Abstract:
A heated or cooled sample holding stage for use in a nanoindentation measurement system is described. The geometry of the design and the selection of materials minimizes movement of a sample holder with respect to a nanoindentation tip over a wide range of temperatures. The system controls and minimizes motion of the sample holder due to the heating or cooling of the tip holder and/or the sample holder in a high temperature nanoindentation system. This is achieved by a combination of geometry, material selection and multiple sources and sinks of heat. The system is designed to control both the steady state and the transient displacement response.

Description:
RELATED APPLICATIONS 
       [0001]    This application claims priority to provisional U.S. patent application Ser. No. 62/136,930, filed Mar. 23, 2015, titled “Structure to Achieve Active Dimensional Stability During Temperature Changes.” 
     
    
     FIELD 
       [0002]    This invention relates to any field in which dimensional stability is required. This includes but is not limited to nanoindentation measurements. More particularly, this invention relates to compensating for dimensional changes due to temperature variations in such systems. 
       BACKGROUND 
       [0003]    In applications involving various high-precision measurement instruments, such as scanning electron microscopes, precision optical systems, alignment systems and nanoindentation testing systems, maintaining the position of a sample holding stage with respect to a microscope focal point or the tip of a nanoindentation test probe is critical. Dynamic variations in temperature over time can cause undesirable movements of a sample platform with respect to a focal point or a measurement tip in a measurement system. Temperature variations can be particularly problematic in sample holding platforms that include heaters or coolers for making high or low temperature measurements. 
         [0004]    What is needed, therefore, is a reliable system for heating or cooling the various components of the system while also compensating for movement of system components due to temperature variations. 
       SUMMARY 
       [0005]    In various embodiments described herein, the above and other needs are met by a heated or cooled holding stage for holding a sample or a measurement tip or both for use in a nanoindentation measurement system. The geometry of the design and the selection of materials minimizes movement of the sample holder with respect to a nanoindentation tip over a wide range of temperatures. Preferred embodiments control and minimize motion of the sample and/or motion of the indentation tip due to the heating of the tip and/or the sample in a high temperature nanoindentation system. This is achieved by a combination of geometry, material selection and multiple sources and sinks of heat. Both the steady state and the transient displacement response can be controlled. 
         [0006]    In embodiments described herein, a design goal is to minimize the net linear expansion or contraction of structural elements along a heat flow path that traverses one or more 180 degree changes in direction—in other words, a path that folds back on itself one or more times. The net linear expansion/contraction along the path depends on the lengths of the various components of the structure in the path, their thermal expansion coefficients, and the temperature gradient across each component. For purposes of modeling, one-dimensional heat flow is assumed, so that component lateral dimensions are not critical. The net linear expansion/contraction can be described as: 
         [0000]      net linear expansion/contraction= L   i α i    ΔT   i  
 
         [0000]    where, L i , α i  and ΔT i  are the corresponding length along the direction of the path, the thermal expansion coefficient, and the temperature gradient across the component, respectively, for each component in the path. In the above equation, some values of ΔT i  are positive (in the +y direction) and some are negative (in the −y direction), depending on the direction of heat flow. As one skilled in the art will appreciate, the design goal is net zero expansion/contraction. From the above equation, it is apparent that there are multiple combinations of component lengths, component material properties, and component temperature gradients that can achieve a net zero expansion/contraction for steady-state or transient heat flow conditions. This equation also accounts for additional contributions to the expansion/contraction from radiation, especially at higher operating temperatures. 
         [0007]    Some embodiments described herein provide a sample holding stage for a measurement instrument. The sample holding stage includes a sample holder, a support structure, and a housing. The sample holder includes a sample platform and a tubular support stem. The sample platform has an upper surface upon which a sample may be placed and a lower surface disposed below the upper surface. The tubular support stem has an upper portion that is rigidly affixed to the lower surface of the sample platform and a lower portion disposed below the upper portion. The support structure includes a base member, a tubular wall member, and a lip member. The base member is rigidly affixed to the lower portion of the tubular support stem. The tubular wall member has a lower portion that is rigidly affixed to the base member and an upper portion disposed above the lower portion. The lip member is rigidly affixed to the upper portion of the tubular wall member and has a central opening. The lip member is also rigidly affixed to the housing. The housing includes a central bore and an upper ledge that surrounds the bore. The central bore receives the base member and the tubular wall member of the support structure. 
         [0008]    In preferred embodiments, at least a portion of the sample platform is disposed inside the central opening of the lip member, and the tubular support stem of the sample holder is disposed inside the tubular wall member of the support structure. When there is thermal expansion or contraction, the sample platform can move axially with respect to the tubular wall member, and the base member of the support structure can move axially with respect to the housing. 
         [0009]    In some embodiments, the sample platform, the tubular wall member, the central opening of the lip member, and the central bore of the housing are all cylindrical. The inner diameter of the tubular wall member is greater than the sample platform diameter, so that the sample platform can move axially with respect to the tubular wall member. The inner diameter of the central opening of the lip member is greater than the sample platform diameter, so that the sample platform can move axially with respect to the central opening of the lip member. The diameter of the central bore of the housing is greater than the outer diameter of the tubular wall member, so that the tubular wall member can move axially with respect to the central bore of the housing. 
         [0010]    In some embodiments, the sample holder is formed of molybdenum, the support structure is formed of stainless steel, and the housing is formed of copper. 
         [0011]    In some embodiments, a heat transfer element is disposed within the sample platform for transferring heat into or removing heat from the sample platform. 
         [0012]    In another aspect, embodiments described herein provide an indentation tip holding stage for a measurement instrument. The indentation tip holding stage includes a housing, a support structure, and a tip holder. The housing has an outer surface and a central bore extending into the housing from its outer surface. The support structure includes a central portion disposed at least partially inside the central bore of the housing. A central bore in the support structure, which extends into the central portion, has a bore opening in an outer surface of the central portion and a bore end spaced apart from the bore opening. A lip member, which extends outwardly from the central portion, is rigidly affixed to the outer surface of the housing. The tip holder, which is disposed at least partially inside the central bore of the support structure, includes a receiving portion and an attachment portion. The receiving portion, which is disposed adjacent the bore opening in the central portion, receives and holds an indentation tip. The attachment portion, which is disposed inside the central bore of the support structure, is rigidly affixed to the central portion of the support structure adjacent the bore end. When there is thermal expansion or contraction, the central portion of the support structure can move axially within the central bore in the housing, and the receiving portion of the tip holder can move axially within the central bore of the support structure. 
         [0013]    In some embodiments, the tip holder is formed of molybdenum, the support structure is formed of stainless steel, and the housing is formed of copper. 
         [0014]    In some embodiments, a heat transfer element is disposed within the central portion of the support structure for transferring heat into or removing heat from the tip holder. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0015]    Further advantages of the invention are apparent by reference to the detailed description in conjunction with the figures, wherein elements are not to scale so as to more clearly show the details, wherein like reference numbers indicate like elements throughout the several views, and wherein: 
           [0016]      FIGS. 1-3  depict a sample holding stage according to an embodiment of the invention; 
           [0017]      FIG. 4  depicts a plot of displacement versus distance along a heat flow path in the sample holding stage depicted in  FIGS. 1-3 ; 
           [0018]      FIGS. 5A and 5B  depict a tip holding stage according to an embodiment of the invention; and 
           [0019]      FIGS. 6A and 6B  depict a sample holding stage according to an alternative embodiment. 
       
    
    
     DETAILED DESCRIPTION 
       [0020]    As the terms are used herein, “upper,” “lower,” “above,” and “below” indicate spatial positions or relationships of various components of the structure with reference to the y-axis (vertical axis) of an x-y-z coordinate system. Thermal expansion and contraction, and compensation therefor, are also described as occurring along component axes that are disposed in the y-direction. It will be appreciated that the structures described herein could be rotated such that the component axes are disposed in the x-direction or z-direction (or any other direction), in which case the terms above that describe spatial positions or relationships are transformed to the relevant component axes. Thus, the invention is not limited to a vertical orientation, nor is it limited to any other particular orientation of the structure with respect to any particular axis of a coordinate system. 
         [0021]      FIGS. 1, 2 and 3  depict a cutaway view of a preferred embodiment of a sample holding stage  10 , comprising a sample holder A, a support structure B and a housing C. The sample holder A, which may be heated or cooled, includes a sample platform  12  and a support stem  14 . 
         [0022]    The sample platform  12  and the support stem  14  are both preferably formed from molybdenum, which has a coefficient of thermal expansion of 2.8×10 −6  in/(in R). The sample platform has an upper surface  12   a  for receiving a sample and a lower surface  12   b  for engaging the support stem  14 . In a most preferred embodiment, the sample platform  12  is cylindrical. Generally, the diameter of the sample platform  12  depends on the size of sample to be accommodated. From a heat compensation standpoint, the diameter of the platform is generally not critical, as only axial displacements are of interest. However, it will be appreciated that the outer diameter of the platform must be less than the inner diameter of the lip  20  of the support structure, so that the platform  12  can move freely in the axial direction with respect to the lip  20  as the structures expand and contract with changes in temperature. In one embodiment, the diameter of the sample platform is 12.5 mm. 
         [0023]    A heat transfer element  13  may be disposed within the platform  12 . In some embodiments, the heat transfer element  13  is an electric heater element for providing heat to a sample material disposed on the platform. In some embodiments, the heat transfer element  13  is a heat sink for cooling the sample. The thickness (axial height) of the platform  12  is preferably determined by the minimum space required to accommodate the heat transfer element  13 . 
         [0024]    The support stem  14  includes an upper portion  14   a  and a lower portion  14   b . In a most preferred embodiment, the support stem  14  is cylindrical. However, it should be appreciated that the support stem  14  could have any other tubular shape. Because one purpose of the support stem  14  is to throttle heat flow, its axial height (y direction) is as small as possible while still accommodating structures at either end that may be needed to attach the stem  14  to adjacent components. In one embodiment, the total axial height of the support stem is 7.8 mm. The thickness of the tubular wall of the stem  14  is preferably as small as possible while still providing sufficient mechanical strength. In a preferred embodiment, the upper portion  14   a  of the stem  14  is attached to the lower surface  12   b  of the platform  12  by high-temperature brazing. 
         [0025]    The support structure B comprises a base portion  16 , a tubular wall member  18  and an upper lip member  20 , which are all preferably formed from stainless steel (such as type  304 ) having a coefficient of thermal expansion of 9.6×10 −6  in/(in R). 
         [0026]    The tubular wall member  18  has a lower wall portion  18   a  and an upper wall portion  18   b . In a most preferred embodiment, the tubular wall member  18  is cylindrical. However, it should be appreciated that the tubular wall member  18  could have any other tubular shape. The axial height (y direction) of the tubular wall member  18  depends on the choice of materials and lengths of other components in the heat flow path. In one embodiment, the axial height of the tubular wall member is 11.7 mm. The effective height of the tubular wall member  18  can be adjusted by replacing the upper lip member  20  with a similar-sized circular clamp  38  that can slide onto the tubular wall member  18 , such as shown in  FIGS. 6A and 6B . The wall thickness of the tubular wall member  18  is preferably as small as possible to throttle heat flow, while not compromising needed mechanical strength. In one embodiment, the wall thickness of the tubular wall member is 0.38 mm. From a heat compensation standpoint, the diameter of the tubular wall member  18  is generally not critical, as only axial displacements are of interest. In one embodiment, the outer diameter of the tubular wall member is 14.5 mm. It will be appreciated that the inner diameter of the tubular wall member  18  must be greater than the outer diameter of the platform  12 , so that the platform  12  can move freely in the axial direction with respect to the tubular wall member  18  as the structures expand and contract with changes in temperature. The upper lip member  20  and the upper wall portion  18   b  can be made as one continuous piece, such as by machining the structure from a single piece of stainless steel. Alternatively, the upper lip member  20  may be shrink fit onto the upper wall portion  18   b . In one embodiment, the outer diameter of the upper lip member member is 22 mm. 
         [0027]    The thickness (axial height) of the base portion  16  is preferably as small as possible while still permitting the fastening of the base portion to the lower portion  14   b  of the stem  14 , and preventing excessive distortion of the lower wall portion  18   a  to which the base portion  16  is fastened. In one embodiment, the axial height of the base portion is 3.5 mm. The lower portion of the stem  14   b  can be attached to the base portion  16  in various ways, such as by welding, fastening by a set screw, shrink fit, or a combination of these. The base portion  16  and the lower wall portion  18   a  can be made as one continuous piece, such as by machining the structure from a single piece of stainless steel. Alternatively, the base portion  16  may be shrink fit into the lower wall portion  18   a.    
         [0028]    The housing C, which is preferably formed from copper (coefficient of thermal expansion=9.3×10 −6  in/(in R)), has a central bore  22  and an upper ledge portion  24 . In a most preferred embodiment, the central bore  22  is cylindrical. However, it should be appreciated that the central bore  22  could have any other tubular shape. The upper lip member  20  of the support structure B is fixedly attached to the upper ledge portion  24  of the housing C, such as with threaded bolts. 
         [0029]    As depicted by the arrows in  FIG. 3 , heat generated by a heat transfer element  13  in the sample platform  12  flows through the walls of the support stem  14 , through the base portion  16 , tubular wall member  18 , and upper lip member  20  of the support structure B, and finally into the copper housing C. Because the support stem  14  of the sample holder is fixed to the base portion  16  of the support structure, the upper surface  12   a  of the platform  12  moves in the +Y direction due to thermal expansion of the platform  12  and stem  14 . Because the lip  20  of the support structure B is fixed to the ledge  24  of the housing C, which is maintained at a constant lower temperature, the base portion  16  of the support structure B moves in the −Y direction due to thermal expansion of the support structure. 
         [0030]    The offsetting +Y and −Y movements of the structure result in the upper surface  12   a  of the platform  12  maintaining an essentially constant position as the structure heats up or cools down. This offsetting effect is illustrated in  FIG. 4 , which is a plot of net displacement versus distance along the heat flow path over a temperature range of 100° C. to 400° C. 
         [0031]    With reference to  FIG. 2 , for perfect temperature compensation at the upper surface of the sample platform, assuming that the housing C is at room ambient temperature, 
         [0000]        L   1 ×α 1   ×ΔT   1   =L   2 ×α 2   ×ΔT   2 ,
 
         [0000]    where, α 1  is the coefficient of thermal expansion of the material used for the sample platform  12  and the support stem  14 , and α 2  is the coefficient of thermal expansion of the material used for the tubular wall member  18 , and L 1  and L 2  are their respective lengths along the y direction, and ΔT 1  and ΔT 2  are the respective temperature gradients across the corresponding components. 
         [0032]      FIGS. 5A and 5B  depict an embodiment of a nanoindentation tip holding stage  26  that includes a tip holder  32  for holding a nanoindentation tip (not shown). In a preferred embodiment, the tip holder  32  is formed from molybdenum. The tip holder  32  has a receiving portion  32   a  for receiving a nanoindentation tip and an attachment portion  32   b . The tip holder  32  is disposed within a central bore  33  of a central portion  30   a  of a support structure  30 , with the receiving portion  32   a  extending out from the bore opening  33   a . In a preferred embodiment, the attachment portion  32   b  of the tip holder is fixedly attached to the bore end  33   b  at the bottom of the central bore  33 . Thus, the tip holder  32  is firmly held and supported by the support structure  30 , which in a preferred embodiment is formed from stainless steel. The receiving portion  32   a  of the tip holder  32  is free to move axially with respect to the bore opening  33   a  due to material expansion or contraction caused by temperature changes. 
         [0033]    In some embodiments, a heat transfer element  31  is disposed within the central portion  30   a  of the support structure  30 . The heat transfer element  31  may be an electric heater element for heating the tip holder  32 , or a heat sink for cooling the tip holder  32 . Multiple heat transfer elements  31  may be strategically placed to alter the transient response as desired. 
         [0034]    The support structure  30  is held and supported by an extension shaft housing  28 . The housing  28  has a central bore  36  that receives the central portion  30   a  of the support structure  30 . An outer lip  34 , which extends outwardly from the central portion  30   a  of the support structure  30 , is fixedly attached to an outer surface  28   a  of the housing  28 . In this configuration, the central portion  30   a  of the support structure  30  is free to move axially with respect to the central bore  36  as materials expand or contract due to temperature changes. 
         [0035]    Thus, as the support structure  30  is heated (or cooled), the central portion  30   a  of the structure  30  moves downward (or upward), thereby compensating for expansion (or contraction) of the tip holder  32 . This controls the steady state response to maintain the position of the receiving end of the tip holder  32 . 
         [0036]    In a preferred embodiment, the shaft housing  28  is formed from copper. It will be appreciated that various other combinations of materials may be used for the tip holder  32 , support structure  30  and extension shaft  28 . 
         [0037]    The foregoing description of preferred embodiments for this invention have been presented for purposes of illustration and description. They are not intended to be exhaustive or to limit the invention to the precise form disclosed. Obvious modifications or variations are possible in light of the above teachings. The embodiments are chosen and described in an effort to provide the best illustrations of the principles of the invention and its practical application, and to thereby enable one of ordinary skill in the art to utilize the invention in various embodiments and with various modifications as are suited to the particular use contemplated. All such modifications and variations are within the scope of the invention when interpreted in accordance with the breadth to which they are fairly, legally, and equitably entitled.