Colloidal ZnO QDs were synthesized at room temperature by a sonochemical

method [14] [15] in which acoustic cavitation precludes the formation of intermediate products, including Zn(OH)₂, converts the reactants into ZnO QDs and calcination steps are not required. This method has proven useful for accelerating chemical reactions in liquid-solid systems [14] . Specifically, ZnO QD synthesis was accomplished by preparing an initial solution of 0.02 M zinc acetate (ZnAc) (99.99%, Sigma-Aldrich) in pure ethanol. A second and independent solution of 0.01 M of lithium hydroxide (LiOH) (≥98% Sigma-Aldrich) was prepared also in pure ethanol. Subsequently, the LiOH solution was incorporated dropwise to the ZnAc solution until a pH value of 10 or 12 was obtained. Once the targeted pH value was reached, the mixture was placed in a sonication bath for 3 hours [16] [17] . The chosen pH values were found to yield stable nanoparticles and relatively minimal agglomeration. Furthermore, the ultimate size of the obtained QDs was determined by the pH value of the final solution employed during synthesis and observed to be in agreement with the dependence of ZnO nanoparticle size on pH reported elsewhere [18] . A summary of the synthesis is shown in Figure 2. The ZnO QDs were then deposited onto the surface of the MM shown in Figure 1.

In order to characterize the synthesized ZnO QDs in the terahertz regime, the nanoparticles were dispersed in a polydimethylsiloxane (PDMS) matrix. To this end, the ZnO QDs were harvested by drying the final solution on a hotplate maintained at 70˚C, and prior to dispersing them in the aforementioned matrix, the QD samples were thoroughly pulverized using a mortar. Once the solvent had completely evaporated, the ZnO QD powder was mixed with a PDMS solution that had been previously prepared by mixing 5 wt% of a curing agent in a silicone elastomer [19] [20] . The mixture of PDMS and ZnO QDs was then cured at 90˚C for 3 hours (see Figure 3).

The UV-vis absorption characterization of the ZnO QDs was performed using

an Ocean Optics Flame-S-UV-VIS spectrometer and the collected absorption spectra corresponding to nanocrystals synthesized with the previously mentioned colloidal solution pH values of 10 and 12, are shown in Figure 4, along with their corresponding photoluminescent response. The emission wavelength is directly related to quantum dot size, therefore, the larger the nanoparticles the longer the wavelength of their characteristic photoluminescent peak [21] [22] . Thus, QDs synthesized with a pH value of 12 have an emission peak located at 510 nm, while QDs synthesized with a pH value of 10 have the peak located at 540 nm, indicating that lower pH values produce larger nanoparticles.

The observed QD absorbance measurements are related to QD bandgap by the following expression

α = ( A h ν ) ( h ν − E g ) m (1)

where α is the absorption coefficient, A is an optical constant, m represents the type of optical transition in the semiconducting material; specifically, m can only take the values of 1/2, 2, 3/2 or 3 corresponding to allowed direct, allowed indirect, forbidden direct and forbidden indirect, respectively [23] , and E g is the band gap of the semiconducting quantum dots. Multiplying Equation (1) by h ν , obtaining the natural logarithm and finally taking the derivative with respect to h ν , the resultant equation is

d ( ln ( α h ν ) ) d ( h ν ) = m h ν − E g (2)

The bandgap can then be estimated by plotting Equation (2) with respect to energy [23] , and this approach permits the identification of the inflection point (i.e., the bandgap value) where the slope changes sign (see Figure 5). In other words, the bandgap value will be determined as a discontinuity at h ν − E g = 0 [23] . The extracted bandgap values were 3.43 eV and 3.62 eV for the ZnO QDs synthesized with the colloidal solutions with a pH of 10 and 12, respectively. The observed emission peaks were located at 510 nm (pH 12) and 540 nm (pH 10).

Since the wavelength emission is directly related to QD size, i.e., the larger the particle, the longer the wavelength of emission, the emission peak wavelength observations corroborate that higher pH values during synthesis indeed lead to smaller ZnO quantum dots.

Once the bandgap value had been calculated, the size of the QDs was estimated employing Brus’ quantum mechanical approximation [24]

E g = E B u l k + ℏ 2 π 2 2 r 2 ( 1 m e * + 1 m h * ) − 1.8 e 2 r ϵ (3)

where E g is the band gap energy of the semiconductor quantum dots, E B u l k is the band gap energy of the bulk semiconductor material, ℏ is the reduced Planck constant, m e * and m h * represent the effective mass of electron and hole of the material under consideration, ϵ is the bulk relative permittivity, and r is the QD radius. For the pH 10 ZnO QDs we estimated a radius of 3.00 nm and for the pH 12 ZnO QDs we obtained a radius of 2.12 nm. To corroborate the estimated sizes, transmission electron microscope (TEM) images for both samples were obtained and are shown in Figure 6. The measured values were approximately 3.2 nm and 1.85 nm radius for the ZnO pH 10 and ZnO pH 12 samples, respectively, in reasonable agreement with the sizes estimated via Equation (3).

From the collected THz-TDS data, optical properties of interest such as refractive index, permittivity and conductivity can be extracted. The real part n ( ω ) and imaginary part κ ( ω ) of the refractive index can be calculated by using the following equations [26]

n ( ω ) = 1 + c ( ϕ s a m ( ω ) − ϕ r e f ( ω ) ) ω d (5)

κ ( ω ) = − ( c ω d ) ln ( | A s a m ( ω ) A r e f ( ω ) | ) (6)

respectively. Similarly, the permittivity and the index of refraction are related by

ϵ ˜ ( ω ) = ϵ ′ ( ω ) + i ϵ ″ ( ω ) = ( n ( ω ) 2 − κ ( ω ) 2 ) + i ( 2 n ( ω ) κ ( ω ) ) (7)

where ϵ ˜ is the complex permittivity, ϵ ′ is the real part of the permittivity, ϵ ″ is the imaginary part of the permittivity. The extracted real effective refractive index of the PDMS + QDs membrane at 1 THz (see Figure 8), was of ~1.50 for the smaller QDs synthesized with a pH value of 12 (blue dotted line), and to ~1.85 (green solid line) for the larger QDs synthesized with a pH value of 10. Subsequently, the samples were exposed to UV excitation of 400 nm wavelength (see Figure 9 and Figure 10). The intensity of the UV source was measured using

an ILT2400 Light Meter and observed to be 2.5 × 10⁻⁴ W/cm². The observations indicate that larger quantum dots exhibit a relatively more pronounced response to UV excitation. This can be explained on the grounds that the synthesized semiconducting nanoparticles exhibit quantum confinement effects where exciton polarizability, reported to be proportional to the fourth power of the radius ( α ~ R 4 ), can be defined as [27]

α = Δ χ s ( ϵ Q D + 2 ϵ ) 2 9 n s ϵ 2 (8)

were Δ χ s is the susceptibility of the material (related to the permittivity by χ s = 1 − ϵ ), ϵ Q D is the permittivity of the quantum dots, ϵ is the permittivity of the medium and n s is the sheet excitation density. This result is in agreement with the extracted real part of the effective refractive index of the media with the incorporated ZnO QDs shown in Figure 8. Ostensibly, studies of polarizability as a function of frequency and quantum dot dimensions can be performed employing THz-TDS.

The experimental characterization of the metamaterial array previously described and shown in Figure 1, corroborated the anticipated resonant frequency at 1 THz (dotted lines Figure 11 and Figure 12). Subsequently, the synthesized ZnO QDs were deployed directly on the MM surface, and the resonance frequency was observed to shift to 0.95 THz and to 0.96 THz for the ZnO QDs synthesized with pH values of 10 and 12, respectively. The observed variation in the resonance frequency reflects the permittivity value trends presented in Figure 8, thus, larger permittivity values are associated with lower resonant frequencies.

In order to measure the modulation of the metamaterial arrays with the deployed quantum dots, the samples were excited with a UV source of 400 nm while being tested with the THz-TDS (results are shown in Figure 13). The experimental observations yielded a modulation of 4.55% for the ZnO QDs synthesized with colloidal solutions with a pH value of 10, while the nanoparticles synthesized with a pH value of 12 exhibited a relatively large modulation of 9.21%. The observed results are thought to be due to a higher degree of confinement effects in smaller quantum dots [27] . These changes in modulation depth demonstrate the capability of hexagonal MM via the deployment of ZnO QDs to tune THz electromagnetic signals.