Terahertz Sensing of Å‐scale Thin Dielectric Film Via Electron Tunnelling

Precise sensing of ultrathin dielectric films is paramount in various fields including nanoscale dielectric characterization, advanced material development, and quality control in microelectronics manufacturing. However, achieving this with conventional detection techniques within the terahertz (THz) frequency range has remained challenging due to their limited sensitivity and resolution. In this study, a novel approach is reported that utilizes Fowler‐Nordheim (FN) tunnelling at a metal‐dielectric junction, which drastically improves the sensitivity to changes in dielectric film thickness down to the Angstrom scale. Through a detailed analysis of both experimental and simulated data, it is demonstrated that the FN tunnelling‐based THz sensing technique exhibits exceptional sensitivity. This finding not only overcomes the limitations of traditional detection techniques, but also paves the way for novel ultrathin film sensing capabilities in the rapidly advancing field of THz technology.


Introduction
Terahertz (THz) sensing is a rapidly emerging field with potential applications in non-destructive imaging and spectroscopy for material characterization, [1] security screening, [2] biomedical diagnostics, [3] and biosensing. [4,5]The fact that THz waves are non-destructive and non-ionizing, [6] penetrative through a range of materials [7] and are sensitive to hydrogen bonds and van der Waals forces [8] makes THz sensing via THz time-domain spectroscopy (THz-TDS) an attractive field of research. [9,10]owever, many of the above-mentioned applications often require sensing in a small volume deep below the wavelength of the THz waves. [11]Whereas classical THz-TDS [8] is typically applied to samples of a significant thickness to resolve temporal features, metallic resonators help to overcome this as their fine structures confine the electric field to potentially sub-wavelength DOI: 10.1002/adom.202302841dimensions, making them highly sensitive to local variations of the refractive index. [12]An evaluation of the sensing performance with a thin film of dielectric, such as photoresists, [13][14][15][16][17] metal oxide, [16,18] or germanium [16,19,20] utilized as a sensing layer has become a standard in studies in this field, similarly to other sensor types. [21]owever, in most of these studies the analyte film is several μm thick and sensing a sub-10 nm film is challenging even with the use of metasurfaces.
Sensing of an ultrathin dielectric film has previously been demonstrated using tight field confinement of the electric field in an ultranarrow 2-nm gap [22] and high-Q bound-states-in-continuum metasurfaces. [20,23]While fabrication constraints limit the former approach, the latter has yet to be applied effectively to sub-5-nm films.In parallel, there have been significant strides in studying THzinduced tunnelling, [24,25] fueling the development of a novel class of THz optical detectors. [26,27]This innovative approach employs THz metasurfaces, leading to a local field enhancement and subsequent electron emission via Fowler-Nordheim (FN) tunnelling.Here, we show a distinct sensing of Angstrom (Å)-scale thin dielectric film realized via FN electron tunnelling at THz frequencies.This method does not require elaborate fabrication or high-Q resonances.To the best of our knowledge, this is the first study that shows the sensing of Å-scale dielectric films utilizing THz waves.

Results
Figure 1a shows the experimental scheme featuring an array of gold antennas with and without an ultrathin dielectric overlayer exposed to single-cycle THz waves of variable field strength inside a vacuum chamber equipped with a multichannel plate (MCP) for electron multiplication.The sample comprises an array of gold (Au) dipole antennas, each with a length of 81.5 μm, width of 4.0 μm, and thickness of 200 nm, designed to resonate at a frequency of 0.66 THz.The resonant frequency has been selected based on the peak spectral intensity of the THz waves.The antennas are arranged with spacings 269 and 420 μm in the x and y directions, respectively.The samples are exposed to THz pulses generated via intra-pulse difference frequency generation by the tilted pulse front method in a lithium niobate (LiNbO 3 ) crystal, [28,29] with its polarization linearly aligned along the antennas.Electron emission from the sample occurs due to the FN tunnelling effect, a quantum mechanical phenomenon in which electrons tunnel through a potential barrier under an applied electric field, in this case provided by the pulsed THz field with field strength of several tens to hundreds of kVcm -1 .An ultrathin Al 2 O 3 film with thicknesses ranging from 4 -52 Å introduces a second tunnelling barrier, and hence, is used to modify the optical properties of the array.
Figure 1b illustrates the electric potential profiles as a function of distance from the gold surface, taking into account the applied electric field, F = *F 0 , with F 0 being the maximum electric field of the incident waveform, and  representing the enhancement of the electric field at the gold antenna tip's surface.The potential can be expressed as: here, V 0 = E F + Φ, where E F and Φ are the Fermi level and work function of the metal respectively,  is the electron affinity of the dielectric, and F diel is the electric field inside the Al 2 O 3 film, which is given by F/ϵ, where ϵ is the dielectric function of Al 2 O 3 .In the THz regime, ϵ is approximately constant in frequency at ϵ = 9. [30] Figure 1c displays a micrograph of the gold dipole antenna array fabricated on a 525 μm thick high-resistivity silicon substrate, with an SEM image of the sample provided in the inset, highlighting the 400 nm diameter tip.The dipole antennas are connected to a contact pad via thin gold wires, enabling the application of a bias voltage within a vacuum chamber equipped with an MCP.The bias voltage ensures a well-defined electrostatic potential that accelerates the emitted electrons toward the MCP.The dipole antennas provide tight confinement and significant enhancement of the THz electric field at the tip.A finite element method (FEM) simulation, shown in Figure 1d, demonstrates the effectiveness of the antennas in enhancing the electric field, with a maximum simulated enhancement factor of  ≈ 457 with the electric field polarized parallel to the antennas.The simulation is performed in the frequency domain, which provides insights into the metasurface response to each frequency component.The validity of such a simulation arises from the linearity of the terahertz metasurfaces, allowing the electromagnetic response at specific frequencies to be considered independently, making it suitable for predicting the response to realistic broadband terahertz pulse waveforms.
The dielectric coating was deposited over the gold antennas using a standard atomic layer deposition (ALD).For consistency, the reference sample without any coating was also subject to the vacuum annealing treatment in the ALD chamber but with no precursor pulses.Figure 1c shows the thickness of the dielectric film measured with ellipsometry as a function of the number of cycles of the ALD process and the respective growth rate.The thickness exhibits a linear relationship with the number of cycles, indicating a consistent deposition process.Additionally, to confirm the thickness, we performed X-ray reflectometry as seen in Figure S4 (Supporting Information).An AFM analysis of the surface morphology of antennas coated with 5 and 50 Å of Al 2 O 3 in Figure S1a,b (Supporting Information) show that the morphology of the gold surface does not change significantly.
Figure 2a presents the THz-TDS transmittance for multiple samples with varying coating thicknesses.While the data shows a resonance dip close to the designed frequency, there is no significant difference observed among the spectra of the samples with different coating thicknesses.To analyze the spectra, we fitted each resonance dip with a Gaussian function.The fitted central frequency shown in Figure 2b is, within the experimental uncertainties, independent of the coating thickness.The resonance frequency of the gold dipole antenna measured using THz-TDS is found to be approximately 0.71 THz, which slightly deviates from the simulated value of 0.66 THz obtained through FEM analysis (see Figure S6, Supporting Information).This discrepancy could be attributed to fabrication imperfections and variations in the material properties, as well as the accuracy of the THz-TDS system, which has a frequency-resolution of 50 GHz, limited by the thickness of the substrate, which leads to echoes in the time-trace.These observations suggest that the coating thickness does not have a significant effect on the THz-TDS spectra of the samples and we conclude that sensing of sub-5-nm dielectric film via THz-TDS spectroscopy using the presented antenna array is not feasible.An extended data can be found in the Figure S5 (Supporting Information).
Figure 3a displays the electron tunnelling current as a function of THz field strength for dipole antennas coated with various thicknesses of Al 2 O 3 , ranging from 0.4 to 5.2 nm, and an uncoated antenna for reference.The emitted electrons are multiplied by a multichannel plate, and the amplified current pulse is detected by an anode formed by a phosphorus screen, situated within a vacuum tube.We record the current due to the incident electrons going through the circuit connected to the phosphor  screen.The detected current represents the number of incident electrons on the anode, which depends on the number of emitted electrons from the metasurface, the MCP collection efficiency, and its gain factor.The experimental setup also includes a pair of wire-grid polarizers, which enable the adjustment of the incident THz field strength, without altering the polarization state of the light.This arrangement facilitates the investigation of the tunnelling current field threshold and its field dependence.The results demonstrate clearly, that both the tunnelling current threshold and density decrease with increasing thickness of the coating.Furthermore, the tunnelling current in Figure 3a exhibits distinct differences among the various coatings, with no overlap among the 1- error bars, indicating that the difference in tunnelling current between samples is statistically significant.
The double-barrier FN plots in Figure 3b provide insights into the tunnelling behavior of antennas with different Al 2 O 3 thicknesses by linearizing the double-barrier FN equation: [31,32] where J is the emitted current, F is the electric field at the emitter, 3qℏ are the FN constants, and Φ = 5.1eV is the workfunction of Au.The constants B and C are In these equations, Φ eff = Φ −  is the effective work function at the metal-dielectric interface, is the electric field inside the dielectric layer, d is the thickness of the dielectric layer,  diel = 9 [30] is the relative permittivity of the Al 2 O 3 dielectric layer, and H(x) is the Heaviside step function.Defining y = ln (J/F 2 ) and x = 1/F, yields a straight line for data following the doublebarrier FN tunnelling model.In this manner, we generally find a good fit of the double-barrier FN model to the experimental data with high R 2 values (see Table S1, Supporting Information) indicating a strong relationship between emitted current and electric field. [31]nterestingly, for the uncoated case and the sample coated with 0.4 nm Al 2 O 3 , the plot can be fitted with two different linear functions with distinct slopes as indicated by the black dashed lines in Figure 3b.The smaller slope of the linear function at higher F, points to the presence of the space charge effect, which becomes significant in electron tunnelling at high field strengths, as the accumulation of charge alters the local electric field and consequently impacts the tunnelling process. [33,34]These findings provide strong evidence for the accuracy of the double-barrier FN law in describing tunnelling behavior across different Al 2 O 3 thicknesses.
Complementing these findings, Figure 3c presents the tunnelling current thresholds as a function of the Al 2 O 3 thickness.This trend clearly distinguishes the threshold difference even for the case of a 0.4 nm coating.The consistency in the threshold trends and distinct differences in tunnelling current across different coating thicknesses highlight the impact of the dielectric film on the tunnelling behavior of the antenna.Figure 4a illustrates the profile of the potential barrier for various dielectric coating thicknesses.Specifically, we determine a tunnelling distance of 2.3 nm for electrons at the Fermi level for the uncoated case from Equation (1).By considering the potential barrier profile and using the experimentally derived emission threshold of the applied field, we calculate the field strength required to achieve a tunnelling distance of 2.3 nm as a function of coating thickness d using Equation (1), which yields the calculated emission threshold shown as grey, dashed curve in Figure 3c.This calculation is valid if the field enhancement  is invariant to d.To explore this, we have performed a FEM simulation for coated antennas as shown Figure S6 (Supporting Information), which indicates a slight increase in .This is consistent with a calculation by Xiong et al. [35] In contrast to the significant enhancement reported by Xiong et al. in the visible range, our study reveals that the far-off resonance of terahertz antennas with the metal's plasmonic frequency, coupled with the less confined nature of the electric field in this regime, results in a negligible enhancement effect from ultrathin coatings.It may, however, explain slight deviations of the trend of the experimentally measured threshold from the calculated one.
The tunnelling current from a gold surface coated with Al 2 O 3 of various thicknesses calculated with the double-barrier FN equation is depicted in Figure 4b.The field strength range considers the field enhancement  obtained from FEM simulation, where F = F 0 , with F 0 representing the field strength range of the THz radiation used in the experiment, measured and calibrated to be incident on the backside of the substrate.Figure 4b shows the tunnelling current as a function of the field strength, calculated using the double-barrier FN equation for different thicknesses of the dielectric coating.The calculated tunnelling current follows the trend observed in the experimental measurements, confirming that the current decreases as the coating thickness increases.

Conclusion
In conclusion, this study has successfully harnessed single-cycle THz waves and the Fowler-Nordheim tunnelling effect to develop a sensitive detection mechanism for ultrathin dielectric films covering metal structures.Our results emphasize the impact of dielectric layer thickness on the THz-field driven electron tunnelling behavior, highlighting the potential of our technique for precise thickness measurements at the Angstrom scale, six orders of magnitude below the wavelength of the THz wave.The theoretical model concurs well with the experimental results, validating the effectiveness of our methodology.
The electric field strength of the THz waveform used in this study is relatively high.There are several strategies to increase the sensitivity of the electron tunnelling response from the sample.First, changing the material composition of the antennas to one with a lower work function can result in improved tunnelling characteristics due to the reduced energy barrier for electron tunnelling.Second, optimizing the geometrical design of the metasurface, such as the shape, size, and arrangement of the microstructures, can lead to better field enhancement and, consequently, electron tunnelling.Finally, by designing metasurfaces that exploit resonant effects, such as surface plasmon polaritons or Fabry-Perot resonances, it is possible to enhance the local electric field and increase the sensitivity of the electron tunnelling. [36,37]

Figure 1 .
Figure 1.Scheme of the experiment a) shows THz pulse incident to the back side of the substrate that induces electron tunnelling from the Au dipole antenna.The electron tunnelling of the Al 2 O 3 coated antenna is weaker than that of its uncoated counterpart.b) A simplified band diagram explains the lower tunnelling current from the coated dipoles due to increased tunnelling distance.The antenna array is shown in micrograph of the sample c) and an SEM image in the inset shows the tip of the antenna.Scale bars are 100 and 1 μm, respectively.The spatial distribution of the electric field enhancement at a frequency of 0.66 THz is shown in FEM simulation in the frequency domain d).For clarity, the figure shows a cut-out of the whole unit cell.e) The Al 2 O 3 coating thickness measured by ellipsometry as a function of the number of ALD cycles.

Figure 2 .
Figure 2. THz time-domain spectroscopy of the ultrathin dielectric coating.a) THz-TDS transmission spectra of the antennas with Al 2 O 3 coating of various thicknesses.b) Resonance frequencies obtained by the Gaussian fits to the data do not show any discernible trend.

Figure 3 .
Figure 3. Characterization of THz-induced electron tunnelling a) Measured electron tunnelling current J as a function of electric field F for uncoated and Al 2 O 3 coated antennas with the grey dashed line indicating the noise floor, b) FN plot for respective electron tunnelling current data with the black dashed lines indicating a linear fit to the data, and c) tunnelling current threshold as a function of coating thickness with calculated hyperbolic trend in dashed gray.

Figure 4 .
Figure 4. Theoretical calculation a) Potential barrier profiles according to Equation (1) for different thicknesses of the dielectric coating, with F 0 = 48 kVcm -1 representing the experimental tunnelling current threshold of the uncoated sample and  = 457.As the coating thickness increases, the tunnelling distance also increases, leading to changes in the tunnelling current threshold for coated samples.b) Electron tunnelling current as a function of dielectric coating thickness, calculated using the double-barrier FN equation.The calculated tunnelling currents follow the experimental measurements, showing a decrease in tunnelling current with increasing coating thickness.