key: cord-0468104-8z9bwicm
authors: Mishra, Rishabh Bhooshan
title: Design criteria of flexible capacitive pressure sensors using DIY-techniques and household materials
date: 2021-06-21
journal: nan
DOI: nan
sha: 53d93b231948342c2c71769a46a7c4d5ec87199a
doc_id: 468104
cord_uid: 8z9bwicm

The flexible capacitive pressure sensors are one of the most essential and famous devices with vast applications in automobile, aerospace, marine, healthcare, wearables, consumer, and portable electronics. The fabrication of pressure sensors in a cleanroom is expensive and time-consuming; however, the sensitivity, linearity, and other performance factors of those pressure sensors are exceptional. Moreover, sometimes we require sensors that are not expensive and can be fabricated rapidly where the other performance factors do not need to be highly remarkable. In this modern era, household materials and DIY (Do-it-yourself) techniques are quite helpful, highly utilized. They are recommended to fabricate low-cost sensors and healthcare devices for personalized medicine and low-cost consumer electronics. Different flexible capacitive pressure sensors are presented and experimentally characterized for acoustic and air-pressure monitoring in this thesis. The design criteria of a cantilever-based capacitive pressure sensor are discussed. The three different designs are analysed with aspect ratios of 1.5, 1.0, and 0.67. The sensor with an aspect ratio of 0.67 shows maximum sensitivity (mechanical and electrical), better response time, and the 1st and 2nd mode of resonant frequencies is comparatively less than the other two. The cantilever designs are susceptible to slight pressure; therefore, the diaphragm-based normal mode capacitive pressure sensor is introduced in the second chapter, which defines the design criteria of diaphragm shapes. The five different diaphragms analysed are circular, elliptical, pentagon, square, and rectangular shapes. The circular capacitive pressure sensor shows maximum sensitivity, however, maximum non-linear response.....

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These three different types of pressure have been monitored previously in pervasive and advanced ways using piezoresistive [2] , capacitive [1] , resonant [11] , and optical [12] techniques.

The piezoresistive sensing is most utilized for sensing technique for pressure monitoring among all four types mentioned above. The MEMS piezoresistive pressure sensors, the piezoresistive element, are placed at the micro-mechanical component's highly stressed region, which is sensitive to pressure application. The deflection in the mechanically sensitive part causes stress, and the piezoresistive details, which are placed in this region, change resistivity that defines applied pressure. Measuring the change in resistivity is performed using the Wheatstone Bridge method, which monitors the change in resistance when the bride unbalances due to pressure application [2] , [13] , [14] . The piezoresistive pressure sensor is highly applicable to monitor change in pressure with high sensitivity, provides linear response for extended dynamic range, high reliability, and small size [2] , [13] , [14] . However, mass fabrication and temperature sensitivity are the significant problems with the piezoresistive pressure sensors, which capacitive pressure microsensors have covered. On the other hand, the capacitive pressure sensors offer high sensitivity, precise measurement, and less temperature drift [2] , [13] , [14] .

MEMS-based devices are popular due to their outstanding performances and high reliability; however, they are rigid and can't be applicable for non-curvilinear surfaces. The freeform (physically flexible, stretchable, and reconfigurable) CMOS electronics are becoming in trend to make devices flexible, stretchable and expandable, which is not only limited to control, computation, communication and display, healthcare, and Internet of Everything (IoE) [15] - [22] even it is utilized for killer applications, vehicular technology, marine ecology, harsh environment applications and solar cells as well [15] , [17] , [20] - [26] . The freeform CMOS enabled electronics to become popular due to the technological advancement and requirement of placing the electronics on soft surfaces (like human skin or skin of other species and plants) for various environmental monitoring. This technology revolutionized healthcare with wearables and implantable electronics (glaucoma monitoring and brainmachine interface). To overcome with the multiple challenges of contemporary electronics, the freeform CMOS electronics became popular however it requires some cleanroom processing which increases the cost of the device and requires time for mass fabrication; therefore, some other fabrication technique is being adapted like rapid/additive manufacturing, DIY and garage fabrication techniques.

Design, fabrication, and performance enhancement of low-cost MEMS-based pressure sensors are in trend in the last few years. The development of low-cost MEMS-based devices is significant in the modern era to reduce the cost of devices without performance degradation. However, sometimes the devices' performance is as essential as the cost-effectiveness; therefore, device fabrication from household materials using DIY-technique became very popular, and paper electronics evolved. The paper-like materials and other household materials became very useful to design the sensors [27] - [32] , actuators [33] , [34] , microfluidic devices [35] , and transistors [36] , [37] .

The DIY technique is becoming popular because it is beneficial for rapid manufacturing and helps to design low-cost flexible and printed electronic systems. These techniques suggest that everyone in this world could be able to make their electronics device [38] . D. A. Mellis from MIT Media Lab presented DIY based radio, speaker, cellphones, and mouses from low-cost materials, which gave a new introduction to digital fabrication, embedded and passive computation [38] . J. M. Nassar et al. presented pressure, temperature, and humidity sensors from household materials like Al-foil, double-sided tape, a microfiber wipe, conductive ink, and sponge and then designed the electronic skin [29] and paper watch out of these materials [39] . The pressure sensor is designed after using the capacitive pressure sensing principle. Al-foil acts as parallel plate electrodes; however, air, a microfiber wipe, sponge, and doublesided tape are utilized as dielectric materials. In the capacitive pressure sensing principle, the mechanically sensitive element (i.e., Al-foil in this case) deflects, which causes the change in the separation gap. That shift in the separation gap causes a change in capacitance. Moreover, that change in capacitance provides information about applied pressure. After analyzing these dielectric materials, the pressure sensor with air dielectric shows the highest sensitivity however saturates faster than others [29] .

The pressure sensor of Al-foil with microfiber wipe and double-sided tape as dielectric materials are utilized for pulse rate monitoring in another work of J. M. Nassar et al. [39] . Moreover, S. M. Khan et al. from MMH Labs at KAUST presented the pill counter for personalized medicine/healthcare [40] .

The pill counter consists of anisotropic conductive tape with the silver particle in between and sandwiched between two Cu electrodes and characterized for 0 -40 kPa pressure.

Since the microfabrication technique requires cleanroom facilities because the devices are very time-consuming and expensive, to analyze the multiple types and modes of the capacitive pressure sensor, we have utilized household materials and DIY-technique, a.k.a. garage fabrication process.

Household materials such as paper like materials, printable ink, Al-foil, and tapes (single-sided, double-sided and posted) are utilized to design and fabricate multiple electronic devices. The contents of all these chapters are published in the following research articles: [Link]

Chapter -2

Cantilevers are one of basic element in MEMS technology for pressure sensors [41] , microphones [42] , flow sensors [43] , gyroscope [44] , accelerometers [45] , energy harvester [46] , resonators [47] , grippers [48] and ultrasonic transducers [49] . These devices/sensors utilize different sensing techniques i.e. piezoresistive [50] , piezoelectric [46] , capacitive [41] , electrothermal [51] , chemical and biological [52] . Among all these techniques the capacitive one using cantilevers is most utilized among all for automotive [53] , aerospace [54] , robotics [55] , industries (chemical and biological both) [52] , consumer and portable electronics [42] , [43] , [56] .

Proceeding with this approach of research, techniques of Do-it-yourself (DIY) like folding, printing, and cutting [28] , [29] , [33] , [50] , [57] , [58] for designing and analysis of cantilever capacitive pressure sensor is presented for various applications using paper and polymer composites, e.g. Al-foil, Cu-foil, Kapton-tape, metal-coated polymers sheets, scotch tape, and glass. Paper-based cantilever pressure sensors, using piezoresistive sensing, are fabricated from paper, carbon, and silver ink. A square-shaped diaphragm, which is clamped at all edges using four cantilevers, presents a weighing machine [50] . Hygroxpensive electrothermal paper actuators (HEPAs) of a different type; straight, recurved, and released, which is fabricated using paper, conducting polymer (PEDOT: PSS), and adhesive tape, operate due to change in resistance or dimensional parameter when the cellulose paper absorbs humidity/moisture [59] . Laser-induced graphene (LIG) is printed on Kapton polymer sheets which linearized for pressure measurement of extensive dynamic range (20 MPa), which have a sensitivity of 1.23 Pa and resolution of 10 Pa with extremely excellent long-term stability of a minimum 1of 5,000 measurement cycles [60] .

In this chapter, Al coated Kapton (PI) sheet, scotch tape, and glass sheet piece are used for designing, fabricating, and analysis is presented. The pressure sensor's sensitive element and backplates manufactured using the Al coated Kapton foil, scotch tape is used to clamp one edge of the cantilever, and the backplate is fixed at a glass sheet piece. The resonant frequency, response time, stability of the system, mechanical and capacitive sensitivity after acoustic/sound pressureapplication.

Kirchhoff's plate theory for the thin or thick mechanically sensitive element is a unique and remarkable method to the mathematical analysis of sensors which is very much utilized in designing micro and nano-sensors. The deflection in mechanically sensitive components has a significant interest and influence on sensors/devices' static and dynamic performance/behavior of sensors/devices. The large deflection theory is being utilized for mathematical analysis of deflection, mechanical and cantilever sensitivity of cantilever capacitive pressure sensor for acoustic pressure measurement which will generate 1 Pa pressure, in this present chapter. The cantilever after pressure application will follow a large deflection theory, due to which the dynamic behavior of the sensor will be non-linear.

The non-linear partial differential equation using Euler-Bernoulli's theory for deflation in cantilever is given by:

where, D, L, m, and qare flexural rigidity of pressure-sensitive cantilever, length of the cantilever, mass per unit length of the cantilever, and distributed load on the cantilever, respectively.

For this initial boundary value problem, the initial conditions are:

Since the cantilever is non-stretchable: The deflection in cantilever due to pressure wave, ( ) = sin( ), can be given by:

where, = √ 2 / 4 and is frequency of vibration.

And the bending moment of the cantilever at the clamped edge can be given by:

The deflection due to pressure application changes the capacitance is given by:

Finite Finite element analysis of deflection in cantilever due to pressure application required before fabrication helps to choose proper sensor dimensions, i.e. separation gap between electrodes, the overlapping area between parallel plates, and clamping of edges, which reduces material wastage, leading to minimise sensor's cost and time consumption. 

The cantilever, which is fabricated using our approach, requires DIY-technique or garage fabrication process and low-cost materials like Al coted Kapton foil (Liren's LR-PI 100AM of 25 ¬µm polyimide coated with 200 nm aluminium), double-sided scotch tape, and glass pieces (7.5 cm×5 cm×0.5 cm). The steps to fabricate sensors is as follows: 

The experimental setup is prepared for acoustic pressure sensing. The fabricated pressure sensor is placed underneath the Bluetooth speaker (JBL Go Portable Speaker) and connected to the Keithley Semiconductor Characterization System (Model -4200 SCS) for measuring capacitance change/variation after the deflection in the mechanically sensitive cantilever diaphragm. In addition, the Bluetooth speaker is connected to the source (Moto one power mobile), which can play the sound of different frequencies. 

A frequency sweep from 20 Hz -20 kHz is given on all three designs for obtaining resonant frequencies in the designed acoustic pressure measuring setup. The first and second mode of frequencies (f1 and f2) is obtained for all different design of cantilever pressure sensors [ Figure   3-(a-c) ]. The aspect ratio for design D3 is minimum; therefore, the f1 and f2 are less, and the change in capacitance is maximum for the design with the smallest aspect ratio among all designs.

It is observed that the experimental result trends replicate the trends in all three designs from finite element analysis. The resonant frequency is the smallest in the design, which has the smallest aspect ratio among all designs and increases as the aspect ratio of the cantilever increases [ Figure 3-(a-c) ].

We observed that the design which has the smallest aspect ratio has the smallest gap between the occurrence of the first and second mode resonant frequencies (f2 − f1) among all designs, due to which this design can be considered as the 

Paper/polymer/foil-based sensing materials have gained significant importance in this emerging electronics area. Herein, we have presented a metal-coated polymer-based cantilever pressure sensor for acoustic pressure sensing using a simple garage fabrication and DIY approach with radially available raw ingredients. The analysis provides an insight on how the geometrical parameters play an essential role for any cantilever pressure sensor and what design shall be preferred based on the frequency spectrum according to applications. After analyzing all three different cantilever designs whose aspect ratios are 0.67, 1, and 1.5, we conclude, the capacitive pressure sensor, which has a maximum aspect ratio, gives a rapid response, possesses maximum sensitivity, and is applicable to respond to low-frequency sound (f2 -f1=183 Hz).

However, the sensitivity and response time decrease as the aspect ratio gets lower. Furthermore, the first and second mode of resonant frequencies is undershot for the sensor of maximum aspect ratio, which is advantageous for designing the stable system, which decreases as aspect ratios get lower. Furthermore, more studies according to applications can be performed in the future, such as human health monitoring, flow-sensing, and environmental monitoring.

Diaphragm based capacitive pressure sensors

Apart from cantilevers, different diaphragm shapes, i.e. square, circular, rectangular, elliptical, pentagon and hexagon are also one on the mechanical element which is being utilized in MEMS sensor/device arena in broad sense according to the application and/or specifications for fabrication of pressures sensors, accelerometers, gyroscopes, capacitive micromachined ultrasonic transducers (CMUT) and piezoelectric micromachined ultrasonic transducers (PMUT) [2] , [28] , [32] , [61] . The cantilevers are very sensitive to pressure which are compatible with a small range of pressure measuring applications. In large pressure range measurement, then diaphragms of different shapes are a better option that plays a significant role in terms of the sensor's performance, sensitivity, and non-linearity [4] , [8] . Three different diaphragm shapes, i.e. circular, square, and rectangular, for surface acoustic wave measurement in which the circular shape diaphragm-based sensors show maximum sensitivity [61] . The mathematical modelling, FEManalysis, and comparison of elliptical capacitive pressure microsensor with circular capacitive pressure microsensor are presented [4] , [8] , [62] . The elliptical shape of the diaphragm is also utilized for the fabrication of the SiGe CMOS capacitive pressure sensor with the signal processing circuitry [63] .

In paper electronics, different diaphragm shapes have also been utilized in designing pressure sensors for healthcare, acoustic pressure, and air pressure monitoring [28] , [29] , [32] . The square shape pressure sensor is presented as paper-like materials, i.e. Al-foil (used as parallel plate electrode of the sensor), double-sided tape (for clamping the edges of square pieces), a microfiber wipe, and sponge (for dielectric material) is utilized in which the sensor with air as the dielectric medium has maximum sensitivity among all these designs [29] . The circular, square, and 

The maximum deflection in all different shapes of diaphragms that are clamped at the edges is given in Table 1 .

The deflection equation is obtained from a partial differential equation which is being solved after considering multiple boundary conditions like deflection at the edges is zero, the slope of deflection at the edges is zero, deflection is maximum in the center of the diaphragm, and slope of the deflection at the center of diaphragm is zero. zero.

The fabrication of normal mode capacitive pressure sensor starts with cutting the Al-coated 3( 2 + 2 ) + 2 2 

The COMSOL Multiphysics simulation tool is utilized to compare the mathematical analysis with finite element simulation. The finite element simulated values of deflection in various diaphragms are shown in Figure 6 . The trend in diaphragm deflection, which is being obtained from mathematical modelling, is the same as the trend obtained from simulation, and the plot is shown in Figure 7 -a.

To mimic the acoustic sensor setup conditions, we put all the diaphragm shapes under an equivalent sound pressure level (SPL) intensity of 94 dB, which is equivalent to a loud sound produced by human beings. To find the equal value of pressure is Pascal (Pa), we convert the value of Sound Pressure Level (SPL) into Pascal (Pa).

( ) = 20 10 

where the reference pressure was set to 20 μPa, which is the threshold of human hearing.45

An SPL of 94 dB corresponded to 1 Pa. The FEM simulation results to visualize the deflection behaviour in each diaphragm are shown in Figure 6 . The deflection at the centre of each diaphragm against each shape is plotted in Figure 7 -a. The mathematical values of deflection in terms of "D" ( ℎ × )for each shape are plotted in the same graph to verify that the simulation results follow the same performance trend as indicated by the respective equations.

The identical diaphragms are then subjected to an equal pressure as used in the air pressure sensing experimental setup to observe the deflection response for enormous pressures (∼40 Pa).

The results of FEM simulations, along with maximum deflection, are shown in Figure 6 . The trend remains the same for this more considerable pressure, albeit with a much larger deflection. 

We self-designed a set-up to exert pressure on the top electrode for the air pressure experimental set-up, a mechanically sensitive diaphragm. A 5 mm diameter plastic pipe was connected to the air valve. A custom scale was made on the valve with 0 -50 such that the value is 0 for a fully closed valve and 50 for a fully opened valve. The end of the pipe was then inserted into a hole inside the top layer of an acrylic box such that the air coming out of the nozzle will apply pressure on the bottom surface of the acrylic box the rectangular diaphragm provides the most linear response. Therefore, if we are looking for a susceptible sensor, we should go with circular shape diaphragms; however, a rectangular shape sensor should be preferred for linear response.

In this chapter, the normal mode of capacitive pressure sensors with different diaphragm shapes (i.e. circular, elliptical, square, pentagon, and rectangular) are presented. The mathematical and FEM simulation results are verified with two experimental setups, i.e. acoustic pressure and air pressure. After characterization, it is found that the circular shape diaphragm deflects maximum among the five shapes, which mean circular shape capacitive pressure sensor shows maximum mechanical sensitivity.

If sensitivity is essential for a required application, a circular or less elliptical diaphragm shape should be chosen. However, the circular shape capacitive sensor response is highly non-linear than the other five shapes of diaphragms. We have used low-cost, recyclable materials, which can result in reduced financial and environmental costs. The ellipticalshaped diaphragm has less material wastage while having a comparable performance in comparison with circular-shaped diaphragms. For scalable manufacturing techniques with the least material wastage, a square-shaped diaphragm is more beneficial. In addition, square-shaped diaphragms show a linear response. The response becomes nonlinear as we move toward circular-shaped diaphragms.

Singleanddouble touch mode capacitive pressure sensors

Apart from different cantilever/diaphragm shapes based on capacitive pressure sensors, the modes also play an essential role in pressure measurement. For example, the cantilever or diaphragm-based normal mode capacitive pressure sensors are very suitable for a small range of pressure measurement; however, if we try to measure the large range of pressure, the sensors will not be the highly sensitive and non-linear response. Moreover, in the double-touch mode capacitive pressure sensor [ Figure 8 -b], the mechanically sensitive diaphragm is separated in such a way so that we get two touchpoints.

Another layer will have a small hole; first, the diaphragm touches the bottom electrode, and that pressure is known as first touchpoint pressure. However, when the same diaphragm touches another thin dielectric with a small hole that provides second touchpoint pressure. The advantages of touch mode capacitive pressure sensor (single and double both) have multiple following properties over the normal mode of capacitive pressure sensors [30] , [31] , [64] , [65] : 

The governing partial differential equation of deflection in diaphragm is given by partial differential equation:

where, h, D, Φ, and W are diaphragm thickness, the flexural rigidity of diaphragm, airy stress, and diaphragm deflection at radius r respectively. The flexural rigidity is a function of young's modulus of elasticity, diaphragm thickness, and Poisson's ratio of diaphragm material. If the circular diaphragm, made of elastic, homogeneous, and isotropic material, is clamped at the edges, then after applying the boundary conditions, the deflection in the diaphragm at any distance r due to uniform pressure application is given by:

where W0 is the diaphragm deflection at the center and R is the diaphragm radius. A large deflection due to the application of pressure in the circular diaphragm is given by: where, h, σ, D, P are diaphragm thickness, build-in-stress, flexural rigidity, and applied pressure respectively. A small deflection in circular diaphragm with build-in stress is given by:

The base capacitance of the parallel plate capacitive pressure sensor is given by:

where ɛ0 is the permittivity of air, ɛr is the permittivity of the medium. The capacitance variation due to the application of pressure on the circular diaphragm (for both small and large deflection) is given by:

The section is divided into two subsections which explain the fabrication of single and double touch mode capacitive pressure sensors.

The The single-touch mode capacitive pressure sensor is fabricated using our approach 

The double touch mode capacitive pressure sensor is fabricated in the same way as above;

however, one more dielectric layer, Kapton-tape, has one small concentric circular hole of 5 mm.

The fabrication steps are shown in Figure 10-(a-f) , which are almost the same as the fabrication steps of single-touch mode capacitive pressure sensor except for the dielectric layer (Kapton-tape)

with a small hole of 5 mm diameter, which is being confirmed from the SEM-images which are taken and shown in Figure 10-(g-h) . 

Anexperimental setup is manually designed to reach high pressures on the diaphragm to 

The fabricated sensor was placed under the nozzle, and the knob was opened from 0 -100 while taking the reading at intervals of 10 [ Figure 11 -a]. It can be experimentally observed that the fabricated single touch mode pressure sensor [ Figure 12 ] provides a non-linear response in the pressure range of 1 -8 kPa. This is expected from a capacitive sensor in the normal range of operation as long as the deflection in the mechanically sensitive diaphragm of the pressure sensor is less than 1/3rd of the separation gap and follows Kirchhoff's plate theory of deflection. As we reach higher pressure values (more than 8 kPa), the sensor goes into transition mode (8-10 kPa) of operation. In this mode, the pull-in phenomena occur, and the mechanically sensitive diaphragm touches the backplate of the sensor, which is fixed. After that, a further increase in pressure (more than 10 kPa), transfers the sensor into touch mode operation. After that, the response becomes linear for a wide range (from 10 -40 kPa), and the capacitance increases as the large area of the diaphragm touch the backplate. After that, the response saturates as the maximum portion of the diaphragm is now stuck to the bottom plate. plate. 

The response of the sensor started with nonlinear behavior when the sensor was operating in the normal region (shown in red) for the 0 -7.5 kPa range [ Figure 13 ]. At a pressure of 7.5 kPa, the pull-in phenomena occurred, and the diaphragm touched the bottom electrode. This pressure is known as the first touch pressure point (TP1). At TP1, the sensor entered the transition region (for pressure more than 7.5 kPa), in which the diaphragm touched the bottom cavity, which is at a depth of. As the pressure increased to 9.7 kPa, the diaphragm touched the PI tape with a small concentric hole. This pressure is known as the second touch pressure point (TP2). The fabricated capacitive pressure sensor started operating in the linear region from 14.24 kPa, which is our range of interest for designing the integrated circuitry for any efficient and high precision application. Beyond the 54.9 kPa pressure point, the sensor operated in the saturation region because the maximum area of the mechanically sensitive diaphragm was already touching the bottom. In the linear region, the sensor has a sensitivity of 0.674 fF/Pa. 

In this chapter, the single and double touch mode of capacitive pressure sensors are fabricated from household materials, i.e., Al coated Kapton sheet and double-sided tape, and experimentally characterized using air-pressure set-up. In double touch mode, the pressure sensitivity is almost the same as the touch mode capacitive pressure sensor. However, the linear operating range for the specified pressure range is increased for the same diaphragm radius. As a result, the linear range of operating pressure range for touch mode is 10 -40 kPa which is 14.24 -54.9 kPa for double touch mode capacitive pressure sensor. 

In the presented thesis, I explored cantilever, normal mode (with different diaphragm shapes), single and double touch mode capacitive pressure sensors. In chapter two, i.e., cantilever capacitive pressure sensor, I explored the design analysis, mathematical modelling, finite element simulations (using COMSOL Multiphysics and CoventorWare  ) with fabrication and characterization and application for extensive range of pressure variation. After exploring different shapes and design of sensors, this research work concludes that as we increase the length of the cantilever, the sensitivity increases; however, response time decreases and resonates at the low frequency. However, the cantilever sensor designs do not apply to non-curvilinear surfaces and susceptible to noise. Therefore, the diaphragm shape designs based on normal mode capacitive pressure sensors are characterized and discussed the sensitivity and linearity of sensors; however, less applicable for high-pressure monitoring. Moreover, the circular shape capacitive pressure sensor shows maximum sensitivity; however, the response will be highly non-linear than other shape-based normal mode capacitive pressure sensors. After that, a single touch mode capacitive pressure sensor is fabricated and experimentally characterized. The touch mode capacitive pressure sensor is linear however saturates very fast. Therefore, a double touch mode pressure sensor is fabricated and experimentally characterized to increase the linear regime.

Herein, the capacitive pressure sensor is utilized to design the flexible capacitive pressure sensor using household materials using DIY-techniques for fabrication. The advantage of capacitive pressures is low-temperature drift, high sensitivity, and ease in fabrication; however, it

like piezo-resistive sensing) can be utilized and explored a bit more for the design criteria and shape analysis and can be utilized for multiple applications like controlling drones, healthcare monitoring, consumer and portable electronics, and robotics [67 -70]. The advantage of paper and paper-like materials like easy availability, low-cost and biodegradability might be a very fantastic option over the conventional electronic materials

Therefore, it might help to proceeds with a big step towards democratized

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