Quadratic Voltage Research Articles

Dielectric Relaxation and Reliability of Al<sub>2</sub>O<sub>3</sub>-HfO<sub>2</sub>-Al<sub>2</sub>O<sub>3</sub> Sandwiched Metal-Insulator-Metal (MIM) Capacitor

. In this paper, dielectric relaxation and reliability of high capacitance density metal-insulator-metal (MIM) capacitor using Al2O3-HfO2-Al2O3 sandwiched structure were analyzed. It is shown that multilayer MIM capacitor provides high capacitance density and low dissipation factor at room temperature. The dielectric relaxation voltage shows little dependence on the capacitor area. The capacitance density (C0) increases and quadratic voltage coefficient (α) decreases as a function of stress time under constant voltage stress (CVS) because of the charge trapping effect in the high-k dielectric.

Dielectric Stacking Effect of $\hbox{Al}_{2} \hbox{O}_{3}$ and $\hbox{HfO}_{2}$ in Metal–Insulator–Metal Capacitor

The dielectric stacking effects of Al2O3 and HfO2 thin layers in metal-insulator-metal capacitors are investigated for their leakage current, breakdown voltage, and voltage linearity of the dielectrics. The stacked dielectrics over three layers show the enhancement of dielectric permittivity and voltage linearity of quadratic voltage coefficient compared to one-layer dielectrics. Stacking over five layers attributes to improving leakage current density and breakdown voltage characteristics than three layers.

$\hbox{ZrLaO}_{x}\hbox{/ZrTiO}_{x}\hbox{/ZrLaO}_{x}$ Laminate as Insulator for MIM Capacitors With High Capacitance Density and Low Quadratic Voltage Coefficient Using Canceling Effect

Metal-insulator-metal (MIM) capacitors with ZrLaO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> /ZrTiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> /ZrLaO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> laminate as the insulator were explored in this work. Single ZrTiOx dielectric was found to have a negative quadratic voltage coefficient of capacitance (VCC-α) with a high κ value of 22.5. By integrating this dielectric with ZrLaOx which provides a positive VCC-α and a high κ value of 25.8, the “canceling effect” of VCC-α can be achieved while a high capacitance density can be maintained. MIM capacitors with the laminated structure display desirable characteristics in terms of a capacitance density of 14.6 fF/μm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , a low VCC-α of 33 ppm/V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , negligible frequency dispersion, and satisfactory leakage current of 1.6 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> A/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> at -1.5 V. These results also well meet the International Technology Roadmap for Semiconductors requirement set for 2020.

Flexible metal–insulator–metal capacitors on polyethylene terephthalate plastic substrates

Realization of flexible electronic devices on polyethylene terephthalate flexible plastic substrates is reported. Metal–insulator–metal capacitors have been fabricated using radio frequency sputtered deposited thin films of Nb2O5 on the flexible substrate. Good electrical characteristics have been obtained in terms of quadratic voltage coefficient of capacitance, high capacitance density (∼ 11 fF µm−2), high dielectric constant (∼37) and low dissipation factor (<0.1). Besides, in repetitive bending test, the devices show excellent electrical stability and high mechanical flexibility due to the high ductility of niobium and low-temperature processing used in this study.

Effect of Nitrogen Passivation on the Performance of MIM Capacitors With a Crystalline- $\hbox{TiO}_{2}/\hbox{SiO}_{2}$ Stacked Insulator

TiO2/SiO2 stacked dielectric-based metal-insulator-metal capacitors with different thermal and nitrogen plasma treatments (NPTs) were explored in this letter. As the TiO2 dielectric crystallizes from amorphous phase after a thermal treatment, capacitance density increasing from 7.7 to 11.9 fF/m2 was obtained at the price of aggravating leakage current and wider distribution in device characteristics. With NPT to well passivate grain-boundary-related defects in the crystalline TiO2 film, devices still keep a satisfactory capacitance level of 11.2 fF/μm2 while exhibiting suppressed leakage current by a factor of 53, a lower quadratic voltage coefficient of capacitance (VCC-α) of 30 ppm/V2, near frequency dispersion-free capacitance, a better temperature coefficient of capacitance of 82 ppm/°C, and more controllable device uniformity. The mechanism for the improved electrical characteristics was further confirmed by atomic force microscope. These results suggest that NPT paves a new avenue to further advance the performance of crystalline dielectric-based devices.

Structural and Electrical Characteristics of $ \hbox{Lu}_{2}\hbox{O}_{3}$ Dielectric Embedded MIM Capacitors for Analog IC Applications

In this study, we develop a high-performance metal-insulator-metal (MIM) capacitor using a high- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> Lu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> amorphous film for radio-frequency and mixed-signal applications. The Ni/ Lu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> /TaN capacitor exhibited a high capacitance density, a low leakage-current density, and a relatively low quadratic voltage coefficient of capacitance. The leakage current at the low electric field (<; 1.4 MV/cm) was dominated by the Schottky emission, whereas the Poole-Frenkel effect plays in the high electric field. In addition, the effects of constant voltage stress on leakage current and voltage linearity were comprehensively investigated, and excellent device reliability was also demonstrated. The Ni/ Lu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> /TaN MIM capacitor appears to be very promising for future IC technologies.

High-Performance Metal–Insulator–Metal Capacitors Using Europium Oxide as Dielectric

We report the first demonstration of metal-insulator-metal (MIM) capacitors with Eu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> dielectric for analog and DRAM applications. The influence of different anneal conditions on the electrical characteristics of the fabricated MIM capacitors is studied. FG anneal results in high capacitance density (7 fF/μm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), whereas oxygen anneal results in low quadratic voltage coefficient of capacitance (VCC) (194 ppm/V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> at 100 kHz), and argon anneal results in low leakage current density (3.2 ×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-8</sup> A/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> at -1 V). We correlate these electrical results with the surface chemical states of the films through X-ray photoelectron spectroscopy measurements. In particular, FG anneal and argon anneal result in sub-oxides, which modulate the electrical properties.

Capacitance–voltage and leakage-current characteristics of sol–gel-derived crystalline and amorphous SrTa2O6 thin films

SrTa2O6 (STA) is a promising high-dielectric-constant (ε) material. In this study, STA thin films were fabricated using the sol–gel method. The capacitance–voltage and leakage-current characteristics of crystalline and amorphous STA thin-film capacitors were investigated. STA thin films crystallized at an annealing temperature of 800°C. Crystalline STA thin films exhibited a high ε of about 110, whereas amorphous STA thin films showed a much lower ε of about 26–41. However, amorphous STA thin films had a much more constant capacitance as a function of voltage. Of the amorphous thin films, the one annealed at 700°C had the highest ε of about 41, the lowest leakage current of 10−8A/cm2, and a very constant capacitance as a function of voltage with a quadratic voltage–capacitance coefficient (α) of 27ppm/V2. The crystalline STA thin film had a negative α that was independent of frequency, which suggests that dipolar relaxation occurs and is responsible for the large change in the capacitance. The amorphous thin films had a positive α that decreased with increasing frequency, which implies that electrode polarization occurs.

Semi-Active Control Using Magnetorhelogical Dampers with Output Feedback and Distributed Sensing

Control of seismic response of a building fitted with magnetorheological dampers is considered using Optimal Static Output Feedback (OSOF) for desired damper forces. The Modified Bouc-Wen damper model is used and two control voltage laws based on the MR constraint filter, i.e., Semi-inverse Quadratic Voltage Law and Semi-inverse On-Off Voltage Law, are proposed. These appear to perform at least as well as an existing Clipped Voltage Law. Comparisons with available results from a robust reliability-based controller show OSOF control to be quite effective. Controlled response using OSOF is compared with Linear Quadratic Guassian (LQG) and passive-on controllers. Moderate to substantial reduction in maximum peak/RMS responses is mostly obtained with base configuration of sensors when using OSOF control, and controller CPU time reduces by two orders of magnitude. Parametric studies regarding sensor configuration and state/control weighting matrices are performed in order to obtain effective control. Effective OSOF control requires drift feedback with drift sensor preferably collocated with damper.

Semi-Active Control Using Magnetorhelogical Dampers with Output Feedback and Distributed Sensing

Control of seismic response of a building fitted with magnetorheological dampers is considered using Optimal Static Output Feedback (OSOF) for desired damper forces. The Modified Bouc-Wen damper model is used and two control voltage laws based on the MR constraint filter, i.e., Semi-inverse Quadratic Voltage Law and Semi-inverse On-Off Voltage Law, are proposed. These appear to perform at least as well as an existing Clipped Voltage Law. Comparisons with available results from a robust reliability-based controller show OSOF control to be quite effective. Controlled response using OSOF is compared with Linear Quadratic Guassian (LQG) and passive-on controllers. Moderate to substantial reduction in maximum peak/RMS responses is mostly obtained with base configuration of sensors when using OSOF control, and controller CPU time reduces by two orders of magnitude. Parametric studies regarding sensor configuration and state/control weighting matrices are performed in order to obtain effective control. Effective OSOF control requires drift feedback with drift sensor preferably collocated with damper.

MIM Capacitors With Crystalline-$\hbox{TiO}_{2}/ \hbox{SiO}_{2}$ Stack Featuring High Capacitance Density and Low Voltage Coefficient

Metal-insulator-metal (MIM) capacitors with crystalline-TiO2/SiO2 stacked dielectric are explored in this letter. The crystalline TiO2 possesses a high permittivity while the SiO2 provides a negative quadratic voltage coefficient of capacitance (VCC-α) to cancel out the positive VCC-α from the crystalline TiO2. These desirable properties render MIM capacitors with high performance in terms of a capacitance density of 11.9 fF/μm2 with a VCC-α of 90 ppm/V2. With additional N2 plasma treatment on the crystalline TiO2, because of the effective passivation of grain-boundary-related defects and, consequently, a lower leakage current by a factor of 50, the VCC-α can be further lowered to 30 ppm/V2 with slight degradation in capacitance density to 11.2 fF/μm2, which well meets the requirement in 2018 set by ITRS.

Structural and Electrical Characterization of Lu2O3 Dielectric Layer for High Performance Analog Metal–Insulator–Metal Capacitors

The structural and electrical properties of Lu2O3 dielectric films deposited by radio frequency (RF) magnetron sputtering on TaN electrode have been studied for metal–insulator–metal (MIM) capacitor in analog/RF applications. From X-ray diffraction study, it is observed that the deposited films remain amorphous within the thermal budget (400°C) of back-end-of-line process. The root mean square value of surface roughness of the Lu2O3 film decreases after annealing at 400°C using atomic force microscopy. The chemical composition of the Lu2O3 film was characterized by X-ray photoelectron spectroscopy. The MIM capacitor using a Lu2O3 dielectric film exhibited better electrical characteristics, such as a low leakage current of 5 × 10−8 A/cm2 at −1 V and a high capacitance density of 7.5 fF/μm2 with a low quadratic voltage coefficient of capacitance of 75 ppm/V2. The current conduction mechanism was found to be dominated by Schottky emission mechanism in low electric field (<1 MV/cm) region and hence further improvement in the leakage characteristics can be realized by employing a high work-function electrode or a large bandgap oxide as a barrier layer.

Modeling the Negative Quadratic VCC of $\hbox{SiO}_{2}$ in MIM Capacitor

The electrical performance of metal-insulator-metal capacitors with thicknesses from 3 to 13 nm was investigated. The magnitude of the negative quadratic voltage coefficient of capacitance (VCC) of was found to be inversely proportional to the square of its thickness. A postdeposition anneal at 400 reduced substantially. An equation based on the orientation polarization of the dipole moments in was derived, which fits the measured normalized capacitance density versus voltage across very well. This suggests that the negative quadratic VCC of is due to the orientation polarization.

High-Performance $\hbox{Ni}/\hbox{Lu}_{2}\hbox{O}_{3}/ \hbox{TaN}$ Metal–Insulator–Metal Capacitors

We fabricate the Ni/Lu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> /TaN metal-insulator-metal capacitor with a high capacitance density of 7.5 fF/μm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , a relatively small quadratic voltage coefficient of capacitance (VCC) of 75 ppm/V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , a low leakage current of 5 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-8</sup> A/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> at -1 V, and an excellent ten-year reliability with a very low Δ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> of 0.51% at 3 V. These small VCC value and good reliability are attributed to a reduction of carrier injection and trapping into the dielectric.

Comparison of Multilayer Dielectric Thin Films for Future Metal–Insulator–Metal Capacitors: Al2O3/HfO2/Al2O3 versus SiO2/HfO2/SiO2

In this paper, two kinds of multilayered metal–insulator–metal (MIM) capacitors using Al2O3/HfO2/Al2O3 (AHA) and SiO2/HfO2/SiO2 (SHS) were fabricated and characterized for radio frequency (RF) and analog mixed signal (AMS) applications. The experimental results indicate that the AHA MIM capacitor (8.0 fF/µm2) is able to provide a higher capacitance density than the SHS MIM capacitor (5.1 fF/µm2), while maintaining a low leakage current of about 50 nA/cm2 at 1 V. The quadratic voltage coefficient of capacitance, α gradually decreases as a function of stress time under constant voltage stress (CVS). The parameter variation of SHS MIM capacitors is smaller than that of AHA MIM capacitors. The effects of CVS on voltage linearity and time-dependent dielectric breakdown (TDDB) characteristics were also investigated.

Comparison of Reactively Sputtered HfO&lt;sub&gt;2&lt;/sub&gt; and HfSi&lt;sub&gt;x&lt;/sub&gt;O&lt;sub&gt;y&lt;/sub&gt; Dielectrics for High Density Metal-Insulator-Metal Capacitor Applications

The reactively sputtered HfO2 and HfSixOy dielectrics have been investigated comparatively for metal-insulator-metal (MIM) capacitor applications. X-ray photoelectron spectroscopy analyses reveal the presence of Hf-O, Hf-O-Si and Si-O chemical bonds in the HfSixOy films as well as lots of oxygen vacancies. The relative concentrations of Hf-O-Si and Si-O bonds increase with an increment of the power applied to the Si target. Further, it is found that the quadratic voltage coefficient of MIM capacitor decreases with increasing the Si content in the HfSixOy dielectric in despite of a decrease in the resulting capacitance density. The HfSixOy dielectric MIM capacitors with a capacitance density of ~8.4fF/μm2 exhibit a quadratic voltage coefficient of 1840 ppm/V2 at 100kHz, which is much smaller than 2750 ppm/V2 for the HfO2 dielectric MIM capacitors with a density of ~11.8fF/μm2.

A Model of Electrowetting, Reversed Electrowetting, and Contact Angle Saturation

While electrowetting has many applications, it is limited at large voltages by contact angle saturation, a phenomenon that is still not well understood. We propose a generalized approach for electrowetting that, among other results, can shed new light on contact angle saturation. The model assumes the existence of a minimum (with respect to the contact angle) in the electric energy and accounts for a quadratic voltage dependence ∼U(2) in the low-voltage limit, compatible with the Young-Lippmann formula, and an ∼U(-2) saturation at the high-voltage limit. Another prediction is the surprising possibility of a reversed electrowetting regime, in which the contact angle increases with applied voltage. By explicitly taking into account the effect of the counter-electrode, our model is shown to be applicable to several AC and DC experimental electrowetting-on-dielectric (EWOD) setups. Several features seen in experiments compare favorably with our results. Furthermore, the AC frequency dependence of EWOD agrees quantitatively with our predictions. Our numerical results are complemented with simple analytical expressions for the saturation angle in two practical limits.

Characterizing Voltage Linearity and Leakage Current of High Density &lt;formula formulatype="inline"&gt;&lt;tex Notation="TeX"&gt;$\hbox{Al}_{2}\hbox{O}_{3}/\hbox{HfO}_{2}/\hbox{Al}_{2}\hbox{O}_{3}$&lt;/tex&gt; &lt;/formula&gt; MIM Capacitors

It was found that the quadratic voltage coefficient of the capacitance (VCC) of Al2O3-based metal-insulator-metal (MIM) capacitors is inversely proportional to the square of the insulator thickness, i.e., ~t-2, whereas HfO2-based MIM capacitors exhibit the inverse cube relationship, i.e., ~t-3. Using each of their voltage linearity characteristics in combination with the VCC calculation method, the quadratic VCC of Al2O3/HfC2/Al2O3 (A/H/A)-structured MIM capacitors, with various thickness ratios of the Al2O3 and HfO2 insulators, could be well estimated. A large portion of the HfO2 insulators in the A/H/A structures improved the voltage linearity of the MIM capacitors, whereas it deteriorated the dielectric breakdown and the leakage current characteristics.

A New Cost-Effective Metal–Insulator–Metal Capacitor Processed at 350 $^{\circ}\hbox{C}$ Using $ \hbox{Ni}_{2}\hbox{Si}$ Fully Silicided Amorphous Silicon Electrodes

Without requiring noble metal materials, a novel low-cost Ni <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Si/TiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /Ni <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Si metal-insulator-metal (MIM) capac itor processed at 350°C has been developed using nickel fully sili cided (Ni-FUSI) amorphous silicon electrodes. A high capacitance density of 17 fF/μm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> along with a low top-electrode resistivity of ~38 μΩ · cm were achieved. At 25°C, this MIM capacitor also displays a good leakage current density of 6.4 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> A/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> at -1 MV/cm (-2.5 V) and a quadratic voltage coefficient a of 4110 ppm/V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Schottky emission dominates the leakage current in low negative field (<;1 MV/cm), whereas Poole-Frenkel effect appears in high negative field (>;1.4 MV/cm). The Schottky barrier height Φ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> at the Ni <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Si/TiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> interface was first extracted to be 0.8 eV, whereas the trap barrier height Φt in the TiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> film was 0.39 eV. Material characterization further reveals that this structure is highly appropriate for future ultralarge-scale-integration technologies.

High-performance metal-insulator-metal capacitor with Ge-stabilized tetragonal ZrO2/amorphous La-doped ZrO2 dielectric

A Ge-stabilized tetragonal ZrO2 dielectric with a permittivity (κ) value of 36.5 has been obtained by annealing a ZrO2/Ge/ZrO2 laminate at 500 °C and it is a more reliable approach toward stabilizing a tetragonal ZrO2 film. However, metal-insulator-metal (MIM) capacitors with the sole tetragonal ZrO2 film as an insulator achieve a high capacitance density of 27.8 fF/μm2 at the price of a degraded quadratic voltage coefficient of capacitance (VCC) of 81 129 ppm/V2 and unacceptably high leakage current. By capping an amorphous La-doped ZrO2 layer with a κ value of 26.3 to block grain boundaries-induced leakage paths of the crystalline ZrO2 dielectric, high-performance MIM capacitors in terms of a capacitance density of 19.8 fF/μm2, a VCC of 3135 ppm/V2, leakage current of 6.5×10−8 A/cm2 at −1 V, as well as a satisfactory capacitance change of 1.21% after ten-year operation can be realized.