from one period of the DSD stack, which does not obey the theoretical prediction that the generated SHG intensity scales quadratically with the interacting length. The discrepancy can be attributed to a lower transmittance in the two periods of the DSD stack due to the absorption in the a-Si layer at both wavelengths, the fundamental (i.e., 800 nm) and the second-harmonic (i.e., 400 nm) signals.³² Considering absorption (i.e., the imaginary part of the refractive index) in the Maker fringe analysis, we predict a SHG power ∼1.6 times larger for the two periods of the DSD stack, within the error bars of our experiment.²⁷ Small discrepancies may occur due to the actual values of the real and imaginary parts of refractive indices considered in our study. It should be noted that this loss can be significantly reduced when operated with wavelengths where a-Si is transparent.

In the theory, the magnitude of the effective χ⁽²⁾ in the DSD metamaterial can be further enhanced by either increasing the magnitude of the built-in electric field or choosing semiconductors that exhibit higher χ⁽³⁾.³³ To induce a higher electric field within the a-Si layer, an efficient way is to increase the magnitude of the Q_f density at dielectric/semiconductor interfaces by treating as-deposited samples with an annealing process. The heating treatment offers sufficient energy for inactive charge centers to contribute more to the separation of ions and free carriers, thus increasing the density of Q_f. To understand the influence of annealing treatment on the density of Q_f, we fabricated test samples and performed C-V measurements on SiO₂/a-Si and Al₂O₃/a-Si interfaces shown in Figs. 4(a) and 4(b) for the as-deposited samples and the samples annealed at different temperatures (i.e., 200, 300, and 400 °C) for 15 min (supplementary material: sample preparation). As the plots show, the flat-band voltage, V_fb, for both cases shifts away from the work function difference between a-Si and the aluminum electrodes, indicating that the magnitude of Q_f in both SiO₂ (positive) and Al₂O₃ (negative) increases with an increase in annealing temperature. This increase in Q_f leads to a higher built-in electric field, which is in turn expected to lead to a larger effective χ⁽²⁾_zzz.

To validate the enhanced magnitude of the effective χ⁽²⁾_zzz, we carried out experiments on analyzing the p-polarized SHG signals from samples with one and two periods of the DSD stack annealed under different conditions as shown in Figs. 4(c) and 4(d), respectively. In both cases, the samples annealed at 400 °C (blue circle) show the highest second-harmonic intensity, which matches the prediction from the results of C-V measurement. In Fig. 5, we summarize the calculated Q_f at SiO₂/a-Si (in blue squares) and Al₂O₃/a-Si (in red squares) interfaces and the extracted values of the effective χ⁽²⁾_zzz from one (brown circle line) and two periods (green square line) of metamaterials for samples with different annealing treatments. The magnitude of both positive and negative Q_f generated at either top or bottom interfaces increases with the annealing process at higher temperature, and the calculated effective χ⁽²⁾_zzz in one period and two periods of the asymmetric annealed metamaterial also shows the same trend. The highest effective χ⁽²⁾_zzz is calculated to be 8.5 pm/V for the sample treated by the 400 °C annealing process, which shows 4 times enhancement than that obtained from the as-deposited sample (i.e., 2 pm/V).

In summary, we have theoretically and experimentally demonstrated an approach to engineer CMOS-compatible nonlinear metamaterials by exploiting the generated fixed charges at dielectric/semiconductor interfaces. Asymmetrical DSD metamaterials exhibit an average effective χ⁽²⁾_zzz of 2 pm/V in the bulk via exploiting the charges existing at interfaces, and the magnitude can be further enhanced up to 8.5 pm/V with proper thermal annealing treatment. In the theory, larger effective χ⁽²⁾ can be achieved by either increasing Q_f with optimization of fabrication processes or replacing the a-Si with other semiconductor candidates exhibiting both larger break down fields and larger χ⁽³⁾. Since the composite films are all CMOS-compatible and grown by magnetron sputtering at room temperature, the proposed formation of nonlinear metamaterials can be customized with various dielectric and semiconductor materials for variant applications. We have also demonstrated that if the number of periods is increased, the effective χ⁽²⁾_zzz is the same in the multiple semiconductor layers composed of the DSD metamaterials. Indeed, this feature enables using such metamaterials as waveguide cores provided that large optical mode-metamaterials overlap, which offers efficient nonlinear behaviors exploiting the induced effective χ⁽²⁾. With further optimization of their optical linear and nonlinear properties, the demonstrated DSD metamaterials exhibiting large effective second-order optical nonlinearities can be fabricated into waveguides for efficient on-chip devices such as modulators, nonlinear switches, and wavemixers.

See supplementary material for the details of C-V measurement, sample preparation, and the Maker fringe analysis for characterizing the optical nonlinearities.

This work was supported by the Defense Advanced Research Projects Agency (DARPA), the National Science Foundation (NSF), the NSF ERC CIAN, NSF's NNCI San Diego Nanotechnology Infrastructure (SDNI), the Office of Naval Research (ONR) Multidisciplinary University Research Initiative (MURI), the Army Research Office (ARO), and the Cymer Corporation. We thank UCSD's staff Ryan Anderson for the discussion on the equipment for electrical characterization.