tip - based creation of nano - scale features by mechanical removal has been considered since the 1990s . motivated by the agility , geometric capability , and wide - range material applicability of mechanical removal processes , surface characterization instruments such as scanning tunneling microscopes ( stms ) , atomic force microscopes ( afms ) , and nano - indenters have been applied to create nano - scale features on various materials . using afms at the force levels significantly higher than those used for topography measurements , simple features such as lines and pockets have been created on semiconductor , metal , and polymer / photoresist   surfaces through scratching or indenting . various applications of mechanical removal at the nano - scale has been identified , including shaping of mask layers for lithography , fabrication of single - electron transistors ( sets ) , and creation of coulomb blockades , quantum point contacts , quantum nano - dots , quantum wells , and nano - wires [ 8 - 10 ] . although the basic capability of afm - based surface modification has been established , its wide - range of applicability as a viable nanomanufacturing technique has been hindered by several issues . first , the material removal mechanism is dominated by ploughing ( i.e. , plastic deformation ) rather than shearing ( i.e. , removal of material in the form of a chip ) . this causes accumulation , rather than removal , of the material around the created features ( i.e. , ridge formation ) . second , the throughput of the process is low due to the limited removal speeds , large force requirements , and associated rapid tool wear . third , the depth of removal is dictated indirectly by prescribing the force by monitoring the deflection of the relatively low - stiffness afm cantilever . since the material removal force depends on factors such as material ( surface ) properties , probe geometry , and removal conditions ( e.g. , removal speed ) , the resultant removal depth can not be well - controlled through indirect prescription of depth using force monitoring . while several approaches have been proposed to address these issues , including the use of high - stiffness cantilevers , vibrating cantilevers , and vibrating workpiece   or diamond tips ( to reduce wear ) , significant process improvements that will make tip - based mechanical material removal as a fully controllable nanomanufacturing technique have not yet been realized . in this letter , we present a tip - based mechanical nanomanufacturing process , referred to here as nanomilling , in which an afm tip rotated at high frequencies is used as the nanotool to remove the material in a manner similar to that of the conventional milling process . the rotary motions are obtained by out - of - phase motions of the axes of a three - axis piezoelectric actuator that hosts the afm tip . by assembling the tip directly onto the actuator , and thereby eliminating the high compliance arising from the afm - beam connection , a high - stiffness configuration is realized . the feeding motions in three directions , which define the overall geometry , are obtained by moving the sample using a nano - positioning stage . the combined use of high - stiffness tip and nano - positioning stage enables direct prescription of feature depth and shape . as such , the nanomilling process has the potential to advance tip - based nanomanufacturing by enhancing the shape capability and accuracy , increasing the removal speed , and reducing the removal forces and nanotool wear . two possible configurations of rotational motions of the tip ( in - plane and out - of - plane ) are depicted in fig . these motions are obtained by supplying out - of - phase sinusoidal excitations to the axes of the piezoelectric actuator in mutually perpendicular directions . the material removal process in nanomilling is accomplished by rotating the tip in an elliptical pattern , while moving the sample along the feeding direction at a prescribed removal depth ( obtained by the nanopositioning stage ) . for the in - plane configuration , the piezoelectric actuator is used to induce an elliptical pattern ( nanotool path ) to the tip within the sample - surface plane . the tip ( nanotool ) is represented with a circular cross - section in the top view shown in fig . as the nanotool follows the nanotool path , the material is removed by combined feeding and rotary motions . the width of the channel can be modified by changing the diameter of the elliptical nanotool motion normal to the feeding direction . two fundamental rotational motions of the tip : a in - plane motion , and b out - of - plane motion . two instants of the cross - section of the nanotool are indicated as 1 and 2 . continued nanotool rotation will remove the dark - shaded portion of the sample for the out - of - plane configuration ( see fig . 1b ) , the nanotool is rotated in a plane perpendicular to the surface . in this case , the prescribed depth can be changed by varying the nanotool - path diameter along the sample - surface normal . combined motion of nanotool rotation and feeding causes a portion of material ( the shaded region in fig . the amount of material removed per revolution ( the size of the shaded region ) depends on the prescribed feed . to demonstrate the nanomilling process , a nanomilling testbed has been designed and constructed ( see fig . an afm tip is assembled onto an acrylic nanotool - post in a reverse configuration , where the tip is directly supported . since the compliant afm beam is not used as a connection element , a high - stiffness nanotool - attachment is attained . as described below , the free - standing portion of the afm beam , along with the piezo shaker , are used for contact detection . the nanotool - post is attached to a three - axis piezoelectric actuator ( physik instrumente l.p . the sample is attached to a piezoelectric element ( i.e. , the piezo shaker ) that is fixed to the nanopositioning stage ( physik instrumente l.p . the nanopositioning stage provides the feeding motions and prescribes the depth with 1 nm resolution and 5 nm rms repeatability ( with the closed - loop position control ) . the motion directions of the nanopositioning stage and the piezo actuator are characterized using a laser doppler vibrometer ( ldv ) system ( polytec gmbh msa-400 ) and optical reference surfaces , and are subsequently aligned using a compensation algorithm . a three - dimensional rendering of the nanomilling testbed , showing different components of the system the nanomilling process is performed within the nanomilling testbed through the following procedure : first , the sample surface is located through a nanotool - sample contact algorithm using the nanotool cantilever . the piezo shaker placed under the sample is vibrated at the first resonant frequency of the nanotool cantilever ( determined a priori through ldv measurements ) with a sub - nanometer vibration amplitude . the sample is then slowly approached to the tool using the nanopositioning stage , while measuring the vibrations of the tool cantilever using the ldv . a contact between the tool and the sample surface causes a significant ( an order of magnitude or more ) increase in cantilever vibrations at the first resonant frequency and thus , can be detected . second , the nanotool is rotated with selected frequency using the piezoelectric actuator . and third , the nanopositioning stage is used to prescribe the depth and feeding motions to create a particular feature . one of the premises of the nanomilling process is the effective removal of the material mainly in the form of a chip , rather than only ploughing the material . to demonstrate the material removal characteristics , an su-8 sample surface was nanomilled to create channels with 5 m length and 100 nm depth using each of the in - plane and out - of - plane configurations ( see fig . 3 ) . for the in - plane configuration , the nanotool was rotated using a 100 nm circular motion at 3 khz frequency . for the out - of - plane configuration , the elliptical nanotool motion included a normal ( to the surface ) diameter of 40 nm and a feeding - direction diameter of 100 nm at 3 khz frequency . as a reference , channels were also fabricated without a nanotool motion ( i.e. , by scratching ) . a commercial silicon probe tip with a pyramidal shape and 10-nm nominal tip radius was used as the nanotool . due to the potential effect of nanotool orientation , three feeding directions were tested . it can be seen that the in - plane and out - of - plane nanotool motions facilitated material removal in the form of long , curled chips , and produced well - defined edges of the channels . the scratch ( no - motion ) configuration , on the other hand , did not produce chips in a consistent manner , and resulted in reduced edge definition , indicating a removal process dominated by ploughing effects . the long and curled chips observed for the cases with nanotool motions indicate that the material removal mechanism is shearing dominated . no - motion ( scratch ) case does not produce chips consistently , indicating the dominance of the ploughing mechanism to evaluate the capability of the nanomilling process and the testbed in directly prescribing the removal depth , a set of three side - by - side parallel pockets with increasing depth were created on pmma using the in - plane configuration . circular nanotool motions with 200 nm diameter were utilized at 3 khz rotational frequency . to eliminate the uncertainty arising from the contact detection , the first pocket was considered as the reference . two subsequent pockets were nanomilled by setting the depth to 50 and 100 nm , respectively , from the reference surface . figure 4 shows the afm image of the fabricated pockets and the associated line scan . in order to calculate the average depths , three parallel planes were fitted to the afm scans of each created pocket , and the first plane was taken as the reference . the average depths of the second and third pockets were obtained by calculating the distances between their corresponding fitted planes and the reference plane . the standard deviation of measured surface points around the fitted planes for each pocket were also calculated . the average depth of the second and third pockets were calculated as 48.4 and 98.5 nm , respectively . the calculated standard deviation of the surface for both pockets was found to be 4 nm . the difference between the prescribed and actual depths are within the repeatability of the nanopositioning stage . an afm image of the created depths and associated cross - sectional topography in contrast to scratching , when used in the in - plane configuration , the nanomilling process is capable of creating a range of channel widths in a single pass . to demonstrate this capability , four channels with different width value were created on su-8 , each in a single pass , by providing circular nanotool motions with 100 , 200 , 300 , and 400 nm diameter for each case , the rotational frequency was kept at 3 khz , and the channel depth was set to 100 nm . an afm image of the created channels and their cross - sectional topography data is presented in fig . although the channel widths can not be accurately measured due to the steep channel walls , it is seen that the width consistently increased in each successive channel . an afm image and cross - section topography of four channels with different widths , each created in a single pass using the circular in - plane motions with increasing diameter ( chips around the created features are cleaned prior to imaging ) to show the capability of nanomilling process in creating complex shapes , a set of shapes were fabricated on su-8 . figure 6 shows sem images of sample shapes , including a 5 m diameter circle with 30 nm depth , fabricated by in - plane motions ( see fig . 6a ) ; an equilateral triangle with 5 m side length and 30 nm depth , fabricated by out - of - plane motions ( see fig . 6b ) ; and a 4.5 m by 4.5 m square pocket with a 100 nm depth ( see fig . shape capability of the nanomilling process : a a circular trench nanomilled using the in - plane configuration , b a triangular trench nanomilled using the out - of - plane configuration , and c a square pocket nanomilled using the in - plane configuration in summary , this letter demonstrated the viability of a nanomanufacturing technique , nanomilling , that uses piezoelectrically induced rotary motions of a nanotool ( afm tip ) to create nano - scale features by mechanical material removal . two configurations of the nanomilling process that use in - plane and out - of - plane elliptical nanotool rotations were described . the components of the nanomilling testbed and the procedure for the nanomilling were then outlined . the material removal in nanomilling was observed to be dominated by shearing the material in the form a ( continuous / curled ) chip . it is shown that the nanomilling process possesses a high level of geometric control , including direct prescription of the feature depth ( due to the high nanotool - stiffness ) , creation of different feature widths in a single pass , and fabrication of shapes with complex geometries . it is concluded that , although further improvements are needed to increase the process efficiency and accuracy , the nanomilling process has a potential to become a controllable nanomanufacturing process for fabricating nano - scale features with complex geometries . it is expected that , when compared to afm scratching , the nanomilling process will yield lower forces , reduced nanotool wear , and improved feature quality . the future work will include an in - depth analysis of the effect of nanomilling parameters on the material removal mechanism , feature quality , and nanotool life . the nanomilling parameters of interest are the nanotool shape , nanomilling orientation , motion shape , frequency , and feed rate . the future work will enable identifying the optimal nanomilling parameters that will yield improved feature quality and minimum tool wear , thereby optimizing the overall throughput of the nanomilling process . this work was supported in part by the national science foundation award cmmi-0602401 ( ozdoganlar ) . this article is distributed under the terms of the creative commons attribution noncommercial license which permits any noncommercial use , distribution , and reproduction in any medium , provided the original author(s ) and source are credited . this article is distributed under the terms of the creative commons attribution noncommercial license which permits any noncommercial use , distribution , and reproduction in any medium , provided the original author(s ) and source are credited .
we present a rotating - tip - based mechanical nanomanufacturing technique , referred to here as nanomilling . 
 an atomic force microscopy ( afm ) probe tip that is rotated at high speeds by out - of - phase motions of the axes of a three - axis piezoelectric actuator is used as the nanotool . by circumventing the high - compliance afm beam and directly attaching the tip onto the piezoelectric actuator 
 , a high - stiffness arrangement is realized . 
 the feeding motions and depth prescription are provided by a nano - positioning stage . 
 it is shown that nanomilling is capable of removing the material in the form of long curled chips , indicating shearing as the dominant material removal mechanism . 
 feature - size and shape control capabilities of the method are demonstrated .