Nanotechnologies have advanced numerous research fields such as fundamental science and have provided various applications in microelectronics, mechanical, and optics and plasmonics fields. Nanofabrication techniques are critical to the implementation of nanotechnologies for various application needs. Nanofabrication usually refers to the manufacture of structures, components, and materials within 1 and 100 nm [1] , and lithography techniques among all the nanofabrication methods are the core of cutting-edge nanotechnologies [2] . Compared with electron beam lithography (EBL) and focused ion beam (FIB) method which must be operated under a vacuum environment [3] , atomic force microscopy (AFM) has emerged and used in nanofabrication due to its relatively convenience in operation, with comparable high resolution and flexibility in maskless processes. Various surface structures including small organic molecules, proteins, metals, polymers, ceramics, and semiconducting materials have been successfully fabricated [4] , [5] . An AFM probe consists of a microscale cantilever, and a nanoscale tip with the shape of an inverted pyramid attached to the free end of the cantilever, which can be used as a sharp cutting tool for material removal when a constant or dynamic load is applied [5] .
Among all of the AFM-based nanomachining approaches, direct mechanical scratching processes were implemented with a simple and flexible setup [6] , but it is barely compatible with other nanofabrication methods due to its low scribing speed [7] , typically less than 1.2mm/min [8] . Also, the interaction between a sharp tip and sample during direct mechanical scratching is hard to control, which degrades the fabrication performance [9] .
Nanotechnologies have advanced numerous research fields such as fundamental science and have provided various applications in microelectronics, mechanical, and optics and plasmonics fields. Nanofabrication techniques are critical to the implementation of nanotechnologies for various application needs. Nanofabrication usually refers to the manufacture of structures, components, and materials within 1 and 100 nm [1] , and lithography techniques among all the nanofabrication methods are the core of cutting-edge nanotechnologies [2] . Compared with electron beam lithography (EBL) and focused ion beam (FIB) method which must be operated under a vacuum environment [3] , atomic force microscopy (AFM) has emerged and used in nanofabrication due to its relatively convenience in operation, with comparable high resolution and flexibility in maskless processes. Various surface structures including small organic molecules, proteins, metals, polymers, ceramics, and semiconducting materials have been successfully fabricated [4] , [5] . An AFM probe consists of a microscale cantilever, and a nanoscale tip with the shape of an inverted pyramid attached to the free end of the cantilever, which can be used as a sharp cutting tool for material removal when a constant or dynamic load is applied [5] .
Among all of the AFM-based nanomachining approaches, direct mechanical scratching processes were implemented with a simple and flexible setup [6] , but it is barely compatible with other nanofabrication methods due to its low scribing speed [7] , typically less than 1.2mm/min [8] . Also, the interaction between a sharp tip and sample during direct mechanical scratching is hard to control, which degrades the fabrication performance [9] .
Nanotechnologies have advanced numerous research fields such as fundamental science and have provided various applications in microelectronics, mechanical, and optics and plasmonics fields. Nanofabrication techniques are critical to the implementation of nanotechnologies for various application needs. Nanofabrication usually refers to the manufacture of structures, components, and materials within 1 and 100 nm [1] , and lithography techniques among all the nanofabrication methods are the core of cutting-edge nanotechnologies [2] . Compared with electron beam lithography (EBL) and focused ion beam (FIB) method which must be operated under a vacuum environment [3] , atomic force microscopy (AFM) has emerged and used in nanofabrication due to its relatively convenience in operation, with comparable high resolution and flexibility in maskless processes. Various surface structures including small organic molecules, proteins, metals, polymers, ceramics, and semiconducting materials have been successfully fabricated [4] , [5] . An AFM probe consists of a microscale cantilever, and a nanoscale tip with the shape of an inverted pyramid attached to the free end of the cantilever, which can be used as a sharp cutting tool for material removal when a constant or dynamic load is applied [5] .
Among all of the AFM-based nanomachining approaches, direct mechanical scratching processes were implemented with a simple and flexible setup [6] , but it is barely compatible with other nanofabrication methods due to its low scribing speed [7] , typically less than 1.2mm/min [8] . Also, the interaction between a sharp tip and sample during direct mechanical scratching is hard to control, which degrades the fabrication performance [9] .
Nanotechnologies have advanced numerous research fields such as fundamental science and have provided various applications in microelectronics, mechanical, and optics and plasmonics fields. Nanofabrication techniques are critical to the implementation of nanotechnologies for various application needs. Nanofabrication usually refers to the manufacture of structures, components, and materials within 1 and 100 nm [1] , and lithography techniques among all the nanofabrication methods are the core of cutting-edge nanotechnologies [2] . Compared with electron beam lithography (EBL) and focused ion beam (FIB) method which must be operated under a vacuum environment [3] , atomic force microscopy (AFM) has emerged and used in nanofabrication due to its relatively convenience in operation, with comparable high resolution and flexibility in maskless processes. Various surface structures including small organic molecules, proteins, metals, polymers, ceramics, and semiconducting materials have been successfully fabricated [4] , [5] . An AFM probe consists of a microscale cantilever, and a nanoscale tip with the shape of an inverted pyramid attached to the free end of the cantilever, which can be used as a sharp cutting tool for material removal when a constant or dynamic load is applied [5] .
Among all of the AFM-based nanomachining approaches, direct mechanical scratching processes were implemented with a simple and flexible setup [6] , but it is barely compatible with other nanofabrication methods due to its low scribing speed [7] , typically less than 1.2mm/min [8] . Also, the interaction between a sharp tip and sample during direct mechanical scratching is hard to control, which degrades the fabrication performance [9] .
48th SME North American Manufacturing Research Conference, NAMRC 48 (Cancelled due to To improve efficiency and throughput of AFM-based nanomachining processes, ultrasonic vibration assisted techniques were developed [9] , [10] . The in-plane circular motion of the sample and ultrasonic vibration in Z direction enable high speed nanofabrication [11] and complex 3D patterns [12] with effectively reduced setpoint force [13] and smaller tool wear [14] .
Another method to advance the AFM-based nanomachining is to use thermal-mechanical nanopatterning technique, which mostly uses the cantilever heating method. Cantilever heating is applied to locally remove the resist material [15] , [16] , by heating up the tip through an integrated resistive heater [17] , [18] . As soft polymers are widely used as masks or resists in electronics device fabrication [19] , thermal heat can assist the mechanical deformation through decreasing the viscosity of less fluid polymers, hence lower normal force is required for the nanopatterning process [20] .
In addition to the tip heating method, sample heating is a potential candidate but with limited research results. It can soften the entire sample other than only the AFM tip by applying the Joule heating on substrates [21] . However, it is not easy to fabricate nanopatterns with controllable dimensions due to significant adhesion forces between the sample and the tip. In our previous study [22] , uniform nanopatterns with controllable dimensions were fabricated with lower normal force than only using vibration or only using thermal sources. We demonstrated that the integration of the in-plane vibration with the substrate heating, the nanopatterning capabilities were enhanced. The in-plane vibration can reduce the elevated adhesion force resulted from the Joule heating and produce uniform features. And the Joule heating can decrease the normal force needed for the vibration assisted nanomachining on thermoplastics.
In this study, to provide cantilever selection guidance for this novel nanomachining system and to understand the effect of cantilever stiffness and sample temperature on feature dimensions, we used both soft and stiff probes for the nanomachining processes. By applying the same normal force (50 nN) with different types of AFM cantilevers, nanotrenches with different dimensions were fabricated. We also designed and conducted full factorial experiments to statistically investigate the main effects and interaction effects of two factors, types of probes and heating temperatures, on the dimensions of the lithographic nanopatterns.
The experimental setup includes a commercial AFM (XE7, Park Systems Corporation, Suwon, South Korea) and an inhouse fabricated nanolithography stage, as shown in Fig. 1 . There are two piezoelectric actuators placed on the stage in X&Y direction, which are mounted between the extruded centre and side part of the aluminium stage. A signal generator (USB-6259, National Instruments, Austin, TX, USA), together with two signal amplifiers (PX200, PiezoDrive, Shortland, NSW, Australia), both have a gain of 20, were used to drive the piezos. A heating element is attached beneath the sample holder to provide Joule heating on the sample surfaces. When applying different voltages to the heating element, the temperature of the sample can be controlled. Distance between the center and side aluminium parts are exactly the same with the length of both piezoelectric actuators when no voltage is applied on. Directions of the two vibrations created by piezoelectric actuators are orthogonal, which can generate inplane circular motion of the sample under the same vibration frequency and amplitude.
The dynamic behaviours of the two piezoelectric actuators is also vital to the lithography performance. Desired pattern width and material removal rate is acquired under the frequency of 2 kHz, with 0.8 V amplitude of the input sinusoidal wave (16 V amplitude for the amplifier output signal), which produces trenches with 40 nm widths when depths are 10 nm. The in-plane sample motion provided by piezoelectric actuators can regulate the pattern shape in lateral dimensions and can increase the machining efficiency. As for the heating element, 4.6 V and 6 V of the power supply can generate 35°C and 42°C on the sample surface, respectively. The actual sample surface temperature was measured by a thermocouple thermometer (HH802W Digital Thermometer, Omega Engineering Inc., Norwalk, CT, USA). The polymer surface is softened under elevated temperatures and thus facilitates the machining process. With the integrated vibration and thermal AFM-based nanomachining system, nanopatterns can be fabricated on the polymer surface with the feature depth controlled by setting force and temperature.
This nanomachining experiment was conducted on 200 nm PMMA (950PMMA A4) films, which was spin coated on clean silicon wafers. The PMMA was spin coated on the substrate for 60 seconds at 4000 rpm and then post baked at 180 °C for 90 seconds. The sample was fixed on the top of the aluminum stage. A stiff cantilever with diamond like coating on the tip side (Tap190DLC), and a soft cantilever with Au coating (CSG10/Au) are used in this experiment. Table 1 describes general information about the probes, which refers to parameters including cantilever force constant, resonant frequency, tip radius, and tip height. Other than lithography part, the same tip is also used in scanning the topography images of the lithographic area before and after the nanomachining process.
Using the setpoint control function of the nanolithography software provided by Park Systems, a constant force is applied on the sample surface by the AFM tip in contact mode during lithography processes. Vector mode of the software enables lithography patterns to be designed using basic shapes (lines, rectangles, ellipses, polylines, etc). During lithography processes, AFM tip will draw the patterns along the designed trajectories in the loaded lithographic area under constant force until finishing all patterns.
The lithography experiments include several procedures. 1) Take a topography image of the lithographical area under contact mode. 2) Load the AFM image in the nanolithography software and input the designed patterns. 3) Elevate the temperature of the heating device. 4) Open the vibrators and start the lithography process. 5) Turn off the heating device and both vibrators after the lithography finished. 6) Reimage the lithographic area to acquire nanomachining results. 
In order to study the effect of cantilever stiffness and sample temperature on nanofabrication, we designed a two-level full factorial experiment. Two factors are the spring constant of the cantilever and the temperature of the sample surface, each with two levels, as is shown in Table 2 . The high and low level of the spring constant are 48 and 0.11 N/m (for Tap190DLC and CSG10/Au, respectively), and the two levels of temperature are 35°C and 42°C (corresponding to 4.6 V and 6 V DC voltage supplies, respectively). The displacement of piezoelectric actuators is in accordance with its input sinusoidal signal, which has the frequency of 2 kHz and the amplitude of 16 V. Constant force of 50 nN is applied in each experiment for every lithography pattern. Three lines, each with 1.6 μm length were designed in a 2 μm x 2 μm lithographic area. Moving rate of the tip during lithography is 0.5 μm/s. Fig. 2 shows the topography images and the height profiles of the lithography patterns. As is shown in the height profiles of Fig. 2 , there is no trench but only shallow marks showing in the topography image of the lithography experiment of the CSG10/Au cantilever under 4.6 Volts (35°C), indicating that no patterns can be machined using 50 nN normal force and 16 V in-plane vibration. Apart from that, the trenches machined by CSG10/Au cantilever under 6 V (42°C) are the shallowest ones compared with the others, with depths less than 10 nm and widths around 40 nm. The trenches in the lithography experiments performed by Tap190DLC tip under 4.6 V (35°C) and 6 V (42°C) have significantly increased depths and widths. Fig. 3 compares the depth of trenches machined in the four experiments through the cross-sectional height profiles of the trenches, one from each of the experiments. As the force constant of the tip increases, a deeper trench is machined using the same experimental settings. Similarly, using the same type of cantilever, the trench depth will also increase under an elevated temperature. Fig. 3 shows that under 50 nN normal force and 42°C on the sample surface, the maximum depth of trench fabricated by CSG10/Au tip is around 8 nm, and that for Tap190DLC cantilever is around 80 nm. As one cantilever is much stiffer than the other one, they may react differently under the same heat flux. Therefore, even though the same normal force is applied, it is possible to get trenches with different depth using different probes in the machining process. Different extent of deflection for the two cantilevers can lead to different bending angles of the tips, which might be another reason of the difference in depth. To further study the effect of tip categories and temperature on the depth and width of the nanopatterns machined in this experiment, Fig. 4 summarizes the main effects and interaction plots for different factors on trench depth and width. Fig. 4 (a) and (b) show similar trend that both tip category and temperature can affect the trench depth and width because all the four lines are not horizontal. Generally, Tap190DLC tip can fabricate trenches with larger width and depth comparing with CSG10/Au tip under same experimental settings. In the meantime, depth and width of the nanopatterns will increase as the temperature elevates. Through comparing the slope of the left and right figure, we can also draw the conclusion that the main effect of tip categories is bigger than that of the temperature. Fig. 4 (c) and (d) show the two factors (tip categories and temperature) have interaction effects on trench depth and width as the two lines in both figures are not parallel. The interaction effect between the two variables indicates that the effect of temperature on the trench depth depends on the type of the tip categories. The depth of trenches fabricated by Tap 190DLC tip greatly increases at higher temperature, comparing with that of the CSG10/Au tip. Meanwhile, the change in trench width of Tap 190DLC tip under different heating temperature is subtle, much less than that of the soft tip. Besides, interaction effects might because of the soft and stiff cantilevers react differently under the same vibration and heat flux. The interaction effect on trench width is larger than that on depth. Table 3 and Table 4 include more statistical analysis results of the factorial design. As is shown in Table 3 , both factors (the tip force constant and the temperature) have significant effect on the response (the depth of trench), with p values all less than 0.05. The interaction between the two factors also has a significant effect, which means the trench depth over different temperatures is significantly different depending on tip categories. Trench depth increases along with the increase of the tip spring constant and temperature, which shows the nanomachining ability of various trench dimensions using different AFM cantilevers under elevated temperatures. Similarly, in Table 4 , both factors (the tip force constant and the temperature) and their interactions have significant effect on the response (the width of trench), indicating when the experimental setting changes from the low level to the high level of the factor (i.e. tip category from CSG10/Au to Tap190DLC, and temperature from 35°C to 42°C), the trench width increase. 
In this study, we employed a multiple energy assisted AFMbased nanomachining system with both mechanical vibration and sample heating to study the lithography capabilities of AFM cantilevers with different spring constants under different elevated temperatures using the same setpoint force. Nanopatterns with small and large depths were successfully fabricated on PMMA films under elevated temperature using AFM probes with very low and high stiffness (0.11 and 48 N/m). Through the analysis of the effect of tip categories and temperature on the depth and width of nanopatterns machined in the lithography process, the results indicate that tip categories, heating temperature, and their interactions all have significant effect on trench depth and width. As the same constant force is applied during the lithography processes, the dimensions of nanotrenches fabricated by tips with different stiffnesses should be similar. However, the differences in trench depths turn out to be over 50 nm under the exact same experimental settings. The reason might be different cantilever deflection and tilting angle due to the cantilever stiffness, effects of the vibration and the heat flux, which needs to be further investigated. The contributions of this approach are twofold: First, it helps to identify the most appropriate tip and parameters used for machining trenches with different dimensional requirements of the nanopatterns. Second, it investigates the effect of different factors (including tip categories and temperature) on the sample heating lithography performance in vibration and thermal induced AFM-based nanomachining.