Dielectric Properties Investigation of Metal–Insulator–Metal (MIM) Capacitors

This study presents the construction and dielectric properties investigation of atomic-layer-deposition Al2O3/TiO2/HfO2 dielectric-film-based metal–insulator–metal (MIM) capacitors. The influence of the dielectric layer material and thickness on the performance of MIM capacitors are also systematically investigated. The morphology and surface roughness of dielectric films for different materials and thicknesses are analyzed via atomic force microscopy (AFM). Among them, the 25 nm Al2O3-based dielectric capacitor exhibits superior comprehensive electrical performance, including a high capacitance density of 7.89 fF·µm−2, desirable breakdown voltage and leakage current of about 12 V and 1.4 × 10−10 A·cm−2, and quadratic voltage coefficient of 303.6 ppm·V−2. Simultaneously, the fabricated capacitor indicates desirable stability in terms of frequency and bias voltage (at 1 MHz), with the corresponding slight capacitance density variation of about 0.52 fF·µm−2 and 0.25 fF·µm−2. Furthermore, the mechanism of the variation in capacitance density and leakage current might be attributed to the Poole–Frenkel emission and charge-trapping effect of the high-k materials. All these results indicate potential applications in integrated passive devices.


Introduction
As an increasing trend for next-generation radio-frequency (RF) and analog mixedsignal integrated circuits (ICs) applications, a higher level of energy storage and integration performance are required for on-chip system components to reduce chip size and fabrication cost. Metal-insulator-metal (MIM) dielectric capacitors (DCs), as one of the crucial and typical components, have been widely used in silicon integrated RF and ICs devices due to their low resistance and low parasitic capacitance [1][2][3][4][5][6][7][8]. In recent years, a great number of research studies have been devoted to developing energy and capacitance densities in energy storage fields, especially for supercapacitors (SCs) [9][10][11]. Nonetheless, the intrinsic characteristics of SCs, such as low operation voltage and poor working frequency, have greatly limited their electronic applications [12][13][14]. Compared with SCs, DCs adopt dielectric materials sandwiched between the top and bottom electrodes to achieve higher working frequency and voltage due to their fast-moving charges and high-power discharge, which can achieve MHz and exceed 5 V [15,16], respectively. The high capacitance density of MIM capacitors can be realized by using high-k dielectric materials or with a lower film thickness [17,18]. Yu et al. investigated a high-density (13 fF·µm −2 ) MIM capacitor using HfO 2 dielectrics through atomic layer deposition (ALD) [19]. Ding and 2 of 12 co-workers reported the use of Al 2 O 3 dielectric film (13 nm thickness) as the insulator of a dielectric capacitor with a capacitance density of 6.05 fF·µm −2 , intended for RF and mixed-signal integrated circuits applications [20]. Boris's group focused on the dynamic random access memory application of a capacitor with TiO 2 -based high-k dielectrics [21]. Due to their increased integration application, most previously reported works focused on how to stack or laminate different kinds of high-k dielectric materials to achieve high capacitance density and other critical parameters, such as low leakage characteristic, good voltage linearity, and reliability. For instance, Wu et al. utilized the stack composition of TiO 2 and SiO 2 to achieve desirable performance in terms of a capacitance density of 11.9 fF·µm −2 with a VCC-α of 90 ppm·V −2 [22]. Additionally, Sung and co-workers proposed a laminated Al 2 O 3 /HfO 2 /Al 2 O 3 MIM capacitor to estimate the leakage current and voltage linearity [23].
In these studies, HfO 2 , Al 2 O 3 , and TiO 2 are regarded as the representative materials for fabricating MIM capacitors due to their high-k and relatively large bandgap energy. However, one of the great challenges is the constraint trade-off between high capacitance density and breakdown field strength because of the direct effect of the dielectric layer thickness on the leakage current and breakdown voltage [24,25]. Herein, we systematically study the synergistic effect of different dielectric material types and their thicknesses on the performance of DCs. Moreover, the physical morphology features and electrical characteristics of the DCs are further investigated. It is found that the Al 2 O 3 -based dielectric capacitor exhibits superior comprehensive electrical performance compared to the DCs based on HfO 2 and TiO 2 . Moreover, the thickness of the Al 2 O 3 -based dielectric capacitor is further investigated. Accordingly, the optimized Al 2 O 3 -based dielectric capacitor with a thickness of 25 nm demonstrates a lower leakage current, a larger breakdown voltage, a stable frequency and voltage retention, and an ideal secondary voltage coefficient, providing new insights for silicon integrated RF and ICs devices.

Experimental Section
The basic information of the selected silicon substrate for the experiment includes crystal orientation (<100> = 0.5 • ), diameter (100 ± 0.2 mm), and thickness (500 ± 10 µm). Aluminum (A1 13503) used in vacuum thermal evaporation process is a specimen (∅3 × 3 mm) with a purity of 99.999%. Firstly, a layer of photoresist (PR) was spincoated on the silicon substrate, and the bottom electrode was patterned by laser direct writing technology with a four-axis laser-pattern direct writing system (see Figure S1 for scalable electrode pattern design, Supporting Information); the final bottom electrode patterned structure was fabricated by the subsequent development process. Subsequently, about 100 nm-thick metal Al was deposited by vacuum thermal evaporation process using a JSD300 vacuum thermal evaporation coating system as a bottom electrode layer, where Al was employed to enhance conductivity while reducing the parasitic resistance of the electrode. During the entire ALD deposition process, the remaining photoresist could be decomposed spontaneously in a high-temperature environment. The dielectric layers, Al 2 O 3 , TiO 2 , and HfO 2 , were deposited by ALD with the equipment of an NCE-200R atomic layer deposition system at different temperature conditions. In detail, nitrogen gas was used as a carrier to feed the reaction sources Al(CH 3 ) 3 /H 2 O, TiCl 4 /H 2 O and HfCl 4 /H 2 O precursors into the reaction chamber, and the temperature of the reaction chamber was 200 • C, 60 • C, and 100 • C, respectively. Additionally, the corresponding reaction rate was 0.667 nm per cycle for Al 2 O 3 , 0.031 nm per cycle for TiO 2, and 0.125 nm per cycle for HfO 2 , respectively. Two different dielectric types (Al 2 O 3 and TiO 2 ) of MIM capacitors with thicknesses of 12.5 nm, 25 nm, and 50 nm were fabricated; simultaneously, HfO 2 MIM capacitors with thicknesses of 12.5 nm and 25 nm were also prepared for comparisons. Then, the photoresist was secondary spin-coated on each dielectric layer, and the top electrode was patterned again using laser direct writing technology. Finally, Al of 150 nm was prepared as the top electrode with the same method described above for depositing the bottom electrode.
In the experiment, the electrode patterning equipment used a four-axis laser-pattern direct writing system (Microlab), the top and bottom electrode evaporation equipment was a JSD300 vacuum thermal evaporation coating system, and the dielectric layer deposition equipment was employed by an NCE-200R atomic layer deposition system. The morphology and roughness of the MIM capacitors were characterized by a Carl Zeiss SIGMA HD scanning electron microscope (SEM) and a Dimension Icon atomic force microscope (AFM). Insulator thicknesses of Al 2 O 3 , TiO 2, and HfO 2 were evaluated via an SE-VE spectroscopic ellipsometer. The entire parameter test of the samples was carried out on the low-temperature vacuum probe station, where the capacitance-voltage (C-V) and capacitance-frequency (C-Q) characteristics were measured using an Agilent 4294A semi-conductor parameter analyzer, and leakage current-voltage (J-V) characteristic measurements were carried out with a Keysight B2912A parameter tester.

Results and Discussion
The planar area of the MIM capacitors is designed to be 80 µm × 80 µm on an n-type single-side polished (100) silicon wafer with a resistivity of 0.01 Ω·cm, and the fabrication process is schematically illustrated in Figure 1, where the detailed preparation process corresponds to the above-mentioned fabrication of MIM silicon capacitors. Moreover, combined with micro/nanofabrication technology, the actual size can be adjusted larger according to different practical applications of the dielectric capacitors, which enables the possibility of mass production. Different from other deposition technologies for dielectric layers, such as electron beam deposition, electrodeposition, and magnetron sputtering, ALD can prepare highly pure and dense thin film, accurately controlling the thickness and composition of the required dielectric layer through reaction conditions simultaneously. In the experiment, the electrode patterning equipment used a four-axis laser-pattern direct writing system (Microlab), the top and bottom electrode evaporation equipment was a JSD300 vacuum thermal evaporation coating system, and the dielectric layer deposition equipment was employed by an NCE-200R atomic layer deposition system. The morphology and roughness of the MIM capacitors were characterized by a Carl Zeiss SIGMA HD scanning electron microscope (SEM) and a Dimension Icon atomic force microscope (AFM). Insulator thicknesses of Al2O3, TiO2, and HfO2 were evaluated via an SE-VE spectroscopic ellipsometer. The entire parameter test of the samples was carried out on the low-temperature vacuum probe station, where the capacitance-voltage (C-V) and capacitance-frequency (C-Q) characteristics were measured using an Agilent 4294A semi-conductor parameter analyzer, and leakage current-voltage (J-V) characteristic measurements were carried out with a Keysight B2912A parameter tester.

Results and Discussion
The planar area of the MIM capacitors is designed to be 80 µm × 80 µm on an n-type single-side polished (100) silicon wafer with a resistivity of 0.01 Ω·cm, and the fabrication process is schematically illustrated in Figure 1, where the detailed preparation process corresponds to the above-mentioned fabrication of MIM silicon capacitors. Moreover, combined with micro/nanofabrication technology, the actual size can be adjusted larger according to different practical applications of the dielectric capacitors, which enables the possibility of mass production. Different from other deposition technologies for dielectric layers, such as electron beam deposition, electrodeposition, and magnetron sputtering, ALD can prepare highly pure and dense thin film, accurately controlling the thickness and composition of the required dielectric layer through reaction conditions simultaneously.  In detail, 100 nm and 150 nm Al work as the top/bottom electrode, which are uniformly evaporated by the vacuum thermal evaporation process, and 25 nm Al2O3 deposited by ALD acts as the dielectric layer. As can be seen, the manufactured MIM capacitors exhibit a step effect with the patterning of the top and bottom electrodes and the uniformity of the vacuum thermal evaporation coating in Figure 2a. Figure 2b shows a clear boundary at the interface between different layers, indicating the outstanding advantage of the compact high-k dielectric layers by low-temperature ALD deposition, film composition control, and outstanding semi-conductor   Figure 2a. Figure 2b shows a clear boundary at the interface between different layers, indicating the outstanding advantage of the compact high-k dielectric layers by lowtemperature ALD deposition, film composition control, and outstanding semi-conductor compatibility [26]. Moreover, the prepared low-temperature ALD dielectric layers are amorphous, which can reduce the leakage current along the edge of the grain boundaries [27].
The dielectric capacitors based on Al 2 O 3 , TiO 2 , and HfO 2 with controllable thicknesses are successfully fabricated by ALD, and the thicknesses of the dielectric film are measured with a spectroscopic ellipsometer. The relevant test principle is shown in Figures S2-S5, Supporting Information. Figure 2c proves that the curve fitted by the model is consistent with the experimental test curve, indicating the accuracy of the test data. The relationship between the refractive index n 2 of the film layer to be measured and the thickness d can be obtained. Figure 3d shows the XPS survey spectrum to determine the chemical composition of the dielectric layer Al 2 O 3 prepared by ALD. The XPS survey spectra represent mainly Al, O, and C contributions. The XPS measurement spectrum shows that typical peaks appear at 74 eV, 118 eV, 285 eV, 532 eV, 979 eV, and 1230 eV, representing the binding energies of Al 2p, Al 2s, and C 1s, O 1s, O KLL, and C KLL, respectively [28]. The peaks corresponding to the plasmon losses are also observed [29]. As can be seen from Figure Figure 2f). Further deconvolution revealed four/three distinct components, the strongest peak located at 531.2 eV originated from Al-O bonds, and the other peak at 532.0 eV associated with Al-O-H hydroxyl groups appeared because of the water-containing raw materials for Al 2 O 3 film growth due to ALD [30]. The peak at 532.9 eV for the Al 2 O 3 film is due to C=O radicals. The peak at 530.5 eV for the Al 2 O 3 film could be related to adsorbed oxygen [31].
compatibility [26]. Moreover, the prepared low-temperature ALD dielectric layers are amorphous, which can reduce the leakage current along the edge of the grain boundaries [27]. The dielectric capacitors based on Al2O3, TiO2, and HfO2 with controllable thicknesses are successfully fabricated by ALD, and the thicknesses of the dielectric film are measured with a spectroscopic ellipsometer. The relevant test principle is shown in Figures S2-S5, Supporting Information. Figure 2c proves that the curve fitted by the model is consistent with the experimental test curve, indicating the accuracy of the test data. The relationship between the refractive index n2 of the film layer to be measured and the thickness d can be obtained. Figure 3d shows the XPS survey spectrum to determine the chemical composition of the dielectric layer Al2O3 prepared by ALD. The XPS survey spectra represent mainly Al, O, and C contributions. The XPS measurement spectrum shows that typical peaks appear at 74 eV, 118 eV, 285 eV, 532 eV, 979 eV, and 1230 eV, representing the binding energies of Al 2p, Al 2s, and C 1s, O 1s, O KLL, and C KLL, respectively [28]. The peaks corresponding to the plasmon losses are also observed [29]. As can be seen from Figure  3d Figure 2f). Further deconvolution revealed four/three distinct components, the strongest peak located at 531.2 eV originated from Al-O bonds, and the other peak at 532.0 eV associated with Al-O-H hydroxyl groups appeared because of the water-containing raw materials for Al2O3 film growth due to ALD [30]. The peak at 532.9 eV for the Al2O3 film is due to C=O radicals. The peak at 530.5 eV for the Al2O3 film could be related to adsorbed oxygen [31].   To further verify the morphology and roughness of the dielectric layer after ALD deposition, the as-prepared samples with different dielectric materials and thicknesses are measured by AFM. Figure 3a-c shows the topographies of Al2O3, TiO2, and HfO2 film with a thickness of 25 nm-based MIM capacitors. The analysis result reflects that the root-meansquare (Rq) roughness values of these three materials are only 2.18 nm, 2.57 nm, and 2.22 nm, which can indirectly depict the special surface area [32][33][34]. It was noticed that there are certain white "defects" in the film itself after ALD deposition, and these white "defects" actually refer to the peaks of the surface undulation of the dielectric layer. The defects of the TiO2 film in Figure 3b are more pronounced, indicating that the film quality of TiO2 is inferior to that of Al2O3 and HfO2, which is mainly due to a lower deposition temperature. Figure 3d shows the linear contour fluctuations in the directions indicated by the black, red, and blue lines in Figure 3a-c. It can be seen that the linear fluctuation of TiO2 is the largest, while the profile fluctuations of Al2O3 and HfO2 are relatively more stable. Additionally, it can be concluded that the 25 nm dielectric films deposited by ALD display better uniformity and compactness compared to the 12.5 nm and 50 nm deposition (Figures S6 and S7, Supporting Information). Figure 4 indicates the typical J-V characteristics of the leakage current density and breakdown voltage under positive and negative voltages. In general, the breakdown strength of the MIM capacitor reflects the device lifetime [35]. Therefore, a continuously increasing voltage is applied to the capacitor until electrical breakdown occurs. With the increase in the voltage, the resulting high electric field broke down the layer of dielectric capacitors. Take the diagram of Al2O3 dielectric capacitors in Figure 4a as an example for detailed analysis, it is found that the MIM capacitor with a 12.5 nm Al2O3 dielectric structure has a low leakage current density of about 5.3 × 10 −9 A·cm −2 at 4.3 V, which meets the requirement of high-density capacitor applications [36]. Simultaneously, the structures of 25 nm and 50 nm capacitors were measured for high breakdown voltages rising from 12 V to 21.6 V, and the corresponding leakage current densities up to 1.4 × 10 −10 A·cm −2 and 2.4 × 10 −11 A·cm −2 , respectively. High capacitance density is one of the vital indicators for evaluating the quality of capacitors, and its variations are mainly caused by the chargetrapping effect between the electrode and the surface of the dielectric [37,38]. However, the increase in the breakdown voltage is largely at the expense of capacitance density. Therefore, in different applications (power supply bypass, high-density, high-precision To further verify the morphology and roughness of the dielectric layer after ALD deposition, the as-prepared samples with different dielectric materials and thicknesses are measured by AFM. Figure 3a-c shows the topographies of Al 2 O 3 , TiO 2 , and HfO 2 film with a thickness of 25 nm-based MIM capacitors. The analysis result reflects that the root-mean-square (Rq) roughness values of these three materials are only 2.18 nm, 2.57 nm, and 2.22 nm, which can indirectly depict the special surface area [32][33][34]. It was noticed that there are certain white "defects" in the film itself after ALD deposition, and these white "defects" actually refer to the peaks of the surface undulation of the dielectric layer. The defects of the TiO 2 film in Figure 3b are more pronounced, indicating that the film quality of TiO 2 is inferior to that of Al 2 O 3 and HfO 2 , which is mainly due to a lower deposition temperature. Figure 3d shows the linear contour fluctuations in the directions indicated by the black, red, and blue lines in Figure 3a-c. It can be seen that the linear fluctuation of TiO 2 is the largest, while the profile fluctuations of Al 2 O 3 and HfO 2 are relatively more stable. Additionally, it can be concluded that the 25 nm dielectric films deposited by ALD display better uniformity and compactness compared to the 12.5 nm and 50 nm deposition ( Figures S6 and S7, Supporting Information). Figure 4 indicates the typical J-V characteristics of the leakage current density and breakdown voltage under positive and negative voltages. In general, the breakdown strength of the MIM capacitor reflects the device lifetime [35]. Therefore, a continuously increasing voltage is applied to the capacitor until electrical breakdown occurs. With the increase in the voltage, the resulting high electric field broke down the layer of dielectric capacitors. Take the diagram of Al 2 O 3 dielectric capacitors in Figure 4a as an example for detailed analysis, it is found that the MIM capacitor with a 12.5 nm Al 2 O 3 dielectric structure has a low leakage current density of about 5.3 × 10 −9 A·cm −2 at 4.3 V, which meets the requirement of high-density capacitor applications [36]. Simultaneously, the structures of 25 nm and 50 nm capacitors were measured for high breakdown voltages rising from 12 V to 21.6 V, and the corresponding leakage current densities up to 1.4 × 10 −10 A·cm −2 and 2.4 × 10 −11 A·cm −2 , respectively. High capacitance density is one of the vital indicators for evaluating the quality of capacitors, and its variations are mainly caused by the chargetrapping effect between the electrode and the surface of the dielectric [37,38]. However, the increase in the breakdown voltage is largely at the expense of capacitance density. Therefore, in different applications (power supply bypass, high-density, high-precision capacitors), the selection of the optimal parameters should be considered comprehensively.
Molecules 2022, 27, x FOR PEER REVIEW 6 of 12 capacitors), the selection of the optimal parameters should be considered comprehensively. The J-V curve can be divided into two regions at 4.6 V, where the leakage current densities increase sharply with the bias voltage (breakdown voltage). This can be explained by the different conductive mechanisms of leakage current, namely Schottky emission and Poole-Frenkel emission at low and high electric fields [5,36,39], which are shown by (1) and (2), respectively.
where A and C are constants; T is the temperature in kelvin, 298 K; E is the electric field; E = U/d; q is the electron charge; ∅S is the barrier height of the interface between the dielectric and injecting electrode for Schottky emission; ∅PF is the trap height in the dielectric for PF emission; k is the Boltzmann constant; βS and βPF are (q 3 /πε0n 2 ) 1/2 and (q 3 /πε0n 2 ) 1/2 , respectively, in which ε0 is a permittivity in a vacuum; and n is the refractive index.
Equations (1) and (2) are fitted to the experimental data and extract the n value of the refractive index from the slope of the fitted curve, which further indicates that the conduction mechanism of the MIM capacitor is dominated by PF emission at high electric region. In fact, the neutral electron traps in high-k materials are abundantly generated under an applied electric field, resulting in an increase in leakage current. Hence, the leakage current is dominated by the trap-assisted-tunneling in the low electric field region. As can be seen, the leakage currents decrease with the increasing dielectric thickness. On the contrary, in the case of the same film thickness, the increase in the bias voltage proves that the traps still exist within the films prepared by ALD, which is possibly related to the parameters of the preparation process, including temperature, vacuum, and substrate crystallinity [40]. In particular, the breakdown voltages and leakage current densities for TiO2 of 13.52 nm, 26.10 nm, and 52.54 nm are 0.44 V and 2.3 × 10 −8 A·cm −2 , 0.58 V and 1.7 × 10 −8 A·cm −2 , and 0.85 V and 1.4 × 10 −9 A·cm −2 . Moreover, for HfO2, the breakdown voltages and leakage current densities of 10.51 nm and 21.29 nm-thick dielectric capacitors are 0.8 V and 2.4 × 10 −9 A·cm −2 and 9.9 V and 8.4 × 10 −10 A·cm −2 , respectively. From the perspective of dielectric materials, the J-V curves indicate that Al2O3 holds better withstand voltage characteristics, which is possibly due to the superior compactness of dielectric film fabricated at 200 ℃. Figure 5a-c demonstrates the dependence of capacitance density as a function of frequency. As can be seen, the capacitance density of Al2O3 MIM capacitors with different thicknesses (12.10 nm, 24.72 nm, and 49.73 nm) exhibit a slight degradation from 0 to 1 MHz, and the maximum change values are only 1.45, 0.54, and 0.17 fF·µm −2 , which reflects the excellent dielectric characteristic of Al2O3 MIM capacitors with frequencies. Nevertheless, under the same preparation conditions, the capacitance densities of TiO2 vary in the The J-V curve can be divided into two regions at 4.6 V, where the leakage current densities increase sharply with the bias voltage (breakdown voltage). This can be explained by the different conductive mechanisms of leakage current, namely Schottky emission and Poole-Frenkel emission at low and high electric fields [5,36,39], which are shown by (1) and (2), respectively.
where A and C are constants; T is the temperature in kelvin, 298 K; E is the electric field; E = U/d; q is the electron charge; ∅ S is the barrier height of the interface between the dielectric and injecting electrode for Schottky emission; ∅ PF is the trap height in the dielectric for PF emission; k is the Boltzmann constant; β S and β PF are (q 3 /πε 0 n 2 ) 1/2 and (q 3 /πε 0 n 2 ) 1/2 , respectively, in which ε 0 is a permittivity in a vacuum; and n is the refractive index.
Equations (1) and (2) are fitted to the experimental data and extract the n value of the refractive index from the slope of the fitted curve, which further indicates that the conduction mechanism of the MIM capacitor is dominated by PF emission at high electric region. In fact, the neutral electron traps in high-k materials are abundantly generated under an applied electric field, resulting in an increase in leakage current. Hence, the leakage current is dominated by the trap-assisted-tunneling in the low electric field region. As can be seen, the leakage currents decrease with the increasing dielectric thickness. On the contrary, in the case of the same film thickness, the increase in the bias voltage proves that the traps still exist within the films prepared by ALD, which is possibly related to the parameters of the preparation process, including temperature, vacuum, and substrate crystallinity [40]. In particular, the breakdown voltages and leakage current densities for   [23]. The large bandgap leads to a higher energy requirement of the electrons in the semi-conductor material when the energy level transition occurs, thereby providing a relatively stable capacitance density capability for the MIM capacitor. As can be seen from Figure 5b,c, there are a large number of charge traps near the interface between electrodes and dielectric layers, and the electrons still become inactive when the frequency increases [41]. Therefore, the high bandgap barrier capacitor has fewer charge traps near the surface of the dielectric layer, or these traps make the capacitance density only function in the low-frequency range [42,43]. In either case, the above two situations are conducive to maintaining the capacitance density of Al 2 O 3 MIM capacitors stable with frequency. As confirmed in Figure 5a- [23]. The large bandgap leads to a higher energy requirement of the electrons in the semi-conductor material when the energy level transition occurs, thereby providing a relatively stable capacitance density capability for the MIM capacitor. As can be seen from Figure 5b,c, there are a large number of charge traps near the interface between electrodes and dielectric layers, and the electrons still become inactive when the frequency increases [41]. Therefore, the high bandgap barrier capacitor has fewer charge traps near the surface of the dielectric layer, or these traps make the capacitance density only function in the low-frequency range [42,43]. In either case, the above two situations are conducive to maintaining the capacitance density of Al2O3 MIM capacitors stable with frequency. As confirmed in Figure 5ac, the capacitance densities for 12.10 nm, 24.72 nm, and 49.73 nm Al2O3 capacitors are 13.19 fF·µm −2 , 7.89 fF·µm −2 , and 4.62 fF·µm −2 , respectively. Figure 5d-f reflects the variation of capacitance with applied voltage for Al2O3 MIM capacitors at different frequencies. It can be inferred from Figure 5d,e that the overall capacitance density of the 12.5 nm-thickness Al2O3 dielectric capacitor decreases slightly with the bias voltages, and the 25 nm-thickness capacitor increases slightly, whereas the increase and decrease in the maximum values are only 1.19 fF·µm −2 and 0.25 fF·µm −2 . The reason for the different variation trends may be related to the thickness of the amorphous structures prepared by low-temperature ALD deposition. As is well-known, capacitance density is significantly sensitive to dielectric (Al2O3) thickness due to the relatively low dielectric constant of Al2O3. It can be seen from Figure 5d-f that the 12.5 nm and 25 nmthick Al2O3 MIM capacitors show a slight change with voltage, while the 50 nm-thick Al2O3 MIM capacitors remain almost unchanged at the same voltage bias. In general, the capacitance densities of Al2O3 capacitors change by 0.45% under the frequency of 10 3 Hz, 10 4 Hz, 10 5 Hz, and 10 6 Hz, indicating exceptional stability. At the same time, they show higher capacitance characteristics under the low-frequency region, which is related to the Figure 5d-f reflects the variation of capacitance with applied voltage for Al 2 O 3 MIM capacitors at different frequencies. It can be inferred from Figure 5d,e that the overall capacitance density of the 12.5 nm-thickness Al 2 O 3 dielectric capacitor decreases slightly with the bias voltages, and the 25 nm-thickness capacitor increases slightly, whereas the increase and decrease in the maximum values are only 1.19 fF·µm −2 and 0.25 fF·µm −2 . The reason for the different variation trends may be related to the thickness of the amorphous structures prepared by low-temperature ALD deposition. As is well-known, capacitance density is significantly sensitive to dielectric (Al 2 O 3 ) thickness due to the relatively low dielectric constant of Al 2 O 3 . It can be seen from Figure 5d-f that the 12.5 nm and 25 nm-thick Al 2 O 3 MIM capacitors show a slight change with voltage, while the 50 nmthick Al 2 O 3 MIM capacitors remain almost unchanged at the same voltage bias. In general, the capacitance densities of Al 2 O 3 capacitors change by 0.45% under the frequency of 10 3 Hz, 10 4 Hz, 10 5 Hz, and 10 6 Hz, indicating exceptional stability. At the same time, they show higher capacitance characteristics under the low-frequency region, which is related to the charge trapping effect on the surface of the electrode and the dielectric layer. That is, when a bias voltage is applied to the electrode, the traps in the dielectric layer cause the charge trapping of the carriers, leading to the change of capacitance with frequency [44].
Previously, we measured and analyzed the C-Q and C-V characteristic curves of MIM capacitors with three thicknesses represented by Al 2 O 3 . Combined with C-Q and C-V curves, a higher dielectric layer thickness has better stability in terms of bias voltage and frequency. Nonetheless, the obtained capacitance density will be reduced, due to the working principle of planar capacitors, and the conclusion is in line with our expectations. For this reason, taking a 25 nm dielectric layer thickness as an example, the variation trends of three kinds of dielectric materials with increasing bias voltage and frequency are also discussed. Figure 6a-c reflects the dependence of capacitance density with Al 2 O 3 , TiO 2 , and HfO 2 dielectric materials as a function of frequency. It is observed that the capacity densities of the three dielectric capacitors decrease slightly with frequency, but the values do not change much. Among them, the maximum change rate for Al 2 O 3 , TiO 2 , and HfO 2 is only 0.5 fF·µm −2 , 3.5 fF·µm −2 , and 1.9 fF·µm −2 , respectively. At the same time, the capacitance density of the TiO 2 dielectric films has large fluctuations with frequency, which is related to a large number of defects on the surface of TiO 2 films prepared by ALD deposition under 60 • C and vacuum conditions. The calculated average capacitance densities are 7.89 fF·µm −2 (24.72 nm Al 2 O 3 ), 21.08 fF·µm −2 (26.20 nm TiO 2 ), and 12.29 fF·µm −2 (21.29 nm HfO 2 ). Figure 6d-f exhibits the voltage stability with different dielectric materials. It should be pointed out that the capacitance density of TiO 2 has a relatively large fluctuation at 1 kHz, which further proves the structure morphology's direct impact on the electrochemical performance of the MIM capacitors.
charge trapping effect on the surface of the electrode and the dielectric layer. That is, when a bias voltage is applied to the electrode, the traps in the dielectric layer cause the charge trapping of the carriers, leading to the change of capacitance with frequency [44].
Previously, we measured and analyzed the C-Q and C-V characteristic curves of MIM capacitors with three thicknesses represented by Al2O3. Combined with C-Q and C-V curves, a higher dielectric layer thickness has better stability in terms of bias voltage and frequency. Nonetheless, the obtained capacitance density will be reduced, due to the working principle of planar capacitors, and the conclusion is in line with our expectations. For this reason, taking a 25 nm dielectric layer thickness as an example, the variation trends of three kinds of dielectric materials with increasing bias voltage and frequency are also discussed. Figure 6a-c reflects the dependence of capacitance density with Al2O3, TiO2, and HfO2 dielectric materials as a function of frequency. It is observed that the capacity densities of the three dielectric capacitors decrease slightly with frequency, but the values do not change much. Among them, the maximum change rate for Al2O3, TiO2, and HfO2 is only 0.5 fF·µm −2 , 3.5 fF·µm −2 , and 1.9 fF·µm −2 , respectively. At the same time, the capacitance density of the TiO2 dielectric films has large fluctuations with frequency, which is related to a large number of defects on the surface of TiO2 films prepared by ALD deposition under 60 ℃ and vacuum conditions. The calculated average capacitance densities are 7.89 fF·µm −2 (24.72 nm Al2O3), 21.08 fF·µm −2 (26.20 nm TiO2), and 12.29 fF·µm −2 (21.29 nm HfO2). Figure 6d-f exhibits the voltage stability with different dielectric materials. It should be pointed out that the capacitance density of TiO2 has a relatively large fluctuation at 1 kHz, which further proves the structure morphology's direct impact on the electrochemical performance of the MIM capacitors. The voltage coefficients of capacitance (VCCs) are one of the most important parameters to evaluate the voltage linearity of the MIM capacitor, and it is the key factor to consider in the application of bypass power supply and the radio frequency circuit, which can be determined by an equation [45] and combined with experimental data to fit VCCs. The voltage coefficients of capacitance (VCCs) are one of the most important parameters to evaluate the voltage linearity of the MIM capacitor, and it is the key factor to consider in the application of bypass power supply and the radio frequency circuit, which can be determined by an equation [45] and combined with experimental data to fit VCCs. C (V) = C 0 (αV 2 + βV + 1) → (C (V) − C 0 )/C 0 = [αV 2 + βV] ppm , where C 0 represents the zero-bias capacitance, α and β are the quadratic and linear voltage coefficients, respectively. Among them, the quadratic voltage coefficient α is the most critical parameter for evaluating voltage linearity, where β can be eliminated by circuit design or canceled out by differential methods [18,46,47]. Figure 7 indicates the normalized capacitance of the 25 nm Al 2 O 3 MIM capacitors with bias voltages of 10 4 Hz, 10 5 Hz, and 10 6 Hz. It can be seen that as the frequency increases, the normalized capacitance slope shows a downward trend, while the quadratic voltage coefficient α values decrease from 329.1 ppm·V −2 to 270.5 ppm·V −2 , which is attributed to the increase in the relaxation time and the smaller capacitance variation caused by the gradually increasing high frequency [48].
age linearity, where β can be eliminated by circuit design or canceled out by differential methods [18,46,47]. Figure 7 indicates the normalized capacitance of the 25 nm Al2O3 MIM capacitors with bias voltages of 10 4 Hz, 10 5 Hz, and 10 6 Hz. It can be seen that as the frequency increases, the normalized capacitance slope shows a downward trend, while the quadratic voltage coefficient α values decrease from 329.1 ppm·V −2 to 270.5 ppm·V −2 , which is attributed to the increase in the relaxation time and the smaller capacitance variation caused by the gradually increasing high frequency [48].

Conclusions
In this work, three types of high-performance MIM dielectric capacitors (Al2O3, TiO2, and HfO2, with an area of 80 µm × 80 µm) on a silicon substrate are successfully fabricated by the combination of vacuum thermal evaporation, laser direct writing technology, and atomic layer deposition (ALD). The physical morphology and electrochemical properties of the as-prepared MIM dielectric capacitors are also systematically investigated. The prepared samples show a certain discrepancy in compactness and surface defects. Among them, the Al2O3 and HfO2 insulators demonstrate better compactness and fewer surface defects, while the TiO2 insulator shows a relatively poor preparation effect, which is related to the fabrication process and substrate defects. Through the precisely controlled micro-machining processes, the manufactured 25 nm Al2O3 capacitor exhibits a capacitance density up to 7.89 fF·µm −2 , a leakage current lower than 1.4 × 10 −10 A·cm −2 , a breakdown voltage of 12 V, and a breakdown electric field of 4.8 MV·cm −1 , which can satisfy the requirements of integrated passive devices for capacitors. Based on the restrictive tradeoff between leakage current and capacitance density, the relationship between dielectric layer material and thickness is further discussed. Three-dimensional (3D) multilayer silicon-based capacitors are believed to achieve a larger capacitance density, and different 3D structures may have a great influence on the current distribution and the performance effect of MIM capacitors, which are directions worth studying in the future.
Supplementary Materials: The following supporting information can be downloaded at: www.mdpi.com/xxx/s1, Figure S1. MIM capacitor electrode structure pattern design, arrange 30 unit patterns in a 3 cm 3 cm area to form an array; Figure S2. Reflection and refraction of light on thin film and substrate systems; Figure S3

Conclusions
In this work, three types of high-performance MIM dielectric capacitors (Al 2 O 3 , TiO 2 , and HfO 2 , with an area of 80 µm × 80 µm) on a silicon substrate are successfully fabricated by the combination of vacuum thermal evaporation, laser direct writing technology, and atomic layer deposition (ALD). The physical morphology and electrochemical properties of the as-prepared MIM dielectric capacitors are also systematically investigated. The prepared samples show a certain discrepancy in compactness and surface defects. Among them, the Al 2 O 3 and HfO 2 insulators demonstrate better compactness and fewer surface defects, while the TiO 2 insulator shows a relatively poor preparation effect, which is related to the fabrication process and substrate defects. Through the precisely controlled micromachining processes, the manufactured 25 nm Al 2 O 3 capacitor exhibits a capacitance density up to 7.89 fF·µm −2 , a leakage current lower than 1.4 × 10 −10 A·cm −2 , a breakdown voltage of 12 V, and a breakdown electric field of 4.8 MV·cm −1 , which can satisfy the requirements of integrated passive devices for capacitors. Based on the restrictive trade-off between leakage current and capacitance density, the relationship between dielectric layer material and thickness is further discussed. Three-dimensional (3D) multilayer siliconbased capacitors are believed to achieve a larger capacitance density, and different 3D structures may have a great influence on the current distribution and the performance effect of MIM capacitors, which are directions worth studying in the future.
Supplementary Materials: The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/molecules27123951/s1, Figure S1. MIM capacitor electrode structure pattern design, arrange 30 unit patterns in a 3 cm × 3 cm area to form an array; Figure S2. Reflection and refraction of light on thin film and substrate systems; Figure S3