Abstract:
A method and a system are disclosed for determining at least one characteristic of a sample that contains a substrate and at least one film disposed on or over a surface of the substrate. The method includes a first step of placing a mask over a free surface of the at least one film, where the mask has a top surface and a bottom surface that is placed adjacent to the free surface of the film. The bottom surface of the mask has formed therein or thereon a plurality of features for forming at least one grating. A next step directs optical pump pulses through the mask to the free surface of the film, where individual ones of the pump pulses are followed by at least one optical probe pulse. The pump pulses are spatially distributed by the grating for launching a plurality of spatially distributed, time varying strain pulses within the film, which cause a detectable change in optical constants of the film. A next step detects a reflected or a transmitted portion of the probe pulses, which are also spatially distributed by the grating. A next step measures a change in at least one characteristic of at least one of reflected or transmitted probe pulses due to the change in optical constants, and a further step determines the at least one characteristic of the sample from the measured change in the at least one characteristic of the probe pulses. An optical mask is also disclosed herein, and forms a part of these teachings.

Description:
STATEMENT OF GOVERNMENT RIGHTS  
       [0001] This invention was made with government support under grant number DOE DE-FG02-86ER45267, awarded by the Department of Energy. The government has certain rights in the invention. 
     
    
     
       FIELD OF THE INVENTION  
         [0002]    This invention relates generally to non-destructive material analysis and characterization systems and methods and, more particularly, relates to optically based materials analysis and characterization systems that employ light pulses of picosecond and sub-picosecond duration to generate a localized stress in a sample that results in propagating strain waves, and that detect changes in optical constants of the sample material due to the propagating strain waves.  
         BACKGROUND OF THE INVENTION  
         [0003]    A number of U.S. Patents exist in the general area of picosecond ultrasonics. In most of these U.S. Patents a pump light pulse is directed at the surface of a sample. The pump light pulse raises the temperature of a layer near the surface of the sample and sets up a stress in this region. A time-varying strain is then generated in the sample. The strain is detected by means of a probe light pulse applied to the sample at a later time. Hereinafter this approach will be referred to as the “standard method”. From the arrival time, amplitude, and shape of the detected signals, a data processor is enabled to determine a number of characteristics of the sample. These characteristics include, but are not limited to, the film thickness, the adhesion between a film and the substrate, the adhesion between one film and another film, the orientation of crystalline grains making up a film, the size of grains, the crystal phase of a film, the electrical resistivity of a film, the rate of electromigration within a film, and the yield stress of a film.  
           [0004]    In some of these U.S. Patents measurements can be made by means of a second method, referred to herein for convenience as a “grating method”. In this approach, the pump light is divided into two beams that are directed onto the sample surface at oblique angles. Because of the constructive and destructive interference between the two beams, the intensity of the pump light varies periodically across the sample surface. Thus, the temperature rise of the sample surface and the induced stress will also vary periodically across the sample surface. This stress launches a strain disturbance into the sample that varies periodically across the sample surface. This strain field causes the optical constants of the sample, and the displacement of the sample surface, to vary across the sample surface and, as a consequence, when a probe pulse is incident onto the surface a fraction of the probe pulse will be diffracted, rather than undergoing specular reflection. Thus, the strain field acts as a diffraction grating. By a measurement of the intensity of the diffracted probe light as a function of the time after the application of the pump light pulse, the propagation of strain in the sample can be investigated, and physical properties of the sample determined. The grating method can also be used to determine the various sample properties that were listed above.  
           [0005]    These two methods each have some limitations. For example, in the standard method, in order to determine the thickness of a film the sound velocity in the film must be known. This value can be taken from measurements made on a bulk sample of the same material composition as the film. In some cases, it is also possible to estimate the sound velocity from a measurement of the reflection coefficient of the strain pulse at the interface between one film and another. This measurement enables a comparison of the acoustic impedances of the two films to be made.  
           [0006]    The grating method also exhibits a number of limitations. For example, it is necessary to build the apparatus in a way that ensures that the phase relation between the two pump beams remains constant. In addition, the diffracted component of the probe light may have a low intensity and thus may be difficult to measure accurately in the presence of light diffusely scattered from the surface of the sample.  
           [0007]    Based on the foregoing, it can be appreciated that a need exists to provide an improved approach to ultrasonic sample characterization that overcomes the foregoing and other problems.  
         OBJECTS AND ADVANTAGES  
         [0008]    It is a first object and advantage of these teachings to provide an improved sample characterization system and method that overcomes the foregoing an other problems.  
           [0009]    It is another object and advantage of these teachings to provide an improved sample characterization system and method that employs an optical mask.  
         SUMMARY OF THE INVENTION  
         [0010]    The foregoing and other problems are overcome and the objects of the invention are realized by methods and apparatus in accordance with embodiments of this invention.  
           [0011]    An improved method and apparatus in accordance with these teachings generates and detects strain pulses in a sample, while retaining many of the advantages of the standard method, while at the same time making it possible to determine the sound velocity in the sample. A transparent plate, referred to herein for convenience as a mask, is placed over the sample. The bottom of the plate has a periodic grating etched into its surface. A pump light pulse is directed through the transparent mask onto the sample. The periodic grating of the mask distorts the wavefront of the light pulse and, as a result, the intensity of the light incident onto the film varies periodically with position across the sample surface. This results in a heating of the film surface that varies periodically with position. The regions of the film that are heated expand and, as a result, spatially distributed strain pulses (disturbances) are launched into the sample. The strain pulses result in a change in the optical constants of the sample, and this change is detected by means of a time-delayed probe pulse also directed onto the sample through the transparent mask. As in the standard method and the grating method, the improved method in accordance with the teachings herein can be used to determine various characteristics of the sample. These characteristics include, but need not be limited to, the film thickness, the adhesion between a film and the substrate, the adhesion between one film and another film, the orientation of crystalline grains making up a film, the size of grains, the crystal phase of a film, the electrical resistivity of a film, the rate of electromigration within a film, and the yield stress of a film.  
           [0012]    In one preferred embodiment, the pump and probe beams are directed through the mask at normal incidence. The probe is delayed relative to the pump by means of a variable optical path provided by a movable stage. The change in the intensity of the reflected probe beam is measured as a function of the time delay between the application of the pump and probe pulses. To improve the signal to noise ratio the intensity of the pulses composing the pump beam is modulated at frequency f by means of an acousto-optic modulator. The output of the detector of the reflected probe beam is fed into a lock-in amplifier for which the reference signal is at the same frequency f. The measured change ΔR(t) in reflectivity of the sample is compared with the results of a simulated reflectivity change ΔR sim (t). The change ΔR sim (t) can be determined as follows: A) An initial estimate is made for the parameters of the sample. These parameters include, but are not necessarily limited to, the thickness, density, sound velocity, thermal expansion, specific heat, and optical constants of the different films, the adhesion between the films, the orientation of crystalline grains making up a film, the size of grains, the crystal phase and electrical resistivity of each film. B) Based on these assumed values, the stress in the structure that is induced by the pump light pulse is calculated. C) The time-dependent strain in the sample is then calculated. D) From this strain, the expected change in reflectivity ΔR sim (t) is found. E) This change is compared with the measured reflectivity ΔR(t). The parameters of the sample are then adjusted and the procedure repeated in order to achieve the best possible agreement between ΔR(t) and ΔR sim (t).  
           [0013]    A method and a system are thus disclosed for determining at least one characteristic of a sample containing a substrate and at least one film disposed on or over a surface of the substrate. The method includes a first step of placing a mask over a free surface of the at least one film, where the mask has a top surface and a bottom surface that is placed adjacent to the free surface of the film. The bottom surface of the mask has formed therein or thereon a plurality of features for forming at least one grating. A next step directs optical pump pulses through the mask to the free surface of the film, where individual ones of the pump pulses are followed by at least one optical probe pulse.  
           [0014]    In accordance with an aspect of these teachings the pump pulses are spatially distributed by the grating for launching a plurality of spatially distributed, time varying strain pulses within the film. The strain pulses cause a detectable change in optical constants of the film.  
           [0015]    A next step detects a reflected or a transmitted portion of the probe pulses, which are also spatially distributed by the grating.  
           [0016]    A next step of the method measures a change in at least one characteristic of at least one of reflected or transmitted probe pulses due to the change in optical constants, and a further step determines the at least one characteristic of the sample from the measured change in the at least one characteristic of the probe pulses.  
           [0017]    In addition to changes in reflectivity arising from the strain pulses that are launched in the sample, there may be components that arise from a spatial variation in temperature, and/or from a spatial variation in a density of electrons and holes in the sample.  
           [0018]    For example, the sample may include at least one region that is implanted during an ion implant process and, using the spatially varying density of electrons and holes in the film, a determined characteristic of the sample can be related to at least one of (A) a number of ions implanted per unit area of the surface of the sample; (B) a kinetic energy of the ions that are directed at the surface of the sample; (C) a direction at which the ion beam is incident onto the surface of the sample; (D) an ion current per unit area during the ion implant process; (E) the species of the implanted ion; (F) the charge on the implanted ion; (G) a duration of time that the ion-implanted sample is annealed; and (H) a temperature at which the ion-implanted sample is annealed.  
           [0019]    An optical mask is also disclosed herein, and forms a part of these teachings.  
           [0020]    Also disclosed is a method for determining the electrical resistivity of a film that comprises part of a sample having an underlying substrate. The method includes steps of: (A) placing a mask over a free surface of the film, the mask having a top surface and a bottom surface that is placed adjacent to the free surface of the film, the bottom surface of the mask comprising a plurality of features having a known feature repeat distance w; (B) directing optical pump pulses through the mask to the free surface of the film, individual ones of the pump pulses being followed by at least one optical probe pulse, said pump pulses being spatially distributed by said at least one grating for generating a spatially distributed temperature variation within the film that causes a change in optical constants of the film; (C) detecting a reflected or transmitted portion of said probe pulses, said probe pulses also being spatially distributed by said at least one grating; (D) measuring ΔR(t) as a function of the time t after the application of the pump pulses using the mask of known repeat distance w; (E) assuming values for the thermal conductivity κ film  of the film, the thermal conductivity κ sub  of the substrate, and the Kapitza conductance σ K  between the film and the substrate; (F) calculating an initial temperature distribution within the film; (G) calculating the temperature distribution within the film at later times based on the assumed values for the thermal conductivity of the film, the thermal conductivity of the substrate, and the Kapitza conductance between the film and the substrate; (H) calculating an expected change in reflectivity ΔR(t) based on the calculated temperature distribution; (I) adjusting the parameters κ film , κ sub , and σ K , and repeating Steps (F)-(H) so as to obtain a best fit to the measured ΔR(t); and calculating the electrical resistivity from the thermal conductivity. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0021]    The above set forth and other features of the invention are made more apparent in the ensuing Detailed Description of the Invention when read in conjunction with the attached Drawings, wherein:  
         [0022]    [0022]FIG. 1 is an enlarged, cross-sectional view, not to scale, of a sample having a substrate, at least one film, and a mask disposed over a surface thereof in accordance with these teachings;  
         [0023]    [0023]FIG. 2 is a simplified block diagram of a material characterization system in accordance with these teachings;  
         [0024]    [0024]FIG. 3 is a logic flow diagram of a method for operating the data processor shown in FIG. 2 for generating a simulation of a change in sample reflectivity, and for comparing the simulation to a measured change in sample reflectivity;  
         [0025]    [0025]FIG. 4 is an enlarged, cross-sectional view, not to scale, of a sample having a substrate, at least one film, and a mask disposed over a surface thereof in accordance with a further embodiment of these teachings, wherein the grating region of the mask is at a different height than all or a portion of the surrounding area of the lower surface of the mask;  
         [0026]    [0026]FIG. 5 is a logic flow diagram of a method for the determination of the electrical resistivity of a metal film using the optical mask in accordance with the teachings herein; and  
         [0027]    [0027]FIG. 6 depicts in an enlarged cross-section a sample having laterally patterned features. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0028]    Referring first to FIG. 1, a sample  10  includes a substrate  12 , such as semiconductor material (e.g., silicon, a Group III-V material, or a Group II-VI material) having at least one film  14 , such as a metal film or semiconductor or a dielectric film, disposed on or over a top surface thereof. A transparent plate, referred to herein as a mask  16 , is placed on top of the sample  10 . The mask  16  has a periodic grating  18  formed on or within a lower surface thereof. A pump light pulse  20  from a pump light source  30  (FIG. 2) is directed through the mask  16  onto the sample  10 , specifically onto the free (upper) surface of the film  14 . The mask  16  distorts the wavefront of the pump light pulse and, as a result, the intensity of the light incident onto the free surface of the film  14  varies periodically with position across the sample&#39;s surface. This causes a heating of the surface of the film  14  that varies in a spatially periodic manner as a function of position. The regions of the film  14  that are heated expand. As a result, strain pulses are launched into the sample  10  from each of the expanding regions. These strain disturbances result in a change in the optical constants of the sample  10 , and this change is detected by means of a time-delayed probe pulse  22 A that is also directed onto the sample  10  through the mask  16 , specifically by detecting (in this embodiment) a reflected portion  22 B of the probe pulse. The probe pulse  22 A originates from a probe source  32 , which could be the pump source  30  as well. Preferably, the pump and probe pulses are laser pulses of picosecond or sub-picosecond duration, and originate from one laser or from two lasers. As in the standard method and the grating method, one or more characteristics of the sample  10  may be determined, such as those listed above.  
         [0029]    In one preferred embodiment, and referring as well to FIG. 2, the pump and probe beams  20 ,  22 A are directed through the mask  16  at normal incidence. The probe beam  22 A is delayed relative to the pump beam  20 , preferably by means of a variable optical path  34  provided by a movable stage or by some other technique. The sample  10  is assumed to be supported by some suitable type of fixed or movable sample stage  36 . The change in the intensity of the reflected probe beam  22 B is sensed by a detector  38  and measured as a function of a time delay t between the application of the pump and probe pulses  20 ,  22 A. To improve the signal to noise ratio the intensity of the pulses composing the pump beam  20  can be modulated at some frequency f by means of an acousto-optic modulator (AOM)  30 A. The output of the detector  38 , which is an electrical signal indicative of the intensity of the reflected probe beam  22 B, is fed into a lock-in amplifier  40  for which the reference signal is at the same frequency f as the modulation frequency of the AOM  30 A. A data processor  42  has an input coupled to an output of the lock-in amplifier  40 , and is further coupled to a memory  44 , such as a hard disk, RAM, ROM, etc., wherein is stored an operating program, simulation results and other required data, constants and the like. The measured change ΔR(t) in reflectivity is compared by the data processor  42  with the results of a simulated reflectivity change ΔR sim (t) stored in the memory  44 .  
         [0030]    The change ΔR sim (t) is preferably determined in accordance with the following method. Reference can also be made to the logic flow diagram of FIG. 3.  
         [0031]    At Step A an initial estimate is made for the parameters of the sample  10 . These parameters include, but are not necessarily limited to, the thickness, density, sound velocity, thermal expansion, specific heat, optical constants of the different films, the adhesion between the films, the orientation of crystalline grains making up a film, the size of grains, the crystal phase and electrical resistivity of each film.  
         [0032]    Based on the assumed values, at Step B the stress in the sample  10  that is induced by the pump light pulse  20  is calculated.  
         [0033]    At Step C, the time-dependent strain in the sample  10  is calculated.  
         [0034]    From the calculated strain, at Step D the expected change in reflectivity ΔR sim (t) is found.  
         [0035]    At Step E, the expected change in reflectivity ΔR sim (t) is compared with the measured change in reflectivity ΔR(t).  
         [0036]    At Step F, the parameters of the sample are adjusted and the procedure iterated one or more times in order to achieve the best possible agreement between ΔR(t) and ΔR sim (t)  
         [0037]    For certain samples, it may be possible to simplify the procedure just described. Consider first a sample  10  that includes a single film  14  deposited onto the substrate  12  (as in FIG. 1), where the thickness d of the film  14  is significantly greater than the spacing w of the grating lines  18  on the mask  16 . For a time t less than the time required for a strain pulse to propagate through the thickness of the film  14  to the substrate  12  and return to the top surface of the film  14 , the reflectivity change ΔR(t) is unaffected by the existence of the substrate  12 , i.e., the response ΔR(t) is the same as would be obtained on a bulk material of the same composition and material properties as the film  14 . The stress set up by the pump pulse  20  excites a Rayleigh surface wave that is confined to the region near to the upper surface of the film  14 . This wave may be considered to be a standing wave of wavelength λ=w. The frequency of this standing wave is given by f R =c R /w, where c R  is the Rayleigh wave velocity. The presence of this standing wave causes a periodic modulation of the elastic strain in the surface layer of the film  14 , which in turn causes a contribution to ΔR(t) that varies in time with the frequency f R . An analysis of the measured ΔR(t) can be used to obtain the frequency f R , and from this frequency, and from the known value of w, the Raleigh wave velocity of the material of the film  14  can be found. This velocity can be expressed in terms of the elastic constants of the film material using a well-known formula.  
         [0038]    One reference for the velocity of a Rayleigh surface wave is L. D. Landau and E. M. Lifshitz, “Theory of Elasticity”, second edition, Pergamon Press, 1970, section 24. The theory of Rayleigh velocity in elastically anisotropic crystals is complicated but, in general, for an elastically isotropic solid, c R  is given as follows. First define the quantity ξ≡c R /c T . It can then be shown (see Landau et al.) that ξ is the solution for the following equation:  
           ξ   6     -     8                   ξ   4       +     8                     ξ   2          (     3   -     2          c   T   2       c   L   2           )         -     16        (     1   -       c   T   2       c   L   2         )         =   0                         
 
         [0039]    where c T  and c L  are the velocities of longitudinal and transverse sound, respectively.  
         [0040]    If the material of the film  14  is elastically isotropic, a knowledge of the Rayleigh velocity, together with an assumed value for Poisson&#39;s ratio, can be used to estimate the longitudinal and transverse sound velocities in the material of the film  14 .  
         [0041]    More specifically, the ratio of the velocity of the transverse and longitudinal sound is given by  
           c   T       c   L       =           1   -     2      σ         2        (     1   -   σ     )           .                           
 
         [0042]    Therefore,  
           ξ   6     -     8                   ξ   4       +     8                   ξ   2            2   -   σ       1   -   σ         -     16        1     2        (     1   -   σ     )             =   0                         
 
         [0043]    Hence, if σ is known, the value of ξ can be calculated from the preceding equation. A measurement of c R  can then be used to give c T  via the relation  
           c   T     =       c   R     ξ       ,                         
 
         [0044]    and c L  can be found from  
         c   L     =         c   T              2        (     1   -   σ     )         1   -     2      σ             =         c   R     ξ                2        (     1   -   σ     )         1   -     2      σ           .                               
 
         [0045]    For this type of sample, a strain pulse will also propagate away from the surface of the film 14 and into the volume of the film  14 . The strain pulse is partially reflected at the interface between the film  14  and the substrate  12 , and returns to the free (upper) surface of the film  14 . The return of the reflected strain pulse results in a sharp feature in ΔR(t) at a time τ L  equal to 2w/c L , where c L  is the longitudinal sound velocity. Hence, this time can be used to determine the thickness of the film  14 . The value of c L  can be estimated from the results of the measurements of the Rayleigh velocity as described above. Alternatively, for films of known composition and elastic properties, the value of c L  can be taken from the scientific literature.  
         [0046]    A simplified analysis can also be made for those samples  10  in which the thickness of the film  14  is much less than the grating period w. In this case the penetration depth of the Rayleigh wave is greater than the thickness of the film  14 . Thus, the Rayleigh wave will not be confined within the film thickness and will penetrate into the substrate  12 . The velocity of the Rayleigh wave is now dependent on the elastic properties and densities of both the film  14  and the substrate  12 , and is also affected by the thickness of the film  14 . Measurement of the frequency of the oscillations in ΔR(t) gives the Rayleigh wave velocity. There is also a component of the strain that propagates through the thickness of the film  14  and that is reflected back at the interface with the substrate  12 , thereby giving the sharp feature in ΔR(t) at a time 2w/c L . Again, from the measured Rayleigh wave velocity c R  and the time τ L , the longitudinal and transverse sound velocity, and the thickness of the film  14 , can be determined.  
         [0047]    It is within the scope of these teachings to make a number of variations in these measurement techniques.  
         [0048]    For example, the pump light pulse  20  and the measuring probe light pulse  22 A can be directed at the surface of the sample  10  at normal or oblique incidence. Furthermore, the angle of incidence of the probe pulse  22 A can be the same as the angle of incidence of the pump pulse  20 , or the angle of incidence of the probe pulse  22 A may be different than the angle of incidence of the pump pulse  20 . Also, the wavelength of the pump and probe beams  20 ,  22 A can be the same, or they can be different. If the wavelengths are different, and for the case where it is desired to detect a diffracted probe beam, the wavelength of the probe beam  22 A is set to be less than the line spacing of the mask  16 .  
         [0049]    In the description given above, the detection of the time varying strain in the sample  10  is made through a measurement of the change in the intensity of the reflected probe light  22 B. However, it is also within the scope of these teachings for measurements to be made of the change in the intensity of transmitted (as opposed to reflected) probe light. Also, measurements can be made of a change in the polarization of the reflected or transmitted probe light, a change in the optical phase of the reflected or transmitted probe light, or a change in propagation direction of the reflected or transmitted probe light. Measurements may be made of more than one of these characteristics, such as a measurement of intensity of the reflected or transmitted probe light and a measurement of optical phase of the reflected or transmitted probe light.  
         [0050]    Further by example, a measurement could be made of the intensity of the transmitted probe light in conjunction with a measurement of optical phase of the reflected probe light.  
         [0051]    The pump and/or the probe light can be brought to the mask  16  through free space or through optical fiber(s). Measurements can be made of the component of the probe light that is specularly reflected from the sample (angle of reflection equal to angle of incidence), or diffracted at an angle as a result of the presence of the grating in the mask  16 , or from that part of the probe light that is scattered diffusely from the surface of the sample  10 .  
         [0052]    The mask  16  can be made of a number of transparent materials, such as silica, other glasses, or polymers. It is straightforward to obtain gratings that have a line spacing as small as 2000 Å, and this distance can be made even smaller through the use of electron beam lithography.  
         [0053]    The mask  16  can also be constructed using a slab of a transparent material with opposing flat surfaces, and the grating  18  formed with a patterned thin film of a dielectric material, or with a metal deposited onto its lower surface. The thickness of the mask  16  need not be uniform, as a wedged or tapered thickness mask could be used as well.  
         [0054]    Furthermore, a single mask  16  could have two or more gratings  18  on the lower surface, where each grating has different line spacings. In this case the pump and probe beams  20 ,  22 A could be directed to different regions of the mask  16  where the spacing of the grating  18  has a chosen value, and in this way a measurement of ΔR(t) can be made for two or more different values of the spacing w of the lines on the grating  18 . Alternatively, the pump and probe beams  20 ,  22 A can be directed to a fixed location on the surface of the sample  10 , and the mask  16  moved, using a mask positioning system  46  (FIG. 4), so that regions of the mask  16  with different grating line spacing are positioned in the region where the pump and probe beams are located.  
         [0055]    In some applications it may advantageous to use a mask  16  having a two dimensional array of grating features (e.g., a square array), rather than a sequence of lines (one-dimensional array).  
         [0056]    The mask  16  can be positioned by the mask positioning system  46  by being placed in direct contact with the sample surface, i.e., with the free (upper) surface of the film  14 . It is also possible through the use of nanomachining techniques to construct a mask  16  that is prevented from coming into direct contact with the free surface of the film  14  by means of an air cushion produced by passing air through small holes  16 A in the mask  16 , as is done, for example, in an air track used in physics teaching laboratories. In this case the spacing of the mask  16  from the surface of the film  14  is preferably no larger than the spacing between the lines of the grating  18 . It is also within the scope of these teachings to construct a mask  16  that has the grating  18  in a center section that is lower than most or all of a surrounding area of the mask  16 , as shown in FIG. 4. That is, the grating portion of the lower surface of the mask  16  is not coplanar with the surrounding surface area. This approach is useful for those samples  10  that have surfaces that are not flat, as it ensures that the grating  18  can be placed in close proximity to the surface of the film  14 .  
         [0057]    The mask  16  can be lowered onto the sample  10  and raised from the surface of the sample  10  by the mask positioning system  46  using a number of different techniques. For example, electrical or magnetic forces can be applied to the mask  16 , or the mask  16  can be raised or lowered by means of air currents.  
         [0058]    Measurements can be made on a single film  14  on a substrate  12 , on a stack of thin films of different thickness and material composition, or on samples  10  that are laterally patterned. For example, FIG. 6 shows a sample  10  having laterally patterned features  10 A, such as embedded metalization lines, and the mask  16  positioned over a surface of the sample  10  in accordance with the teachings herein. The metalization lines need not be embedded, and could as well be located on a top surface of the film  14 . In this embodiment it may be advantageous to make the period of the mask  16  match the period of the features  10 A, or to mismatch the period of the mask  16  with the period of the features  10 A. It may also be advantageous to provide a predetermined relationship between the size(s) of features  10 A and the period(s) of the mask  16  (where the mask  16  can be provided with two or more characteristic periods for the grating  18 , or where more than one mask is used).  
         [0059]    Based on the foregoing it can be appreciated that these teachings overcome the problems discussed above with relation to the prior art. For example, the sound velocity in the sample can be measured directly, and need not be known a priori. Furthermore, the use of the mask relaxes the requirement that the sample characterization apparatus be constructed so as ensure that the phase relation between a plurality of pump beams remains constant, as a single pump beam is sufficient to provide the spatially distributed heating effect at the surface of the sample.  
         [0060]    In addition to the changes in reflectivity arising from the strain pulses that are launched in the sample  10 , there can be changes in reflectivity that arise from the change in the temperature, and in the density of electrons and holes. The change in reflectivity arising from these effects can be distinguished from the change in reflectivity that arises from the propagation of strain pulses.  
         [0061]    More particularly, strain pulses give rise to either sharp pulses (from sound echoing back and forth in a film) or to an oscillatory contribution (from the Rayleigh surface waves), while the contribution to the change in reflectivity that arises from the change in temperature or from the change in the electron and hole concentration varies more smoothly with time.  
         [0062]    The teachings of this invention also make it possible to measure the electrical resistivity of a metal film, provided that the film has a thickness lying within a certain range. In this embodiment, a determination is first made of the thermal conductivity κ film  of the metal film. From κ film  the electrical resistivity ρfilm can be calculated using the Wiedemann-Franz law:  
           ρ   film     =     LT     κ   film         ,                         
 
         [0063]    where L is the Lorenz number and T is the absolute temperature (see, for example, C. Kittel, Introduction to Solid State Physics, 7 th  edition, Wiley, p. 168).  
         [0064]    The following is a method for the determination of the thermal conductivity. Consider a metal film of thickness d deposited onto a substrate. Let the mask have a line spacing w with lines running parallel to the y axis, and let the normal to the substrate be in the z direction. Assume that the intensity I pump (x) of the pump light varies with position on the sample surface according to  
             I   pump          (   x   )       =       I   pump   o          [     1   +     cos        (   kx   )         ]         ,                         
 
         [0065]    where I o   pump  is a constant, k=2π/w, and x is an axis running across the surface in a direction perpendicular to the direction of the lines. The form of the intensity variation across the surface of the sample is dependent on the geometry of the mask  16  and on its optical properties. The particular form given above is for illustration and is not intended to imply that this variation will occur for all masks  16 . The pump light pulse induces a temperature rise ΔT that varies across the sample surface. Again, for illustration, we take this to have the same form:  
         Δ T ( x, z =0)=Δ T   0 [1+cos( kx )],  
         [0066]    where ΔT 0  is a constant. This is the temperature at the surface located on the plane z=0; the temperature rise at a distance below the surface will be less. The variation of the temperature rise with distance z into the film is determined by: 1) the distance ξ that the light penetrates into the metal, 2) by the distance ξ that the conduction electrons that are excited by the light diffuse before they lose their energy to the thermal phonons and come into thermal equilibrium with the lattice (see G. Tas and H. J. Maris, Electron Diffusion in Metals Studied by Picosecond Ultrasonics, Physical Review B 49, 15046 (1994)), and 3) by the film thickness. Note that since the lines on the mask  16  run parallel to the y-axis there is no dependence of the temperature on the coordinate y.  
         [0067]    The change in temperature of the sample surface results in a change in the optical reflectivity that is different at each point on the surface. In the absence of the mask  16  it is reasonable, as a first approximation, to consider that the change in reflectivity of the probe beam due to the temperature change would be proportional to the average_of the change in temperature taken over the area of the surface onto which the probe light is incident. However, it is important to recognize that the mask  16  distorts the probe beam so that, just like the pump beam, it has a greater intensity at some points on the surface of the sample  10  than at others. If one take the intensity of the probe light at the surface of the sample  10  to vary with position as:  
             I   probe          (   x   )       =       I   probe   o          [     1   +     cos        (   kx   )         ]         ,                         
 
         [0068]    where I o  probe is a constant, then the change ΔR in reflectivity is proportional to the average over the surface of the product of the probe intensity with the temperature change at the surface, i.e.,  
         Δ R∝∫dxI   probe ( x )Δ T ( x, z =0) ∝ I   probe   [A+B]   
         [0069]    where  
           A≡∫dxΔT ( x, z =0)  
           B≡∫dx  cos( kx )Δ T ( x, z =0).  
         [0070]    At a time t after the application of the pump pulse, the temperature distribution in the film will have changed because of heat flow. A measurement of ΔR(t) as a function of time_can provide information about this heat flow. It should be noted that the reflectivity change ΔR contains the term A which is proportional to the temperature change of the film averaged across its surface, and also contains the term B that vanishes when the temperature distribution across the film surface is uniform. Thus, ΔR(t) is affected both by heat flow out of the film into the substrate (this primarily affects the term A), as well as by heat flow within the film which tends to make the temperature distribution across the surface of the film uniform, and hence reduces the magnitude of the term B.  
         [0071]    The heat flow within the metal film may have components both parallel and perpendicular to the plane of the film. The heat flux {overscore (q)} at any point is equal to κ film ∇T, where κ film  is the thermal conductivity of the metal film. The heat flow across the interface into the substrate per unit area is equal to σ K ΔT int , where ΔT int  is the temperature jump across the interface and σ K  is the Kapitza conductance at the interface. Note that since ΔT int  is the difference between the temperature of the film and the temperature of the substrate, this heat flow is also affected by the thermal conductivity κ sub  of the substrate.  
         [0072]    Referring now to FIG. 5, one procedure for the determination of the electrical resistivity of the metal film is as follows:  
         [0073]    Step (A): ΔR(t) is measured as a function of the time t after the application of the pump pulse using a mask of known repeat distance w.  
         [0074]    Step (B): Values are assumed for the thermal conductivity κ film  of the film, the thermal conductivity κ sub  of the substrate, and the Kapitza conductance σ K  between the film and the substrate.  
         [0075]    Step (C): The initial temperature distribution within the film is calculated. This calculation is preferably based on the known geometry, line spacing or repeat distance w and on the optical characteristics of the mask  16 . The temperature distribution is affected by the diffusion coefficient of the hot electrons excited by the pump pulse. This diffusion coefficient can be estimated from the assumed value of the thermal conductivity of the film, as described by Tas and Maris in the publication referenced above.  
         [0076]    Step (D): The temperature distribution within the film is then calculated at later times based on the assumed values for the thermal conductivity of the film, the thermal conductivity of the substrate, and the Kapitza conductance between the film and the substrate.  
         [0077]    Step (E): The expected change in reflectivity ΔR(t) based on the temperature distribution determined in Step (D) is then calculated.  
         [0078]    Step (F) The parameters κ film , κ sub , and σ K , are then adjusted, and Steps (C)-(E) are repeated so as to obtain a best fit to the measured ΔR(t).  
         [0079]    The electrical resistivity of the film is then calculated using the thermal conductivity, as described above.  
         [0080]    It is important to note that the optimum choice of the repeat distance w of the mask  16  depends on the thickness d of the film and on the values of κ film , κ sub , and σ K . For example, if w is chosen to be too small, the hot electrons will diffuse so far that the initial temperature distribution will be almost uniform across the surface of the film, i.e., the temperature distribution in the film will be independent of x. The term B will then be absent. Suppose now that it is also true that the thickness of the film d is less than the diffusion length ξ. In this case the initial temperature distribution throughout the film will be uniform. As a result, the temperature at later times, and hence also the reflectivity change ΔR(t), will only be affected by the Kapitza conductance σ K  Under these conditions, the measurement of ΔR(t) generally cannot be readily analyzed to determine the thermal conductivity of the film.  
         [0081]    It is noted that if the mask  16  is not used, the initial temperature distribution would be uniform across the sample surface. For films whose parameters d, κ film , κ sub , and σ K  lie in a suitable range it would be possible to perform an analysis of the measured ΔR(t) to determine κ film  However, the range of film parameters for which the accurate determination of κ film  is possible is greatly increased through the use of a mask  16  of suitably chosen repeat distance w.  
         [0082]    It is within the scope of the teachings of this invention to make measurements on a single sample using a series of masks  16  of different repeat distances w, and to fit the totality of results so obtained by adjustment of the parameters κ film , κ sub , and σ K .  
         [0083]    As an alternate method, one may compare the measured ΔR(t) on a sample of unknown resistance with the results of measurements of ΔR(t).  
         [0084]    The mask  16  can also be used to advantage for the characterization of samples  10  into which ions have been implanted (or, more generally, the mask  16  may be used with altered materials). Reference with regard to such altered materials may be made to U.S. Pat. No. 5,706,094, “Ultrafast Technique for the Characterization of Altered Materials”, by H. J. Maris, as well as to U.S. Pat. No. 6,008,906, “Optical Method for the Characterization of the Electrical Properties of Semiconductors and Insulating Films”, by H. J. Maris.  
         [0085]    In general, the characteristics of a sample  10  that has been ion implanted are affected by the following parameters:  
         [0086]    (A) the number of ions implanted per unit area of the surface of the sample  10 , referred to as the dose;  
         [0087]    (B) the kinetic energy of the ions that are directed at the sample surface, referred to as the energy;  
         [0088]    (C) the direction at which the ion beam is incident onto the sample  10 ;  
         [0089]    (D) the ion current per unit area during the implant process;  
         [0090]    (E) the species of the implanted ion;  
         [0091]    (F) the charge on the ion, e.g., singly or double ionized;  
         [0092]    (G) the duration of time that the ion-implanted sample  10  is annealed; and  
         [0093]    (H) the temperature at which the ion-implanted sample  10  is annealed.  
         [0094]    In the above-referenced U.S. Pat. No. 5,706,094 it was disclosed to investigate as many as possible of these characteristics through measurements of the change in reflectivity ΔR(t) of the probe pulse applied directly to the surface at a time t after the application of the pump pulse. Experimental parameters that were varied included the wavelength of the pump and/or the probe light, where a change in wavelength changes the distance over which the pump and probe light is absorbed; and the intensity of the pump and/or the probe light, which changes the density of electrons and holes excited in the sample.  
         [0095]    While a variation in the wavelength and/or the intensity can be helpful in providing a more extended characterization of a sample, it may be difficult to obtain a complete characterization of a sample  10  by these means alone, given the large number of sample parameters that can affect the measurement. In addition, while it is possible to build an instrument in which the wavelength of the pump and/or the probe light can be selected to have two different values (for example, by the use of a frequency doubling crystal), it can be difficult to build an instrument in which the pump and probe wavelengths are continuously adjustable.  
         [0096]    The use of present invention has the advantage that the repeat distance w of the mask  16  can be selected so as to optimize the amount of information that can be obtained for a particular type of sample. The mask repeat distance can also be selected so as to make the measured ΔR(t) particularly sensitive to one or more of the sample characteristics (A)-(H) listed above. Furthermore, measurements can be made for a number of different mask  16  repeat distances w in order to achieve a more complete characterization. Also, measurements can be made for line masks or for masks  16  with two dimensional arrays of features.  
         [0097]    For the analysis of the data, the most practical method in many applications may be by comparison with data taken on reference samples of known characteristics. However, the data analysis may also be performed by comparison of the data to simulations, together with adjustment of parameters and iteration to achieve a best fit.  
         [0098]    While the invention has been particularly shown and described with respect to preferred embodiments thereof, it will be understood by those skilled in the art that changes in form and details may be made therein without departing from the scope and spirit of the invention.