Patent Publication Number: US-7582490-B2

Title: Controlled fabrication of gaps in electrically conducting structures

Description:
This application claims the benefit of U.S. Provisional Application No. 60/444,471, filed Feb. 3, 2003, the entirety of which is hereby incorporated by reference. This application is a continuation-in-part of U.S. Non-provisional application Ser. No. 10/367,075, filed Feb. 14, 2003 now U.S. Pat. No. 7,258,838, which is incorporated by reference in its entirety and which claims the benefit of U.S. Provisional Application No. 60/357,281, filed Feb. 15, 2002, the entirety of which is hereby incorporated by reference. U.S. Non-provisional application Ser. No. 10/367,075 is in turn a continuation-in-part of U.S. non-provisional application Ser. No. 10/186,105, filed Jun. 27, 2002, now issued as U.S. Pat. No. 6,783,643, the entirety of which is hereby incorporated by reference, and which claims the benefit of U.S. Provisional Application No. 60/301,400, filed Jun. 27, 2001, the entirety of which is hereby incorporated by reference. U.S. Non-provisional application Ser. No. 10/186,105 is in turn a continuation-in-part of U.S. Non-provisional application Ser. No. 09/599,137, filed Jun. 22, 2000, now issued as U.S. Pat. No. 6,464,842, the entirety of which is hereby incorporated by reference and which claims the benefit of U.S. Provisional Application No. 60/140,201, filed Jun. 22, 1999, the entirety of which is hereby incorporated by reference. 
     CROSS REFERENCE TO RELATED APPLICATION 
     This application is related to U.S. Non-provisional application Ser. No. 09/602,650, now issued as U.S. Pat. No. 6,627,067, entitled “Molecular and Atomic Scale Evaluation of Biopolymers,” filed Jun. 22, 2000, and hereby incorporated by reference in its entirety. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH 
     This invention was made with Government support under Contract No. F49620-01-1-0467, awarded by DARPA. under Contract No. DMR-0073590, awarded by NSF, and under Contract No. DE-FG02-01ER45922, awarded by DOE. The Government has certain rights in the invention. 
    
    
     BACKGROUND OF THE INVENTION 
     This invention relates to fabrication of solid state structures, and more particularly relates to dimensional control of solid state structural features. 
     Precise dimensional control of solid state structural features is essential for many applications in fields ranging from biology and chemistry to physics, optics, and microelectronics. The term “solid state” is here meant to refer to non-biological materials generally. Frequently the successful fabrication of a solid state system critically depends on an ability to articulate specific structural features, often of miniature dimensions, within very tight tolerances. Accordingly, as solid state systems evolve to the micro-regime and further to the nano-regime, nanometric dimensional feature control is increasingly a primary concern for system feasibility. 
     There have been established a wide range of microfabrication techniques for producing and controlling structural feature dimensions in micromechanical and microelectromechanical systems. For example, high resolution lithographic techniques and high-precision additive and subtractive material processing techniques have been proposed to enable small-scale feature fabrication. But in the fabrication of many nano-regime systems, in which structural feature dimensions of a few nanometers are of importance, it is generally found that conventionally-proposed techniques often cannot form the requisite nano-scale features reproducibly or predictably, and often cannot be controlled on a time scale commensurate with production of such nano-scale features. As a result, volume manufacture of many systems that include nanometric features, such as gaps between nanoelectrodes, and/or nanometric feature dimension tolerances is not practical or economical. 
     SUMMARY OF THE INVENTION 
     The invention provides techniques for enabling precise, repeatable manufacture of features, particularly nano-scale features. For example, the invention provides a method for controlling the gap in an electrically conducting solid state structure. In this method, an electrically conducting solid state structure is provided, including a gap in the structure. The structure is exposed to a fabrication process environment the conditions of which are selected to alter an extent of the gap in the structure. During the exposure of the structure to the process environment, a voltage bias is applied across the gap in the structure. Electron tunneling current across the gap is measured during the process environment exposure of the structure. The process environment is in turn controlled, during process environment exposure of the structure, based on tunneling current measurement. 
     This method enables in situ, real time fabrication process measurement and control. As a result, the method provides a level of precision and repeatability that is required for nanometric feature fabrication, e.g., for nanoelectrode fabrication. 
     In a further technique provided by the invention for fabricating precision electrodes, there is enabled a method for controlling the gap between electrically conducting electrodes. Here at least two electrodes are provided on a support structure. Each electrode has an electrode tip that is separated from other electrode tips by a gap. The electrodes are exposed to a flux of ions causing transport of material of the electrodes to corresponding electrode tips, locally adding material of the electrodes to electrode tips in the gap. 
     With this technique, nanometric electrodes, i.e., nanoelectrodes, having nano-scale electrode gaps, can be reliably fabricated for incorporation in a wide range of electromechanical, and nanometric applications. 
     Other features and advantages of the invention will be apparent from the following description and accompanying figures, and from the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIGS. 1A-1D  are schematic cross-sectional views of fabrication sequence steps for the production of an aperture in accordance with the invention; 
         FIGS. 2A-2G  are schematic cross-sectional views of an example fabrication sequence of steps for the production of the cavity of  FIG. 1A  in a membrane; 
         FIGS. 3A-3B  are schematic diagrams of an ion beam sculpting system configured in accordance with the invention to implement precision feedback control by ion counting; 
         FIG. 3C  is a schematic diagram of an ion beam sculpting system configured in accordance with the invention to implement precision feedback control by tunneling current measurement; 
         FIG. 4A  is an electron micrograph of a cavity formed in a 500 nm-thick silicon nitride membrane in accordance with the invention; 
         FIG. 4B  is an electron micrograph of a 10 nm-wide aperture formed in a silicon nitride membrane by a process provided by the invention; 
         FIG. 4C  is a plot of detected ion counts as a function of time for the aperture etch process that resulted in the aperture shown in  FIG. 4B ; 
         FIG. 5A  is an electron micrograph of a 37 nm-wide aperture formed in a 500 nm-thick silicon nitride membrane in accordance with the invention; 
         FIG. 5B  is an electron micrograph of the aperture of  FIG. 5A  enlarged to 58 nm in width by a process provided by the invention; 
         FIG. 5C  is a plot of detected ion counts as a function of time for the aperture etch process that resulted in the aperture increase from that shown in  FIG. 5A  to that shown in  FIG. 5B ; 
         FIGS. 6A-6C  are schematic cross-sectional views of stages in the reduction of a limiting aperture diameter by a process provided by the invention; 
         FIG. 7A  is an electron micrograph of a 95 nm-wide aperture formed in a 500 nm-thick silicon nitride membrane in accordance with the invention; 
         FIG. 7B  is an electron micrograph of the aperture of  FIG. 5A  reduced to 3 nm in width by a process provided by the invention; 
         FIG. 7C  is a plot of detected ion counts as a function of time for the aperture etch process that resulted in the aperture decrease from that shown in  FIG. 7A  to that shown in  FIG. 7B ; 
         FIG. 8  is a plot of detected ion counts per second as a function of ion sputtering time of a square aperture, initially of about 72 nm×72 nm in area, in a silicon nitride membrane of 500 nm in thickness, subjected to the mass transport processes of the invention under various temperatures; 
         FIGS. 9A-9B  are plots of aperture area as a function of total ion dose for five different ion fluxes and aperture area decrease per dose as a function of ion flux, respectively, for an aperture having an initial area of about 1400 nm 2 , for the material transport processes provided by the invention; 
         FIGS. 10A-10C  are scanning electron micrographs of a trenched silicon nitride layer exposing the underlying silicon wafer on which the layer was deposited, partial fill-in of the silicon nitride trenches as a result of the material transport process conditions provided by the invention, and partial sputter etch removal of the upper trench layer as a result of the sputtering conditions provided by the invention; 
         FIG. 11A  is a plot of counted ions/second traversing an aperture as a function of time for various ion beam exposure cycles; 
         FIG. 11B  is a plot of the area of a hole in a silicon dioxide membrane experimentally measured as a function of argon ion beam fluence, for the indicated duty cycles of pulsed ion beam exposure and for continuous ion beam exposure; 
         FIG. 11C  is a plot of the area of a hole in a silicon nitride membrane experimentally measured as a function of argon ion beam fluence, for the indicated duty cycles of pulsed ion beam exposure and for continuous ion beam, and at a temperature of −100° C.; 
         FIG. 11D  is a plot of the area of a hole in a silicon nitride membrane and a plot of the area of a hole in a silicon dioxide membrane experimentally measured as a function of argon ion beam fluence, as the ion exposure is switched between continuous ion beam exposure and pulsed ion beam exposure having a 50% duty cycle of pulsed ion beam exposure at 10 ms beam “on” and 10 ms beam “off;” 
         FIG. 12  is an atomic force micrograph of a silicon nitride membrane one surface of which was exposed to a focused ion beam to produce apertures and protrusions on the membrane surface opposite that exposed to the ion beam; 
         FIG. 13  is a schematic view of a solid state structure surface undergoing a material transport and ion sculpting process provided by the invention, identifying physical mechanisms corresponding to various terms of an ion sculpting model provided by the invention; 
         FIG. 14A  is a plot of aperture area as a function of total ion dose for four different ion fluxes and for continuous as well as periodic ion flux exposure, for the material transport processes provided by the invention; 
         FIG. 14B  is a plot of the inverse of adatom diffusion distance as a function of incident argon ion flux; 
         FIG. 15  is a plot of experimentally measured current as a function of time produced as negatively charged DNA molecules were drawn through a nanopore experimentally produced in accordance with the invention in a silicon nitride membrane; 
         FIGS. 16A-16G  are perspective views of structures at various stages of formation provided by the invention for producing a solid state nanopore device in accordance with the invention; 
         FIGS. 16H and 16I  are perspective views of structures for producing a solid state nanopore device in accordance with the invention, here being processed to control the gap between nanoelectrodes of the nanopore device; 
         FIG. 16J  is a cross-sectional view of a solid state nanopore device provided in accordance with the present invention with an electrically insulating layer over nanoelectrodes; 
         FIGS. 17A and 17B  are planar views of a structure including a nanopore and corresponding nanoelectrodes prior to and after ion beam sculpting of the nanopore and nanoelectrodes, respectively; 
         FIG. 18A  is an electron micrograph of an experimental silicon nitride membrane including an aluminum strip that has been processed in accordance with the invention to produce nanoelectrodes, the gap between which is has been ion beam sculpted to 12 nm in extent; 
         FIG. 18B  is a plot of experimentally measured tunneling current as a function of bias voltage between two nanoelectrodes for three different interelectrode gaps; 
         FIG. 18C  is a plot of experimentally measured tunneling current as a function of bias voltage between two nanoelectrodes during ion beam sculpting of the gap between the electrodes for seven different ion beam doses; 
         FIG. 19  is a schematic diagram of passage of ionic current and a polymer through a solid state nanopore provided by the invention; 
         FIG. 20  is a plot of experimentally measured ionic current as a function of applied voltage during the passage of DNA molecules through a solid state nanopore provided by the invention; 
         FIG. 21  is a schematic diagram of an electron tunneling event across a nanopore of the invention through water and a DNA molecule; and 
         FIG. 22  is a plot of experimentally measured tunneling current between nanoelectrodes of a solid state nanopore device of the invention as different nucleotide bases of a single-strand DNA molecule pass through a nanopore provided with the nanoelectrodes. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The processes for dimensional feature control provided by the invention can be directed to a wide range of materials and structural configurations. The example processes here described are meant to be illustrative but not to represent specific limitations in materials or configurations. The processes of the invention are particularly well-suited for precisely controlling structural feature dimensions, and for enabling such control on the scale of nanometers. This control can be especially advantageous for the precise formation and definition of nanometric-sized features and spaces, such as gaps existing as an aperture, e.g., pores, slits, orifices, vents, and holes, as well as trenches, channels, troughs, and in general, the spacing between two or more distinct feature edges. 
     Referring to  FIG. 1 , in one example implementation of a method provided by the invention for precisely and reproducibly defining the spacing of features, there is carried out a process for forming an aperture of a prespecified extent, e.g., diameter, in a structural layer. In a first process step, referring to  FIG. 1A , a starting structure  10  is provided, shown in cross-section in the figure. Such starting structure  10  can be supplied as, e.g., a substrate, a thick or thin layer provided on a support such as a substrate, a membrane, or suitable structure. A cavity  12  is formed in the structure  10  on a selected surface  14  of the structure and in a region at which an aperture is desired. 
     The cavity  12  extends into the bulk of the structure  10  for only a fraction of the structure&#39;s thickness, rather than through the entire thickness of the structure, to an opposing surface  18 . As a result, the deepest level, i.e., the bottom  16 , of the formed cavity lies at some midpoint in the structure&#39;s bulk. As explained in more detail below, the geometry of the cavity bottom  16  and the cavity sidewalls  20  are preferably selected to enable controlled formation of a limiting aperture of controlled transverse and longitudinal dimensions in later processing steps. In the example illustrated, a bowl-shaped cavity is employed. 
     Referring to  FIGS. 1B and 1C , once the cavity is produced, the structure is progressively thinned from the cavity-free surface  18 . As the thinning is continued, a portion  22  of the structure is increasingly removed, shown by dotted lines. This causes the cavity-free surface  18  of the structure to advance toward the bottom  16  of the cavity. 
     Continued thinning of the structure results in the intersection of the cavity-free surface  18  with the bottom  16  of the cavity, as shown in  FIG. 1D . When this intersection occurs, a limiting aperture  24  is formed which transforms the cavity  12  to an aperture extending through the thickness of the structure. Further thinning of the structure causes the cavity-free surface  18  to intersect upper sidewall locations of the cavity, whereby the limiting aperture  24  takes on that profile of the sidewalls which exists at a given cavity intersection depth. In the example illustrated, the diameter of the limiting aperture  24  increases as thinning is continued, given the bowl shape of the cavity. It is to be recognized, however, that the diameter of the limiting aperture can be made to decrease as thinning is continued, for a corresponding cavity sidewall profile. In addition, asperities or other distinct profile features or geometry can be provided along the cavity sidewalls for controlling limiting aperture geometry. 
     This aperture forming process provides distinct advantages in that it does not rely on direct lithographic techniques for defining final limiting aperture and wall dimensions. As a result, the aperture forming process is not constrained by lithographic resolution limits. The process enables production of a limiting aperture dimension or diameter as small as 1-2 nanometers or less without the need for exotic or expensive processing apparatus. 
     As explained above, this aperture formation process can be carried out on any of a wide range of structures, such as substrates, layers, and films provided on a supporting structure or free-standing as, e.g., membranes. Solid state materials in general can be employed as the structural material in which an aperture is formed; microelectronic or semiconductor materials can be particularly effective in enabling efficient processing techniques, as described below. For example, the broad classes of inorganic and organic glassy materials, such as oxides, glasses, plastics, polymers, and organic films, e.g., PMMA, as well as crystalline materials, such as semiconductors, e.g., silicon and silicon nitride, and metals, as well as other materials can be employed. The invention is not limited to a particular structural material or class of structural materials. Preferably, the structural material is selected to meet the criteria of the application specified for the aperture. 
     The method is particularly well-suited for enabling formation of apertures in membranes, and for providing the nano-regime control of aperture formation that is required for many membrane applications. In the formation of a membrane aperture, microelectronic and semiconductor materials and fabrication processes can be advantageously exploited in accordance with the invention to enable cost-effective and efficient manufacturability. 
     Referring to  FIG. 2 , in an example microfabrication process provided by the invention for forming an aperture in a membrane, a starting substrate  30 , e.g., a silicon wafer, is provided, as shown in  FIG. 2A . A selected membrane material, e.g., silicon nitride, is provided as a coating layer  32 ,  34  on the upper and lower surfaces, respectively, of the wafer. The thickness of the coating layer  34  is that thickness selected for the membrane to be formed. In one example, a silicon-rich, low-stress, silicon nitride layer of about 50 nm in thickness is deposited on the silicon wafer by conventional chemical vapor deposition (CVD) processing. It is recognized that additional membrane materials, e.g., silicon dioxide, can be deposited before or after deposition of the silicon nitride layers for mechanical stress control or other consideration. The silicon nitride layer can also be further processed, e.g., by ion implantation, to control mechanical membrane stress or adjust electrical or thermal conductivity of the membrane as desired for a given application. 
     As shown in  FIG. 2B , a layer of photoresist  40  is formed on one of the deposited nitride layers and patterned to define a nitride etch window  38 . The opposing surface of the wafer is blanket coated with a photoresist layer  40 . Then, as shown in  FIG. 2C , the silicon nitride exposed by the nitride etch window  38  is removed by, e.g., conventional reactive ion etching techniques. This exposes a substrate etch window  42 . The opposing nitride layer  34  is protected from this etch by the blanket photoresist layer  40 , which is removed at the etch completion. 
     Next, referring to  FIG. 2D , the silicon wafer is bulk micromachined by a suitable etch procedure, e.g., a conventional anisotropic wet etch process employing KOH. Preferably, the bulk wafer etch process employed is characterized by a high selectivity to the wafer material over the membrane material. In the example illustrated, the KOH etch substantially does not attack the silicon nitride layers. Continuation of the etch through the thickness of the wafer thereby produces a self-supporting nitride membrane  36  in a nitride layer  34 . The nitride membrane forms the bottom of a pyramidal well  39  etched out of the silicon wafer due to the anisotropic, crystallographic-specific nature of the KOH etch. The extent of the nitride membrane is thus determined by the thickness and crystallographic orientation of the starting silicon wafer. As will be recognized, the membrane dimensions can therefore be controlled as-desired. 
     Referring to  FIGS. 2D-2E , the remaining layer  32  of silicon nitride opposite the membrane layer can then removed if desired by, e.g., conventional reactive ion etching, and then a layer of silicon dioxide  41  is optionally grown on the exposed silicon surfaces, if electrical insulation of the silicon wafer is desired for a given application. Conventional wet or thermal oxide growth can be preferred over a CVD oxide layer such that oxide is only formed on the silicon surfaces in the manner illustrated. If, however, a composite membrane is desired, e.g., for mechanical stress control, then a CVD or other deposition process can be employed to produce an oxide layer on both the silicon wafer and the lower silicon nitride membrane surfaces, or on the nitride membrane surface alone. 
     In a next step of the process, referring to  FIG. 2F  and referring back to  FIG. 1A , a cavity is formed in a selected surface of the membrane. In one example cavity formation process, an etching process, as illustrated, a layer of resist  42  is formed on the lower membrane surface, i.e., the membrane surface opposite that in the pyramidal wafer well. The resist is then patterned to define the cavity to be formed in the membrane. This choice of surface for the cavity can be preferable for enabling a selected lithography technique on a flat surface; it can be difficult to effectively pattern a layer of photoresist provided on the membrane surface at the bottom of the silicon pyramidal well. If desired for a given application, however, the cavity can be formed on such a surface with lithographic techniques specific to such a configuration. The invention contemplates the use of photolithography, electron beam lithography, and other suitable lithographic processes for defining the cavity pattern. It is to be recognized that the selected lithographic process is preferably suited to the dimensions of the cavity; e.g., electron beam lithography can be preferred over conventional photolithography for cavities having submicron dimensions. 
     As explained above, the sidewall profile of the cavity to be formed in the membrane can be specified to produce a selected limiting aperture geometry. The lithographic step defining the cavity, as well as the nature of the cavity etch process itself, can also be employed to define the cavity sidewall profile. In one example scenario, the selected lithographic cavity pattern is continuous, e.g., as a circle, and a relatively isotropic etch process, e.g., an isotropic reactive ion etch process, is carried out to form a bowl-shaped cavity  12  in the nitride membrane  36 , as shown in  FIG. 2G . An isotropic reactive ion etch process inherently forms the bowl shape extending from a circular photolithographic pattern. 
     The invention contemplates the use of substantially any cavity pattern for achieving a desired cavity geometry. Square, rectangle, hexagonal, or other pattern, symmetric or asymmetric, can be employed. Due to the batch nature of lithographic processes and other microfabrication processes employed in the aperture forming method, arrays of cavities, of varying extent and geometry, can be defined in a single structure such as the membrane illustrated. Because the aperture formation process of the invention relies on structural thinning, rather than lithography, to define the final limiting aperture geometry, the largest lateral dimension of the cavity can be much greater than the desired limiting aperture extent; in general, the largest cavity pattern dimension can be two or more orders of magnitude larger than a selected limiting aperture diameter. Preferably, given the characteristics of a selected cavity etch process, the cavity pattern extent is correspondingly selected to produce a desired extent at the cavity bottom, and to produce a range of cavity expanses between the cavity bottom and the material surface. 
     Any suitable cavity etch process can be employed, including, e.g., plasma etching, focused reactive ion etching, focused ion beam etching, wet chemical etching, or other selected technique. Whatever etch process is selected, it is to be controlled to enable termination of the etch at a cavity bottom located at some distance within the membrane thickness or other structure in which the cavity is formed, i.e., at a point between the surfaces of the structure. For etch processes that are fully characterized for the structural material being employed, this can be accomplished by a timed etch; conventional diagnostic techniques otherwise can be employed in the conventional manner to produce a cavity bottom at a selected location in a membrane other structure. It is not required in accordance with the invention to precisely position the cavity bottom at a known, a priori depth in the structure. The progressive structural thinning process of the invention is particularly advantageous in this regard; no precise control or knowledge of the depth of the cavity is required to precisely produce an aperture. In addition, a combination of etch processes can be employed as-necessary for cavity formation in a given material or composite of materials. For example, where a composite membrane is formed of silicon nitride and silicon dioxide layers, the chemistry of a selected cavity etch, such as a plasma etch, can be adjusted over the course of the etch based on the material to be etched at a given time in formation of the cavity. Similarly, a combination of etch processes can be employed to alter the cavity sidewall profile as a function of cavity depth. For example, a combination of isotropic and anisotropic wet etches can be employed to produce selected curvature and slant of cavity sidewalls formed in a nitride or silicon layer or membrane. A combination etch such as this enables the formation of asperities or other distinct features to be located at the limiting aperture. 
     Referring back to  FIGS. 1B-1D , once a cavity has been formed in the selected membrane or other structure, thinning of the structure is then carried out on the structure surface opposite that in which the cavity was formed, employing an appropriate procedure to open a limiting aperture in the structure. The invention contemplates a wide range of thinning processes and is not limited to a particular thinning technique; all that is required is the ability to etch back the structure from a surface opposing that in which the cavity was formed. 
     For many applications, a particularly well-suited thinning process is ion beam sputtering. In such a process, a beam of ions is directed to the structure surface to be thinned to sputter etch away material from that surface. In typical ion beam sputtering processes at relatively low beam energies, e.g., in the range of keV, for every incident ion, on average, a single atom of material is ejected from the sputtering target; sputtering may thus be considered as an atomic-scale version of “sand blasting.” In the case of, e.g., a silicon nitride membrane, such sputter etching results in the removal of about one atomic layer of silicon nitride from the membrane per second for incident ion fluxes between about 10 14 -10 15  ions/cm 2 /sec. When the surface exposed to the sputtering beam has been sufficiently thinned that the surface intersects with the cavity bottom, a limiting aperture is formed. 
     The invention contemplates a wide range of additional thinning processes, including ion beam assisted etching, ion beam induced etching, electron beam etching or assisted etching, plasma and reactive ion etching, wet etching such as electrochemical etching, chemomechanical polishing, and other fabrication and manufacturing processes that enable controlled thinning of a structure to intersect a cavity on a surface opposite that being thinned. These aperture formation processes can be advantageous for many applications because during the thinning etch, the etch species, e.g., a sputtering ion beam or reactive plasma environment, need not be focused on a particular location of the structure surface being thinned. A blanket exposure of the structure surface can be employed to thin the entire extent of the structure. All that is required is that the structure surface including the cavity be isolated, i.e., shielded, from the etch species attacking the opposing surface. This results in nano-regime precision in feature formation without the requirement of nano-regime control of the etch apparatus and species. 
     Whatever thinning process is selected, the inventors herein have discovered that highly precise aperture formation can be accomplished by implementing a feedback mechanism during the thinning process. This feedback mechanism is based on detection of a physical species provided during the thinning etch in a manner that is indicative of the physical dimensions of a feature, e.g., an aperture, that is being produced by the etch. Such feedback enables real time control of the aperture formation process, whereby a precise and prespecified aperture diameter can be reliably and reproducibly formed. As explained later in the description, this feedback mechanism can in general enable precise sculpting of nanometric features and nanostructures, and finds wide application for micro- and nano-systems. 
     Considering feedback control in the aperture formation process of the invention more specifically, when an etch species, such as a beam of sputtering ions, thins a structure to the point that an aperture is formed, ions from the beam are at that point in time enabled to pass through the aperture. Thereafter, the number of ions passing through the aperture per unit time is proportionally related to the increasing diameter of the aperture as the thinning etch continues. Detection and quantification, e.g., by counting, of the rate and/or number of ions passing through the aperture thereby is indicative of the aperture diameter at any given time during the etch. 
     As a result, a selected aperture diameter can be prespecified based on a rate and/or number of ions expected to pass through the aperture before the selected diameter is produced. During a thinning etch process, a first passage of ions through a newly-formed limiting aperture can be detected, and the number of ions passing through the aperture as its limiting aperture dimension enlarges can be individually detected and quantified. When the prescribed number of ions pass through the aperture, a controlling signal can be sent to the sputtering ion beam controller to terminate the etch process at the desired aperture dimension. In addition, it is recognized in accordance with the invention that detection of a physical species can be carried even prior to the time at which an aperture is formed. For example, the level of X-rays produced by the ion beam gun that are detected as passing through the structure being thinned can be expected to increase as the thickness of the structure decreases. Detection of ions similarly can be made even prior to aperture opening. This enables control of the process even prior to the final opening of the aperture. 
     Referring to  FIGS. 3A-3B  there is schematically shown a system  50  for implementing this feedback-controlled sputtering process. The system includes an ion gun  52 , e.g., an ion gun capable of producing an ion beam with an energy range and diameter suitable for a given application. In general, an energy between about 0.05 eV and about several hundred KeV and a beam diameter between about a few nanometers to spatially very broad beams can be employed. A vacuum etch chamber  55  is provided in which the etch process can be carried out. Preferably, the etch chamber pressure is well-controlled such that etch environment pressures of less than about 10 −8  Torr can be maintained during the etch process. In addition, it can be preferred to employ a load-lock sample entry system that is vented with, e.g., dry nitrogen, to minimize exposure of the etch chamber to contaminants. A turbomolecular pump  57  is provided for pressure control and maintenance. Optionally, a mass spectrometer can be provided for monitor and analysis of the etch environment species. 
     A structure holder  54  is provided for supporting a structure  10  in which an aperture is to be formed, e.g., employing clips to maintain the position of the structure. Preferably, the holder  54  is thermally conductive and provides structure temperature control, e.g., by a liquid heat exchange loop, employing a thermocouple positioned on the holder or on the structure itself. For many applications, it can be preferable that the holder also be electrically conductive to enable voltage charge control of the structure and to enable monitor of incident ion beam current. It further can be preferable to provide a liquid-nitrogen-cooled copper shroud surrounding the sample holder, as well as the focusing optics, described below, to condense contaminants and to improve the local vacuum near the sample. 
     The holder includes a central aperture  56  corresponding to the location at which an aperture is to be formed in the structure  10 . With this configuration, a beam of ions  58  directed from the ion gun toward the structure  10  thins the structure to form therein an aperture, after which time the ion beam  58  traverses both the structure aperture and the holder aperture. 
     Referring to  FIG. 3B , an electron flood gun  59  can be included in the arrangement to direct a beam of electrons at the structure being etched during the etch process. For structures such as a silicon nitride membrane that are electrically insulating, positive electrical surface charge can accumulate on the structure due to positively-charged ion beam irradiation. Electron beam irradiation of the structure can be carried out to neutralize this surface charge, if necessary for a given application. 
     If the thinning etch process is to be controlled by a feedback mechanism in accordance with the invention, then the stream of a species traversing the etched aperture is to be detected and quantified in the manner described below. If no such feedback control is desired for a given application, then no additional apparatus is necessary, and the sputtering can be carried out in a conventional sputtering chamber under conditions selected for a given etch. 
     In accordance with the invention, species detection and quantification systems can be included to provide a desired degree of feedback control. Given a scenario where the selected sputtering beam ions employed for the thinning etch are electrically charged, ion focusing optics  60  can be provided for focusing the ions once they traverse the aperture, to facilitate ion detection by a detector that is relatively distant from the structure aperture through which the ions traversed. X-Y deflection optics and Einzel lenses can be employed in conventional configurations to produce a desired focusing of the ions. In the conventional manner, optics design software can be employed to produce a customized focusing configuration for a given detection arrangement. It is to be recognized that such focusing configuration may not be required for configurations where the ion detection system is relatively near to the holder aperture. If focusing optics are employed, it can be preferred to mount such, e.g., behind a stainless steel plate supported by an upper flange of the etch chamber  55 , to provide mechanical stability to the optics as well as shield the ion detector, described below, from stray ions from the ion gun. 
     If employed, the focusing configuration preferably directs the output ion beam to an ion energy analyzer  62  for filtering the beam for the selected species to be detected and quantified by, e.g., counting. In general, it can be expected that the ion beam sputtering process will include and produce a wide range of physical species and radiation, including, e.g., sputtered silicon nitride atoms, etch species scattering in the etch chamber, and X-rays emanating from the ion gun. To enable highly precise etch control, the species to be detected is preferably filtered out from the produced radiation, produced etch species, and background radiation. Such background can be minimized by, e.g., isolating the ion beam gun, the structure to be etched, and the downstream optics from further downstream components such as detectors, as described below, by an electrostatic energy filter or other suitable filter. In addition, it can be preferable to maintain the ion beam gun, structure, and optics at reduced temperature conditions in a suitable vessel, as shown in  FIG. 3B , whereby thermal effects can be controlled. Such a cooling configuration is also useful to maximize cleanliness of the etch and beam detection environment and to control structure temperature. It can also be advantageous to maintain the structure at an elevated temperature to influence materials modification phenomena during ion irradiation. 
     The employment of an ion energy analyzer  62  or other species-specific filtering system is advantageous in that it enables redirection of a species to be detected out of the line of sight of the sputtering trajectory. The species detection location can then be distant and out of line from bombardment by background and produced radiation such as X-rays. For example, as shown in  FIGS. 3A-3B , the electrostatic energy analyzer employed produces a 60°-90° bend in the trajectory of the ion species to be detected, whereby that species is separated from the other species and radiation coming from the etched structure. If the detection resolution and speed desired for a given etch process do not require a low background noise environment, then the ion energy analyzer is not required for many applications. 
     The filtered species of interest output from the electrostatic energy analyzer is directed to a detector  64 . For the detection of an electrically charged ion species, it can be preferable to employ a high-resolution, single ion detector, e.g., a Channeltron 4860 detector from Gallileo Electro-Optics of Sturbridge, Mass. Such a detector can be configured to produce one electrical output pulse per detected ion. Such single ion detection and associated counting can be preferred for many applications to enable nanometric-scale precision in production of a solid state feature such as an aperture. While a typical sputtering beam current density is about 10 ions/nm 2 /sec, etching of a nanometer-range aperture requires counting of the passage of no more than about 10-20 ions through the aperture. Thus, a single ion detection and counting system, or another system of equivalent resolution, is preferred to reproducibly implement nano-regime control of feature production. If the features to be produced for a given application do not require nanometric dimensional control, then a more coarse detection mechanism can be employed. It can be preferred for many applications to shield the ion energy analyzer and detector from potential electrical noise sources by encasing such in, e.g., an aluminum can that includes an aperture through which the beam can enter. In this scenario, the ion beam is preferably aligned with a sample to be processed and the encased detector, by adjusting beam focus voltages so as to maximize the transmitted ion count rate through a control sample containing a hole. 
     Given a single ion detector configuration, a fast pulse amplifier  66  can be employed to modify the electrical output of the detector to facilitate an ion counting process. A suitable pulse preamplifier can be constructed in a conventional manner or a suitable commercial system, e.g., the VT120 Fast Preamp from EG&amp;G Ortec of Oak Ridge, Tenn., can be employed. In one example scenario, given the production of a 10 mV ion detection pulse by the ion detector, the pulse amplifier  66  can be configured to amplify the pulse voltage to about 1 V. This amplified detection pulse is directed to a counting system, e.g., a universal counter such as the HF53131A by Hewlett Packard, for producing an electrical signal indicative of the number of detected ions. It is recognized that detection pulse amplification may not be required for a given pulse counter configuration, and that the pulse amplification, if implemented, is preferably controlled based on requirements of the counting system. 
     The electrical output of the pulse counter  68  is directed to a controller  70  that implements, e.g., monitor and control software for enabling an operator to monitor the thinning etch process in real time and for producing an ion gun control signal. In one example, the controller is implemented in software employing, e.g., Labview, from National Instruments, of Austin Tex. Whatever controller implementation is selected, it preferably provides ion beam control signals based on the ion feedback. For example, the controller can be implemented to initiate ion beam sputtering of the structure for a specified time interval and to configure the counter to count the number of ions received at the detector during the specified time interval. At the end of the interval, the number of ions counted is determined by the controller and the extent of the aperture can at that point be calculated based on this ion count and the known ion flux. The number of ions counted during the interval is then employed by the controller to determine if a further interval of ion beam sputtering is to be initiated to continue etch of the structure. 
     In one advantageous configuration, a computer system including monitor, memory, and associated input/output and printing systems is provided for enabling visual monitoring and recording of the etch process progression. Display of the ion count rate and aperture extent over time, and storage of count rate and other system values can be preferable for many applications. 
     The output of the controller  70  is directed to an ion gun control system  72  for controlling the sputtering etch itself. In one example implementation, ion gun feedback control is effected by control of the ion gun&#39;s X-Y deflection plates to deflect the ion beam away from the structure  10  at the time when the desired aperture dimension is produced. This can be a preferable control technique because of the rapid speed at which the beam can be deflected, typically in much less than a millisecond. It is recognized, however, that alternative beam control mechanisms can be employed. For example, an electrostatic grid can be located between the gun and the structure holder. In this scenario, the grid is energized in response to an ion beam termination control signal to return the beam back toward the ion gun. In a further technique, the accelerating electron impact voltage of the ion gun can be controlled in response to an ion beam termination control signal to terminate production of the ion beam. These techniques are advantageous in that they suppress all sputtering after the desired aperture dimension is produced, whereby possible contamination of the sample is eliminated. 
     With a sputtering system and feedback/control hardware configuration in place, a feedback calibration curve can be produced for a given ion beam species, structure material, and aperture geometry to be produced. Such a calibration curve enables specification of the relationship between ion count number and/or rate and limiting aperture dimension, and can be established empirically, to specify for a particular structural material and thickness a relation between number of measured counts per time and actual limiting aperture dimension. 
     It is found that for many configurations, the relationship between limiting aperture dimension and ion count is generally linear. For this and other generally-predictable relationships, an extrapolated calibration curve can be produced based on a few measurements. To produce each such measurement, a thinning etch is carried out for a prescribed duration, during which an ion count is made and at the end of which an aperture dimension is physically measured by, e.g., transmission electron microscopy. Multiple etch durations and dimensional measurements can be carried out on a single aperture as that aperture is increased from etch to etch. A calibration curve can then be produced based on the ion count and aperture measurements and extrapolated to lower and higher ion counts. With such a calibration curve in hand, the controller system of the feedback configuration can be programmed to direct a controlling etch termination signal to the ion gun when the prescribed ion count corresponding to a desired aperture dimension is reached. 
     It is to be recognized that etch environment temperature and pressure, mechanical stress and temperature of the structure being etched, and feature dimensions and structural aspects can influence the relationship between detected ion count rate and physical feature dimensions. For example, the residual mechanical stress in a silicon nitride membrane can impact its etch characteristics. Similarly, the density of apertures in an array to be formed, the aperture proximity to each other, and other aspects can impact etch characteristics. It is therefore to be recognized that the calibration curve preferably is produced with consideration for various physical and etch environment parameters that can impact etch characteristics. 
     EXAMPLE 1 
     A 50 nm-thick silicon nitride membrane having a cavity formed on one surface was produced by the process outlined in  FIGS. 2A-G . The silicon nitride was deposited by low pressure chemical vapor deposition. The cavity bowl was etched in the membrane by a reactive ion etch process.  FIG. 4A  is an electron micrograph of the cavity formed in the membrane. 
     The membrane surface opposite that including the cavity was exposed to an argon ion beam etch at an energy of about 3 KeV, and a flux of about 3 Ar + sec/nm 2 . The ion beam diameter was about 200 μm and the membrane temperature during the etch was maintained at about −120° C. The ion beam was directed toward the membrane for 1 sec during each 5 sec interval. During the etch process, ion detection and counting was carried out. 
       FIG. 4B  is an electron micrograph of the membrane cavity including a 10 nm limiting aperture formed by thinning of the membrane.  FIG. 4C  is a plot of argon ion count/second as a function of sputtering time. This plot includes that time when the ion beam was directed to the membrane, not when the beam was deflected away from the membrane. As indicated by the plot, the number of counted ions/sec was substantially zero until at point in time, at 25 sec, when the limiting aperture was opened. Then as the limiting aperture diameter increased, the ion counts correspondingly increased. This enables control of the aperture formation process. 
     In this example, precise and controlled etch of the aperture was enabled by detection and counting of electrically charged ions that traversed the aperture once it was opened. Here the species operating as an etchant also operated as the species to be detected. In accordance with the invention, this dual role of the ion beam is not in general required. In an alternative scenario provided by the invention, the etchant species is selected and operates distinctly from the detection species. For many applications, such a decoupling of the etchant and detection species can be advantageous in enabling a broader range of candidate species for both etchant and detection species. 
     Considering an atom beam etch species, if the beam is electrically neutral rather than electrically charged, detection of the atoms can be difficult. A distinct non-etching detection species such as an electron beam can in this case advantageously be employed for controlling formation of a prespecified aperture diameter. Such a scenario can be preferable where the structure being etched may become electrically charged by the impinging sputter beam, thereby warranting the use of an electrically neutral beam. For many applications, it can be preferable to employ an electrically charged detection species, for facilitating beam bending, filtering, and detection and counting with conventional techniques. Electrically neutral detection species can be employed, however, when such is optimal for a given application. For example, laser fluorescence of electrically neutral transmitted atoms can be employed for detecting and counting control functions. 
     When employed, a separate detection species is preferably one that can be directed in some manner toward a feature being produced and whose movement in the vicinity of the feature is indicative of changing dimensions of the feature. This enables detection of the species in a manner that is indicative of changes in the feature&#39;s dimensions. For example, in the case of formation of a membrane aperture, direction of an electron beam toward the membrane, such that electrons traverse the membrane aperture once it is formed, enables counting of electrons in the manner of ion counting described above. The invention does not require the use of a single detection species; more than one detection species can be employed. For example, X-rays produced by the ion gun can be monitored as the structure thins to predict and indicate a the time of a further aperture formation event. Thereafter, ions, electrons, or other species can be employed to monitor changes in aperture diameter. Neutral species and other species suited to a given application can similarly be employed together to provide precise detection and feedback mechanisms. 
     In addition, the invention does not require that the detection species be directed orthogonally to the plane of a feature being produced. For example, electron beam diffraction detection and the diffraction patterns produced by a material can be employed as a feedback mechanism. In such a case, e.g., where a feature in an upper layer is formed by removal of the upper layer to expose a lower layer or substrate, detection of the electron beam diffraction pattern characteristic of the lower layer can be employed as the feedback mechanism. Here the electron beam makes a glancing angle with the material. Similarly, in the case of formation of, e.g., an aperture, diffraction can be detected as a function of the aperture diameter by diffraction rings indicative of changes in aperture periphery. The diffraction feedback mechanism here occurs at the aperture periphery rather than as a trajectory through the aperture. 
     In a further example, an electron beam can be directed parallel to the upper structure surface being thinned in formation of an aperture, whereby the withdrawal of surface material is indicated by an increase in electron count in a direction parallel to that surface. 
     The invention contemplates alternative detection species. For example, atoms in a meta-stable state, e.g., an electronic meta-stable state, can be directed toward a feature being formed and detected once past the feature. Such meta-stable atoms, e.g., excited states of helium or argon, are electrically neutral and do not decay until hitting a solid surface, at which time an electron is liberated and can be detected and counted. Whatever detection species is selected, it preferably is one that can be detected and counted on a time scale that is commensurate with the desired dimensional scale of control in the feature being produced. For example, where nanometric feature dimensions are of importance, microsecond detection and counting processes are preferable to enable high sensitivity and resolution in the feedback mechanism. Less strict sensitivity and resolution requirements need be placed on detection species for micro- and macro-scale feature control. 
     The invention contemplates application of physical species detection and counting for feedback control in a wide range of fabrication processes. Many fabrication processes that are conventionally carried out in open loop fashion, i.e., without feedback control, can be adapted to enable nanoscale dimensional feature control with the incorporation of the highly sensitive and precise feedback mechanisms provided by the invention. For example, in the aperture formation process described above, reactive ion etching in a plasma, rather than sputter etching, can be employed to thin a structure surface in formation of a limiting aperture. In such a plasma etch process, the structure surface including a cavity is isolated from the plasma environment by a suitable fixture. The opposing structure surface is fully exposed to the plasma environment. As the plasma etch progresses to thin the structure and eventually produce a limiting aperture and growing aperture, ions traversing the aperture are detected by, e.g., a channeltron positioned on the isolated side of the structure. Accordingly, in the manner of the ion sputtering etch described above, feedback control can be imposed on the plasma etch process based on the detection and counting of plasma ions traversing the aperture. 
     In a further example process contemplated by the invention, physical detection and feedback control can be imposed on a wet etch process employed to produce a feature. For example, in formation of an aperture in a structure, electrodes can be provided near to the cavity formed in the structure. Here the structure surface opposite the cavity is exposed to a wet etch environment, e.g., an electrochemical environment, and the structural surface which includes the cavity is isolated from the etch environment. As the wet etch progresses to thin the structure and open an aperture, ions in the liquid that traverses the aperture can be detected and counted at the cavity-side electrodes. This enables feedback control for terminating the electrical stimulus of the etch at a time when the desired aperture dimension is attained. 
     The invention contemplates implementation of physical species detection and feedback process control for enabling fabrication of a wide range of structural, solid state features. The feedback mechanism is not limited to the aperture formation process described above. As explained above, an aperture, slit, trench, hole, or gap between two feature edges can be precisely formed, by any of a wide range of processes, in a precise and controllable manner with the feedback mechanisms of the invention. 
     For example, in a membrane aperture formation process employing, e.g., focused ion beam or plasma etching techniques where a hole is formed directly through the thickness of the membrane from one surface to the other of the membrane, feedback can be employed to control and monitor the formation. Similarly, the invention contemplates a membrane aperture formation process where a cavity is formed in one surface of the membrane and then that membrane surface, including the cavity, is exposed to, e.g., an ion sputtering etch. Because the thickness of the membrane between the cavity bottom and the opposing surface is much less than at other membrane regions, such etching opens a limiting aperture at the base of the cavity before completely etching away other regions of the membrane. The feedback mechanisms of the invention enable precise control and monitoring of this process. 
     EXAMPLE 2 
     A silicon nitride membrane of about 50 nm in thickness was produced in the manner of  FIGS. 2A-2E . An aperture was formed through the entire thickness of the membrane by reactive ion etch. This resulted in a 37 nm-wide aperture, an electron micrograph of which is shown in  FIG. 5A . The membrane and aperture were then exposed to an argon ion beam at a flux of about 1.7 Ar + /nm 2 /sec and an energy of about 3 KeV. The ion beam was directed toward and away from the membrane to sputter for 1 second during each 5 second interval. The membrane was maintained at a temperature of about −102° C. during the ion beam exposure. 
       FIG. 5B  is an electron micrograph of the 58 nm-wide aperture that resulted from 180 seconds of sputtering.  FIG. 5C  is a plot of counted ions/sec as a function of time. A generally linear relationship between ion counts as a function of time is demonstrated. 
     The invention does not require that the process being controlled by feedback be a subtractive process as in Example 2; additive processes can also be controlled by the feedback techniques of the invention. For example, an aperture, trench, or hole of a given dimension can be diminished or narrowed, by a suitable process, during which the physical species detection and feedback process control of the invention is imposed to control the diminishing process. 
     Sintering, heating, material deposition, material growth, and other suitable processes are contemplated as being controllable by the feedback mechanism of the invention. Similarly, oxidation, swelling, material flow and transport as described in detail below, condensation, evaporation, electroplating, ion- or electron-assisted deposition or growth, and other such additive processes can be controlled in accordance with the invention. The only requirement of the process to be controlled, whether additive or subtractive, is that the process accommodate the introduction of some detection species near to the structural feature being processed in a manner that enables detection of that species as an indicator of changing feature dimensions. As explained above, the features can be produced in a membrane, in a layer or layers provided on a support structure, or in a structure itself, e.g., a silicon wafer. Whether the process being controlled is additive or subtractive in nature, the advantages of the control processes of the invention can be most fully exploited and realized in the formation of nanometric scale feature dimensions and dimensional tolerances. 
     This capability can be particularly advantageous for producing a field of nanometric features, e.g., in formation of a lithographic mask plate. Here, e.g., a starting membrane can be processed with selected geometries to ultimately form wires, pads, and other mask plate geometries by additive or subtractive processes. This enables precise formation of the mask plate features in an efficient and effective process. 
     Referring now to  FIG. 3C , the invention provides an additional process control feedback technique and corresponding apparatus for controlling fabrication processes in real time based on a feedback parameter indicative of the process results. In this feedback technique, a bias voltage is applied across the gap of an electrically conducting feature or features being modified by a fabrication process, as the process proceeds, and the electron tunneling current across the gap that results from the applied voltage bias is monitored as the process proceeds. The monitored electron tunneling current enables a very high resolution, real time measurement of changes in the gap dimensions because the gap extent is directly related to the tunneling current for a given applied voltage bias. 
     In accordance with the invention, a measurement of tunneling current is related to a corresponding gap dimension based on the tunneling regime at which the gap is biased. A first of two tunneling regimes considered in accordance with the invention, the Fowler-Nordheim tunneling regime, is characterized by relatively large gaps, i.e., gap extents greater than about 1-2 nm, and applied voltage biases that are greater than the work function of the material in which the gap exists. 
     The Fowler-Nordheim expression relates a measured tunneling current, I, to an applied voltage bias, V, across a gap, g, as: 
                       I   ⁡     (   V   )       =       aV   2     ⁢     ⅇ       -   b     /   V       ⁢           ⁢   where       ⁢     
     ⁢     a   =         σⅇ   3       16   ⁢     π   2     ⁢     ϕℏg   2         ⁢             ⁢             ⁢   and       ⁢             ⁢             ⁢     
     ⁢     b   =       4   ⁢       (     2   ⁢     m   e       )       1   /   2       ⁢     ϕ     3   /   2       ⁢   g       3   ⁢   ℏ   ⁢           ⁢   ⅇ                 (     1   ⁢   a     )               
where σ is the area of the material at opposite sides of the gap, e is the elementary charge, 1.6×10 −19  C; ℏ=1.1×10 −34  J·s; m e =9.1×10 −31  Kg; φ is the work function of the material at the location of the gap; and g is the gap spacing. With this expression, once the area of the material at the location of the gap and the work function of that material are known, then for a given voltage bias across the gap and a given tunneling current measurement, the corresponding gap can be known.
 
     The second tunneling regime to be considered for correlating measured tunneling current with gap dimension corresponds to relatively smaller gap extents, i.e., less than about 1-2 nm, and applied voltage biases less than the work function characteristic of the material in which a gap is provided. In this regime of tunneling, the tunneling current I, is given as a function of applied voltage bias, V, as: 
                       I   ⁡     (   V   )       =       I   0     ⁢     ⅇ       -   α     ⁢       ϕ   ⁢           ⁢   g               ⁢     
     ⁢   where   ⁢     
     ⁢       I   0     =         σⅇ   2       4   ⁢     π   2     ⁢     ℏ   2         ⁢         2   ⁢     m   e     ⁢   ϕ       g     ⁢   V   ⁢             ⁢             ⁢   and       ⁢     
     ⁢     α   =       2   ⁢       2   ⁢     m   e           ℏ               (     1   ⁢   b     )               
where σ is the area of the material at opposite sides of the gap, e is the elementary charge, 1.6×10 −19  C; ℏ=1.1×10 −34  J·s; m e =9.1×10 −31  Kg; φ is the work function of the material at the location of the gap; and g is the gap spacing.
 
     Given an expected range in gap spacing and an expected range in applied voltage bias, one of the expressions above can be employed to make a correspondence between measured tunneling current and corresponding gap dimension as a process proceeds. For many applications, it can be preferred to preliminarily calibrate the expressions for a given material and given process conditions, based on known gap dimensions so that real time correspondence can be made easily, i.e., so that each tunneling current measurement can be correlated in real time to a previously determined, known gap extent. This enables control of a fabrication process in real time to produce a selected gap extent based on in situ tunneling current measurements as a process proceeds. 
     As shown in  FIG. 3C , a tunneling current feedback control loop can be implemented, in one example, with a computer  70  having a computer control program, e.g., the Labview program described above, configured for a selected fabrication process. The computer control is specified to generate a bias voltage selected for a given process and a gap extent of interest, e.g., based on the selected one of the tunneling current-voltage expressions given above. Application of the bias voltage is to be made across a gap in an electrically conducting feature or features of a sample to be processed  10 . To enable such, the digital voltage output specification from the computer is first converted to an analog voltage signal by a digital-to-analog converter (DAC)  80 . If desired, the analog voltage signal can be amplified by a voltage amplifier  82  if the DAC limits the bias voltage below that required for a given application. 
     The analog voltage is then applied across a gap in an electrically conducting feature or features being processed. Electrical contact can be made to the electrically conducting features in any suitable and convenient fashion that enables a robust electrical connection as the sample is being processed. In the example of  FIG. 3C , electrical contact is made to a sample as the sample is exposed to an ion beam  58  in the manner described above, but this specific processing is not required; as explained above, the feedback techniques of the invention are applicable to a wide range of fabrication processes. Whatever process is carried out, the only requirement is that a robust electrical connection be provided for applying a bias voltage across a gap of interest during the processing. For many applications, it can be preferred that the electrically conducting material at the location of the gap be itself patterned or connected to a material that is patterned as contact pads of a macroscopic scale, e.g., at least about 100 μm square, such that conventional wire bonding, spring clips, or other selected connection technique can be employed. 
     With electrical contact in place for applying a bias voltage across a feature gap, then as processing of a sample proceeds, e.g., during exposure of the sample to an ion beam  58 , electron tunneling current across the gap in an electrically conducting feature is measured and if desired, amplified, by a current amplifier  84  that preferably is characterized by a high acquisition speed and a high gain factor, if desirable for a given application. The measured current is digitized by an analog-to-digital converter (ADC)  86  and delivered to the computer  70 . In one example feedback control scenario, the computer is programmed with a prespecified threshold tunneling current against which the measured tunneling current is compared as the process proceeds. When the measured tunneling current corresponds, in a selected manner, to the threshold tunneling current, the computer directs an ion gun controller  72  to control the ion gun  52 , e.g., to extinguish exposure of the sample to the ion beam. In this manner, the fabrication process is directly controlled in real time based on in situ monitoring of the tunneling current across a gap or gaps in a sample as the sample is processed. 
     The programmed threshold tunneling current can be set in any suitable manner. For example, based on the Fowler-Nordheim expression given above, the tunneling current corresponding to a desired gap size can be determined for a given material and voltage bias application. With the tunneling current thusly determined, the computer can be programmed with that tunneling current value for comparison with tunneling current measurements as the process proceeds. The invention contemplates a wide range of alternatives for providing a tunneling current threshold; such can be determined, e.g., in real time; a programmed look-up table can be employed, or other technique can be implemented for enabling feedback control of a process based on tunneling current measurements. 
     This feedback control technique can be extended to any fabrication process that can accommodate application of a voltage across and measurement of tunneling current across a gap in an electrically conducting material. No specific arrangement is needed for the monitored gap; all that is required is a gap the extent of which will increase or decrease in a manner that relates to a fabrication process to be controlled. The extent of the gap can be made larger or smaller by the fabrication process to be controlled, and/or the gap can be nonexistent at the start of the process or be closed during the process. It is correspondingly not required that a tunneling current measurement be possible at all times during a fabrication process under control. If the process is initiated in a material without a gap and results in the formation of such, tunneling current measurements can be made once the gap appears. Similarly, if the process is initiated in a material including a gap and results in closure of such, tunneling current measurements can be made during the interval of the process when a gap exists. For a given gap extent, tunneling measurements may be possible only during an interval of a fabrication cycle when the gap extent is sufficiently small to enable tunneling. Further, a tunneling current measurement can be made at selected points in time during a fabrication process rather than continuously; as described in detail below, because the tunneling current measurement can under some circumstances itself impact the process; brief, intermittent tunneling measurements can therefore be preferred for some applications. 
     In accordance with the invention, the ion counting feedback technique described previously can be employed in concert with the tunneling current measurement feedback technique. For example, the ion counting feedback can be employed for control of processing larger features that are, e.g., tens of nanometers or more in extent, and the tunneling current measurement feedback control then employed for fine tuning the larger features or producing finer features that are, e.g., tens of nanometers or less in extent. Further, the two feedback control techniques can be employed simultaneously, e.g., for controlling fabrication of electrically conducting and electrically insulating features, or employed sequentially in any order. As explained in detail below with regard to nanoelectrode fabrication, the tunneling current measurement technique of the invention is particularly advantageous for enabling real time fine tuning of a feature, such as a nanoelectrode gap, in a precise and reproducible manner, and therefore for many applications can be advantageously employed after relatively gross dimensional control by the ion counting feedback technique. 
     In another aspect of the invention, the inventors herein have discovered that the conditions of interaction between an ion beam and a solid can be controlled for manipulating nanoscale feature dimensions in solid state materials. These controlled ion beam interaction techniques enable solid state material topology to be adjusted, rather than necessarily removed. Specifically, under selected process conditions provided by the invention, solid state material can be caused to transform such that feature edge locations are precisely and controllably produced and/or modified by atomic transport mechanisms that are locally additive or subtractive. 
     Referring to  FIGS. 6A-6C , in a first example of this ion beam feature control, a limiting aperture  24  in a structure  10  is caused to be adjusted from a first diameter, D 1 , to a smaller diameter, D 2  or D 3 . The starting aperture is formed in a selected structure in any suitable fashion, e.g., by the methods described above and shown in  FIGS. 1A-1D  and  FIGS. 2A-2G , in, e.g., a membrane, layer, substrate, or other structure. The structure surface  18  in which the limiting aperture was formed is then exposed to ion beam irradiation, employing, e.g., the system described above and illustrated in  FIGS. 3A-3B . 
     As shown most dramatically in  FIG. 6C , for selected ion beam irradiation conditions, the inventors have discovered the unexpected result that the material is added to the periphery, or boundary, of the limiting aperture  24  exposed to the irradiation, causing the diameter of the limiting aperture to decrease. This condition can be predictably and precisely imposed by enforcing structure temperature, ion flux rate, and ion energy conditions conducive to material addition at the aperture rim. Given that the ion beam irradiation is generally considered to be a sputtering/material removal process, it is particularly unexpected that this material movement and addition condition can effectively progress, even in the presence of the atomic sputtering erosion, to result in a change in the physical dimensions of a feature. 
     EXAMPLE 3 
     A silicon nitride membrane of about 500 nm in thickness was produced in the manner of the process outlined in  FIGS. 2A-E . An aperture was formed through the entire thickness of the membrane by reactive ion etching.  FIG. 7A  is an electron micrograph of the 95 nm-wide aperture that resulted from the etch. 
     The membrane and its aperture were then exposed to an argon ion beam flux at an energy of about 3 KeV, and a flux of about 47 Ar + /sec/nm 2 . The membrane was maintained at a temperature of about 20° C. during ion flux exposure. The ion beam was directed to the membrane for 250 ms for each 1 sec time interval. 
       FIG. 7B  is an electron micrograph of the membrane after exposure to the argon ion beam reduced the aperture diameter to about 3 nm.  FIG. 7C  is a plot of counted argon ions/sec as a function of time. A generally linear count rate is indicated for midpoints in the process. 
     Without being bound by theory, the inventors herein understand that the mechanisms underlying the ability of an ion beam to cause material build up at an ion-irradiated aperture rim may be related to atomic transport through the bulk of the structure; ion-induced changes in viscosity, electronic surface charge, mechanical stress generation, and lateral swelling of the structure; and/or atomic surface transport caused by ion-induced surface atom excitation or supersaturation of mobile adsorbed ionic species on the structure surface. At sufficiently low ion energies the ion penetration depth is much less than the structure thickness, resulting in a domination of surface transport processes. The invention does not require a specific material transformation mechanism, but rather, provides distinguishing process control parameters that impose predictable material transformation results. 
     Considering the process parameters to be controlled, it is found that the temperature of the structure being exposed to the ion beam irradiation directly impacts the ability to impose material movement and the rate at which material moves. It is found that for a specific structural material, there is a characteristic temperature above which material of the structure is found to move, resulting in an adjustment, or change, in feature dimensions and below which material is instead removed by sputtering from the structure. For given ion beam energy and flux conditions, control between material removal and dimensional feature adjustment can therefore be imposed by structural temperature control. 
     EXAMPLE 4 
     Referring to the graph of  FIG. 8 , there is plotted the ion counts/second detected by an ion sputtering system like that of  FIG. 3A  as a function of time for a 500 nm-thick silicon nitride membrane in which was initially fabricated a square aperture of about 72 nm in length. The membrane was fabricated based on the process shown in  FIGS. 2A-2F  and the aperture was fabricated by a focused ion beam directed at the membrane to form an aperture that extended completely through the membrane. Each region of the graph indicates the temperature at which the membrane was maintained during bombardment by an argon ion beam. The beam flux was 14 Ar + /sec/nm 2  and the beam energy was 3 KeV. The on/off duty cycle of the ion beam being directed toward the membrane was such that the beam was directed to the membrane for 200 msec during each 1 sec interval. 
     As a function of time, an increase in ion count/second indicates an increase in the aperture dimension, while a decrease in ion count/second indicates a decrease in the aperture dimension. The plotted data clearly indicate an increasing rate of aperture shrinkage under the ion beam irradiation as the membrane temperature is increased above about 5° C. In contrast, at membrane temperatures below about 4° C. the aperture dimension increases rather than decreases. At membrane temperatures between about 0° C. and about −10° C. no appreciable temperature dependence in the rate at which the aperture dimension decreases is indicated. 
     With this experimental data, it is indicated that for a silicon nitride membrane, two distinct temperature regimes exist; the first temperature regime, at or above about 5° C., imposes material movement and feature addition by ion beam irradiation, the second temperature regime, at or below about 4° C., imposes material sputtering and removal by ion beam irradiation, both regimes for given ion beam species, flux, and energy conditions. This analysis for a silicon nitride membrane is an example of the empirical analysis contemplated by the invention to determine that temperature above which a material of interest can be made to move and augment features. It is recognized that this transition temperature can vary widely from material to material. 
     The plotted data also indicate that within the regime for imposing material movement and addition, the rate of material transport in altering feature topology is temperature dependent. At relatively higher temperatures, the transport process proceeds more rapidly than at relatively lower temperatures. Knowledge of this temperature-dependent transport rate enables precise process control and characterization. 
     EXAMPLE 5 
     Five silicon nitride membranes of about 500 nm were fabricated in the manner of the process outlined in  FIGS. 2A-E . Apertures each of about 1400 nm 2  in area were produced in the membranes by focused ion beam etching. The membranes were then exposed to an argon ion beam at an energy of about 3 KeV for various total doses at five ion beam fluxes. Each membrane was maintained at a temperature of about 22° C. during the ion beam exposure. Each ion beam exposure was controlled to sputter for 200 msec during each 1 second interval. 
     Referring to the graphs of  FIGS. 9A-9B , there is plotted the area of the apertures in nm 2  as a function of total argon ion beam dose, in ions/nm 2 , for five different argon ion beam fluxes, and the aperture area decrease per dose, as a function of argon ion beam flux, respectively. From the plotted data, it is indicated that as a function of total argon ion beam dose, the aperture shrinks more rapidly at low incident fluxes relative to higher incident fluxes. In other words, the lower the flux, the less dose is required to shrink an aperture. The strong nonlinearity indicates that the amount of material mass transport produced by the ion beam irradiation per incident ion may be suppressed at high incident fluxes. This characterization enables operation at a selected mass transport rate. In a manner analogous to the temperature dependence analysis provided above, the invention contemplates empirical analysis of flux dependence for a selected material, to enable precise control of the material movement. 
     EXAMPLE 6 
     A 50 nm-thick layer of silicon nitride was deposited by low pressure chemical vapor deposition on a silicon wafers. The silicon nitride layer was patterned by electron beam lithography to produce trenches of about 50 nm in width through the entire thickness of the silicon nitride layer. The bottom of each trench thereby exposed the underlying silicon surface.  FIG. 10A  is a scanning electron micrograph of the trenched silicon nitride layer on the silicon wafer. 
     The trenched silicon nitride layer was exposed to an argon ion beam at an energy of about 3 KeV and a flux of about 20 Ar + /nm 2 /sec, where the ion beam was sputtering for 0.5 seconds for each 2 second interval. The silicon wafer was maintained at a temperature of about 20° C. during the ion beam exposure.  FIG. 10B  is a scanning electron micrograph of the trenched silicon nitride layer after about 200 seconds of sputtering. Note that silicon nitride material has been moved to the trenches, whereby the trenches have been partially filled in. This indicates that for the process conditions here employed, material is transported from the silicon nitride layer to the trenches. 
     A second 50 nm-thick trenched silicon nitride layer like the one just described was exposed to an argon ion beam at an energy of about 3 KeV and an ion flux of about 30 Ar + /nm 2 /sec, with the ion beam sputtering for one second during each two second interval, for a total sputtering time of about 300 seconds. The silicon wafer was maintained at a temperature of about −100° C. during the ion beam exposure.  FIG. 10C  is a scanning electron micrograph of the trenched silicon nitride layer. Here, the silicon nitride material at the top of the trenches has been etched away, as indicated by the rounding of the trench edges, but the bottom of the trenches are not at all filled in. 
     This example demonstrates the temperature control that can be imposed to predictably produce material transport and feature adjustment or material removal by sputtering as desired for a given application. 
     Turning to additional material transport control mechanisms provided by the invention, it is understood that the energy of the ion beam can impact the nature of material transport. Specifically, for a given structural material and temperature, a given ion beam current density, and a given time structure of the ion beam exposure, as discussed below, there exists an ion beam energy above which material transport is effectively induced in the manner described above and below which sputtering in the conventional manner occurs. This juncture between the two distinct operational regimes can be empirically determined for a given material and ion beam exposure system, and can be employed as an important control technique for precisely enabling and disabling the material transport processes. 
     Further in accordance with the invention, it is found that the time structure of the ion flux exposure, i.e., the sequence of intervals in which the ion beam is controlled to enable interaction with a material and then controlled to not interact with the material, impacts the nature of material transport and dimensional feature change. Specifically, the imposition of an on/off duty cycle on the ion flux is found to impact the ability to cause material movement and corresponding dimensional feature change. 
     EXAMPLE 7 
     A 500 nm-thick silicon nitride membrane was produced in the manner of the process outlined in  FIGS. 2A-E . A 95 nm-wide aperture was formed through the entire thickness of the membrane by focused ion beam etch. The membrane and aperture were then exposed to an argon ion beam at an energy of about 3 KeV and a flux of about 14 Ar + /sec/nm 2 . The membrane was maintained at a temperature of about 16° C. during the ion beam exposure. During the exposure, the amount of time that the ion beam was directed to the membrane was varied. Six different time structures were employed: 100 msec on for each 1 second interval; 200 msec on for each 1 second interval; 400 msec on for each 1 second interval; 600 msec on for each 1 second interval; 600 msec on for each 2 second interval; and 600 msec on for each 4 second interval. During the ion beam exposure, ion detection and counting was carried out as an indication of the reduction or enlargement of the aperture in response to the various ion beam exposure cycles. 
       FIG. 11A  is a plot of argon ions counted/second as a function of sputtered time. The plot indicates that the 400 msec/1 second interval and the 600 msec/1 second interval time structures increased the aperture diameter, while all other time structures decreased the aperture diameter. This demonstrates that at about room temperature, control between material transport processes and sputtering processes can be achieved by control of the ion beam exposure time structure. 
     In addition, the invention provides an understanding, based on experiments using periodically pulsed ion beams, for directly determining the time scale of material transport on ion sculpted materials, including dielectric materials such as silicon dioxide and silicon nitride. Experimental measurements produced in accordance with the invention demonstrate that ion sculpting can indeed be successfully applied to the technologically important oxide of silicon, and further demonstrate a discovery of the invention, that ion sculpting material transport time scales can be surprisingly long, indicating that the materials do not necessarily relax to their equilibrium condition until seconds after a stimulating ion beam has been extinguished. This effect can be used advantageously in applications of ion sculpting to predictably control the sculpting process for a desired dimensional result. 
     In accordance with the invention, additional samples for ion beam sculpting were prepared as 500 nm-thick, freestanding SiO 2  or SiN membranes supported on a silicon frame. The SiO 2  membranes were thermally grown on Si(100) substrates, then capped for further processing by depositing a 200 nm-thick layer of Si 3 N 4  by low pressure chemical vapor deposition. Photolithography and anisotropic wet chemical etch processing of the silicon substrates was then carried out to create free-standing 90 μm×90 μm SiO 2  membranes. The Si 3 N 4  capping layer was then removed by etching in hot phosphoric acid, and then the oxide surface was cleaned by exposing it to an oxygen plasma. Silicon nitride membranes were fabricated by first depositing a 500 nm-thick layer of low-stress SiN directly on Si(100) substrates by LPCVD, followed by similar photolithography and etching steps as described above for the oxide membranes. A single initial hole of a selected diameter was then milled near the center of each SiO 2  or SiN membrane by a focused ion beam milling process. 
     The thusly produced oxide and nitride membranes were individually exposed to an argon ion beam at an energy of about 3 keV in the apparatus of  FIG. 3A , with the ion beam impinging the membrane surface in the normal direction. Ions transmitted through the open holes were detected by a Channeltron single ion detector after electrostatic focusing and energy analysis in the manner described previously. The ion beam exposure of the membrane was varied in the manner described above, to produce a periodic time structure of pulsed ion exposure. This was specifically controlled by electrostatically deflecting the ion beam on and off a membrane for the desired “on” and “off” times, referred to as T on  and T off , respectively. Pulses of 200 volts were applied to deflection plates at the exit port of the ion gun to steer the beam about 5 mm away from a hole being processed within about one microsecond. The term “pulsed ion exposure” is thus herein meant to refer to the direction and removal of an ion beam at the hole. 
     In a first experiment with a silicon dioxide membrane, a 55 nm-wide hole in an SiO 2  membrane was exposed to the pulsed argon ion beam at a temperature of about 28° C. A range of beam “off” times of 0.1 s, 0.4 s, 0.9 s, and 1.9 s was employed with a constant beam “on” time of 0.1 s per cycle, as shown in the plot of  FIG. 11B . In this experiment, the instantaneous ion beam flux was kept constant at 15.7 Ar + nm −2 s −1 . The initial duty cycle of the beam was 0.1 s “on”, 0.9 s “off”. Without interrupting the experiment, the “off” time was changed to 0.1 s, 1.9 s, 0.1 s, 0 s, i.e., continuous exposure, 0.9 s, 0.1 s, then 0.4 s, each for 100 cycles. 
     The hole area in the SiO 2  membrane was found clearly to decrease with increasing ion beam exposure, at a rate of hole decrease that depended on the “off” time of the pulsed beam. Whereas the continuous beam tended to open the hole, remarkably a pulsed beam with an “off” time of 0.1 s or longer acted to close the hole. The rate at which the hole area closed per unit fluence, referring to the negative slope in the figure, and given as “closing rate” for short, represents the efficiency, ξ, with which the ion beam closed holes. It is clearly an increasing function of “off” time up to 1-2 seconds. 
     In a similar experiment, a 100 nm-wide hole in a SiN membrane, fabricated as described above, was exposed at a temperature of about 28° C. to varying ion beam exposure cycles of a pulsed ion beam having an instantaneous flux of 11.2 Ar + nm −2 s −1 . The resulting hole area is plotted in  FIG. 11C , revealing a duty-cycle dependence similar to that exhibited by the hole in the SiO 2  membrane. The ion sculpting efficiency was found to clearly increase as the ion beam “off” time was increased from 0.5 s through 1.5 s and 3.5 s, and was unchanged at 5.5 s all while the beam “on” time was held constant at 0.5 s. 
     Based on these experimental results, it is understood in accordance with the invention that the rate of hole closure, i.e., the rate of material transport, can be controlled by increasing the beam “off” time, and specifically can increase the material transport rate. The efficiency with which a pulsed ion beam sculpting process reduces a hole diameter is further found to increase with the beam “off” time, i.e., T off , as an increasing function of T off , independent of ion beam flux, processing temperature, or the initial conditions of a hole being ion beam sculpted. In addition, it is found that the efficiency with which a pulsed ion beam sculpting process reduces a hole diameter can be enhanced, to promote reduction of the hole, by lowering the flux of the ion beam or by raising the processing temperature, given a selected ion beam exposure duty cycle. 
     In addition, in the SiN experiments, it was also found that continuous ion beam exposure increased, rather than decreased the hole diameter in the SiN membrane at various temperatures. This demonstrates a discovery in accordance with the invention that the lateral transport of matter by ion sculpting can be “frozen out” at low temperatures, at which point sputter erosion of a pore dominates the process. The 0.1 s “on”, 0.9 s “off” pulsed beam that closed the hole at 28° C. opened it at a rate of 2.9 nm 2 /Ar + nm −2  at −100° C. Thus, in accordance with the invention, an increase in process temperature can be employed to increase the rate of material transport. 
     It is further recognized, based on these experiments, in accordance with the invention, that pulsed ion beam sculpting can be precisely controlled by the initial conditions of a hole being exposed to a pulsed ion beam, as well as the surface topography of the membrane in which the hole is formed, in conjunction with the duty cycle of the pulsed ion beam. More specifically, the closing efficiency of a hole being ion sculpted by a pulsed ion beam is directly controlled by the initial condition of the hole, including the size of the hole and the surface topography of the membrane in which the hole is formed. For example, a large initial hole, e.g., of about 150 nm in diameter, can be enlarged under the same pulsed ion sculpting conditions that reduce the diameter of a smaller hole, e.g., of about 50 nm in diameter, given a fixed ion beam flux and processing temperature. 
     As explained previously, without being bound to theory, it is understood in accordance with the invention that on a microscopic scale ion beam sculpting can involve the motion of independent atoms along the surface of the material, and/or the collective motion of many atoms in a surface layer, to account for the lateral transport of matter under the influence of low-energy ion beams. To describe the time-dependent behavior of pulsed ion beam sculpting of the invention, at first ignoring the effect of sputter erosion, the material response is parameterized with a rise time, τ rise , and a decay time, τ decay . Within the time scale description, the closing rate of a hole approaches a steady-state closing rate value, i.e., a continuous beam closing rate value, R ss , as (1−e (t−to)/     τ     (rise) )R ss  when the ion beam is turned on, and decays as e −t/     τ     (decay)  when the beam is turned off, where t is time and t 0  is the initial time. An exponential rise and decay of the hole closing rate is the simplest phenomenological model that incorporates material response time scales. Such time scales are common to microscopic models that are understood to provide a description of the pulsed ion sculpting phenomenon of the invention, including surface diffusion or viscous flow models. 
     In accordance with the invention it is required that the closing rate of a hole being sculpted be a continuous function of time that is assumed to reach a quasi-steady state condition where the closing rate at the beginning of each ion pulse, given as time t=0 in the equations below, is the same. Then the closing rate of the hole area, A, is given by: 
     
       
         
           
             
               
                 
                   
                     
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     A hole closes during the entire beam pulse cycle, i.e., during both ion beam “on” and “off” durations. The area change induced by the cycle is thus integrated over the “on” and “off” times of (2a) and (2b) above. The ion sculpting efficiency, ξ, for flux φ is: 
                   ξ   =         1     ϕ   ⁢           ⁢     T   on         ⁢       ∫   cycle     ⁢         ⅆ   A       ⅆ   t       ⁢     ⅆ   t           =         R   SS     ϕ     ⁡     [     1   +         (       τ   decay     -     τ   rise       )       T   on       ⁢         (     1   -     ⅇ     -       T   on       τ   rise             )     ⁢     (     1   -     ⅇ     -       T   off       τ   decay             )         1   -     ⅇ       -       T   on       τ   rise         -       T   off       τ   decay                   ]                 (   3   )               
This expression accounts for duty cycle dependence in ion beam sculpting through the relative lengths of the material response time scales. The experimental results in the plots of  FIGS. 11B and 11C  suggest that the intrinsic decay in material response, τ decay , i.e., the material response decay when the ion beam is off during a pulse cycle, for both SiO 2  and SiN, is on the order of seconds, and fitting the results to the exponential time scale model given above indicates that the rise time in material response, τ rise , is shortened by the incident ion beam relative to the decay in material response, τ decay .
 
     In accordance with the invention, it is understood that the pulsed ion beam sculpting process of the invention is characterized by a condition in which ion-stimulated mobile species cause the rise time in material response, τ rise , to decrease with increasing ion beam flux. The mechanism by which τ rise  is reduced by increasing beam flux is understood to be a function of incoming ions ejecting mobile surface species, i.e., sputter erosion, thereby reducing the intrinsic time for such species to be trapped on the surface. Ion sputter erosion is known to arise from momentum transfer in atomic collision cascades that last on the order of a picosecond. But the time scale for a material to respond in ion beam sculpting is unusually long—on the order of seconds. 
     For a given material, the extent to which a pulsed ion beam reduces the material response rise time, τ rise , relative to the material response decay time, τ decay , can be determined by measuring the ratio of ion sculpting efficiency, ξ, for continuous beam exposure and pulsed beam exposure. The expression for ion sculpting efficiency, ξ, can be approximated by ξ≈R ss /φ[1+(τ decay −τ rise )(τ decay +τ rise ) −1 ] for a pulsed beam whose “on” and “off” times are the same and are assumed to be much shorter than τ decay  and τ rise . 
     With this expression, the ion sculpting efficiency, ξ, is given as R ss /φ for continuous ion beam exposure. As the material response rise time, τ rise , decreases, the ion sculpting efficiency of the pulsed beam therefore tends to twice that value, regardless of the material, for a 50% duty cycle of ion exposure. This is a surprising discovery provided by the invention, and implies that the same amount of hole closing can be induced by half the ion fluence in the same amount of time by using a periodically pulsed beam at a 50% duty cycle, in the manner described above. 
     This enhancement of ion sculpting efficiency of a pulsed beam over a continuous beam was experimentally measured in accordance with the invention for the SiO 2  and SiN membranes described above. The measured the results are shown in the plot of  FIG. 11D . The experiment was performed by switching between continuous ion beam exposure and a periodically pulsed beam with 10 ms “on” and “off” times. The incident ion flux was 8.3 Ar + nm −2 s −1  for the nitride membrane hole, and 2.2 Ar + nm −2 s −1  for the oxide membrane hole. 
     The ion sculpting efficiency was found to be clearly enhanced by the periodically pulsed beams in both materials. For the SiO 2  membrane, the measured value of efficiency, ξ, increased from 0.3 for the continuous beam exposure to 1.4 for the pulsed beam exposure, in units of nm 2 /(Ar + nm −2 ). The measurement was repeated on the same SiO 2  sample to find the efficiency, ξ, enhanced from 0.5 for continuous beam exposure to 1.3 for pulsed beam exposure. The measured value of efficiency, ξ, for the SiN membrane was found to increase from 1.6 for continuous ion beam exposure to 5.8 for pulsed beam exposure, then returned to 3.5 when the continuous beam exposure measurement was repeated. 
     Based on the model described above, when continuous ion beam exposure is switched to a pulsed beam exposure, the ion sculpting efficiency, ξ, should be enhanced by at least a factor of 2 if the material response rise time, τ rise , is negligibly small, and again neglecting sputter erosion effects. The experimentally determined ξ-enhancement factors were observed to be 3.4 for the SiO 2  membrane, and 2.3 for the SiN membrane, by averaging the slopes for continuous or pulsed segments of the data from the beginning and the end of each experiment, which likely differ due to surface material changes affected by significant argon irradiation. 
     The measured values of ξ then are preferably corrected for the competing effect of pore opening by sputter erosion by using the low temperature data in  FIG. 11D . Sputter erosion is assumed to contribute a constant hole opening rate of 2.9 nm 2 /(Ar + nm −2 ) because the sputter yields of SiO 2  and SiN are very similar, weakly flux-dependent, and presumed to be independent of duty cycle. The corrected experimental efficiency ξ-enhancement factors are 1.3 for the SiO 2  membrane and 1.6 for the SiN membrane. These values are less than the predicted value of 2 because the material response rise time, τ rise , although significantly diminished relative to the material response decay time, τ decay , is not negligibly small. From equation (3), it is found that the material response rise time, τ rise , is reduced to 0.6 times τ decay  for an SiO 2  membrane by a 2.2 Ar + nm −2 s −1  ion beam. Similarly, a 8.3 Ar + nm −2 s −1  ion beam reduces the material response rise time, τ rise , to one quarter of the material response decay time, τ decay , for the SiN membrane. 
     These experimental results in accordance with the invention indicate that dynamics of hole closing, and correspondingly, material transport, in SiO 2  and SiN membranes are strongly dependent on the rest time between ion beam pulses, indicating that in general, a significant amount of hole closing, and material transport, occurs when no beam is incident on the material surface. This discovery has bearing on ion beam sculpting nanofabrication techniques of the invention in enabling control of ion beam time structure and control of the ion dose necessary to close holes, i.e., to impose material transport, on a feature being ion sculpted. It further determines whether holes can be made smaller at all by influencing the competition between the hole-closing and hole-opening processes of ion-induced lateral matter transport and sputter erosion, respectively. The dynamics of pulsed ion beam sculpting can be described by an exponential rise and decay of the hole closing rate. The incident ion beam must shorten the material response time in order to account for the enhanced sculpting efficiency of pulsed beams. 
     The ion detection and counting mechanism of the invention for imposing feedback control on ion irradiation mass transport is advantageous for many applications for enabling precise feature formation, but is not required by the invention. Once a mass transport process is characterized, and for processes that do not require very fine feature control, feedback control of the system may not be required. All that is required is the exposure of the material to an ion beam under conditions that impose processes such as mass transport for adjusting dimensions of structural features of the material by local material addition or subtraction. 
     This structural material adjustment process provided by the invention can be applied to a wide range of structural features, including holes, slits, apertures, and gaps in general, and in trenches and other such features where a distinct feature rim or wall is present and can be adjusted. It further can be applied to fabrication of protruding features such as hillocks and asperities. 
     In one example of such a fabrication technique, the ion flux and dose and the temperature of a membrane are selected to produce a protrusion on the membrane by exposure to ion beam flux. One membrane surface is exposed to the ion beam flux under the selected conditions. This results in formation of a protrusion on the membrane surface opposite that exposed to the ion flux. 
     EXAMPLE 8 
     A silicon nitride membrane of about 500 nm in thickness was produced by a LPCVD process following the fabrication sequence outlined in  FIG. 2 . The membrane was exposed to a gallium ion beam at an energy of about 50 KeV and a dose of about 4 nanocoulombs/μm 2 . Five different isolated exposure areas on the membrane were defined, namely, 0.12 μm 2 , 0.14 μm 2 , 0.16 μm 2 , 0.18 μm 2 , and 0.20 μm 2 . 
       FIG. 12  is an atomic force micrograph of the nitride membrane surface opposite that which was exposed to the gallium ion beam. In this image, brightness level corresponds to topology; the brighter a region in the image, the “taller,” or higher, is the topology of that region. As noted in the image, both of the 0.16 μm 2 , 0.18 μm 2 , and 0.20 μm 2  membrane areas, and one of the 0.14 μm 2  membrane areas were opened by the ion beam exposure, i.e., an aperture through the thickness of the membrane resulted from the ion beam exposure in that area. The other 0.14 μm 2  membrane area and the 0.12 μm 2  membrane area were not opened by the ion beam exposure and instead exhibit hill-like protrusions formed on the membrane surface opposite that exposed to the ion beam. This example demonstrates that dose can be controlled to cause mass transport in a manner that produces a protrusion on the surface of a structure. This example further demonstrates that the ion beam species can impact the nature of feature formation and adjustment; in this example gallium ions were employed as opposed to the argon ions employed in earlier examples. It is understood in accordance with the invention that ion species can be selected to control aspects of feature formation processing. Similarly, it is understood in accordance with the invention that the ambient gas species present during the ion interaction with a material can be selected to control the nature of the interaction. 
     The features formed by and/or having dimensions adjusted or changed by the processes of the invention can be provided on the surface of a structure, in a layer provided on a support structure or a free-standing membrane, or other surface which can be irradiated by an ion beam. Composite material structures can be processed. There is no restriction on the fabrication sequence employed to produce the starting structures for which dimensional adjustment is to be carried out. 
     The invention provides a model of the various ion beam processes described above for enabling control of the process parameters. Such process control provides an ability to, in effect, ion beam sculpt nanoscale features with a precision not previously attainable. Solutions to analytical expressions of the model, as-obtained with appropriate parameter values for a given sculpting process, can be employed in accordance with the invention to produce prespecified nanoscale features in a precise, predictable manner, and in open-loop fashion, i.e., without the need for closed-loop ion counting rate feedback control like that provided by the feedback system of  FIG. 3A  described above. As explained in detail below, the invention provides a recognition that the ion beam sputtering and mass transport phenomena discussed above compete during an ion beam sculpting process. The methodology of the invention provides the ability to control these phenomena such that one can be made to dominate over the other in a manner to enable production of a desired nanoscale feature or geometry. 
     The invention provides analytical model expressions that are based on process parameters which generally depend on the properties of a material being ion beam sculpted, e.g., the specific material composition, the initial geometry of a structure or feature at the material surface, material defects, and doping impurities, as well the local environment around the sculpting process, for example the gaseous ambient environment, the temperature of the material, the incident ion species, ion flux, and ion energy, and other parameters that characterize the incident ion beam. It is recognized in accordance with the invention that the process parameters therefore are to be adjusted based on a particular ion beam sculpting application to achieve desired process results, in the manner described below. 
     For clarity, the following discussion is directed to a process model based specifically on ion beam sculpting of a nanopore of a selected diameter, or area. As explained in detail below, however, the invention is not limited to such. The analytical process model expressions provided by the invention can be adjusted to control formation of a wide range of geometries, e.g., slits or irregularly-shaped holes, trenches, or other geometry, extending through the entire thickness of a material or through only a portion of the thickness. In addition, positive features, rather than negative features such as apertures, can be formed on a material surface or in a material, in the manner previously described. Features such as lithographic mask features, ion beam doping profiles accompanied by mass transport, or buried layer profiles can further be produced in accordance with the process model provided by the invention. Further, the dimensions of existing features can be controlled, or changed, in accordance with the invention. There is no fundamental geometric symmetry or pattern to which the process control model is limited. Whatever geometry or feature is being formed, controlled, and/or changed, it is the nanoscale control of that geometry by the methodology of the invention that is universally applicable. 
     As explained above, the model employed by the invention for use in controlling ion beam sculpting is based on a recognition that distinct processes are likely to compete during the sculpting. Considering ion beam sculpting of a nanopore to reduce a starting diameter of a pore to a selected reduced diameter, a first such competing process tends to open the pore and is understood to likely be driven by ion beam-sputter erosion of a pore edge. This erosion process is understood to be dominant at low temperatures and high ion beam fluxes. Established sputtering phenomenology can be employed for most applications to account for and control sculpting processes that are dominated by sputtering in this regime. 
     A second, competing process tends to cause motion of matter, i.e., mass transport, and can operate to a degree necessary for reducing the starting pore diameter. Without being bound to theory, it is understood that more than one view can explain this phenomenon. A first theory understood in accordance with the invention takes the view that a very thin, e.g., about 5 nm-thick, stressed viscous surface layer can be created by the energy and matter deposited on a material surface by an ion beam. An enhanced collective motion, driven by a reduced viscosity and/or enhanced stress owing to implantation effects or surface tension, may cause the layer to flow or relax, whereby material is transported across a surface. 
     Although this “viscous flow” model has merit, in accordance with the invention a preferred ion beam sculpting control model reflects a process theory in which incident ions create as well as annihilate excess, independent, and mobile species such as adatoms, ad-dimers, ad-molecules, molecular clusters and surface vacancies that are present at the surface of a material exposed to an ion beam. For most applications, it is understood to be reasonable to assume a single mobile species which, for simplicity, will here be called an “adatom.” The changing concentration of surface adatoms, C(r,t), is modeled in accordance with the invention as a function of distance, r, along the surface, and time, t, governed by a two dimensional diffusion expression as: 
                           ∂               ∂   t       ⁢     C   ⁡     (     r   ,   t     )         =       FY   1     +     D   ⁢       ∇   2     ⁢   C       -     C     τ   trap       -     FC   ⁢           ⁢     σ   C           ,           (   4   )               
where C is the concentration of adatoms on a two-dimensional surface, r=(x,y) is the radial surface position, t is time, F is the ion flux, Y 1  is the number of adatoms created per incident ion, D is the adatom surface diffusivity, τ trap  is the average lifetime of an adatom before thermally-activated adatom annihilation occurs at a surface defect, and σ C  is the cross-section for adatom annihilation by incident ions.
 
       FIG. 13  schematically illustrates the competing mechanisms modeled by this expression. Changes in concentration of surface adatoms, ∂C/∂t, depends firstly on a rate of generation of adatoms that results from the ion flux, F, with Y 1  indicating the number of created adatoms per incident ion. The second modeled term is a mass transport term, driving the adatom transport by diffusion along the surface and within the structure, and thus depending on the adatom surface diffusivity, D, and the adatom concentration gradient. This transport term models the reduction in a nanopore radius by mass transport of material from around the pore, in the manner described and demonstrated above. 
     Further as shown in  FIG. 13 , the surface adatom concentration change is determined by adatom annihilation that can occur at a surface defect, or trap; τ trap  is correspondingly defined as the average lifetime of an adatom before such annihilation at a trap occurs. The final term models ion beam annihilation of adatoms; here σ C  reflects the cross-section for adatom annihilation by the incident ion beam itself. It is also understood that annihilation of adatoms occurs at the pore edge as the pore is filled by the mass transport phenomena; this annihilation mechanism is treated as a boundary condition for Expression (4) above. 
     The first and last terms on the right hand side of Expression (4) above reflect an understanding provided by the invention that each incident ion resets a surface patch of area given as σ C  to an adatom concentration given as Y 1 /σ C  that is independent of its previous state. The presence of a nanopore of an initial diameter in the material being subjected to an ion flux is represented by adding an adatom sink at the nanopore edge, for a nanopore radius, R, and by including the second term on the right hand side of the expression to model long-range material diffusion to the pore edge. Adatoms annihilated at the nanopore boundary are turned into new, stable matter at the boundary. 
     The magnitudes of the parameters Y 1 , D, τ trap , and σ C  can be estimated for a given ion beam sculpting application from experience with suitable materials and can be determined by independent experiments. For example, a matrix of pore-closing experiments can be conducted, preferably including both steady state and transient conditions, and employing the feedback system of the invention described previously for making precise determination of the influence of each parameter on feature formation, e.g., pore-reduction rate, and other characteristics. One or more “test” ion flux exposures of a material structure can be carried out under a variety of test process conditions, with each “test” exposure monitored by the ion counting feedback loop previously described above. This monitoring enables an indication of feature fabrication dependence on the test process conditions. In turn, the magnitudes of the model parameters, and corresponding optimal process conditions, can then be determined and selected based on the accumulated test process results. It is recognized in accordance with the invention that the values of the model parameters can be manipulated by adjusting not only temperature, ion beam flux, and ion beam energy, but also by adjusting the ambient gas species and pressure, ion species, material properties, e.g., concentrations of trace impurities on the material surface, material defects, and impurity doping. The parameters are therefore treated here as being fully adjustable to enable selection based on test process results, if desired, and to enable precise control of the ion beam sculpting process for a given application. 
     By comparison with the trapping annihilation term of the right hand side of Expression (4) above, the ion impingement annihilation term of the right hand side of Expression (4) above corresponds to an average adatom lifetime before ion impingement-induced annihilation as τ ion =1/(Fσ C ). Thus, the effective surface lifetime, τ, of an adatom in the presence of both annihilation mechanisms can be given as: 
                     1   τ     =       1     τ   trap       +     F   ⁢           ⁢     σ   C                 (   5   )               
It is understood that under some circumstances, one of the two annihilation terms of the right hand side of Expression (4) above will be insignificant compared to the other, but this may not necessarily always be the case, and is not required for the analysis of the invention.
 
     An additional annihilation mechanism, namely, adatom annihilation by joining of adatoms and precipitation into adatom islands, is not represented in Expression (4) for simplicity so that this partial differential equation is linear, rather than nonlinear, for ease of analytical mathematical solution. It is understood, however, that applications for which this annihilation channel cannot be neglected are more precisely modeled with the addition of another term to the right hand side of Expression (4) that would be proportional to −C n /τ island , where n is the number of adatoms in an critical island of a critical size, i.e., a size just large enough to be more likely to grow than to shrink, and τ island  is a characteristic time constant for adatom island formation. Thermal generation of adatoms, thermal desorption of adatoms into a surrounding vacuum, and deposition of adatoms from an ambient vapor are additional mechanisms that have also been neglected for clarity but can be readily incorporated, when necessary for a given application, in the manner of the mechanisms described above. 
     Expression (4) above expresses an understanding provided by the invention that far from a feature, e.g., a nanopore, steady ion beam irradiation of a material surface creates on the surface and at the near-surface a spatially uniform, steady state adatom concentration C SS =FY 1 τ. The pore boundary, or nanopore edge, is taken to be a “perfect sink” for adatoms, which are there transformed to a thin layer of accumulating matter that accounts for pore reduction. If the nanopore edge is taken as a sink for adatoms then the adatom supersaturation drops as the nanopore edge is approached. Expression (4) above implies that the normalized difference, n(r,t), between C SS  and C(r,t), given as n(r,t)≡(C SS −C(r,t))/C SS , obeys a diffusion equation as: 
     
       
         
           
             
               
                 
                   
                     
                       ∂ 
                       
                         n 
                         ⁡ 
                         
                           ( 
                           
                             r 
                             , 
                             t 
                           
                           ) 
                         
                       
                     
                     
                       ∂ 
                       t 
                     
                   
                   = 
                   
                     
                       D 
                       ⁢ 
                       
                         
                           ∇ 
                           2 
                         
                         ⁢ 
                         n 
                       
                     
                     - 
                     
                       
                         n 
                         τ 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     The assumption that the pore boundary is a “perfect sink” for adatoms implies that the adatom concentration, C, vanishes at the pore boundary, shown as in  FIG. 13  to be of radius R. This is the simplest boundary condition that accounts for a net accumulation of adatoms at the pore, and thus for reduction of pore diameter. It is recognized in accordance with the invention, however, that because of its interaction with the ion beam, the pore boundary could be a net source of surface vacancies while producing this pore-reducing effect if vacancies, rather than adatoms, dominate surface transport. The invention is therefore not limited to an adatom “perfect sink” boundary condition. An alternative boundary treatment contemplated by the invention employs a surface accommodation velocity to describe a partial sink for adatoms at the pore boundary, in a manner analogous to surface recombination velocity factors employed in semiconductor modeling of charge carriers interacting with surfaces. These pore boundary conditions can be directly generalized to other feature location characteristics. 
     The diffusion model employed by the control method of the invention is thus found to be phenomenological in nature, relying on several idealizations and assumptions to compensate for uncertainty in aspects of many microscopic properties of matter under ion beam exposure. Nevertheless, it is understood by the inventors that studies of pulsed and continuous ion beam exposures at different temperatures, gas ambients, and material conditions can be employed for a given application in conjunction with the model to permit the determination of materials-specific parameters like diffusivity, D, ion-induced adatom population Y 1 , area of adatom annihilation by ion impingement σ, and adatom lifetime prior to trap annihilation, τ trap , for a given application. Such analysis enables prespecified and precise ion beam sculpting of the material in the production of useful nanoscale devices. 
     In addition, practitioners of ion beam sculpting can use the model provided by the invention in both quantitative and qualitative ways. That is, by knowing the qualitative as well as quantitative nature of the solutions to the analytical model expressions and their dependence on various parameters of the model that are subject to experimental control, the parameters can be adjusted to achieve desired dimensional control of structures for large classes of structures. For example, the model demonstrates a qualitative dependence of an ability to increase the rate of pore reduction, and even the possibility of reducing a pore diameter at all with ion sculpting, by increasing the material temperature or by decreasing the incident flux of incident ions. The model also provides a quantitative dependence of the precise degree of temperature increase or flux decrease required for a given application. In these examples, practitioners are guided to such action by noting that both of these actions increase the effectiveness of surface diffusion of adatoms over sputtering, by a temperature enhancement of the surface diffusion constant and a reduction in adatom sputtering, respectively. 
     Other qualitative and quantitative uses of the model include correlations between analytical predictions of the model and ancillary empirical observations. For example, an observation that nanopores, the area of which are reduced to a desired area more quickly under the ion beam sculpting process, may require a minimum initial diameter before the sculpting process can be effective, can be correlated to process conditions via the model. Although the model at any given stage of its solution evolution may not contain the details of the process controlling the pore diameter, it can be used to correlate the process control parameters, and thereby, e.g., control the process mechanisms. 
     In a further example, consider the reduction in diameter of a nanoscale pore from a starting pore diameter down to a selected final diameter in the manner described above with reference to the pore shown in the electron micrographs of  FIGS. 7A-7B . A plot of pore area as a function of ion beam dose, as in  FIGS. 9A-9B , demonstrates that for a given ion beam dose, as the incident ion beam flux is reduced, mass transport of material increases, thereby more quickly reducing the diameter of the pore. As explained above, the strong nonlinearity of this result indicates that at high ion beam fluxes, the mass transport mechanism captured by the model of the invention may become suppressed. Analysis and testing based on the model of the invention enables a correlation of this flux dependence for given material and ion beam characteristics. 
       FIG. 14A  provides a similar plot of pore reduction data, here of nanopore area as a function of total ion beam dose for several ion beam fluxes and for continuous as well as pulsed ion beam exposure. The dotted plot points correspond to experimentally measured results, and the solid lines correspond to results produced by analysis of Expression (4) above, as explained in detail below. The slope of this data demonstrates that for continuous ion beam exposure, where the ion beam flux, F=0.53, 1.17, and 4.7 Ar/sec/nm 2 , the efficiency of pore closing per incident ion is clearly greater at low fluxes than at high fluxes. This plotted data also demonstrates that pulsed ion beam exposure, here at 100 ms/1 s, provides more effective mass transport, and a correspondingly increased rate in pore area reduction, than does a continuous ion beam at the same instantaneous flux. Particular control methodology provided by the invention for the plotted pulsed ion beam exposure data is described below. 
     Thus, as explained above, in accordance with the invention, ion beam sculpting process parameters can be adjusted for a given application, based on the process model provided by the invention, to enable prescription of nanoscale geometries produced by the sculpting process. As explained above, parameters will in general depend on the composition of the material being ion sculpted, the environment around the structure during the sculpting process, temperature, and on the incident ion species, energy, and other parameters that characterize the incident ion beam. The incident ion beam can be supplied as atoms, i.e., neutral ions, ions of a controlled charge state, molecules or clusters of incident atoms, or indeed any controlled energy source. It is recognized that differing model parameters will be required for various energy sources. In addition, the invention contemplates the use of multiple energy sources as well as adjustment of the charge state of the material surface at the start and during the sculpting process. 
     It is recognized in accordance with the invention that both the surface of a structure being ion sculpted and the ion-induced adatoms on the surface may be highly susceptible to the influence of the environment. By environment is meant a background ambient of a gas like oxygen, hydrogen, sulfur hexafluoride, or other selected gas. As a result the interaction of these gasses with surface atoms and/or adatoms, the transport of adatoms and/or the removal of surface atoms and adatoms can be greatly modified, relative to a process carried out in the absence of such gasses. Consequently, the rates and signs of ion sculpting mechanisms captured in the model provided by the invention will be dramatically modified by ambient gas species, and these modifications can be of great utility for precise control of the ion beam sculpting process. 
     It is also to be recognized that the state and chemical reactivity of the ambient gas, as well as the excitation state of the surface or charge state of the surface being acted upon, can be influenced by, or catalyzed by, the incident ion beam. This can result in removal or addition of adatoms and/or creation or elimination of surface defect traps, thereby influencing the mass transport and annihilation mechanisms of the ion sculpting process. Means other than an incident ion beam, such as an electron beam, laser beam, atomic beam, metastable excited atomic beam, mixtures of ion beams, or other energy source, can be used to control the sensitivity of the ion sculpting process to the ambient environment in which the process is carried out. Adjustment and control of these various influences are recognized in accordance with the invention to enable flexibility and reproducibility of prespecified and precise ion beam sculpted geometries of a material in the production of useful nanoscale devices. 
     As mentioned above, the charge state of an ion beam can be adjusted based on a particular ion beam sculpting application to achieve desired ion sculpting process results. Positive, neutral, or negative ions can be employed in accordance with the invention to produce a desired surface force between adatoms that are produced and transported along the surface during the sculpting process. 
     Turning to more quantitative solutions of the analytical model provided by the invention, and referring back to Expression (4) above, it is clear that the ion sculpting process can be specifically controlled by controlling the dominance of adatom creation and transport mechanisms relative to adatom annihilation mechanisms. Specifically, the adatom creation mechanism, represented by the term FY 1 , along with the adatom mass transport mechanism, represented by the term D∇ 2 C, can be controlled to dominate, or alternatively be dominated by, the adatom trapping annihilation mechanism, represented by the term C/τ trap , together with the adatom ion impingement annihilation mechanism, represented by the term FCσ C . This control accordingly enables a “starting” and “stopping” of an ion sculpting process to achieve a desired feature geometry. 
     Specifically, in accordance with the invention, process parameters that influence the ion flux, F, and adatom diffusivity, D, are selected relative to process parameters that influence surface defects and ion impingement characteristics, to control the adatom concentration and transport. For example, material temperature, material surface conditions, and other material dependent characteristics can be selected to increase adatom diffusivity, D, thereby to enhance mass transport to a feature being ion sculpted and to maximize the rate at which an ion sculpted feature is produced. Minimization of surface defects and other material trapping mechanisms can be carried out to minimize annihilation of adatoms by traps, thereby further enhancing the mass transport mechanism of the ion sculpting process. 
     Considering the influence of the ion beam flux, F, as explained above with reference to the plot of  FIG. 14A , as ion beam flux is increased, adatom annihilation by ion impingement also increases, resulting in a reduction of adatom concentration and transport to a feature to be produced. But at the same time, as ion beam flux is increased, the number of adatoms created also increases. Ion beam flux is therefore preferably controlled to influence adatom creation and adatom annihilation, thereby to determine the availability of adatoms for the ion sculpting process. Control of incident ion species and energy, and control of the gaseous process ambient enable control of the factors Y 1  and σ C  similarly to control adatom creation and annihilation. 
     Specific solutions for the spatial adatom concentration profile given by the model in Expression (4) can be achieved under a quasi-stationary approximation in which the left hand side of Expression (4) is set to zero. This scenario is justified for applications in which the adatom concentration profile of a material being processed adjusts rapidly to changes in feature geometry, e.g., changing pore radius, R, and ion flux, F. With this assumption, the model yields a spatially uniform steady-state adatom supersaturation concentration far from the pore edge, decaying over a characteristic mass transport distance, X m , to zero at the nanopore edge. 
     Because adatoms are being removed everywhere on the surface of a material exposed to ion beam irradiation, as well as being created by the ion beam, adatoms created within the mass transport distance, X m , of a feature, e.g., a the pore edge, are more likely to diffuse to and add to the material at the pore edge than be annihilated by incident ions; the opposite is true of adatoms created farther away. The mass transport distance, X m , therefore decreases with increasing flux. 
     Obtaining Y p , the effective cross section for sputter-erosion from the pore edge, from relevant data obtained at low temperature, where diffusion is expected to be insignificant, and taking Y 1 , the number of adatoms created per incident ion, to be of order unity, then for a material thickness of about 10 nm for a silicon nitride sample, the model of Expression (4) yields the solid curves of the plots of  FIG. 14A  for each Argon flux given, at a temperature of about 28° C., which is a temperature experimentally verified to cause pores to be reduced. 
     From this data, a value of diffusivity, D, of about 10 3  nm 2 s −1  is extracted, using a linear fit, with σ C  of about 0.1 nm 2  as a reasonable estimate. From this experimental data, it is found that the model therefore predicts that the maximum distance, X m , from which adatoms are likely to diffuse to and add to material at a feature location, e.g., at the edge of a reducing pore, is linearly proportional to the adatom diffusivity, the trap lifetime, the ion beam flux, and the cross section for adatom annihilation, as: 
                     1     X   m   2       =       1     D   ⁢           ⁢     τ   trap         +         σ   C     D     ⁢   F               (   7   )               
and a linear relation is indeed observed, as demonstrated by the plotted data of  FIG. 14B .  FIG. 14A  provides an indication of the corresponding mass transport distance, X m , for each ion flux considered. The mass transport distance, X m , thus is found to represent a characteristic distance from the pore edge within which adatoms are more likely to reach the pore than be annihilated by traps or ion beam flux erosion. Adatoms beyond a distance X m  from a feature to be formed, such as a pore edge, are more likely to be annihilated before they reach the pore edge.
 
     Considering particular parameter effects, as the ion beam flux is increased, the number of produced adatoms is increased, but the distance from which adatoms can diffuse to and add to a pore edge is reduced. As the average lifetime of an adatom is increased by a reduction in surface defects, the maximum adatom diffusion distance also increases. As the temperature is increased, the diffusivity, and correspondingly, the maximum adatom diffusion distance, is increased. With the analytical understanding of these relationships provided by the invention, the model thereby enables an ability to prescribe a minimum distance, X m , of material that must be provided around a starting feature, such as a nanopore, or around a location at which a feature is to be fabricated, to provide sufficient material for fully forming the feature, e.g., for reducing the radius of the nanopore to a desired final radius, R, under given processing conditions, and enables adjustment of processing conditions to accommodate a maximum diffusion distance X m  that is available for a given application. 
     The adatom flux, or current, j, at any location, r, of a surface being processed is given by
 
 j ( r )=− D∂C/∂r,   (8)
 
with r the radial coordinate, and the concentration gradient evaluated at the edge of the nanopore, at r=R, providing an indication of the adatom flux j(R) to the edge of the nanopore material. Additionally, scraping of material off the edge of the nanopore, tending to increase the pore area, is accounted for by a characteristic cross section for sputter-erosion from the pore edge.
 
     If each adatom reaching the nanopore fills the pore by a volume Ω, thereby reducing the extent of the pore, then the nanopore reduction rate is predicted by a volume balance given as: 
                           ⅆ               ⅆ   t       ⁢     (     π   ⁢           ⁢     R   2     ⁢   H     )       =     2   ⁢   π   ⁢           ⁢   R   ⁢           ⁢     Ω   ⁡     (       -     j   ⁡     (   R   )         +     FY   p       )           ,           (   9   )               
where Y p  is an effective cross section for sputter-erosion from the pore edge, H is the thickness of a film that is formed as the nanopore is reduced, or filled in, and Ω is the atomic volume. Substituting Expression (8) above for the adatom current j(R) at the edge of the nanopore results in:
 
                           ⅆ               ⅆ   t       ⁢     (     π   ⁢           ⁢     R   2       )       =       -       2   ⁢   πΩ   ⁢           ⁢   RF     H       ⁢     (         Y   1     ⁢     X   m     ⁢         K   1     ⁡     (     R     X   m       )           K   0     ⁡     (     R     X   m       )           -     Y   p       )         ,           (   10   )               
where K 0  and K 1  are modified Bessel functions of the second kind.
 
     This expression enables ion beam sculpting control, for a given set of process parameters characteristic of an ion beam environment, to produce a nanopore of a desired radius R. For example, it is found from this model that reduction of pore radius is enhanced with increasing temperature. This can be accounted for by a thermally activated adatom diffusion coefficient in the manner described above. 
     Based on this understanding, if the process parameters that influence adatom creation and mass transport are selected such that the first two terms of the right hand side of Expression (4) above dominate the second two terms of the right hand side of Expression (4), then ion sculpting to form a selected feature in a material being ion-irradiated proceeds. On the other hand, if the process parameters that influence adatom annihilation by traps and adatom annihilation by ion impingement are selected such that the second two terms of the right hand side of the Expression (4) dominate, then material sputtering and removal, rather than mass transport of the material from one surface location to another, is controlled to occur. 
     Thus, in accordance with the control method of the invention, with this methodology, Expression (10) can be employed to specify R max , the largest starting pore radius that can be reduced at all under any particular set of processing conditions. This maximum starting radius, R max , increases with increasing temperature and with decreasing ion beam flux. At a sufficiently high temperature and sufficiently low ion beam flux, R max  becomes infinite, in a scenario that determines the conditions under which an open pore can be closed. The maximum radius, R max  is thus given by: 
     
       
         
           
             
               
                 
                   
                     
                       
                         Y 
                         1 
                       
                       ⁢ 
                       
                         X 
                         m 
                       
                       ⁢ 
                       
                         
                           
                             K 
                             1 
                           
                           ⁡ 
                           
                             ( 
                             
                               
                                 R 
                                 max 
                               
                               
                                 X 
                                 m 
                               
                             
                             ) 
                           
                         
                         
                           
                             K 
                             0 
                           
                           ⁡ 
                           
                             ( 
                             
                               
                                 R 
                                 max 
                               
                               
                                 X 
                                 m 
                               
                             
                             ) 
                           
                         
                       
                     
                     - 
                     
                       Y 
                       p 
                     
                   
                   = 
                   0. 
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     With X m , Y 1 , and Y p  provided as constants, the ratio of 
                 K   1     ⁡     (     R     X   m       )           K   0     ⁡     (     R     X   m       )             
gets smaller with increasing pore radius, R, so that at R=R max  and above, the pore radius cannot be reduced. Analysis of this expression thereby enables adjustment of processing conditions to produce a desired R max  or to accommodate a maximum radius, R max , that is fixed by a given application.
 
     It has been observed empirically that the thickness, H, of a growing membrane or film produced as a nanopore radius is reduced and a pore is filled in depends on the rate of reduction, d(πR 2 )/dt, where R is the radius of the nanopore. Higher pore reduction rates result in thinner films than lower pore reduction rates. In addition, higher ion beam energies result in thicker films than lower ion beam energies. Based on the expressions given above, the invention provides the ability to prescribe a selected film thickness by selecting ion beam sculpting process conditions, and particularly ion beam energy, that result in a desired pore reduction rate and film thickness. 
     As explained above, it is understood in general in accordance with the invention that different regions of the perimeter of an arbitrarily-shaped aperture will also open and close according to Expressions 4-7 above. In addition, Expressions 7-11 above can be generalized in an obvious manner to remove the cylindrical symmetry assumed in the example given here, to enable modeling and process control of arbitrarily-shaped features. Thus, as stated above, the invention is therefore not limited to a particular feature geometry. 
     Time dependent solutions of the adatom diffusion model can be employed in accordance with the invention to describe an ion sculpting process employing a pulsed ion beam having a selected duty cycle. In order to model conditions when the incident ion beam is turned off, a steady state condition is assumed for the initial concentration profile. That is, the ion beam flux is set to F=0, and the initial concentration of the adatoms on the surface is given, for the nanopore example above, as: 
                       C   ⁡     (     r   ,     t   =   0       )       =       C   ss     ⁡     [     1   -         K   0     ⁡     (     r     X   m       )           K   0     ⁡     (     R     X   m       )           ]         ,           (   12   )               
where C ss  is the steady state adatom concentration far from the pore edge. Substitution of this initial concentration into Expression (3) above then provides:
 
                         ∂     ∂   t       ⁢     C   ⁡     (     r   ,   t     )         =       D   ⁢           ⁢       ∇   2     ⁢   C       -     C     τ   Trap           ,           (   13   )               
with assumed boundary conditions for the adatom concentration, C, as:
 
                             C   ⁡     (     R   ,   t     )       =   0                 C   ⁡     (       b   =     NX   m       ,   t     )       =       C   ss     ⁢     ⅇ     -     t     τ   Trap                     ,           (   14   )               
where b is an outer boundary condition, far from the pore edge, i.e., N&gt;&gt;1. In practical calculations, N≈5 is typically sufficiently large, but it is recognized that for some applications, a larger value of N can be required for increased accuracy.
 
     Solutions to Expression (12) above provide time dependent solutions of the adatom concentration on the surface of a material being processed after the beam is off, as: 
                           C   off     ⁡     (     r   ,   t     )       =         C   ss     ⁡     [         ln   ⁡     (     r   R     )         ln   ⁡     (     b   /   R     )         +       ∑     n   =   1     ∞     ⁢       A   n     ⁢       U   0     ⁡     (       α   n     ⁢   r     )       ⁢     ⅇ       -     a   n   2       ⁢   Dt             ]       ⁢     ⅇ     -     t     τ   Trap               ,     
     ⁢   where     ⁢     
     ⁢       A   n     =             π   2     ⁢     α   n   2       2     ⁢         J   0   2     ⁡     (       α   n     ⁢   R     )                   J   0   2     ⁡     (       α   n     ⁢   R     )       -                 J   0   2     ⁡     (       α   n     ⁢   b     )               ⁢       ∫   R   b     ⁢       r   ⁡     [     1   -         K   0     ⁡     (     r     X   m       )           K   0     ⁡     (     R     X   m       )         -       ln   ⁡     (     r   R     )         ln   ⁡     (     b   /   R     )           ]       ⁢       U   0     ⁡     (       α   n     ⁢   r     )       ⁢           ⁢       ⅆ   r     .     
     ⁢     Given   :     
     ⁢       U   0     ⁡     (     α   ⁢           ⁢   r     )                 =           J   0     ⁡     (     α   ⁢           ⁢   r     )       ⁢       Y   0     ⁡     (     α   ⁢           ⁢   b     )         -         J   0     ⁡     (     α   ⁢           ⁢   b     )       ⁢       Y   0     ⁡     (     α   ⁢           ⁢   r     )               ⁢     
     ⁢   and   ⁢     
     ⁢           U   0     ⁡     (       α   n     ⁢   R     )       =             J   0     ⁡     (       α   n     ⁢   R     )       ⁢       Y   0     ⁡     (       α   n     ⁢   b     )         -         J   0     ⁡     (       α   n     ⁢   b     )       ⁢       Y   0     ⁡     (       α   n     ⁢   R     )           =   0       ,             (   15   )               
to provide the roots of α n . J 0  and Y 0  are Bessel functions of the first kind.
 
     The rate at which the area of a pore decreases when the ion beam is off, or the material is not being irradiated by the beam, is given as: 
     
       
         
           
             
               
                 
                   
                     
                       ∂ 
                       
                         ∂ 
                         t 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           R 
                           2 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         - 
                         
                           
                             2 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             π 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             Ω 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             R 
                           
                           H 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       D 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           ∂ 
                           
                             C 
                             off 
                           
                         
                         
                           ∂ 
                           r 
                         
                       
                     
                     ⁢ 
                     
                       | 
                       
                         r 
                         = 
                         R 
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     When a material being processed is not irradiated by the ion beam, i.e., just after the beam is extinguished or the material is shielded from the beam, mobile adatoms remain on the surface of the material, but the adatom annihilation mechanism associated with the incident beam flux is no longer present. Thus, once the material is not exposed to the ion beam, those adatoms remaining on the material surface can diffuse to the pore periphery from a greatly increased X m . This condition is discovered to significantly increase the efficiency per ion for pore radius reduction. Indeed, as shown in the plot of  FIG. 14A , a pulsed ion beam irradiation process is found experimentally to be more efficient in forming a feature, here in reducing the radius of a pore, than continuous exposure conditions. 
     In accordance with the invention, Expression (16) can be employed in combination with Expression (10) above to predict and then control the rate of feature formation or change, e.g., nanopore diameter reduction, when a pulsed ion beam sculpting process is employed. Specifically, the pulsed ion beam time structure, i.e., the pulse rate and duty cycle, can be adjusted in accordance with the invention to achieve control over the sign and rate of change of structural dimensions. 
     It is recognized in accordance with the invention that as with the conditions when the beam is turned off, there is also a transient solution when the beam is first turned back on or the structure is again exposed to the beam. This transient may be important under some conditions, but it is understood that for most applications, the “beam-on” transient is significantly shorter than the “beam-off” transient and therefore can be ignored. If for a given application such is not the case, then the “beam-off” transient analysis given above is preferably extended to the “beam-on” analysis. Then the duty cycle of the ion beam irradiation can be particularly selected to achieve desired ion sculpting results. 
     To demonstrate the effectiveness of the process control methodology of the invention, a nanopore was sculpted in a Si 3 N 4  membrane for use as a single-molecule electronic detector of DNA. Proteinaceous nanopores, or channels, have been inserted into lipid bilayers in aqueous solutions where they serve as electronic sensors to identify and characterize single molecules. But proteins in lipid bilayers are labile and the channel diameters they provide cannot easily be adjusted. Robust, solid-state nanopores provided in accordance with the invention, fashioned to any desired diameter, enable a yield of new data and understanding of transport in confined spaces, and make it possible to produce robust single-molecule-sensing devices to characterize molecules of DNA and other biopolymers at unprecedented speeds. 
     A 5 nm-diameter pore in a silicon nitride membrane was produced in accordance with the process parameters and process control described above. Then, using electrophysiology techniques, the pore was tested with double-stranded DNA. After applying a voltage bias that would draw the negatively charged DNA molecules through the nanopore, diminutions of the ionic current were observed, as shown in  FIG. 15 , in a manner analogous with the ionic-current blockages observed when single strands of DNA are translocated through the channel formed by α-hemolysin in a lipid bilayer. Because no such reductions in current were observed during one hour of monitoring before adding DNA, and because the reductions in current ceased to occur when the voltage bias was reversed, the reductions in current are attributed to interactions of individual DNA molecules with the nanopore. The duration of these reductions in current was found to be on the order of milliseconds, and to consistently fall to a current value of about 88% of the open-pore current value. This last value is commensurate with translocation of a rod-like molecule whose cross-sectional area is 3-4 nm 2 . 
     The experimental observations, model considerations and control methodology, and experimental electronic device results all described above indicate that the ion beam-sculpting control method of the invention represents a superior approach to nanoscale fabrication. Specifically, the invention enables control of sputtering and mass transport processes that compete during an ion beam sculpting process. With the feedback control techniques described above, reproducibility does not depend on precisely matching all conditions and starting dimensions. If, however, such can be achieved, then the control model of the invention enables open loop processing without reliance on ion rate counting or other feedback control. The invention therefore is not limited to features or geometries that can accommodate an ion counting feedback loop. 
     The ion beam-sculpting control method of the invention is particularly useful for fabricating a wide variety of nanoscale semiconductor devices, masks, and mechanical features, and as explained above is not limited to formation of a pore or a through-hole. Slits, trenches, crosses, doping profiles, resist patterning, buried layer profiles, and other geometries and features can be produced and dimensionally controlled, or changed. Similarly, a wide range of materials can be employed, including microelectronic materials such as Si, SiO 2 , Si 3 N 4 , Al, and a wide range of others. Furthermore, it is recognized that next-generation ion-source arrays and mask technologies, combined with multichannel ion detectors, can be employed to enable highly parallel applications of the nanoscale ion beam sculpting control methods of the invention. 
     The process of controlling dimensional features of a structure using ion beam sculpting, as described above, can be extended to solid state structures that include more than one material. According to one advantageous embodiment, ion beam sculpting can be used to control the dimensions of a feature or features of a first and/or of a second material that are either both exposed on a surface or layered with respect to one another, in order to create a feature, e.g., at the edge of a nanopore, even as small as less than 10 nanometers in diameter, bordered by both materials. For example, if the first material is an electrically insulating material and the second material is an electrically conducting material, the dimensions of the materials can be controlled to form electrodes from the conductive material on opposite sides of a nanopore in the insulating material, i.e., laterally insulated by the insulating material and nanopore. The resulting solid state nanopore structure has numerous useful applications due to the electrical properties of this configuration. Such applications include, but are not limited to, molecular probing and detection, nanoscale characterization, near-field optical microscopy, surface enhanced Raman spectroscopy, electron tunneling and ionic probing. 
     In an example embodiment of a method for fabricating such a multi-material solid state nanopore device according to the invention, a starting structure  201 , e.g., as shown in  FIG. 16A  is provided. The starting structure, composed of a first material, can be supplied as a substrate, a membrane, or other suitable solid state structure. The first material can be any selected solid state material, but for many applications in which the second material is electrically conducting, it can be preferred that the first material be characterized as an electrically insulating material, including, e.g., silicon nitride, silicon dioxide, a polymer, an inorganic crystalline material, a plastic, or other suitable material. 
     The structure  201  can be uniform or nonuniform in thickness, and can include various features, e.g., a cavity  206  formed in the structure  201 .  FIG. 16A  illustrates an example of a cavity  206  formed into one surface  202  of the structure. The cavity  206  extends into the bulk of the structure  201  for a fraction of the structure&#39;s thickness, rather than through the entire thickness of the structure  201 , to an opposing surface  209 . As a result, the deepest level, i.e., the highest point, on the arch of the cavity  207  lies at somewhere around a midpoint of the structure&#39;s thickness. The geometry of the cavity  206  can be selected to enable controlled formation of a feature of controlled transverse and latitudinal dimensions in later processing steps, in the manner described previously. It is to be recognized, however, that the cavity  206  is not required, and that other structure configurations and features can be employed as suitable for a given application. 
     In one optional configuration, as shown in  FIG. 16B , a trench feature  211  can be lithographically patterned, e.g., using conventional techniques, on one surface  209  of the structure  201  of  FIG. 16A . The trench  211  can vary from, e.g., about 100 nm to 1 μm in width, and the depth of the trench can extend into the bulk of the structure  201  for a selected fraction of the structure&#39;s thickness, for example, between 40 nm and 100 nm. The depth of the trench  211  is selected so that the trench does not reach the top of the cavity  206  etched into the opposite surface  202 , if such is included. The width, depth and length of the trench  211  can also be selected to enable control and manipulation of a second material that is to be placed into the trench in subsequent processing steps. 
       FIG. 16C  shows an example multi-material and multi-layer structure resulting after a stripe layer  215  or “wire” composed of a second material that is deposited or evaporated onto the structure, and then patterned, e.g., by a conventional lift-off process, so that only the portion of second material deposited into and/or over the trench  211  remains in place, forming a stripe of material. The composition of the second material is different from that of the first material, and can be preferably provided for many applications as, e.g., an electrically conducting material such as, but not limited to, a metal. In particular, metals such as aluminum and gold can be advantageous to use as the second material because such are good conductors and do not oxidize readily. However, other conducting metals, and semiconductors or composites can also be employed for the second material. 
     Considering further optional configurations, after the electrically conducting stripe  215  has been added and patterned into the trench  211  of the structure, a through-hole, longitudinal slit  208 , or other aperture can be formed at a location of the stripe  215  and extending in depth to a point in the structure or through the entire structure, e.g., to the cavity  206  as shown in the figure. In this scenario, as shown in  FIG. 16D , the aperture, e.g., slit  208 , can extend across the entire longitudinal width  231  of the structure, cleaving the structure into two separate parts  201   a  and  201   b  and exposing inner surfaces  220   a  and  220   b . This complete cleaving is not necessary, however, and indeed, for many applications, it can be preferred to instead employ another geometry, such as an aperture or through-hole, that does not extend the entire longitudinal width of the structure, e.g., as shown in  FIGS. 17A and 17B , discussed below. The lateral width of an initial aperture such as a slit can be selected based upon the composition of the first and second materials and to enable control and manipulation of any material that may be moved to the location of the feature in subsequent processing steps, but typically can vary between about 40 nm and 100 nm. Slits or through-holes of this width can be formed by electron-beam or ion-beam lithography in the conventional manner. 
     With this structural arrangement, one or both of the two materials, i.e., the material of the structure  201  and the second material  215  formed on the structure, can be exposed to an ion beam in the manner described above to cause ion sculpting of one or both of the materials. In particular, ion beam sculpting can be employed to adjust or produce features relative to edges of the slit  208  or other edge feature in the structure. Given this scenario, the invention contemplates a wide range of additional structure configurations that can be employed. For example, referring to  FIG. 16E , there can be provided a structure  201  that further can include a surface layer  240  of a differing material or materials. The structure and the surface layer can be considered as the “first” material described above. A second material  215  can be formed on top of the surface layer; here the trench  211  described in the example above is not required, and instead the second material can sit atop the surface. For many applications, it can be preferred that the second material  215  be electrically conducting and the structure or surface layer, if included, be electrically insulating. 
     As shown in  FIG. 16E , the second material  215  can be provided in a selected geometry, e.g., as a stripe or line. An aperture  242  is produced through the second material  215 , the surface layer  240 , and the structure  201 . Although the aperture is here illustrated as being rectangular, the through hole can take on any suitable geometry, as described above. 
     In a further example configuration, as shown in  FIG. 16F , there is provided a structure  201 , again optionally including a surface layer  240 . A second material  215  is provided atop the structure or the surface layer  240 , again, e.g., in the pattern of a stripe or line. A trench  244  extends through the second material and the surface layer to a selected depth in the structure  201 . The depth of the trench can be selected based on requirements of a given application and the properties of the various materials; for many applications, a trench depth of, e.g., about 100 μm is sufficient. 
     Referring to  FIG. 16G , in yet a further configuration, there is provided a structure  201  configured such that the surface layer  240  forms a suspended membrane  246 , e.g., that is self-supported across its extent. There is formed a second material  215  atop the membrane, again, e.g., in the pattern of a stripe or line. An aperture  248  is formed through the second material  215  and the membrane material  240 . As in the previous embodiment, the aperture can be provided in any suitable configuration, e.g., as circular or rectangular. More than one aperture can be included in the membrane or other structure if desired for a given application. Further, the second material can be provided in a trench formed in the structure or surface layer material in the manner of  FIG. 16C  should such a configuration be suitable for a given application. In addition, the second material can be provided in any selected geometry on both sides of the structure or membrane. For example, the second material  215  can be provided on both the top and bottom surfaces of the structure, in alignment with an edge of the structure aperture in  FIG. 16E  or the membrane aperture in  FIG. 16G . 
     With these example structure configurations, ion beam sculpting can be employed in accordance with the invention to precisely adjust the extent of the first material and structure and/or the second material  215 . If the second material  215  is provided as an electrical conductor, this process can be advantageously exploited to precisely adjust the distance between the two separated legs of a conductive stripe on opposite sides of an aperture or trench, with the two separated legs operating as distinct electrodes. In other words, the ion beam sculpting process can be employed to precisely adjust the gap between two electrodes, even down to the nanometer scale, to thereby produce nanoelectrodes. The aperture or trench included in the embodiments just described for separating the two electrode legs is particularly useful for controlling the inter-electrode gap, as well as for enabling transmission electron microscopy (TEM) of the structure. But such is not required; the second material  215  can be deposited and patterned atop a structure surface or surface layer to form two separated electrode legs on a flat and unbroken surface. If two separated electrode legs are not required for a given application, a single electrode leg can be included rather than the two electrode legs illustrated, with ion beam sculpting then employed for precisely controlling the geometry of the single electrode. The following discussion focuses on a specific example for control of the gap between two nanoelectrodes, but it is to be recognized that control of the features of a single electrode can also be carried out with this process. 
     In the various alternative configurations just described, the structure  201 , structure surface layer  240 , and second material can be selected from a wide range of materials. For the example of formation of nanoelectrodes and control of nanoelectrode gap, the structure can be provided as a semiconducting substrate, e.g., a silicon substrate, or as an insulating substrate, e.g., a nitride, sapphire, polymer, oxide, glass, or other selected material, or a composite of materials such as a silicon-on-insulator substrate. If the second material  215  is to be provided as an electrically conducting electrode material, and if no surface layer  240  is to be included, then the substrate preferably is electrically insulating. If a surface layer  240  is included, then the structure  201  can be conducting or semiconducting, if not insulating. Given a conducting second material  215 , a surface layer, if included, is preferably insulating; provided as, e.g., silicon nitride, silicon dioxide, a polymer, or other selected material or composite of materials. The electrode material can be provided as gold, aluminum, or other suitable material, or a composite of conducting materials. 
     With these material selections, conventional microfabrication processes can be employed to produce the various configurations described above. Given a silicon substrate, conventional bulk micromachining by a suitable etch procedure, e.g., a conventional anisotropic wet etch process employing KOH, can be employed to form an aperture or a trench in the substrate or to remove a selected portion of the substrate in the formation of a suspended membrane. The techniques described above with reference to  FIG. 2  are here applicable in this regard, and further applicable for formation of an aperture through the surface layer or membrane as well as the conducting stripe. Conventional electroplating, sputtering, evaporation, or other deposition technique can be employed for producing the electrode material, and photolithography and lift-off processes can be employed for patterning the electrode material. 
     Whatever configuration is selected, once the electrode structure is in place, ion beam exposure of the structure is then carried out to ion sculpt a nanoelectrode gap. The incident ion beam can be supplied as atoms, i.e., neutral ions, ions of a controlled charge state, molecules or clusters of incident atoms, or indeed any controlled energy source. As discussed above, exposure of the surface to the ion beam causes competing processes of adatom creation and annihilation to occur at the surface of the structure. Depending upon the particular selection of the various controllable ion exposure parameters, as explained earlier, the creation and mobility of adatoms of the materials at the edge of a feature, e.g., a trench or aperture, can be stimulated to a greater extent relative to annihilation mechanisms. With this control, adatoms from the structure, a surface layer material provided on the structure, and/or a second material, e.g., electrodes, can be caused to move, e.g., toward the edge of a trench or aperture, thereby altering the material dimensions at the location of the features. 
     In accordance with the invention, the ion exposure conditions can be selected to cause a selected one or both of the structure materials to be ion sculpted. Referring now to  FIG. 16H , in a first example technique, the surface  209  of the structure, including the electrode legs  215   a ,  215   b , is exposed to a blanket ion beam  245  in the manner described above. In general, with this blanket exposure, both the electrode leg material and the structure material will flow as a result of ion beam exposure, if the exposure conditions for causing material transport are relatively similar for the two materials. If the exposure conditions favor, e.g., material transport of the electrode material but not the structure material, then only the electrode material will flow, as shown in  FIG. 16H . 
     It is found experimentally, for example, that the conditions for material transport of aluminum and silicon nitride are relatively similar. Therefore, given an aluminum stripe on a silicon nitride membrane, it can be expected that both the aluminum stripe and the membrane material adjacent to the stripe will flow in response to ion beam exposure. If it is desired that the structure material underlying the electrode material flow, then the stopping distance of the selected species for ion exposure in the electrode material should be considered. For example, it can be determined by conventional MonteCarlo simulation that the stopping distance of 50 KeV Ga ions in aluminum is about 350 Å and the stopping distance of 3 KeV Ar ions in aluminum is about 62 Å. If it is desired to cause a structural material underlying an aluminum electrode leg to flow with the electrode leg, then the aluminum stripe should be less than about 350 Å-thick, in the case of Ga ion exposure, or be less than about 62 Å-thick, in the case of Ar ion exposure for the example ion energies given. As can be easily recognized, this analysis can be extended to any ion species and any surface material to determine the maximum electrode thickness for enabling ion sculpting of material underlying the electrode. 
     Further in accordance with the invention, the energy of an ion beam and the stopping distance of a second material can be selected such that only the structural material beneath the second material, and not the second material, is ion sculpted. For example, given an aluminum stripe provided on an oxide membrane, for sufficiently high ion energy and sufficiently thin aluminum layer, only the oxide membrane below the aluminum can be made to flow in response to blanket ion beam exposure of the entire structure. 
       FIGS. 17A and 17B  illustrate pre-ion sculpting and post-ion sculpting configurations in which both materials in a multi-material configuration are sculpted. In  FIG. 17A  is illustrated a planar view of an insulating membrane  301  like that of  FIG. 16G , here composed of, silicon nitride, for example, and including a patterned electrically conducting electrode element  305 , e.g., an aluminum stripe, on the surface  302  of the structure. A circular aperture, or pore, having an initial diameter D 31  of between, e.g., 40 nm and 100 nm, is etched through the entire thickness of a region of the electrode  305 , and extends laterally beyond the electrode, and through the thickness of the membrane beneath the electrode, by, e.g., focused e-beam lithography and/or focused ion beam etching. 
     Ion-beam sculpting conditions are selected, in the manner described previously, for the combination of materials  303 ,  305  so that adatoms of both the insulating material and conducting material flow inwardly along radii for equal total lengths, toward the center of the pore  315 . In this manner, the flow of material shrinks the diameter of the pore from D 31  to D 32  while retaining the circular shape of the pore. The resulting diameter D 32  can be as small as 1 nm. This fabrication process provides a solid state nanopore device having nanoelectrode tips that taper inwardly and contact only a small portion of the circumference  313  of the pore  315 . 
     It is to be recognized, in considering the example of  FIGS. 17A-17B , that when simultaneously ion sculpting multiple materials, precise modeling and prediction of the interaction of an ion beam with the surface of a structure and/or surface layer is more complex than that for a single material, in general because many of the parameters of the modeling expressions above are material-dependent. For example, as noted above, material temperature, material surface conditions, and other material-dependent characteristics can be selected to increase adatom diffusivity, D, thereby to enhance mass transport of material to a feature being ion sculpted and/or to maximize the rate at which an ion sculpted feature is produced. Minimization of surface defects and other material trapping mechanisms can be carried out to minimize annihilation of adatoms by traps, thereby further enhancing the mass transport mechanism of the ion sculpting process. 
     In general, particularly when acting on different types of materials such as insulators and conductors, it is to be expected that for a given ion flux, F, for an average ion energy, for an ion beam pulse duty-cycle, and for a given exposure temperature, each distinct material will undergo different rates of adatom production and annihilation due to respective differences in the molecular structure and other properties of each material. For example, the mobility of the adatoms caused by the mechanisms of surface diffusion and viscous flow of a given material may depend on the crystalline structure and the presence of defects within the material as well as the relative mobility of atoms within the material when freed from a surface by ionic collisions. In addition, the effective depth that an ion beam penetrates a material can vary to some extent between materials. With this recognition, in accordance with the invention, a multi-material structure such as  201  can be exposed to an ion beam multiple times with varying exposure conditions to control the adatom flow of each material separately in sequence, or simultaneously, to achieve a desired ion sculpting result. 
     For the example of ion sculpting to control dimensions of a feature in a conducting material, e.g., for controlling the gap between two conducting electrodes, then, referring to  FIG. 16H , exposure of the surface  209  of a structure  201  to an ion beam  245  is carried out at exposure conditions that are selected to cause the electrically conducting material from the two legs  215   a ,  215   b  of the conductive stripe to advance toward the slit  208 . This results in portions  205   a ,  205   b  of the legs  215   a ,  215   b , respectively, extending beyond the edge of the structure into the slit, thereby reducing the width of the slit in that region and adjusting the gap between the conductor legs  215   a ,  215   b . For this application, it is preferred that the ion exposure conditions minimize flow of adatoms from the structure  201 , in contrast to the multi-material ion sculpting process illustrated in  FIGS. 17A-B , but such is not required; features and dimensions of both materials can be sculpted. 
     Referring also to  FIG. 16I , it is preferred in accordance with the invention that when ion sculpting a conducting material for adjustment of the gap between nanoelectrodes, the ion beam exposure be provided as a focused ion beam  245  that is rastered in a rastering pattern  250  along a portion or the entire extent of the length of the electrode legs  215   a ,  215   b , crossing the slit  208  or other gap between the legs. It is found that lateral scanning along the length of the conductor legs  215   a ,  215   b , as shown in the figure, by a focused ion beam can produce a higher adatom flow rate than longitudinal rastering along the width of the conductor legs. The focused ion beam need not be directed to the structure surface  209  and instead can be rastered only along the electrode legs as shown. With this technique, the material of the structure  209  is not ion sculpted and does not flow, and only the material of the electrode legs flows. The material of the structure underlying the electrode legs does not flow so long as the electrode leg material is thicker than the stopping distance characteristic of the ion species selected for the ion exposure. As shown in  FIG. 16I , as the rastering proceeds, electrode material is caused to transport toward the slit  208 , thereby reducing the gap size between the electrodes. 
     If only a limited portion of the width of the conductor legs is included in the raster scan by the focused ion beam, it is found that only that rastered portion is ion sculpted and alters its extent in the vicinity of the slit feature. As a result, the rastering can be selectively applied to produce localized protrusions  252   a ,  252   b  of each conductor leg  215   a ,  215   b , respectively, at the slit location. This can be particularly advantageous for producing a localized nanoelectrode gap at a precise location that is at a selected point along the width of the electrode, rather than extending across the entire electrode width. 
     In general, it is preferred that the focused ion beam rastering be controlled to minimize the beam exposure time at each pixel location of the raster pattern. Specifically, it can be preferred to adjust the ion beam control to employ whatever minimum pixel exposure is achievable for a given FIB machine. As explained previously, it has been experimentally shown that adatom transport to a feature can depend strongly on the time structure, or duty cycle, of a pulsed ion beam exposure. For the nanoelectrode gap ion sculpting process here, it is preferred that the focused ion beam system be controlled to maximize the beam “off” time between raster columns as a technique for producing an ion exposure duty cycle that maximizes the beam “off” time. For example, it can be preferred to control the “off” time between raster columns to be at least about 0.1 sec, where under conventional focused ion beam rastering control, such intercolumn beam “off” time might be 1000 times shorter. Further, as explained previously, it is recognized that adatom flow can occur over second-long time scales after an ion beam has been extinguished, and that an on-off beam duty cycle of 0.1 s “on” and 0.9-1.9 s “off” can produce a high flow rate toward the through-hole/slit feature, whereas continuous exposure tends to cause the aperture to enlarge. 
     After ion beam rastering of the electrode legs to produce a desired nanoelectrode gap, subsequent ion sculpting steps can be employed, e.g., under differing ion beam exposure conditions, to further adjust the dimensions of the conducting material  215  as well as to adjust the dimensions of the structure or a surface layer material, if such is included, in the vicinity of the slit  208  or other feature. Under typical ion beam exposure conditions, it is expected that most adatom production occurring at the structure surface material is localized to within a thin surface layer of approximately 5 nm in depth. However, if the ion beam energy is raised to a sufficient level, adatoms can be created by the ion beam at greater depths within the structure material. With this control, it is possible to achieve multi-layer flow of the structure, any surface layer material, and the electrode material. For example, adatoms from a location  227  ( FIG. 16H ) of the structure beneath the electrodes can be caused to flow by impact of high energy ions that penetrate the electrode material. In addition, the structure can be reoriented with respect to the ion beam, e.g., by turning the structure over to expose the bottom surface, to carry out ion beam sculpting at that surface of the structure. This technique can be particularly preferable for arrangements in which, e.g., electrode legs are provided on both front and back surfaces of a structure or membrane. Once ion sculpting is complete at a first of the surfaces, the structure can be reoriented to enable ion sculpting at the second surface. 
     Whatever ion beam exposure control is employed, it is preferred in accordance with the invention that the ion beam species be selected based on the materials to be exposed. For example, given ion beam exposure of an electrically conducting material such as a metal, it can be preferred to employ an inert gas or noble metal ion species that will not oxidize the metal. Otherwise, the ions introduced into the metal by the ion beam exposure can diffuse to the metal surface be oxidized, thereby diminishing the electrical properties of the material. For example, in a scenario of Ga ion beam exposure of a metal, the resulting implanted Ga ions can diffuse to the metal surface and be oxidized, forming a very stable surface oxide, and therefore is not optimum, but Ar ion beam exposure of the metal does in general form an oxide on the metal, and therefore can be preferred. 
     With this ion sculpting process, employing exposure parameters in the manner previously described, a nanoelectrode gap or other feature of interest can be controlled, e.g., reducing a gap in a second material layered on a structure from a large starting dimension to a precisely controlled smaller dimension that is on the nanoscale, e.g., under 10 nanometers in extent. In order to control such feature dimensions as precisely as possible, it is preferred in accordance with the invention that a closed-loop feedback control technique be employed as the ion sculpting is carried out. 
     In a first feedback control example, the ion counting feedback loop of  FIG. 3A  is employed, e.g., while an ion beam is rastered along the length of two nanoelectrodes atop a structure. Ions from the beam that pass through the aperture or slit in the structure between two nanoelectrodes during ion beam rastering across the aperture or slit can be detected by a detector as in  FIG. 3A , and counted in real time. Such ion counting can be employed as an indication of the width of a feature, such as gap between nanoelectrodes, because the ion count, i.e., number of ions traversing a feature, e.g., passing through a slit, is proportional to the extent of the feature. In the manner previously described, with this closed-loop feedback control technique, the ion beam rastering can be shut down when the feature reaches a particular dimension, or alternatively, if it is indicated by the ion counting that the feature is not changing as desired, the ambient temperature can be increased to boost adatom production. Similarly, when the lateral dimensions of the feature, e.g., a nanoelectrode gap, vary along its longitudinal width, the closed-loop system can be preferably controlled, e.g., for detection at a particular longitudinal location along the feature. Alternatively, the detector can accept ions from the entire feature width and thereby determine various lateral widths to accurately assess a two-dimensional contour across a feature landscape as the feature is sculpted. 
     EXAMPLE 9 
     A silicon nitride membrane of about 500 nm thickness was provided with an upper layer of aluminum having a thickness of about 55 nm. The aluminum was lithographically patterned to produce an aluminum stripe, or “wire” of about 200 nm in width along the length of the silicon nitride membrane in the manner described above. With the wire in place, the silicon nitride membrane and the upper aluminum layer were etched through their entire thicknesses by focused ion beam processing to produce an initial slit feature having an initial width of about 54 nm, as shown in the micrograph of  FIG. 18A . The slit was positioned so as to cut through the width of the aluminum line at a selected location along the silicon nitride membrane, with the membrane remaining intact. The etched silicon nitride membrane and upper aluminum line were then exposed to an ion beam provided in the closed-loop feedback apparatus of  FIG. 3A  and  FIG. 3B . 
     An argon ion beam species was employed for blanket ion exposure, controlled for a flux of about 0.2 ions/nm 2 /sec and an ion beam energy of about 3 keV. The aluminum stripe and nitride membrane were cyclically exposed to the ion beam, with the duration of each “on” cycle being about 100 ms and the duration of each “off” cycle being about 900 ms. As exposure of the structure to the ion beam was carried out, an ion counting feedback loop implemented as in  FIG. 3A  was monitored to determine the corresponding width of the slit in the membrane and the aluminum line. It was found that as the structure was exposed to the ion beam flux, both the silicon nitride membrane and the upper aluminum layer flowed, reducing the extent of the etched slit. During ion beam exposure the original 54 nm-wide slit was reduced to a 12 nm-wide slit. As the ion beam exposure was continued the slit correspondingly closed. It is recognized in accordance with the invention that this process could be continued to reduce the width of the feature to less than 10 nanometers, which is beyond the resolution of conventional etching techniques, and which results in a “nanopore” sized feature. 
     In a further feedback control technique provided by the invention, the electron tunneling detection and measurement method described previously with regard to  FIG. 3C  can advantageously be employed here given the nanometer scale achievable by the multi-material ion sculpting process. In an example of a process monitored and controlled by tunneling feedback, an electrically conducting material, e.g., an aluminum stripe, is provided on an insulating substrate, e.g., in the membrane arrangement of  FIG. 16G , in the manner described above. As shown in  FIG. 16I , an initial aperture  208  through the conducting stripe and membrane, forming two distinct electrodes  215   a ,  215   b , can be provided of relatively large dimensions, e.g., 50 nm-1000 nm in width, and can be poorly controlled, i.e., the width dimension can be imprecise. As a result, the initial aperture can be relatively easily produced with conventional microfabrication techniques in the manner previously described. 
     Each of the two electrode legs  215   a ,  215   b  is connected in a closed-loop circuit across the gap between the legs, with a voltage source, e.g., as in the arrangement of  FIG. 3C , and with a current measuring device. A voltage is applied across the aperture between the two electrodes as the gap is sculpted by exposure to ion beam rastering along the length of the electrodes and across the aperture under selected ion exposure conditions. The tunneling current across the aperture that results from the voltage application is then monitored and if desired, employed to automatically control ion beam exposure of the electrodes. 
     If desired, the tunneling measurement process can be employed during an entire sculpting process or alternatively only for a selected duration, and can be carried out during selected tunneling regimes, e.g., as a tunneling current develops in the Fowler-Nordheim regime of tunneling described above in connection with Expression (1a) or as the tunneling current develops in the opposing regime, described above in connection with Expression (1b) above. 
     As explained in detail previously, the tunneling feedback control expression employed for a given application is preferably selected based on the tunneling regime expected for a given process to be controlled. The Fowler-Nordheim control relationship is useful for monitoring adjustment of relatively large gaps, and corresponds to applied bias voltages that are above the work function of the electrode material. For smaller gaps, the applied voltage is preferably on the order or less than the material work function, and the alternative expression (1b) above is here preferably employed. It is recognized that mechanisms of conduction other than conduction that are associated with transport on the quantum scale can also be monitored, e.g., for producing one or more contributions to tunneling current signal for feedback control. 
     For a selected voltage bias to be applied between the electrodes across a gap, a prespecified current can be selected as a feedback “switch” signal indicative of production of a gap extent at which the ion exposure is to be terminated, in the manner described previously. It is recognized that such a prespecified current can be set by carrying out one or more calibration processes in which the correspondence between tunneling current and gap size is determined for selected materials and ion exposure conditions, in the manner described previously. With a calibration correspondence in hand, a tunneling current feedback system can be implemented for automated control of an ion sculpting process. 
     EXAMPLE 10 
     An aluminum stripe of about 300 nm in width and about 50 nm in thickness was provided on a silicon nitride membrane in the configuration of  FIG. 16G . An initial aperture of about 100 nm in extent was produced through the aluminum stripe and through the entire thickness of the membrane by a conventional focused ion beam etch technique. Electrical leads were attached to the left and right legs of the aluminum stripe and connected in the feedback loop of  FIG. 3C . The temperature and ion beam conditions were selected to induce closure of the gap by ion beam sculpting of the aluminum in the manner described previously. A focused Ga ion beam was rastered along the aluminum in the manner of  FIG. 16I . This process was continued until the gap between the electrodes was reduced to about 17 nm. 
     In a similar process, an initially large gap between aluminum electrode legs of about 1 μm in width and 100 nm in thickness on a silicon nitride membrane was narrowed by successive brief periods of focused ion beam sculpting. During each sculpting period, a DC voltage bias of about 20 V was applied across the gap and the resulting tunneling current was monitored as the structure was exposed to rastering by a focused Ga ion beam at a flux of 6.25 ions/s·nm 2  at room temperature. The two open-dot curves of  FIG. 18B  plot the measured current-voltage relationship. These experimental curves could be fit to the Fowler-Nordheim tunneling relationship, given an aluminum work function estimate of about 1 eV, yielding reasonable estimates of the corresponding minimum width along the extent of the gap; these “fit” curves are indicated by the dark, closed-dot curves of  FIG. 18B . 
     Plots like that of  FIG. 18B  produced for a given application can be employed as calibration tools for setting tunneling current levels in an automatic feedback-controlled ion sculpting process. For example, with the “fit” data, theoretical current-voltage relationships can be estimated for a given process. In one example of such, given a selected applied voltage bias of 5 volts, indicated by the arrow in the plot, as the tunneling current between two electrodes is monitored during ion beam sculpting of the electrodes, a 0.36 nm-wide gap can be expected to be formed when the measured tunneling current across the gap reaches 4 nA, as indicated in the plot, for the given exposure conditions. The calibration curve thereby indicates that control of the ion beam can be correspondingly set to automatically stop the ion sculpting process when measured tunneling current reaches 4 nA for a 5 V electrode bias to produce a 0.36 nm nanoelectrode gap. Thus, in accordance with the invention, it can be preferred to produce such calibration curves for a selected structure, materials, and ion sculpting conditions such that automatic feedback control of the ion sculpting process can be implemented. 
     EXAMPLE 11 
     An aluminum stripe of about 2 μm in width and about 150 nm in thickness was provided on a silicon nitride membrane in the configuration of  FIG. 16G . An initial aperture of about 100 nm in extent was produced through the aluminum strip and through the entire thickness of the membrane by a conventional focused ion beam etch technique. Electrical leads were attached to the left and right legs of the aluminum strip and connected in the feedback loop of  FIG. 3C . The structure was exposed to ion beam rastering of the aluminum at room temperature by a Ga ion beam at a flux of about 28.4 ion/s·nm 2 . The temp and ion beam conditions were selected to induce closure of the gap by ion beam sculpting of the aluminum in the manner described previously. The ion beam was rastered along the aluminum in the manner of  FIG. 16I . This process was carried out for a range of ion beam doses, during which the tunneling current was monitored as a function of applied voltage across the nanoelectrodes. Specifically, a DC voltage was applied across a gap at the level shown, and then as the focused ion beam was rastered along the aluminum, the resulting tunneling current was monitored. When the current significantly changed, e.g., by one nA or more, the ion beam rastering was halted and a current-voltage analysis of the given gap extent was made. 
       FIG. 18C  is a plot of each of these tunneling current-voltage characteristics. For a given bias voltage, as the ion beam dose was increased, the tunneling current increased, corresponding to a smaller gap. This correspondence is due to an enhancement in material movement of the sculpting process by the dose increase, and demonstrates that the tunneling measurement technique of the invention is a good indicator of changes in the dimensions of a feature that are caused by changes in process parameters. 
     It has been discovered in accordance with the invention that the application of a voltage bias across a gap between electrodes for making tunneling current measurements can itself effect the ion sculpting process in situ, specifically by enhancing the motion of matter during the sculpting process. It is understood that processes like electromigration, caused by high local current densities, electric fields, and/or temperatures, can be induced by the local application of a voltage bias to electrodes being ion sculpted. The electric field resulting from the voltage bias application can influence the shape of a final gap, e.g., by inducing the formation of a sharp points, e.g., asperities, across the gap at a location along the gap edge. Thus it is discovered that the application of a bias voltage for enabling a tunneling current feedback measurement across a gap also facilitates controlled reduction in the gap. 
     It is understood that the application of a bias voltage across a gap being ion sculpted can induce nanoscale material modification that would not be possible in its absence. In situ influence of an applied voltage on material transport during an ion sculpting process is understood to be measurable at 1 nm-100 nm length scales with applied voltages in the range of about 1 V to about 100 V. 
     It is further discovered in accordance with the invention that an applied bias voltage can also modify electrical characteristics, e.g., tunneling current-voltage characteristics, for ion sculpted materials before or after formation of a desired feature dimension has been effected, e.g., after an ion beam sculpting process has been completed. In other words, once a nanoelectrode gap is produced, the application of a voltage across the gap can itself alter the gap by causing material movement in the manner described above. In accordance with the invention, this material movement resulting from an ex situ voltage application can be calibrated in the manner given above to enable a controlled application of voltage for producing prespecified material movement. 
     Both in situ and ex situ feature dimension modifications by a voltage application can be employed in accordance with the invention in the manufacture of nanostructures with desired structural, chemical, and electrical characteristics, using feedback control to determine the final structure, function, or device characteristics of the nanostructure. There is provided by this process an ability to control material movement by a combination of ion beam sculpting and voltage-induced material movement. For example, a nanoelectrode gap sculpting process can consist of a first duration of focused ion beam rastering of the nanoelectrode structure, followed by a duration of voltage application across the nanoelectrode gap. A combination of ion beam exposure and voltage application can also be employed. For example, a first duration of focused ion beam rastering can be carried out without feedback control, followed by a duration of ion beam rastering including voltage application for enabling tunneling current feedback control, subsequently followed by ion beam rastering without feedback control and voltage application without ion beam exposure. There is contemplated in accordance with the invention all possible combination scenarios of the two processes for causing material movement. 
     It is further recognized in accordance with the invention that for some applications, it can be preferred to minimize material transport due to voltage application while at the same time implementing the tunneling current feedback provided by the invention. In such a situation, it is preferred in accordance with the invention that a tunneling current measurement be made only at discrete times during a sculpting process, rather than continuously during the process. It further can be preferred that each tunneling current measurement be made as fast as possible, i.e., without prolonged application of a voltage. Such can be achieved by employing, e.g., the high-speed current amplifier  84  in the feedback loop of  FIG. 3C . With this configuration, the effects of voltage application are minimized and a feedback control measurement is enabled. 
     In a further nanoelectrode ion sculpting control scenario, a combination of feedback control techniques and measurements can be employed. For example, the ion counting measurement and feedback control technique discussed above can be employed in combination with a tunneling measurement and feedback control technique. Such a combination enables both relatively gross and fine feedback control. With calibration data for each measurement technique, an ion sculpting process can be run in an automated mode for stopping the processes at a point of desired nanoelectrode gap formation. 
     Once an ion sculpting process is complete, further fabrication processes can be carried out to adapt a structure for a selected application. For example, once the gap between nanoelectrodes is ion sculpted to a selected dimension, the electrodes can be coated with, e.g., an insulating layer, by chemical vapor deposition, or other suitable conventional solid state deposition process.  FIG. 16J  is a cross-sectional view of the region of a structure near to the slit feature  208 , illustrating an insulating layer material  260  over the electrode layer  215 . The added layer  260  effectively “sandwiches” the electrode layer  215  between the structure  201  and the insulating layer  260 , such that the electrode material is exposed only at nanoelectrode tips  262   a ,  262   b  at edges of the slit  208 . This arrangement is particularly advantageous where the electrode layer is configured as two distinct electrodes across which a potential difference is to be applied for a given application. As will be discussed further below, the depicted arrangement of insulated electrodes across a nanopore can serve as a particularly effective molecular probing device because of the intense electrical field strengths and quantum level effects that can be achieved at the nanometer dimensional scale. 
     One particularly important application of molecular probing using the solid state nanopore device including nanoelectrodes at the location of the nanopore in accordance with the present invention is in probing chain polymer molecules such as DNA. According to an example method, the solid state nanopore device can be submerged in a medium containing mobile ions and contacted with a polymer molecule. If a voltage is applied across the device, the ions and the polymer molecule are attracted, or induced to move, through the nanopore of the solid state device. Owing to the minute diameter of the nanopore, monomers of the polymer can only pass through the nanopore in strictly single file order. The passage of ionic current and monomers of a polymer through the nanopore of a solid state nanopore device is shown schematically in  FIG. 19 . 
     According to one embodiment of the method, ion current through the nanopore can be detected and used to determine or evaluate molecular structure and/or species. Because molecules of the polymer effectively block amounts ionic current from the medium as they pass through the nanopore depending upon the proportion of the nanopore that they occupy as they pass, reduction of ion flux in the limiting aperture of the nanopore depends on the stereospecific and chemical properties of the polymer, e.g., a polynucleotide. 
     As a polymer molecule passes through the nanopore, each monomer of the polymer can be monitored. Individual polymeric molecules in a sample thus can be evaluated in rapid succession. Using this method, any suitable polymeric molecule that is a strand of monomers, which generally are arranged in linear strands, can be evaluated. The method is particularly useful for characterizing biological polymers such as polynucleotides, including, e.g., deoxyribonucleic acids and ribonucleic acids, polypeptides, and oligosaccharides, although other polymers can be evaluated. In some embodiments, a polymer that carries one or more charges, e.g., a polynucleotide or polypeptide, can particularly facilitate implementation of the invention. This method of the invention can be particularly advantageous for evaluating biological molecules that are a polynucleotide or a polypeptide. 
     The polymers employed for evaluation do not need to be present in a homogenous mixture. When the mixture is heterogeneous, however, only one molecule can interact with the nanopore at a time. Monitoring of such a heterogeneous population yields a size distribution of molecules in the mixture and/or sequence data for multiple polymeric molecules in the mixture. In order to identify the monomers, evaluation conditions preferably are appropriate to avoid secondary structure in the polymer to be sequenced, e.g., a polynucleotide; if necessary, this can be achieved by using a recording solution that is denaturing. 
     In one embodiment, two separate pools of medium, which can be electrolyte solutions, are provided at opposite sides of the nanopore of the solid state device. By applying a voltage differential between the two pools of medium, conductance of the nanopore can be monitored following passage of each monomer of the polymer molecule through the nanopore. For example, as shown in  FIG. 20 , measurements of ion currents through a solid state nanopore can achieve real-time discrimination between polynucleotides. In this example, a salt solution of 1M KCl, 10 mM Tris, of a pH 8 was employed, with a 120 mV bias applied across a nanopore membrane. Double-stranded DNA was here employed at 2868 base pairs long. In general, in laboratory experiments, of 999 conductance events recorded in four minutes, a nanopore configuration like that shown in  FIG. 19  unambiguously, e.g., &gt;90%, identified 98% of the molecules as poly(dA)100 or poly(dT)100. 
     The media employed on opposite sides of the nanopore can be any suitable material that permits adequate polymer mobility for nanopore interaction. For most applications, the medium can be provided as a liquid, e.g., as an aqueous solution or other liquid solution in which the polymers can be distributed. When an electrically conducting medium is preferred, such can be provided as any medium capable of carrying an electrical current in the form of ions such as, e.g., sodium, potassium, chloride, calcium, cesium, barium, sulfate, or phosphate ions. 
     In one embodiment of the method of the invention, ionic conductance across a nanopore is determined by measuring the flow of current across the nanopore via the conducting medium. A voltage difference can be imposed across the pore between the media pools by conventional means. Alternatively, an electrochemical gradient can be established by a difference in the ionic composition of the two pools of media, either with different ions in each pool, or with different concentrations of at least one of the ions in the solutions or media of the pools. In this embodiment of the invention, the measured conductance changes are indicative of monomer-dependent characteristics. 
     Alternatively, a voltage can be applied to nanoelectrodes formed at the location of the nanopore in the manner just described, with the nanopore forming a gap between the nanoelectrodes. In this scenario, molecular detection can be carried out via measurement of changes in tunneling current across the nanoelectrodes that result from the applied voltage during passage of monomers of a polymer molecule through the nanopore. Because the space between the nanoelectrodes, i.e., the nanopore diameter, in the solid state nanopore device is on the scale of nanometers, tunneling currents that jump from one electrode across the nanopore to the other are detectable because the tunneling current is related directly to the inter-electrode distance, e.g., in the manner given above with regard to Expressions (1a) and (1b), modified to account for the molecular and atomic species positioned in the nanopore between the electrodes at any given time. In this context it is noted that to maximize the detectable tunneling current that overcomes the tunneling barrier of the nanopore and a probed molecule of interest in the nanopore, it is preferable that the edges of the nanoelectrodes bordering the nanopore, i.e., the nanoelectrode “tips” be electrically insulated to the greatest extent possible. This ensures that tunneling electrons that are available to jump across the nanopore between nanoelectrodes do not have parallel conductive paths to tunnel through and thereby by-pass the nanopore in transit to the opposite electrode. 
     Owing to the exponential relationship between tunneling current and nanoelectrode distance given above in Expressions (1a) and (1b), it is found that detectable variations in tunneling current across nanoelectrodes provided at the site of a nanopore can be as much as three orders of magnitude greater than detectable variations in ionic current flowing through the nanopore. Because any variation in detected tunneling current is typically attributed to the effective tunneling barrier, φ, which depends on the molecular species passing through the nanopore and therefore contributing to the corresponding tunneling barrier, such variation can very effectively be employed as a molecular probe to determine molecular species as they pass through the nanopore. 
       FIG. 21  schematically illustrates the tunneling mechanism that can be imposed in accordance with the invention as a DNA molecule traverses a nanopore having nanoelectrodes at edges of the pore. An electron, e −  jumps from a first electrode  410  at which a high electrical potential  412  is applied, through an electrical potential due to a water barrier  415   a  to a DNA molecule at a lower electrical potential  414 , and then tunnels again through a water barrier  415   b  to a second electrode  430  which is at a lower electrical potential  418  as determined by an applied voltage between the nanoelectrodes, i.e., the high potential  412  minus the applied voltage=the low potential  418 . 
     As a DNA polynucleotide passes through the nanopore, each nucleotide is associated with a different barrier energy, and therefore with a particular “signature” measurement of tunneling current. This signature can be a specific length of time during which the polymer interacts with the nanopore as it is drawn through the nanopore at a known rate or by measuring some feature of the interaction as each monomer of the polymer is sequentially drawn through the nanopore. The interactions can also be sufficient to ascertain the identity or sequence of individual monomers in the polymer due to physical configuration, size/volume, charge, interactions with the medium, or other characteristic. 
     For example, the amplitude or duration of a measured variation in tunneling current can be used to identify the characteristics of a polymer passing through a nanopore. Such changes can be used to identify the monomers in sequence, as each monomer in general has a characteristic conductance change signature. This condition is illustrated in the plot of  FIG. 22 , which shows measured tunneling current levels associated with the various ATCG nucleotide bases. The volume, shape, electrical charge or other characteristic of each monomer is understood to affect electrical tunneling conductance in a characteristic way. Likewise, the size of an entire polymer can be determined by observing the length of time, i.e., duration, that monomer-dependent conductance changes occur. 
     Alternatively, the number of monomers in a polymer, which also is a measure of size or length, can be determined as a function of the number of monomer-dependent electrical tunneling conductance changes for a given polymer traversing the nanopore. The number of monomers may not correspond exactly to the number of conductance changes because there may be more than one conductance level change as each of monomer of the polymer passes sequentially through the nanopore. However, there will be a proportional relationship between the two values that can be determined by preparing a standard of known sequence. 
     There are a variety of suitable electronic devices that can be used in conjunction with the solid state nanopore device of the present invention for organizing, acquiring and analyzing the measurements made according to the described methods of the present invention, and computer acquisition rates and storage capabilities are adequate for the rapid pace of sequence data accumulation. 
     A solid state nanopore device including nanoelectrodes provided in accordance with the present invention also finds particular utility in the field of near-field optical microscopy, and specifically to the technique of surface-enhanced Raman spectroscopy. It is understood that optically-excited metallic nanoparticles can be used as near-field optical probes because such nanoparticles can enhance the electromagnetic field of incoming radiation on their surface by several orders of magnitude. It has been reported that silver nanoparticles can enhance surface fields by a factor of 10 14 , e.g., S. Emory et al., “Near Field Surface-Enhanced Raman Spectroscopy on Single Silver Nanoparticles”,  Anal. Chem.  69, 2631-2635 (1997). 
     In accordance with the invention, nanoparticles can be provided by extending the tips of conducting nanoelectrodes disposed at the edges of a nanopore several nanometers into the interelectrode gap formed by the nanopore. This condition is illustrated in  FIG. 16I  at tips  252   a ,  252   b . Excitation of the nanoelectrode tips by an optical source such as a laser causes the tips to behave in the same manner as free-standing metallic nanoparticles in enhancing the electromagnetic field near to the nanoelectrode tips. Through this surface enhancement mechanism, the near-optic field of atoms or molecules passing near to the surface of the electrode tips can be enhanced to the point where their optical fields can be “seen”. Thus, the solid state nanopore device including nanoelectrodes in accordance with the invention can be used as a key component in extremely sensitive optical detection instruments. 
     This discussion highlights the wide range of applications of the solid state feature formation and dimensional control processes of the invention. The subtractive and additive materials processing techniques of the invention, in conjunction with the physical species detection and feedback control of the invention, enable reproducible and highly precise feature formation. The advantages of this precision and control are most apparent when applied to nanometric feature dimensions and dimensional tolerances. It is recognized, of course, that those skilled in the art may make various modifications and additions to the processes of the invention without departing from the spirit and scope of the present contribution to the art. Accordingly, it is to be understood that the protection sought to be afforded hereby should be deemed to extend to the subject matter of the claims and all equivalents thereof fairly within the scope of the invention.