Field Enhancement Factor Research Articles

Joule heating of an emitter on the cathode surface by field electron emission current with an account of the nonisolation of the apex

This work is devoted to the investigation of the nonstationary problem of the thermal conductivity of a nanoemitter on the surface of a massive copper cathode when a field electron emission current passes through it. At the same time, the dependence of volume resistivity, thermal conductivity on temperature, and size effects have been taken into account. The influence of the Nottingham effect has been considered. The dependence of the equilibrium temperature of the emitter apex on the field enhancement factor for different values of the electric field strength has been found. Based on the assumption that the initial stage of the breakdown begins when the emitter apex melts, the conditions for the occurrence of a vacuum breakdown and the influence of the Nottingham effect have been analyzed.

Proton-Induced Displacement Damages in 2-D and Stacked CMOS SPADs: Study of Dark Count Rate Degradation

Dark count rate (DCR) degradation is measured on 40-nm 2D and stacked CMOS SPADs after proton irradiations. Mean DCR increase is plotted for different displacement damage doses (DDD) for two biasing conditions. Due to field enhancement effects such as Poole-Frenkel and phonon-assisted-tunneling, Non-Ionizing Energy Loss (NIEL) scaling is found to be dependent on the excess bias. Moreover, the associated damage factors are higher compared to pixels with unity gain photodiodes. A model predicting DCR increase with DDD based on field enhancement factor equations and damage energy deposited by the proton induced recoil spectrum is established and fits well with experimental data. Finally, activation energies are extracted: low values between 25 °C and 60 °C confirm the domination of field effects over thermal generation. Furthermore, large energy discrepancies seen at a fixed DCR increase are suggesting that defect structures could also have an impact on DCR distributions.

Electric Field-Enhanced Generation Current in Proton Irradiated InGaAs Photodiodes

Dark current degradation due to 49.7 MeV proton irradiation is studied on lattice-matched InGaAs PIN photodiodes. This degradation is described in terms of electric field enhanced Shockley-Read-Hall generation current in the depletion region. In this paper we present a model of the radiation-induced generation current which includes the role of the electric field through the generation rate field enhancement factor (GRFEF). Using a combination of dark current-voltage ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I_d – V</i> ) and capacitance-voltage ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C – V</i> ) measurements, an experimental GRFEF is extracted for the thermal generation rate. This GRFEF has been used to define a new damage factor for InGaAs at low electric field that has been compared to previous literature studies. As a final result, the low-field generation lifetime degradation as a function of the fluence has been extracted.

Local field enhancement factor of spheroidal core–shell nanocomposites with passive and active dielectric cores

We studied the effects of depolarization factor (L), metal fraction (p), and dielectric function of host matrix (ε h ) on the local field enhancement factor (LFEF) of spheroidal core–shell nanocomposites (NCs) with passive and active dielectric cores. Solving Laplace’s equations in the quasi-static limit, we obtained expressions of electric potentials for spheroidal core–shell NCs. Then, by introducing L and the Drude-Sommerfeld model into these expressions, we derived the equation of LFEF in the core of spheroidal core–shell NCs. The results show that whether L, p, and/or ε h vary or kept constant, LFEF of the spheroidal core–shell NCs possesses two sets of peaks with passive dielectric core, whereas only a set of peak is observed with active dielectric core. In NCs with passive dielectric core, an increase in any of these parameters resulted in a more pronounced LFEF peaks in the first set of resonances. With both passive and active dielectric cores, increasing L increases the peaks of LFEF of spheroidal core–shell NCs, whereas increasing p shows decreasing tendency on the peaks of LFEF of the same material with active dielectric core. Moreover, the highest peak of LFEF is obtained by increasing L than p or ε h indicating that change in the geometry of spheroidal core–shell NCs has the highest effect on the LFEF than the metal concentration and host dielectric function. With the same increase in ε h , intensities of LFEF of the spheroidal core–shell NCs decrease when the dielectric core is passive and increase when the dielectric core is active. Briefly, the number and intensities of peaks of LFEF of spheroidal core–shell NCs vary greatly when its core is made either passive or active dielectric. Furthermore, by changing parameters like L, p, and ε h , adjustable LFEF could be obtained and used for applications in optical sensing, nonlinear optics, and quantum optics.

Enhancement of pattern quality in maskless plasmonic lithography via spatial loss modulation

Plasmonic lithography, which uses the evanescent electromagnetic (EM) fields to generate image beyond the diffraction limit, has been successfully demonstrated as an alternative lithographic technology for creating sub-10 nm patterns. However, the obtained photoresist pattern contour in general exhibits a very poor fidelity due to the near-field optical proximity effect (OPE), which is far below the minimum requirement for nanofabrication. Understanding the near-field OPE formation mechanism is important to minimize its impact on nanodevice fabrication and improve its lithographic performance. In this work, a point-spread function (PSF) generated by a plasmonic bowtie-shaped nanoaperture (BNA) is employed to quantify the photon-beam deposited energy in the near-field patterning process. The achievable resolution of plasmonic lithography has successfully been enhanced to approximately 4 nm with numerical simulations. A field enhancement factor (F) as a function of gap size is defined to quantitatively evaluate the strong near-field enhancement effect excited by a plasmonic BNA, which also reveals that the high enhancement of the evanescent field is due to the strong resonant coupling between the plasmonic waveguide and the surface plasmon waves (SPWs). However, based on an investigation of the physical origin of the near-field OPE, and the theoretical calculations and simulation results indicate that the evanescent-field-induced rapid loss of high-k information is one of the main optical contributors to the near-field OPE. Furthermore, an analytic formula is introduced to quantitatively analyze the effect of the rapidly decaying feature of the evanescent field on the final exposure pattern profile. Notably, a fast and effective optimization method based on the compensation principle of the exposure dose is proposed to reduce the pattern distortion by modulating the exposure map with dose leveling. The proposed pattern quality enhancement method can open new possibilities in the manufacture of nanostructures with ultrahigh pattern quality via plasmonic lithography, which would find potentially promising applications in high density optical storage, biosensors, and plasmonic nanofocusing.

Synthesis and Physical Characteristics of Undoped and Potassium-Doped Cubic Tungsten Trioxide Nanowires through Thermal Evaporation.

We report an efficient method to synthesize undoped and K-doped rare cubic tungsten trioxide nanowires through the thermal evaporation of WO3 powder without a catalyst. The WO3 nanowires are reproducible and stable with a low-cost growth process. The thermal evaporation processing was conducted in a three-zone horizontal tube furnace over a temperature range of 550-850 °C, where multiple substrates were placed at different temperature zones. The processing parameters, including pressure, temperature, type of gas, and flow rate, were varied and studied in terms of their influence on the morphology, aspect ratio and density of the nanowires. The morphologies of the products were observed with scanning electron microscopy. High resolution transmission electron microscopy, X-ray photoelectron spectroscopy, and X-ray diffraction studies were conducted to further identify the chemical composition, crystal structure and growth direction of the nanostructures. Additionally, the growth mechanism has been proposed. Furthermore, we investigated the potassium doping effect on the physical properties of the nanostructures. Photoluminescence measurements show that there were shorter emission bands at 360 nm and 410 nm. Field emission measurements show that the doping effect significantly reduced the turn-on electric field and increased the enhancement factor. Furthermore, as compared with related previous research, the K-doped WO3 nanowires synthesized in this study exhibited excellent field emission properties, including a superior field enhancement factor and turn-on electric field. The study reveals the potential of WO3 nanowires in promising applications for sensors, field emitters and light-emitting diodes.

Efficient field emission from ultrafine nanostructured lanthanum sulfide synthesized by chemical route

Lanthanum sulfide having a rocksalt structure has attracted lots of research interest because of its tremendous applications in the field of display devices, optoelectronic, field emission, and thermoelectric devices due to their low work function, and excellent chemical and physical properties. In the present work, we have synthesized LaS2 ultrafine nanostructures using anisotropic nanostructures of La(OH)3. The synthesis of anisotropic La(OH)3 has been attempted by the micellar-assisted hydrothermal route. The obtained La(OH)3 was further heated with elemental Sulfur at ambient pressure, leading to the stabilization of LaS2 of size ∼25 nm. Further, the as-obtained lanthanum disulfide was used for making LaS2 ink and spin-coated over a silicon substrate to fabricate LaS2 film. Field emission study of LaS2 film shows the lowest turn-on field (<3.9 V/μm), high field enhancement factor (β = 14,594), and high current density of 7.15 μA/cm2 has been obtained, which is around 10 times higher than earlier reports.

Mechanism analysis of field electron emission of titanium

Field electron emission (FEE) is generally considered to be closely correlated with radio frequency (RF) breakdown in accelerating structures and high-power microwave (HPM) devices. In this study, the field emission characteristics of titanium are investigated by using a field emission test system. With the increase of the number of field emission tests and stability tests, the repeatability of the field emission characteristic curve of titanium tends to be better, and the amplitude of the current oscillation in the stability tests gradually decreases, indicating that the field emission performance of titanium gradually becomes stable. Subsequently, the field emission characteristic curve of titanium is analyzed by adopting the field emission theory of metal microprotrusions. Combined with the analysis of the electric field enhancement effects caused by the surface morphology, the dominant effect of the metal microprotrusions on the FEE of titanium is excluded from the two aspects of the electric field enhancement factor and local maximum emission current density. At last, the field emission theory of dielectric micropoints is introduced to analyze the field emission characteristics of titanium. The electric field enhancement factor of 102 ∼ 103 are explained theoretically. Simultaneously, the reasonable effective emission area and local emission current density are given, which can better explain the field emission phenomena of titanium, such as the sharp decrease in emission current and repeatability of the field emission curve. Hence, it is revealed that the key factor that dominates the FEE of titanium is the dielectric impurities on the surface, rather than the metal microprotrusions.

Proposal that interpretation of field emission current–voltage characteristics should be treated as a specialized form of electrical engineering

This article proposes that we should think differently about predicting and interpreting measured field electron emission (FE) current–voltage [Im(Vm)] characteristics. It is commonly assumed that Im(Vm) data interpretation is a problem in emission physics and related electrostatics. Many experimentalists then apply the Fowler–Nordheim plot methodology, developed in 1929. However, with modern emitting materials, this 90-year-old interpretation methodology often fails (maybe in nearly 50% of cases) and yields spurious values for characterization parameters, particularly field enhancement factors. This has generated an unreliable literature. Hence, validity checks on experimental Im(Vm) data are nearly always needed before use. A new check, supplementing existing checks, is described. Twelve different “system complications” that, acting singly or in combinations, can cause validity-check failure are identified. A top-level path forward from this unsatisfactory situation is proposed. The term “field electron emission system (FE system)” is defined to include all aspects of an experimental system that affect the measured Im(Vm) characteristics. The analysis of FE systems should now be regarded as a specialized form of electronic/electrical engineering, provisionally called “FE Systems Engineering.” In this approach, the Im(Vm) relationship is split as follows: (a) the current is expressed as a function Im(FC) of the local surface-field magnitude FC at some defined emitter surface location “C,” and (b) the relationship between FC and measured voltage Vm is expressed and determined separately. Determining Im(FC) is mostly a problem in emission physics. Determining the relationship FC(Vm) depends on system electrostatics and (for systems failing a validity check) on the other aspects of FE Systems Engineering, in particular, electrical-circuit modeling. The scope of FE Systems Engineering and some related research implications and problems are outlined.

Field emitter electrostatics: Efficient improved simulation technique for highly precise calculation of field enhancement factors

When solving the Laplace equation numerically via computer simulation, in order to determine the field values at the surface of a shape model that represents a field emitter, it is necessary to define a simulation box and, within this, a simulation domain. This domain must not be so small that the box boundaries have an undesirable influence on the predicted field values. A recent paper discussed the situation of cylindrically symmetric emitter models that stand on one of a pair of well-separated parallel plates. This geometry can be simulated by using two-dimensional domains. For a cylindrical simulation box, formulas have previously been presented that define the minimum domain dimensions (MDD) (height and radius) needed to evaluate the apex value of the field enhancement factor for this type of model, with an error-magnitude never larger than a “tolerance” εtol. This MDD criterion helps to avoid inadvertent errors and oversized domains. The present article discusses (in greater depth than previously) a significant improvement in the MDD method; this improvement has been called the MDD extrapolation technique (MDDET). By carrying out two simulations with relatively small MDD values, it is possible to achieve a level of precision comparable with the results of carrying out a single simulation using a much larger simulation domain. For some simulations, this could result in significant savings of memory requirements and computing time. Following a brief restatement of the original MDD method, the MDDET method is illustrated by applying it to the hemiellipsoid-on-plane and hemisphere-on-cylindrical-post emitter shape models.

Gap distance dependence on field emission at the nanogap between silicon cleavage surfaces

In this study, we developed a model of field emission at a vacuum nanogap composed of semiconductor electrodes and conducted numerical calculations to evaluate its field emission characteristics. The current at the silicon nanogap was also measured, and the results were compared with the calculated results. Large-area vacuum nanogaps are expected to be used for highly efficient room-temperature thermionic power generation owing to their good thermal insulation, and their electrical conduction of tunneling current is sufficient for practical use. Because vacuum nanogaps should be parallel and smooth with a large area, we proposed and examined the use of cleavage to fabricate nanogaps in single-crystal materials. A nanogap with a nominal area of 26.5 μm2 was fabricated in a microelectromechanical device to evaluate its properties, and the model was used for the analysis. The calculated current–voltage characteristics of the semiconductor nanogap of both n-type and p-type silicon were affected by the bandgap and the presence of carriers, i.e., electrons and holes. Moreover, the Fowler–Nordheim plot was confirmed to be valid for semiconductor nanogaps based on the calculated results. We proposed an effective work function that compensates for the discrepancy between semiconductor nanogaps and the Fowler–Nordheim theory and enables a more accurate analysis. Field-emission currents flowing through a 1.1 nm nanogap were measured and matched with the calculated results by adjusting the field enhancement factor and emission area. The model developed and confirmed experimentally in this work will be helpful in examining field emissions at semiconductor nanogaps.

Effects of shape on the optical properties of CdSe@Au core-shell nanocomposites

We studied the local field enhancement factor (LFEF), absorption, and extinction cross sections of spherical, cylindrical, oblate, and prolate core–shell nanocomposites (NCs) theoretically and numerically using the quasi-static approach. By solving Laplace’s equations, we obtained expressions for the LFEF, polarizability, absorption, and scattering cross sections for each of the core–shell NCs. We found that the LFEF, absorption, and extinction cross section of spherical and cylindrical core–shell NCs possess two peaks whereas oblate and prolate spheroids show three observable peaks. Moreover, the prolate core–shell spheroid shows greater tunability and larger intensity of the LFEF than its corresponding oblate structure. Furthermore, spherical nanoshells are characterized by the higher LFEF than cylindrical and spheroidal core–shells of the same size and composition. When compared, even the smallest value of the LFEF of the spherical core–shell is 11.42 and 10.09 times larger than the biggest values of oblate and prolate core-shells, respectively. The study also indicated that for spherical and cylindrical NCs, the first two peaks of the LFEF and extinction cross sections are achieved at the same corresponding frequencies. Furthermore, all peaks of the extinction cross sections of the prolate spheroid are found to be the lowest while those of the cylindrical peaks are the highest. Where there are an equal number of peaks of different shapes, the peak values are different, showing that shapes of core–shell NCs determine the intensity, the number, and the positions of peaks of the LFEF and optical cross sections. Such NCs are promising for applications in optical sensing, bio-sensing, and electronic devices. Especially, gold coated core–shell spheroids have good potential applications in multi-channel sensing.

Electric-Field Emission Mechanism in Q-Carbon Field Emitters.

In this paper, we report the excellent field emission properties of Q-carbon and analyze its field emission characteristics through structural, morphological, and electronic property correlations, supported by density functional theory (DFT) simulation studies. The Q-carbon field emitters show impressive and stable field emission properties, such as a low turn-on electric field of ∼2.38 V/μm, a high emission current density of ∼33 μA/cm2, and a critical field of ∼2.44 V/μm for the transition from a linear region to the saturation region in the F-N plot. The outstanding field emission properties of Q-carbon are attributed to (i) a unique sp2/sp3 mixture in Q-carbon, (ii) sp2-bonded highly conductive amorphous carbon-rich channels inside the Q-carbon cluster, (iii) a large local field enhancement due to the local geometry and microstructure of Q-carbon, and (iv) the presence of sp2-bonded amorphous carbon regions in the composite film. The temperature-dependent field emission properties, such as extreme sensitivity and an enhancement in the emission current density with temperature, can be explained by the local density of states near the Fermi level and the excellent thermal stability of the Q-carbon field emitters. From DFT simulation studies, the computed work function and the field-enhancement factor were determined to be 3.62 eV and ∼2300, respectively, which explains the excellent field emission characteristics of Q-carbon. The obtained field emission properties, in most cases, were superior to those from other carbon/diamond-based field emitters, which will open new frontiers in field emission-based electronic applications.

The effect of DRIE notching on field emission enhanced breakdown in SOI based MEMS electrodes

Microscale (<5 μm) gas breakdown is usually dominated by field emission, which is influenced largely by electrode surface morphology. At present, there is a large number of studies on the breakdown and discharge of different metal electrode geometry and electrode spacing as well as micro-electro-mechanical system (MEMS) device structures, but few studies on the breakdown of MEMS electrodes affected by notching, which will greatly change the electrode surface morphology but is difficult to completely avoid in deep reactive ion etching process based on silicon on insulator (SOI) wafer. In response to this situation, this paper conducted breakdown tests and field emission tests on MEMS samples with and without notching. It was found that samples with notching could withstand more breakdowns of about 6–13 times before the formation of internal resistance, increased by 200%–300% compared with samples without notching, and have a lower breakdown voltage of about 210 V, 16% lower than that of samples without notching. In addition, it was also found that for the samples with notching, the field enhancement factor gradually decreases with the increase of the number of breakdown events. When the field enhancement factor decreases to about 100, the subsequent breakdown is highly likely to cause the sample to form electrical connection, thus completely damaging the sample. Above conclusions have certain reference value for designing the actuation voltage of MEMS devices based on SOI wafers.

Field electron emission behavior of pristine and Au nanoparticles decorated Sb2Te3-rGO heterostructure emitters

A facile one-pot hydrothermal method was used to synthesize pristine Sb2Te3 and its heterostructure with reduced graphene oxide (rGO). A novel approach dealing with high energy (6 MeV) electron irradiation has been efficiently used for synthesis of gold nanoparticles (Au- NPs) and their in-situ decoration on Sb2Te3-rGO heterostructure. From an application point of view, we have investigated the field electron emission characteristics of pristine Sb2Te3 and Sb2Te3-rGO heterostructures, with and without Au-NPs decoration. The Au-NPs decorated Sb2Te3-rGO heterostructure emitter showed enhanced electron emission behavior in terms of reduced value of turn-on field, delivery of large emission current density (∼1171 µA/cm2) at relatively lower applied field (∼3.1 V/µm), and excellent emission stability. The improvement in emission characteristics upon decoration of Au-NPs is attributed to noticeable increase in the number of emission sites, higher value of field enhancement factor (β = 4562), and betterment in the electronic properties due to Au-NPs-Sb2Te3-rGO interface effects. The obtained results suggest that Au-NPs decorated Sb2Te3-rGO heterostructure emitter has potential towards practical applications in various vacuum microelectronic devices. Furthermore, the present approach dealing with high energy electron irradiation for synthesis and in-situ decoration of nanoparticles can extended to other inorganic heterostructures towards improving their functionality.

Enhancement and redshift of vortex harmonic radiation in epsilon-near-zero materials.

The harmonic radiation from a vortex laser field interacting with an epsilon-near-zero (ENZ) material is numerically investigated via solving the Maxwell-paradigmatic-Kerr equations. For a laser field of long duration, the harmonics up to the seventh-order can be generated with a low laser intensity (∼109 W/cm2). Moreover, the intensities of high order vortex harmonics at the ENZ frequency are higher than at other frequency points due to the ENZ field enhancement effects. Interestingly, for a laser field of short duration, the obvious frequency redshift occurs beyond enhancement in high order vortex harmonic radiation. The reason is that the strong change of the laser waveform propagating in the ENZ material and the non-constant field enhancement factor around the ENZ frequency. Because the topological number of harmonic radiation is linearly proportional to its harmonic order, the high order vortex harmonics with redshift still possess the exact harmonic orders indicated by the transverse electric field distribution of each harmonic.

Bias dependent NDR in TiO2/NiO heterojunction diodes

TiO2/NiO thin film heterojunction diodes are fabricated using electron beam evaporation and DC sputtering techniques. Three different thicknesses of NiO (58, 82, and 160 nm) are combined with a TiO2 film of about 80 nm thick. The common device configuration is FTO/TiO2/NiO/Au with a 4 mm sq. device area. The thickness dependent diode I-V characteristics were analyzed; with the increase in thickness, the diode knee voltage, series resistance, and ideality factor have reduced. All the devices exhibit a high diode ideality factor, which means the diode currents are not limited by drift, diffusion, or recombination at the space charge region. The high ideality factor points to the presence of interface states, spatial inhomogeneities, or tunneling in the devices. Further, the bias dependent negative differential resistance (NDR) in I-V characteristics and the presence of an anomalous peak in C-V characteristics were analyzed, which claimed the presence of interfacial trap states, defects, or tunneling in the diodes. The Fowler-Nordheim tunnel model was applied to the devices and the field enhancement factors were calculated as −14.3, −9.3, and −9.2 for the diodes in the increasing order of thickness. The tunneling phenomenon was confirmed as trap-assisted indirect tunneling. Also, the temperature dependence of NDR was studied.

All field emission experiments are noisy, … are any meaningful?

Representing field emission data on a Fowler–Nordheim plot is both very common and strongly not recommended. It leads to a spurious estimation of the emitter parameters despite a very good data fit. There is a lack of a reliable method of analysis and a proper estimation of the uncertainty in the extracted parameters. In this article, we show that the uncertainty in the estimation of the field enhancement factor or the emission area can be as high as ±50% even for a tungsten single emitter in good ultrahigh vacuum conditions analyzed by the Murphy–Good model. Moreover, the choice of the exact Murphy–Good method can have a noticeable impact. We found that advanced analysis methods, based on the measurement of the differential conductance of the emitter, are so demanding in terms of emitter stability that up to now its requirements are probably out of reach in any field emission laboratory.

High-Q multiple Fano resonances with near-unity modulation depth governed by nonradiative modes in all-dielectric terahertz metasurfaces.

Reducing radiative losses for a high quality factor resonance based on the concept of nonradiative states including anapole mode and bound states in the continuum mode has been attracting extensive attention. However, a high quality factor resonance is obtained at the expense of its modulation depth. Here, an asymmetric metasurfaces structure consisted of silicon double D-shaped resonator arrays that can support both an anapole mode and two bound states in the continuum modes in terahertz band is proposed, which has not only ultrahigh quality factor but also near-unity modulation depth. A resonance derived from anapole mode with stronger electromagnetic field enhancement and higher quality factor can be achieved by increasing the gap of resonator. Meanwhile, two Fano resonances governed by bound states in the continuum modes can be identified, and their quality factors can be easily tailored by controlling the asymmetry of resonator. Such an all-dielectric metasurfaces structure may give access to the development of the terahertz sensors, filters, and modulators.

Thickness-dependent loss-induced failure of an ideal ENZ-enhanced optical response in planar ultrathin transparent conducting oxide films.

Ultrathin planar transparent conducting oxide (TCO) films are commonly used to enhance the optical response of epsilon-near-zero (ENZ) devices; however, our results suggest that thickness-dependent loss renders them ineffective. Here, we investigated the thickness-dependent loss of indium tin oxide (ITO) films and their effect on the ENZ-enhanced optical responses of ITO and ITO/SiO2 multilayer stacks. The experimental and computational results show that the optical loss of ITO films increases from 0.47 to 0.70 as the thickness decreases from 235 to 52 nm, which results in a reduction of 60% and 45% in the maximum field enhancement factor of a 52-nm monolayer ITO and 4-layer ITO/SiO2 multilayer stack, respectively. The experimental results show that the ENZ-enhanced nonlinear absorption coefficient of the 52-nm single-layer ITO film is -1.6 × 103 cm GW-1, which is 81% lower than that of the 235-nm ITO film (-8.6 × 103 cm GW-1), indicating that the thickness-dependent loss makes the ultrathin TCO films unable to obtain greater nonlinear responses. In addition, the increased loss reduces the cascading Berreman transmission valley intensity of the 4-layer ITO/SiO2 multilayer stack, resulting in a 42% reduction in the ENZ-enhanced nonlinear absorption coefficient compared to the 235-nm ITO film and a faster hot electron relaxation time. Our results suggest that the thickness and loss trade-off is an intrinsic property of TCO films and that the low-loss ultrathin TCO films are the key to the robust design and fabrication of novel ENZ devices based on flat ultrathin TCO films.