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3-D finite element calculation of electric field enhancement for nanostructures fabrication mechanism on silicon surface with AFM tip induced local anodic oxidation Barayavuga Theogene, Jianlei Cui, Xuewen Wang, Wenjun Wang, Xuesong Mei, Peiyun Yi, Xinju Yang, Xiaoqiao He & Hui Xie To cite this article: Barayavuga Theogene, Jianlei Cui, Xuewen Wang, Wenjun Wang, Xuesong Mei, Peiyun Yi, Xinju Yang, Xiaoqiao He & Hui Xie (2018) 3-D finite element calculation of electric field enhancement for nanostructures fabrication mechanism on silicon surface with AFM tip induced local anodic oxidation, Integrated Ferroelectrics, 190:1, 129-141, DOI: 10.1080/10584587.2018.1457346 To link to this article: https://doi.org/10.1080/10584587.2018.1457346
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INTEGRATED FERROELECTRICS , VOL. , – https://doi.org/./..
-D finite element calculation of electric field enhancement for nanostructures fabrication mechanism on silicon surface with AFM tip induced local anodic oxidation Barayavuga Theogenea,b , Jianlei Cuia,b,c,d , Xuewen Wanga , Wenjun Wanga , Xuesong Meia , Peiyun Yib , Xinju Yangc , Xiaoqiao Hed,e , and Hui Xief a
State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an, P. R. China; State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai, P. R. China; c State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai, P. R. China; d Department of Architecture and Civil Engineering, City University of Hong Kong, Kowloon, Hong Kong; e Center for Advanced Structural Materials, City University of Hong Kong Shenzhen Research Institute, Shenzhen, P. R. China; f State Key Laboratory of Robotics and Systems, Harbin Institute of Technology, Harbin, P. R. China b
ABSTRACT
ARTICLE HISTORY
The atomic force microscope (AFM) can be used in dynamic tipping mode as an effective lithography technique capable of manufacturing nanometer sized devices on the surface of a silicon wafer with a higher resolution surface characterization. The most difficult challenge in fabrication of nanostructure based on AFM nano-oxidation approach is the way of controlling an electric field between a cantilever probe tip and a silicon wafer. A water bridge builds up between the tip and the wafer, resulting in the oxidation due to the high electric field in the region. A reconstructive AFM system for nano-oxidation with a tapping model, implemented in an air, was developed. The presented AFM implements the increasing of electric field intensity by analyzing the impact voltage from −1 V to −5 V, electric field, and ion concentrations at the ambient/oxide and oxide/silicon interfaces, while the growth of thin oxides assumes a single liquid/silicon interface, which is modeled as an infinitely long conducting plane. Therefore, particle distribution for the surface charge density is generated for topography simulations. Based on the control-parameters, an enhanced electrical field of up to 1010 V/m can be obtained, which provides a powerful support for controllable experimental study of nanostructures fabrication with AFM tip induced local anodic oxidation. This showed the dependence of applied voltage types and various nanostructures and life time of AFM tip, by controlling tip-sample position in nanolithography processes is an important factor for controlling the aspect electric field distribution. And the effect of different parameters on enhancement distribution was performed and analyzed in this paper.
Received September Accepted February KEYWORDS
Electric field enhancement; scanning probe tip; nanolithography based on tip (NBT); nano dot; AFM and surface characterization
CONTACT Jianlei Cui
[email protected]; Hui Xie
[email protected]; Xiaoqiao He
[email protected] Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/ginf. © Taylor & Francis Group, LLC
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1. Introduction Over the past decade, nanotechnology becomes the promising research area which may bring significantt breakthrough in nanofabrication of many devices and systems used in modern industry that are becoming progressively smaller and have reached the nanoscale domain [1–6]. Nanofabrication is the central theme in the realization of the potential benefits of these modern devices and systems nanotechnology based on tip (NBT) uses a nanometer-scale tip to interact with a sample and fabricate nanostructures. NBT has the potential for fabricating nanostructures with controlled size, shape, and orientation at precise substrate locations and nanometer-scale precision and resolution [7–9]. A tip can interact with the sample to fabricate nanostructures, with the tip influencing the surface through any of a number of mechanisms, including mechanical electrochemical, optical, chemical diffusion, thermal, electrical polarization, and plasma [10, 11].To overcome limitations, many processes such as e-beam lithography, focused ion beam lithography, imprint lithography and scanning probe microscope (SPM) lithography have been developed. For many patterning processes, SPM lithography was introduced and studied by several research teams. SPM lithography has been studied with a scanning tunneling microscope (STM) and an atomic force microscope (AFM). Anodic oxidation nanolithography is only suitable for conducting materials while AFM lithography can process semiconductor and metal substrates. AFM anodization lithography is a promising process for making nanostructures on metals and semiconductors. Recently, it has been used to fabricate Nano-electronic devices and sensor in local area with low damage direct to patterning of sample the previous researchers demonstrated that the AFM tip is in contact with silicon sample surface or not in order to generate oxidation process .Bring the metallic tip close to the silicon sample in humidity environment was enough to generate electric field in the region and concluded that the height of oxide dots increased by increasing applied voltage .AFM anodization lithography was performed by inducing electrochemical reactions between the tip and the silicon sample surface. The driving force is Colombian’s attraction force; the current in the water column formed by capillary force when the current flows into the water column, H2 O molecules are decomposed into oxyanions (OH− , O− ) and protons (H+ ). These ions penetrate into the oxide layer because of the electric field (order 108 V/m to 109 ). The penetrated hydroxyl ions (OH− ) grow SiO2 on a Si surface. Moreover, hydroxyl ions can form an alcohol bridge between the tip and the substrate. The hydroxyl ions penetrate the substrate, enhancing the aspect ratio of protruded oxide patterns compared to the water environment. Therefore, the penetrated and reduced hydroxyl ions are important factors for fabricating SiO2 on a Si surface in AFM anodization lithography. Several physical parameters influence the fabrication of oxide structure in AFM anodization nanolithography [12–17]. Both the oscillating frequency of nanolithography and time of exposure nanolithography are important kinetic factors in electrochemical oxidation reactions. Humidity is related to the height of oxide nanostructure [18–23].
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Figure . The overview of geometry for analytical model.
The tip geometry has also significant meaning [24]. In AFM anodization lithography, applied voltage type is the most important factor for characterize the size of the oxide structure. Most studies are performed under dc pulse in AFM anodization lithography. Applied voltage types have been investigated to determine diffusion of oxyanions is restricted by the short duration time of the pulsed bias [25]. Pulsed bias voltage is synchronized with the resonance frequency of the cantilever in lithography processes using non-contact model [26, 27]. The finite element method is used to solve electrostatic problem of AFM tip sample interaction in better to analyze the problem it is important to think about near electric field effect and the distribution of electric field enhancement and its distribution for AFM tip shape. Finally, AFM was the first tool that could perform high-resolution imaging and a vacuum free working environment. Nowadays, AFM has been playing a more important role in various research areas, which is still a formidable challenge for us to discover [28–38].
2. Computational modeling A fundamental analysis of electrochemical and electromechanical processing at the nanoscale Surface of Si film begins to oxidize when enough positive voltage is added between surface of Si film and conductive AFM tip in air ambient [39]. In order to simulate electric field around the tip, the conductive AFM Probe tip and the surface of substrate are separated by few nanometer and the samall radius of hemiellipsaidal shape [40, 41]. In this paper to estimate the electric field enhancement by AFM Tip sample new structure system shown on the Figure 1 is computation modeling by using Finite element method (FEM) in order to evaluate the influence of applied voltage and tip-sample distance on tip-induced electric field, we performed 3-D simulation (comsol- multiphysics software5.2) by using the following mathematical equations. The electric field intensity at a distance from the silicon sample are calculated as follows. cos θ− q cos θ+ Ex = (1) − 4π ε0 (Dt − s)2 (Dt − s)2
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q Ey = 4π ε0 where sin θ− =
sin θ− sin θ+ 2 − (Dt − s) (Dt − s)2
(2)
x y , cos θ+ = and (Dt − s)2 ± = (Dt − s)2 + a2 Dt − s Dt − s 2 ±2 (Dt − s) a cos θ+ = x2 + y ± a .
Ex and Ey are the electric field strength distributions along x and y-axis. Similarly to the Cartesian coordinates the above equation becomes: r is the distance between two opposite charges the same as tip sample position. ⎧ ⎫ ⎪ ⎪ ⎬ q ⎨ x x Ex = − (3)
3/2 2 3/2 ⎪ 4π ε0 ⎪ ⎩ x2 + y − a2 ⎭ x2 + y + a ⎧ ⎫ ⎪ ⎪ ⎨ ⎬ q y+a y−a − Ey = (4)
3/2
2 3/2 ⎪ 4π ε0 ⎪ ⎩ x2 + y − a2 ⎭ 2 x + y+a We shall make a polynomial expansion for the electric field by using the binomial 1 theorem and then we collect terms that are proportional to (Dt−s) 3 , and ignore the 1 term that are proportional to (Dt−s)5 , where(Dt − s) = (x2 + y2 )
Let’s start with the equation below: [x2 + (y ± a)2 ]− 2 = (Dt − s)−3 a2 ±2ay − 3 [1 + (Dt−s) 2] 2 The limit whenDt − s a, we can use the binomial theorem to express a polynoa2 ±2ay 3 15 2 −3 mial functionS ≡ (Dt−s) 2 ,(1 + S) 2 = 1 + 2 S + 8 S − ... the above equations for the components of electric field distribution becomeDt − s a. 3
(r, θ ) = E
P 2 3 3 cos θ i + 3cos θ − 1 j 4π ε0 (Dt − s)
(5)
Using a little algebra, the intensity of electric field distribution is given E (Dt − s, θ ) =
12 P 2 3cos θ + 1 4π ε0 (Dt − s)3
(6)
Where P → qa called electric dipole moment where a → Dt − s by assumption. The electric dipole moment is in relation with electric potential difference U (a, θ ) =
1 kqcosθ ,k → Dt − s 4π ε0
(7)
The relationship between electric field and electric dipole moment is shown on the equation (6) clearly the electric field strength is a linear function of dipole at a fixed tip-sample position. According to above equations we can simulate the field distribution under various parameters and analyze the influence of these parameters on the silicon surface modification. Electric field induced is an important
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phenomenon utilized in probe-based nanofabrication as well as a potential factor in contact reliability of surface science in nanometer size. By varying the tip-sample distance, the voltage intensity and the tip geometry indicated by semi-angle the simulation of electric field can be done according to the equation (6). As indicated on the equation the electric field distribution intensity is the function of tip-sample distance and tip geometry, in our model that prediction has a significant meaningful electric field and the horizontal axis represent tip-sample distance, as the tip-sample distance increased from 0nm to 8nm the effect of electric field distribution on silicon substrate reduced. Our model suggested the formation of nanostructures that are depended on how much voltage needed to induce enough Electric Field. Electric field distribution along a surface could be used as a diagnostic tool to investigate the possible oxide structure height and service life of an AFM probe tip. According to above equations we can simulate the field distribution under various parameters and analyze the influence of these parameters on the silicon surface modification. Electric field induced is an important phenomenon utilized in probebased nanofabrication as well as a potential factor in contact reliability of surface science in nanometer size. By varying the tip-sample distance, the voltage intensity and the tip geometry indicated by semi-angle θ the simulation of electric field can be done according to the equation (6). As indicated on the equation the electric field distribution intensity is the function of tip-sample distance and tip geometry, in our model that prediction has a significant meaningful electric field and the horizontal axis represent tip-sample distance, as the tip-sample distance increased from 0nm to 8nm the electric field distribution on silicon substrate reduced. Our model suggested the formation of nanostructures that are depended on how much voltage needed to induce enough Electric field; we studied the influence of controlled local anodic oxidation by AFM tip as a surface modification mechanism for miniaturization. Electric field stress distribution along the surface of silicon influenced by the applied voltage for modification process. Electric field distribution along a surface could be used as a diagnostic tool to investigate the possible oxide structure height and service life of an AFM probe tip. 3. Results and discussion 3.1. Effect of biased voltage on electric field generation to the AFM tip apex
The influence of bias voltage on the electric field distribution on silicon substrate was observed by applying voltage −1 V, −2 V, −3 V, −4 V, and −5 V. The highest voltage induced stronger electric field which caused interaction between both AFM tip and silicon sample to be strongest. The laws of electrostatics are now used for the comparison with the results of finite element model we consider the results for gold (Au) tip with radius 6 nm, semi-angle of the tip angle of 7° and at tip sample distance of 1 nm. For our presented results, the electric field is a function of voltage
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and tip sample separation distance. The technique is applied for only short time scale expressed in milliseconds. The surface charge density on silicon surface is deduced from the electric field and the height of oxide structure is grown according to the distribution electric field. The results described in the Figure 1 indicate the impact of biased voltage on the electrical field distribution the strongest electric field was generated by -5V and when no biased voltage acting on the tip the electric field is zero any generation of electric field. When the tip-substrate distance is a constant the AFM probe tip of the same characteristic (radius of curvature) generate electric field with linear relationship to the biased voltage acting on the tip. 3.2. Influence of tip–sample distance
The tip-sample distance effect on electric field distribution was analyzed through to its influence on electric field distribution the simulation results indicated that the highest electric field is produced when tip is bright towards near to the silicon surface indicated by the Figure 2 and it becomes lower for several nanometers above the substrate. 3.3. Effect of tip apex radius on the electric field enhancement
In this paper we address the imapct of tip geometry on electric field distribution. AFM probe tip of the following apex radius are considered to investigate the dependence of sharped apex radus in Rc = 6 nm,Rc = 7 nm,Rc = 8 nm, Rc = 9 nm and Rc = 10 nm in Figure 3. the bised voltage and the tip sample distance was fixed. To understand the influence of AFM tip apex radius on electric field distribution the probe tip was place at fixed distance above the substrate of 4nm, bias voltage U = −1 V, the electric field distribution decreased from a AFM tip of small apex radius to a higher apex radius. The Figure 4 shows the dependance of electric field enhancement on the tip apex radius is very stronger for the sharped tip. Our simulation results show a nonlinear relationship between of the electric field enhancement
Figure . The attraction forces between two charged particles induce electric field enough to make silicon oxide structure.
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Figure . Electric field distribution on AFM tip apex is a function of biased voltage.
on the tip apex radius and substrate in the electrostatic field regime. The electric field increased several nanometer near to the sample material that the dependence of electric field enhancement on the tip apex and the electric field intensity calculated at distance of 8nm from the sample by considering tip apex radius of 6,7,8,9 and 10 nm it is indicated on it; the electric field distribution is high 1.19 × 109 V/m for RC = 6 nm and it is lower 9.81 × 108 V/m for RC = 10 nm.
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Figure . Electric field distribution on AFM Tip Apex is a function of its Radius of curvature.
3.4. Effect of tip apex semi-angle on the electric field enhancement
The increased electric field distribution could be explained mainly by the smaller cone angle. However, this concept changed for tip-sample spacing above 1nm. The simulation results show for a 31º cone angle of AFM tip, that in comparison to a 31º cone angle of AFM tip, the electric field grows stronger for the smallest cone angle. For sharper tips, the emission occurs over a larger range, and thus the tip-sample gap increases stronger the electric field distribution decreased. Roughly speaking, low bias voltages are targeted for all tips to achieve minimum electric field and thus minimum structure size Figure 5 indicates the impact of semi-angle of AFM Probe tip found in our simulation results: higher electric field arose when using sharpness’s
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Figure . Electric field distribution on AFM tip apex is a function of semi-angle for applie.
AFM tip, the distance less than 1nm and for larger than 1nm the impact of AFM tip shape on electric field distribution decreases. The model reflected to the observed reduction dependence of tip sample distance on the electric field distribution and the voltage dependence is relatively linear. The fixed tip sample distance, the voltage of 5 V is required in order to generate electric field intensity which is enough for fabrication of nanostructures of higher oxide height.
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Figure . Electric field distribution decreases from lower to higher tip -sample distance.
Figure . Electric field distribution increases linearly with biased voltage.
Table . Name of materials and their electrical properties. Material Silicon Si(solid bulk) Gold (Au) Air
Electrical conductivity
Relative permittivity
.E(S/m) .E-(S/m) .E-(S/m)
. .
Figure 6 describes in details that electric field distribution on silicon sample decreases exponentially with respect to the tip moving away several nanometers from considering fixed silicon sample. Figure 7 indicates that electric field intensity distribution increases linearly with higher biased voltage. Table 1 describes the electrical and optical properties of materials used in the modeling process.
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4. Conclusions In this article, we demostrated the electric field enhancement on local induced oxidation by AFM gold tip and the electric field distribution around the tip apex. The field distribution mainly depends on the applied voltage, tip curvature radius, semiangle and tip–substrate distance. Therefore, the electric field distribution on silicon sample has been analyzed by finite element method. The simulation results show that high field enhancement appears around the AFM tip and is mainly concentrated underneath the apex of the AFM tip when Bias voltage applied on the AFM gold tip.The results indicated that electric field enhancement easily appears when an AFM gold tip is stimulated by higher voltage. The tip geometry and tip–substrate distance also determine the electric field distribution. High electric field enhancement can be achieved using a relatively sharp tip with small apex radius and semiangle. As the tip–substrate distance increased, the maximum electric field distribution underneath the tip apex decreases. When the tip–substrate distance reached 1nm, the electric field dramatically drops to the order of 1010 V/m to 108 V/m. When the tip–substrate distance is greater than 1 nm, the electric field enhancement of the tip apex is mildly reduced Through the analysis of electric field distribution, we propose a new promising scheme with some advantages which combines an AFM metal probe for and mechanical processing nanolithography.
Funding This project was supported by the National Key Research and Development Program of China (2017YFB1104900), National Natural Science Foundation of China (51505371, 11372264), Hong Kong Scholars Program (XJ2015038), a research grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (CityU 114013), Young Elite Scientists Sponsorship program by CAST (2016QNRC001), Natural Science Basic Research Plan in Shaanxi Province of China (2017JM5015), Research Project of State Key Laboratory of Mechanical System and Vibration (MSV201713) and State Key Laboratory of Surface Physics and Department of Physics, Fudan University (KF2016_11). All the authors gratefully acknowledge their support.
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