Film Thickness Scales Research Articles

Nanoscale ferroelectric domain switching and thickness scaling impact in undoped hafnium-oxide ferroelectric devices

In this work, we investigated the polarization characteristics of nanoscale undoped hafnium oxide (HfO2) ferroelectric film. The nanoscale domain switching behavior of undoped HfO2 is mainly dominated by mixed ferroelectric/nonferroelectric crystalline phases and interface domain pinning by oxygen vacancies or defect traps. Our experimental results confirm that these issues can be improved by film thickness scaling and well-controlled mechanical stress. We demonstrated a 4-nm-thick undoped HfO2 negative capacitance thin film transistor (NCFET) with an energy-efficient switch characteristic of a low overdrive voltage of -0.6 V, a steep subthreshold swing of sub-60 mV/dec and a uniform hysteresis distribution of sub-60 mV.

Steady-state simulation of the film-casting process for Newtonian and viscoelastic fluids

Thin polymeric films are usually produced in an extensional flow between an extrusion head and a chill roll. The final product is prone to several defects, such as reduced width and non-uniform thickness, and a better understanding of the whole process can improve the final product quality and reduce wastes. This work revisits the film-casting process by exploring the scaling relation between different variables, with particular focus on the width reduction (neck-in). The numerical simulations are carried out for Newtonian, Upper-Convected Maxwell and Giesekus fluids in isothermal and steady-state conditions, for varying film aspect ratio (AR; film width over length), draw ratio (DR) and Deborah number (De). The governing equations are discretized with finite-volumes in their full form (3D model) and using an approximate 2.5D model. However, the latter has been mainly used in this study, as it offered similar accuracy as the 3D model, at a much lower computational cost. The results show that the normalized film shape is independent of the aspect ratio for sufficiently high values of this parameter and that the film thickness scales with DR according to the theoretical prediction for planar and uniaxial extensional flows, in the centre and edge regions, respectively. The neck-in grows logarithmically with the draw ratio for high AR, with a De-dependent growth rate (higher De leads to lower neck-in and lower dependence on DR). There is a reasonable correlation between the neck-in and the ratio between the planar and uniaxial extensional viscosities, as well as between the neck-in and dimensionless variable M = ln(DR)/(De+δ), where δ is a constant which depends on the fluid rheology. However, none of the correlations offer a perfect fit to the neck-in and the search for such a correlation (or master curve) shall be pursued in future works.

The influence of an outer bath on the dewetting of an ultrathin liquid film

We report a theoretical and numerical investigation of the linear and nonlinear dynamics of a thin liquid film of viscosity μ sandwiched between a solid substrate and an unbounded liquid bath of viscosity λμ. In the limit of negligible inertia, the flow depends on two non-dimensional parameters, namely, λ and a dimensionless measure of the relative strengths of the stabilizing surface tension force and the destabilizing van der Waals force between the substrate and the film. We first analyze the linear stability of the film, providing an analytical dispersion relation. When the viscosity of the outer bath is much larger than that of the film, λ≫1, the most amplified wavenumber decreases as km∼λ−1/3, indicating that very slender dewetting structures are expected when λ becomes large. We then perform fully nonlinear simulations of the complete Stokes equations to investigate the spatial structure of the flow close to rupture revealing that the flow becomes self-similar with the minimum film thickness scaling as hmin=K(λ)τ1/3 when τ→0, where τ is the time remaining before the singularity. It is demonstrated that the presence of an outer liquid bath affects the self-similar structure obtained by Moreno-Boza et al. [“Stokes theory of thin-film rupture,” Phys. Rev. Fluids 5, 014002 (2020)] through the prefactor of the film thinning law, K(λ), and the opening angle of the self-similar film shape, which is shown to decrease with λ.

30.2: Invited Paper: Universal Description of FET Mobility of TFTs in Terms of Debye Length, Accumulation Layer Thickness and Film Thickness

A material agnostic modeling framework is presented for predicting film thickness and Debye length scaling of electrical performance in TFTs. Material parameters for a‐IGZO are used to demonstrate the predictive capability of the model, which is applied to identify theoretical maxima of field effect mobility within a large parameter space of Debye length and film thickness. Since FET mobility is a key performance metric in contemporary a‐IGZO TFTs for AMOLED applications, the utility of this approach is timely in its ability to provide clearer direction to optimize performance within a highly sensitive parameter space.

Reliability Study of 1T1C FeRAM Arrays With Hf0.5Zr0.5O₂ Thickness Scaling

We have reported that film thickness scaling of ferroelectric Hf0.5Zr0.5O2 (HZO) allows hafnium-based one-transistor and one-capacitor (1T1C) ferroelectric random-access memory (FeRAM) to obtain higher cycling tolerance for hard breakdown with lower voltage operation in prior reports. This paper is an extension of the previous works including a review of recent works on FeRAM-related devices from a film thickness scaling point of view. We experimentally verified the cycling tolerance advantage of film thickness scaling by 1T1C FeRAM array with different HZO thicknesses of 8 nm and 10 nm using different small capacitors areas (0.20, 0.40, and 1.00 lm2) at practical operation conditions for the first time, demonstrating higher reliability at the 8-nm sample with smaller capacitance area. To support the result, time zero dielectric breakdown (TZDB) and time dependent dielectric breakdown (TDDB) were conducted for both 8-nm and 10a-nm samples.

Dynamics of liquid drops levitating on superheated surfaces

The determination of the spreading dynamics and Leidenfrost temperature of drops impacting on a superheated surface is very complicated because it needs the rigorous determination of relevant time and length scales. We experimentally measured the parameters related to these phenomena for different fluid drops (water, ethanol, and FC-72). Although the drop spreading dynamics, which are represented by the maximum spreading ratio, can be qualitatively modeled by existing energy (kinetic, surface, and viscous dissipation energies) conservation theory, we find that the estimates for the surface area of the drop and the relevant length and time scales should be modified for the accuracy and generality of the model. For drops with a low Weber number, the side surface area should be considered. Further, using experimental data, we reveal that the minimum drop thickness and time scale expressed by the thickness are more suitable for describing the spreading dynamics than the drop diameter and relevant time scale. Moreover, we present a scaling procedure for the Leidenfrost temperature, for which a proper scale for the vapor film thickness is essential. As a result of the scaling analysis, the vapor film thickness scale is expressed in terms of the drop diameter and as a power function of the Weber number. Together with the scaling result, we propose a Leidenfrost temperature scale relation.

Spin coating of capillary tubes

We present the results of a combined experimental and theoretical study of the spin coating of the inner surface of capillary tubes with viscous liquids, and the modified Rayleigh–Plateau instability that arises when the spinning stops. We show that during the spin coating, the thinning of the film is governed by the balance of viscous and centrifugal forces, resulting in the film thickness scaling as . We demonstrate that the method enables us to reach uniform micrometre-scale films on the tube walls. Finally, we discuss potential applications with curable polymers that enable precise control of film geometry and wettability.

Atomically interface engineered micrometer-thick SrMoO3 oxide electrodes for thin-film BaxSr1-xTiO3 ferroelectric varactors tunable at low voltages

In the field of oxide electronics, there has been tremendous progress in the recent years in atomic engineering of functional oxide thin films with controlled interfaces at the unit cell level. However, some relevant devices such as tunable ferroelectric microwave capacitors (varactors) based on BaxSr1−xTiO3 are stymied by the absence of suited compatible, very low resistive oxide electrode materials on the micrometer scale. Therefore, we start with the epitaxial growth of the exceptionally highly conducting isostructural perovskite SrMoO3 having a higher room-temperature conductivity than Pt. In high-frequency applications such as tunable filters and antennas, the desired electrode thickness is determined by the electromagnetic skin depth, which is of the order of several micrometers in the frequency range of a few gigahertz. Here, we report the pulsed laser deposition of a fully layer-by-layer grown epitaxial device stack, combining a several micrometers thick electrode of SrMoO3 with atomically engineered sharp interfaces to the substrate and to the subsequently grown functional dielectric layer. The difficult to achieve epitaxial thick film growth makes use of the extraordinary ability of perovskites to accommodate strain well beyond the critical thickness limit by adjusting their lattice constant with small shifts in the cation ratio, tuned by deposition parameters. We show that our approach, encompassing several orders of magnitude in film thickness scale whilst maintaining atomic layer control, enables the fabrication of metal-insulator-metal (MIM) varactors based on 50–100 nm thin BaxSr1−xTiO3 layers with high tunability above three at the Li-ion battery voltage level (3.7 V).

MoS2 thin films from a (N t Bu)2(NMe2)2Mo and 1-propanethiol atomic layer deposition process.

Potential commercial applications for transition metal dichalcogenide (TMD) semiconductors such as MoS2 rely on unique material properties that are only accessible at monolayer to few-layer thickness regimes. Therefore, production methods that lend themselves to scalable and controllable formation of TMD films on surfaces are desirable for high volume manufacturing of devices based on these materials. We have developed a new thermal atomic layer deposition (ALD) process using bis(tert-butylimido)-bis(dimethylamido)molybdenum and 1-propanethiol to produce MoS2-containing amorphous films. We observe self-limiting reaction behavior with respect to both the Mo and S precursors at a substrate temperature of 350 °C. Film thickness scales linearly with precursor cycling, with growth per cycle values of ≈0.1 nm/cycle. As-deposited films are smooth and contain nitrogen and carbon impurities attributed to poor ligand elimination from the Mo source. Upon high-temperature annealing, a large portion of the impurities are removed, and we obtain few-layer crystalline 2H-MoS2 films.

Uniform trend in layer-by-layer deposition of heteropolytungstates

HypothesisThe layer-by-layer deposition of films including polyoxometalates (POMs) results in a very interesting range of applications in various fields such as electrochemical devices and as photochromic coatings. However, the fundamental knowledge of the parameters responsible for tuning the properties of the film (i.e. relation between the structure and composition of the POM and the properties of the final film) is still lacking. ExperimentsThe current work establishes the relationship between the film thickness, the quantity of POM incorporated in each layer and the electrochemical response of the (PAH-POM)x coatings, where PAH is poly(allylamine hydrochloride). FindingsThe results presented in this work show that the film thickness, composition and electrochemical activity scale proportionally with the number of W atoms in a series of heteropolytungstates ranging from 5 to 48 (P2W5, PW12, P2V3W15, P2W18, P5W30, P8W48). The obtained results allow us to establish a method to predict the behavior as well as the properties of the film based on the nature of the POM used.

Dewetting of Thin Liquid Films Surrounding Air Bubbles in Microchannels.

As an air bubble translates in a microchannel, a thin film of liquid is formed on the bounding walls. In a microchannel with a rectangular cross-section, the liquid in the film leaks toward the low-pressure corners of the geometry, which leads to the appearance of local minima in the film thickness in the cross-sectional plane. In such a configuration, theory suggests that the minimum film thickness scales with Ca and Ca4/3 depending on the distance from the nose of the bubble, where Ca = μUb/γ is the flow capillary number based on the bubble velocity Ub, liquid viscosity μ, and surface tension γ, and Ca ≪ 1. We show that the film of a partially wetting liquid dewets on the channel wall at the sites of the local minima in the film thickness as it acquires thicknesses around and below 100 nm. Our experiments show that the distance Lw between the nose of the bubble and the initial dewetting location is a function of Ca and surface wettability. For channels of different wettability, Lw always scales proportional to Caα, where 1.7 < α < 2 for the range of 10-5 < Ca < 10-2. Moreover, Lw increases up to 10 times by enhancing the wettability of the surface at a given Ca. Our present measurements of Lw provide a design constraint on the lengths of bubbles to maintain a liquid wet channel without dry patches on the wall.

Dual-material double-gate tunnel FET: gate threshold voltage modeling and extraction

A new analytical model for the gate threshold voltage ($$V_\mathrm{TG}$$VTG) of a dual-material double-gate (DMDG) tunnel field-effect transistor (TFET) is reported. The model is derived by solving the quasi-two-dimensional Poisson's equation in the lightly doped Si film and employing the physical definition of $$V_\mathrm{TG}$$VTG. A numerical simulation study of the transfer characteristics and $$V_\mathrm{TG}$$VTG of a DMDG TFET has been carried out to verify the proposed analytical model. In the numerical calculations, extraction of $$V_\mathrm{TG}$$VTG is performed based on the transconductance change method as already used for conventional metal---oxide---semiconductor FETs (MOSFETs). The effects of gate length scaling, Si film thickness scaling, and modification of the gate dielectric on $$V_\mathrm{TG}$$VTG are reported. The dependence of $$V_\mathrm{TG}$$VTG on the applied drain bias is investigated using the proposed model. The proposed model can predict the effect of variation of all these parameters with reasonable accuracy.

Crystalline to amorphous phase transformation of Ta2O5 quantum dots driven by residual stress

Simple vacuum thermal evaporation technique was used to grow Ta2O5 quantum dots. The small dots with large voids between them in ultra-thin films were found to gradually grow in size with decreasing voids with increase in film thickness. The development of residual stress was observed with increasing dot size or film thickness. Residual stress effect on band gap of orthorhombic Ta2O5 quantum dots is studied. Both SAED and XRD confirm that the films thicker than 45 nm become amorphous. Significantly varying optical band gap with film thickness was observed by studying optical absorption of the films. The variation of residual stress with film thickness scales linearly very well with the varying band gap with film thickness. Stress free band gap (3.94 eV) and pressure coefficient of band gap (∂Eg/∂P)T = −26.4 meV/GPa) were determined from this study. Transformation from crystalline to amorphous phase in orthorhombic form of Ta2O5 has been determined to be at about 18 GPa. Both crystalline to amorphous transition and pressure coefficient of band gap for orthorhombic Ta2O5 driven by residual stress have been determined for the first time in the literature.

Influence of substrate temperatures on the properties of GdF(3) thin films with quarter-wave thickness in the ultraviolet region.

High-quality coatings of fluoride materials are in extraordinary demand for use in deep ultraviolet (DUV) lithography. Gadolinium fluoride (GdF3) thin films were prepared by a thermal boat evaporation process at different substrate temperatures. GdF3 thin film was set at quarter-wave thickness (∼27 nm) with regard to their common use in DUV/vacuum ultraviolet optical stacks; these thin films may significantly differ in nanostructural properties at corresponding depositing temperatures, which would crucially influence the performance of the multilayers. The measurement and analysis of optical, structural, and mechanical properties of GdF3 thin films have been performed in a comprehensive characterization cycle. It was found that depositing GdF3 thin films at relative higher temperature would form a rather dense, smooth, homogeneous structure within this film thickness scale.

Residual stress induced crystalline to amorphous phase transformation in Nb2O5 quantum dots

Nb2O5 quantum dots (QDs) were grown using a simple technique of vacuum thermal evaporation. QDs were found to be crystalline in nature by selected area electron diffraction (SAED) in TEM. Samples with thickness up to 20 nm did not show any significant residual strain. Residual stress effect on band gap of crystalline Nb2O5 was studied for films thicker than 20 nm. Residual strain was determined using SAED of the films with reference to powder X-ray diffraction (XRD). Films thicker than 45 nm become amorphous as analyzed by both SAED and XRD. The optical absorption of films in the range 25–60 nm indicates significantly varying optical band gap of films. The varying band gap with film thickness scales linearly very well with the variation of residual stress with film thickness. The residual stress dependence of band gap of crystalline films yields stress free band gap as 3.37 eV with pressure coefficient of band gap (∂Eg/∂P)T = −29.3 meV/GPa. From this study, the crystalline to amorphous transformation in tetragonal form of M-Nb2O5 has been determined to be at about 14 GPa. Both pressure coefficient of band gap and crystalline to amorphous transition for tetragonal M-Nb2O5 have been determined for the first time in the literature.

Crystal structure and epitaxial relationship of Ni4InGaAs2 films formed on InGaAs by annealing

The structural, compositional, and electrical properties of epitaxial Ni4InGaAs2 (denoted as Ni-InGaAs) film formed by annealing sputtered Ni film on InGaAs were investigated. It was found that Ni-InGaAs adopts a NiAs (B8) structure with lattice parameters of a = 0.396 ± 0.002 nm and c = 0.516 ± 0.002 nm, and exhibits an epitaxial relationship with InGaAs, with orientations given by Ni-InGaAs[1¯10]//InGaAs[001] and Ni-InGaAs[110]//InGaAs[110]. The epitaxial Ni4InGaAs2 film has bulk electrical resistivity of ∼102 μΩ·cm, which increases as the film thickness scales below 10 nm. The results of this work would be useful for the development of contact metallization for high mobility InGaAs metal-oxide-semiconductor field-effect transistors.

How crucial is back gate misalignment/oversize in double gate MOSFETs for ultra-low-voltage analog/rf applications?

In the present work, by investigating the influence of source/drain (S/D) extension region engineering (also known as gate-underlap architecture) in planar Double Gate (DG) SOI MOSFETs, we offer new design insights to achieve high tolerance to gate misalignment/oversize in nanoscale devices for ultra-low-voltage (ULV) analog/rf applications. Our results show that (i) misaligned gate-underlap devices perform significantly better than DG devices with abrupt source/drain junctions with identical misalignment, (ii) misaligned gate underlap performance (with S/D optimization) exceeds perfectly aligned DG devices with abrupt S/D regions and (iii) 25% back gate misalignment can be tolerated without any significant degradation in cut–off frequency ( f T) and intrinsic voltage gain ( A VO). Gate-underlap DG devices designed with spacer-to-straggle ratio lying within the range 2.5 to 3.0 show best tolerance to misaligned/oversize back gate and indeed are better than self-aligned DG MOSFETs with non-underlap (abrupt) S/D regions. Impact of gate length and silicon film thickness scaling is also discussed. These results are very significant as the tolerable limit of misaligned/oversized back gate is considerably extended and the stringent process control requirements to achieve self-alignment can be relaxed for nanoscale planar ULV DG MOSFETs operating in weak-inversion region. The present work provides new opportunities for realizing future ULV analog/rf design with nanoscale gate–underlap DG MOSFETs.

On the thickness of soap films: an alternative to Frankel's law

The formation of soap films by vertical withdrawal from a bath is typically described by Frankel's law, which assumes rigid film ‘walls’ and shear-like dynamics. Since most soap films have interfaces that are not rigid, and as the flow in the withdrawal of thin free films is typically extensional, we reconsider the theory of soap film formation. By assuming extensional flow dominated by surface viscous stresses we find that the film thickness scales as the two-thirds power of the withdrawal speed U. This speed dependence is also predicted by Frankel's law; the difference lies in the origin of the viscous resistance which sets the pre-factor. When bulk viscous stresses are important the speed dependence can vary between U2/3 and U2.

Thickness dependence of electrical properties in (0 0 1) oriented lead zirconate titanate films by laser ablation

Highly (0 0 1)-oriented Pb(Zr 0.52Ti 0.48)O 3 (PZT) thin films with LaNiO 3 (LNO) bottom electrodes have been fabricated on amorphous TiN buffered Si substrates by pulsed laser deposition. The polarization–electric field ( P– E) hysteresis of the deposited PZT films with different thickness ranging from 25 to 850 nm was measured. Results showed that the coercive field increases with the film thickness scaling down. No P– E loops could be obtained for the film of thickness of 25 nm. The deterioration of ferroelectric property in the thinnest film was attributed to extrinsic effect other than intrinsic size effect. Current–voltage ( I– V) characteristics measurement showed the increase in leakage current of the PZT films with the decrease in the thickness of the films under the same bias voltage. At a high field regime, the leakage current of the PZT films of 25 nm thickness remained unchanged with increasing applied voltage. A totally depleted back-to-back Shottky barrier model was used to explain the effect of electrode interfaces on leakage current in the PZT films. It is believed that ferroelectric/electrode interfaces play an important role in the electrical properties of ferroelectric thin films with thickness at nanometer level.

Thickness-dependent pinning in a superconductor thin film

The dependence of critical current density jc on film thickness (d) is calculated for the simple configuration of a semi-infinite finite-thickness superconductor film and a single vortex. This film-thickness dependence reflects the impact of vortex broadening in a thin film on its pinning by the film’s edge or an internal surface. The calculated film-thickness variation of jc in the range d∕λ<2, where λ denotes the penetration depth, is found to be proportional to d−1∕2. A parameter-free estimate of the ensuing critical current is within a factor of 3 of observed values in YBa2Cu3O7 coated conductors. It is argued that this type of film-thickness scaling applies beyond the simple configuration considered here.