Abstract:
An electromagnetic wakefield detector placed in close proximity to a design trajectory of a non-relativistic charged particle beam produces an optical signal in response to passage of the charged particle beam without interrupting the charged particle beam. A photon detector receives the optical signal and produces a corresponding output. The wakefield detector may be based on the electro optic effect. Specifically, the detector may measure the effect of the charged particle beam a beam of radiation on the phase of radiation travelling parallel to the beam in a nearby electro optic waveguide. This abstract is provided to comply with rules requiring an abstract that will allow a searcher or other reader to quickly ascertain the subject matter of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims.

Description:
CLAIM OF PRIORITY 
       [0001]    This application is a nonprovisional of and claims the priority benefit of commonly owned, co-pending U.S. Provisional Patent Application No. 61/878,609, to Tomas Plettner and John Gerling, filed Sep. 17, 2013, and entitled “ELECTRO-OPTIC ELECTRON BEAM MONITOR”, the entire disclosures of which are incorporated herein by reference. 
     
    
     FIELD OF THE DISCLOSURE 
       [0002]    Aspects of the present disclosure relate to charged particle beam diagnostics, and more particularly, to an apparatus and a method for miscellaneous non-invasive beam diagnostic capabilities for SEM tools and other charged particle based systems. 
       BACKGROUND 
       [0003]    In traditional SEM tools, beam current is determined by intercepting the beam at some plane either in the gun or column. This invasive beam monitoring requires the beam to be intercepted for its current to be determined, and thus no beam is striking at the image plane and the SEM column is not imaging. To get around this, a certain “duty cycle” is imposed on the system if the beam current is to be monitored periodically. This negatively impacts the throughput of the SEM system. 
         [0004]    In current methods of obtaining beam position, the beam position with respect to the optical axis inside the column is determined by a “wobble” function that deliberately perturbs one or more elements in the column from their nominal value to determine the beam position. When set in the wobble function the column, cannot be employed for imaging. Hence, this method also imposes a duty cycle, where a fraction of the useful imaging time is lost to a specific monitoring or tuning function that has to be implemented periodically as the beam drifts. 
         [0005]    Another important beam characteristic many SEM tools can collect is an energy spectrum of the primary electron beam. All present methods of energy spectrum collection known to the inventors of the present disclosure involve an invasive means of energy spectrum detection such as directing the beam into a detector array placed at a dispersive plane in the beam path. The electron beam is captured and ends at the detector plane of a spectrometer. 
         [0006]    In particle accelerators you use a pair of plates that produce an image charge as a beam containing a bunch of charges passes through it. The image charges produce pulses as the beam passes through it. The difference between pulses from the two plates can determine the position of the beam relative to the axis between the plates. The sum of the pulses at the two plates is proportional to the bunch charge. This works well if the beam is pulsed and the peak current is quite larger, e.g., of order 1 amp to 1 kiloamp. For many charged particle beam tools, such as electron microscopes, the beam is continuous and the current is very weak (nanoamps). 
         [0007]    For very charged particle beam short pulses (e.g., femtoseconds) electro-optic crystals are sometimes used to sample fields from bunched electron beams in particle accelerators. The change to the index of refraction of the electro-optic crystal can be probed with a laser beam. 
         [0008]    It is within this context that aspects of the present disclosure arise. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0009]    Objects and advantages of the invention will become apparent upon reading the following detailed description and upon reference to the accompanying drawings in which: 
           [0010]      FIG. 1  schematically illustrates how interaction between a charged beam and an electro optic material can be used to probe beam characteristics in accordance with aspects of the present disclosure. 
           [0011]      FIG. 2  depicts an electron optic charged particle beam detector implemented using an interferometer set-up according to an aspect of the present disclosure. 
           [0012]      FIG. 3  depicts an electron optic charged particle beam detector implemented using polarization rotation for noise-cancellation according to an aspect of the present disclosure. 
           [0013]      FIG. 4A  shows a bulk EO material being probed by a laser beam directed perpendicular to a charged particle beam to measure the effect of a passing single charged particle. 
           [0014]      FIG. 4B  shows a laser propagating along an EO material parallel to a charged particle beam according to an aspect of the present disclosure. 
           [0015]      FIG. 5  is a schematic diagram of a waveguide electron detector in accordance with aspects of the present disclosure. 
           [0016]      FIG. 6  is a graph depicting an expected pulse profile from detection of a single electron in a waveguide electron detector of the type shown in  FIG. 5 . 
           [0017]      FIG. 7  is a graph plotting an expected number of dark port photons per electron detected given a certain wavelength of the probing light for a waveguide electron detector of the type shown in  FIG. 5 . 
           [0018]      FIG. 8  is a schematic diagram of an alternative charged particle detector system in accordance with an aspect of the present disclosure. 
           [0019]      FIG. 9A  is a schematic diagram of a charged particle beam system in accordance with an aspect of the present disclosure. 
           [0020]      FIG. 9B  is a block diagram of the charged particle beacon system of  FIG. 9A . 
           [0021]      FIG. 9C  illustrates a numerical example for determining the aperture size and the waveguide and the length of the waveguide for a given beam geometry in an axial plane in accordance with an aspect of the present disclosure. 
           [0022]      FIGS. 10A-10B  illustrate a beam position monitor in accordance with an aspect of the present disclosure. 
           [0023]      FIG. 11  illustrates an energy spectrometer according to an aspect of the present disclosure. 
           [0024]      FIG. 12  details another implementation of an energy spectrometer according to an aspect of the present disclosure. 
           [0025]      FIG. 13  illustrates a beam profile monitor according to an aspect of the present disclosure. 
       
    
    
     DETAILED DESCRIPTION 
       [0026]    In the following Detailed Description, reference is made to the accompanying drawings, which form a part hereof, and in which is shown by way of illustration specific embodiments in which the invention may be practiced. The drawings show illustrations in accordance with examples of embodiments, which are also referred to herein as “examples”. The drawings are described in enough detail to enable those skilled in the art to practice the present subject matter. The embodiments can be combined, other embodiments can be utilized, or structural, logical, and electrical changes can be made without departing from the scope of what is claimed. In this regard, directional terminology, such as “top,” “bottom,” “front,” “back,” “leading,” “trailing,” etc., is used with reference to the orientation of the figure(s) being described. Because components of embodiments of the present invention can be positioned in a number of different orientations, the directional terminology is used for purposes of illustration and is in no way limiting. It is to be understood that other embodiments may be utilized and structural or logical changes may be made without departing from the scope of the present invention. 
         [0027]    In this document, the terms “a” and “an” are used, as is common in patent documents, to include one or more than one. In this document, the term “or” is used to refer to a nonexclusive “or,” such that “A or B” includes “A but not B,” “B but not A,” and “A and B,” unless otherwise indicated. The following detailed description, therefore, is not to be taken in a limiting sense, and the scope of the present invention is defined by the appended claims. 
         [0028]    As used herein, the term “light” generally refers to electromagnetic radiation characterized by a frequency somewhere in a range of frequencies running from the infrared through the ultraviolet, roughly corresponding to a range of vacuum wavelengths from about 1 nanometer (10 −9  meters) to about 100 microns. 
         [0029]    Introduction 
         [0030]    An electro-optic (EO) detector for a scanning electron microscope (or similar tool) that uses a continuous wave (CW) probe beam is basically attempting to detect single electrons using EO effect. For example, the electrons in a 1 keV nanoamp electron beam are spaced about 3 mm apart. If the detector includes an EO material about 1 mm long in the direction of the charged particle beam, only about one electron is passing by the detector at any given time. 
         [0031]    The field for a single electron is very weak and therefore the index modulation in the EO material is very weak. According to aspects of the present disclosure, the path length over which the refractive index or probe beam polarization is modulated may be increased by directing a probe beam through the EO material more or less parallel to the direction of the nearby charged particle beam. The idea is for the frequency modulation of the probe beam to co-propagate with the charged particles. This can be implemented by incorporating the EO material into part of a waveguide-type structure. A probe beam of electromagnetic radiation (e.g., from a laser) may be coupled into a thin EO crystal slab waveguide. It is desirable to use an EO material with a large EO coefficient. By way of example, and not by way of limitation, KTaLiNbO3 has an electro-optic coefficient r33 of about 1400 pm/V. The group velocity of the probe beam in the waveguide may be matched to the charged particle velocity in the beam. By way of example, and not by way of limitation, the charged particle beam energy may be adjusted to match the group velocity. Alternatively, the cross-sectional size and/or shape of the waveguide may be adjusted to control the group velocity of the probe beam in the waveguide. In broad and general terms, the group velocity of the probe beam in the waveguide depends in a somewhat inverse manner on the broadest transverse dimension of the waveguide. A photon detector may be located at the dark port of an interferometer so that modulation of the refractive index produces a signal resulting from disturbance of a dark fringe. 
         [0032]    According to aspects of the present disclosure, the proposed architecture for a charged particle beam sensor may include a set of one or more electromagnetic wakefield detectors placed in close proximity to a design trajectory of a non-relativistic charged particle beam, wherein the set of one or more wakefield detectors is configured to produce one or more optical signals in response to passage of the charged particle beam without interrupting the charged particle beam; and a set of one or more photon detectors configured to receive the one or more optical signals and produce one or more corresponding outputs. In some implementations, the set of one or more electromagnetic wakefield detectors is configured to implement a multi-function beam monitor that implements two or more of the following functions: beam current monitoring, beam position monitoring, beam energy spectrometry, or beam profile monitoring. 
         [0033]    According to another aspect of the present disclosure a set of one or more electro-optic materials placed in close proximity to a charged particle beam&#39;s design trajectory. One or radiation sources and polarizer/analyzer arrangements may be configured to probe the effect on the EO material of the passage of a charged particle of the beam and its electromagnetic wake field due to the electro-optic effect. A set of one or more photon detectors that register a change of phase or polarization of the probe beam as a result of the electron affecting the electro optic material&#39;s index of refraction. The photon detector(s) may be coupled to the optics dark port of the polarizer/analyzer arrangement to detect the electron&#39;s passage. 
         [0034]    The exact configuration and geometrical construct of the foregoing elements depends on the targeted detection application. 
         [0035]    For higher beam current the beam density of a pulsed or CW charged particle beam could be imaged in transverse direction by passing the probe beam across two EO crystals and a gap between the crystals through which the charged particle beam passes. 
         [0036]    According to aspects of the present disclosure an electro optic apparatus may be configured to operate as an in-line beam current monitor. In one such configuration, a pair of electro-optic crystals is placed facing a charged particle beam trajectory from opposite sides. An optical probe beam traverses both crystals and probes their refractive indexes. A polarizer-analyzer optics arrangement may be used to detect passage of charged particles through the gap between the two crystals. The arrangement of two crystals may be chosen such that the dependence of the magnitude of the electro-optic signal is minimized with the beam position. 
         [0037]    The detected optical phase shift (either inteferometric or polarization rotation) is proportional to the amount of charged particle beam current and can be deployed to cancel noise in a primary beam. This detection method is limited by the laser photon beam shot noise which can be made smaller than the charged particle beam shot noise if the number of photons per detection event is greater than the number of charged particles per detection event. Therefore this could provide for a noise cancellation method for the electron beam shot noise, and allow for throughput increase (less electron per pixel required since primary beam current is now measured). 
         [0038]    According to another aspect of the present disclosure an electro optic apparatus may be configured to operate as a beam-position monitor (BPM). Signals of electro-optic rotation occurring in the EO materials on either side of a vacuum gap through which the charged particle beam passes are read separately in each material and subtracted. The resulting signal is linearly dependent to the charged particle beam&#39;s position relative to the two crystals. Hence the processed signal corresponds to the position of the beam centroid. The sum of the signals on the other hand would also provide a beam current reading. By using pairs of crystals oriented along the x and the y directions, the position of the center of the charged particle beam can be read without stopping the beam. 
         [0039]    According to another aspect of the present disclosure an electro optic apparatus may be configured to operate as a beam profile monitor. In one such configuration, the charged particle beam traverses a gap between two EO crystals in one direction and a collimated optical probe beam travels through both crystals and across the gap in an orthogonal direction. The collimated probe beam is transported to a detector array in a way that images the face of one of the EO crystals onto a detector array (e.g., in a polarizer-analyzer mode and in the dark-port configuration). The beam current density near the crystal face generates a spatially dependent polarization rotation proportional to the beam current density. This spatially dependent polarization rotation at the crystal face is the imaged onto the photo-detector array. To allow for a shallow depth-of-focus for the probe beam and to image the beam profile a quadrupole (line-focusing) beam transport scheme may be used for the charged particle beam. 
         [0040]    According to another aspect of the present disclosure an electro optic apparatus may be configured to operate as an energy spectrometer. In one such configuration, beam current monitoring performed at a dispersive plane (like a chicane) yields the beam&#39;s energy spectrum, and if there is beam energy jitter a monitor constructed from this reading could serve as a servo signal to beam control electronics to stabilize the beam energy. If it is required to match the group velocity of the EO waveguides to the electron velocity, and the waveguides have fixed physical dimensions, the energy spectrometer may only permit one waveguide design per beam velocity. In such a case, the energy spectrometer may utilize a multi-waveguide arrangement similar to the X-Y arrangement containing several waveguides of different dimensions to accommodate different group velocities. 
         [0041]    According to another aspect of the present disclosure an electro optic apparatus may be configured to operate as discussed above for a beam of electrons or for any other charged-particle beam (e.g. ions, muons, positrons). 
         [0042]    In some alternative implementations of the method, other possible pseudo-nonradiative schemes involve formation of an image-charge of the free electron by a nearby set of conductive plates (a classical beam-position monitor or BPM). The current pulse generated from the image charge is very small compared to the beam current being monitored, but the pulse may be detected with sufficient electronic amplification has to be amplified electronically. 
         [0043]    With this new measurement method, the electron beam is not destroyed. As a result, the method can provide for beam servo mechanisms that don&#39;t affect duty cycle, improving throughput. Additionally, applications of this method in noise cancellation and corresponding signal-to-noise for the acquired image are the main impetus for this IP application. This method allows for the possibility of signal-to-noise improvement without altering the fundamental architecture of an existing SEM platform. As a result, and with an EO detection scheme sensitive enough to detect single electrons, application of shot noise cancellation and for a given beam current at the image plane a corresponding improvement in the signal to noise. Alternatively, the SIN could be kept fixed and the beam dose per pixel could be dropped, resulting in the possibility of higher throughput and better resolution from lower beam current (lower Coulomb interaction, aberration from larger NA beams, etc.). 
       EXAMPLES 
       [0044]      FIG. 1  illustrates the basic concept behind an electro optic device as used in accordance with aspects of the present disclosure. In an electro optic (EO) device, the optical properties of a material change in response to a change in electric field in the material. Since charged particles, such as electrons produce electric fields, electro optic materials can be used to detect electrons in a continuous beam, as in a scanning electron microscope (SEM). 
         [0045]    Specifically, as seen in  FIG. 1 , an electron e carries with it an electromagnetic field E that interacts with the nearby electro optic material EOM. For a linear electro-optic material its index of refraction experiences a change that is linear with the electric field component of the electron&#39;s retarded field. This effect is commonly referred to as the Pockels effect. A beam of radiation R (e.g., a laser beam) traversing an electro optic material experiences a phase change (optical retardation) due to the change in the index of refraction resulting from the electric field of a passing charged particle beam. The phase change is proportional to the electric field, which is in turn proportional to the charge or current in the particle beam. Aspects of the present disclosure relate to detection of the passage of as little as a single free nonrelativistic electron by detecting the phase change of a probe laser beam traversing an electro optic medium in close proximity to a charged particle beam. 
         [0046]    The index of refraction n ij ({right arrow over (E)}) is given by: 
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         [0047]    The phase change is given by: 
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         [0048]    Electro optic materials have been used to measure beam pulses in charged particle accelerators.  FIG. 2  schematically illustrates a type of apparatus  200  used for such purposes. In the apparatus  200 , an EO medium  202  is placed alongside a path of a charged particle beam  201 . A beam of radiation R from a laser L is split into a reference beam  203  and a probe beam  205  in a Mach-Zehnder interferometer  204 . The probe and reference beams pass across the EO medium  202  in a direction perpendicular to the direction of travel of the charged particle beam  201 . The reference beam  203  follows a path from the first beam splitter  206  to a first mirror  208  and from the first mirror to a second beam splitter  210 . The probe beam  205  follows a path from the first beam splitter  206  to a second mirror  212  and from the second mirror to the second beam splitter  210  where light from the reference and probe beams recombine and interfere. Part of the light is sent to an optical detector  214  located at a dark port and part of the light travels to a beam dump  216  at a bright port. The interferometer  204  is aligned so that a dark interference fringe is present at the dark port in the absence of a phase disturbance difference between the reference and probe beams. A pulse of charged particles from the beam  201  passing near the probe beam causes a phase disturbance due to the electro optic effect in the EO medium  202 . The phase disturbance is registered by the optical detector  214 , which produces a beam signal A that is proportional to the input beam charge or current. 
         [0049]    The beam of charged particles  201  strikes a target  218  producing secondary particles  221 , which could be, e.g., secondary electrons, backscattered particles from the beam, secondary ions, Auger electrons, or X-rays. The secondary particles  221  are detected by a secondary particle detector  222  that produces a specimen signal B. The beam signal A and specimen signal B are coupled to a signal processor  224 , which produces an output signal  225  that is proportional to the ratio of the specimen signal B to the beam signal A. This normalizes the specimen signal B with respect to the magnitude of the input particle beam current. Therefore, the output signal  225  is more sensitive to variations in the interaction between the charged particle beam and the target and relatively insensitive to variations in the intensity of the charged particle beam. 
         [0050]    The arrangement shown in  FIG. 2  is suitable for measurement of relatively intense pulsed charged particle beams. For example, in particle accelerators average beam currents of one ampere or more and pulse durations on the order of femtoseconds (10 −15  seconds) are common In an electron beam at an average current one ampere, approximately 6.24×10 18  electrons pass a given point per second. For charged particle systems commonly used for materials characterization in the semiconductor industry, e.g., SEM systems, Auger electron spectroscopy systems and energy dispersive X-ray spectroscopy (EDX) systems, the beam currents are continuous and much smaller (e.g., of order 10 −9  amperes). Such low currents typically involve the passage of a relatively small number of charged particles over the time scales of interest. For sufficiently low currents, the variation in beam current is dominated by shot noise, which results from statistical variation due to the discrete nature of the charged particles in the beam  201 . For example, if the electronic circuitry of the secondary particle detector  222  operates on time scales of less than a nanosecond and if the average current in the beam  201  is 16 nanoamps, only about 100 electrons strike the target  218  every nanosecond. According to Poisson statistics the actual number of electrons in any nanosecond could vary by about 10 electrons rms. When such a small current is observed over such a time scale the shot noise amounts to 1/10 of the average beam current. 
         [0051]    According to an aspect of the present disclosure, an alternative apparatus based on electro optics principles may be used to account for the effects of shot noise at low beam currents in charged particle beam systems. As seen in  FIG. 3 , an alternative apparatus  300  includes a light source L (e.g., a laser), an electro optic material  302 , a polarizing beamsplitter  304 , and an optical detector  314 . The laser L produces a polarized beam of radiation R. The polarization direction can be adjusted by passing the radiation R through a retardation waveplate W before the radiation passes through the electro optic material  302  in a direction perpendicular to a charged particle beam  301 . The polarizing beamsplitter  304  (e.g., a Glan-Thompson prism or other polarizing beam-splitter) then splits the radiation R into two beams R 1 , R 2  of different polarizations, which are usually mutually orthogonal. Radiation R 1  having the initial polarization (i.e., the polarization of the radiation R prior to entering the EO material  302 ) passes through the polarizing beamsplitter to a beam dump  316 . Radiation R 2  having a polarization orthogonal to that of the initial polarization is reflected toward the optical detector  314 . The apparatus  300  is initially configured such that, in the absence of the charged particle beam  301 , the EO material does not modulate the polarization of the radiation R and therefore there is no radiation R 2  of an orthogonal polarization to reach the optical detector  314 . In other words, the optical detector  314  is at a dark port and the detector signal is nominally zero (or some other fixed value) in the absence of the beam  301 . 
         [0052]    When the beam  301  passes near the EO material  302 , the electric field from the charged particles in the beam induce an electro optic effect in the EO material that causes a change in the polarization of the radiation R that emerges from the EO material. The amount of change in polarization depends on the electric field in the EO material  302 , which, in turn, depends on the average current in the beam  301  over a time scale of interest. The change in polarization causes some of the radiation R 2  to be directed toward the optical detector  314 , which generates a beam signal A as a result. The beam signal A is proportional to the average current in the charged particle beam  301 . By way of example, and not by way of limitation, the optical detector  314  may be a standard silicon based photodetector, a photomultiplier tube (PMT) or a multi-channel plate (MCP). 
         [0053]    When the charged particle beam  301  strikes a target  318 , secondary particles  321  are produced, e.g., secondary electrons, backscattered particles from the beam, secondary ions, Auger electrons, or X-rays. The secondary particles  321  are detected by a secondary particle detector  322 , which produces a specimen signal B, as a result. By way of example, the secondary particle detector  322  may be a PIN diode detector or a scintillator combined with an MCP or PMT. The beam signal A and specimen signal B are coupled to a signal processor  324 , which produces an output signal  325  that is proportional to the ratio of the specimen signal B to the beam signal A. This normalizes the specimen signal B with respect to the magnitude of the average current in the charged particle beam  301 . Therefore, the output signal  325  is more sensitive to variations in the interaction between the charged particle beam and the target and relatively insensitive to variations in the intensity of the charged particle beam  301  due to shot noise. By way of example, and not by way of limitation, the functions of the signal processor  324  may be implemented in software, e.g., by executable instructions implemented on a general-purpose computer or in hardware, e.g., by a programmable circuit, such as an Application Specific Integrated Circuit (ASIC) or a Field Programmable Gate Array (FPGA). 
         [0054]    In the interferometer shown in  FIG. 2  the probe beam and reference beam pass through the electro optic material in a direction perpendicular to the direction of a charged particle beam  201 . Although this may work for large beam currents, as in particle accelerators, the beam signal A may be too small to be useful for low beam current applications, such as SEM. The reason for this may be understood by referring to  FIG. 4 . 
         [0055]    In  FIG. 4A  a charged particle beam  401  follows a path P parallel to an optical axis A proximate an electro optic (EO) material  402 . The charged particle path is at a distance x from the axis A and a nearby surface of the EO material  402  is at a distance a from the axis. A beam of laser radiation R is directed across the EO material  402  perpendicular to the axis A and path P. By way of example, consider a charged particle beam  401  made up of electrons traveling in free space at non-relativistic speeds. 
         [0056]    At an arbitrary distant x′ from the axis A, the electric field E x (x′) from a non-relativistic electron in free space is given by 
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         [0000]    where e is the charge on the electron (1.6×10 −19  Coulombs) and ε 0  is the permittivity of free space (8.85×10 −12  C 2 /N·m 2 ). For low currents and moderate voltage, e.g., about 1 nanoampere (nA) and about 10 kV, the electrons in the beam are sufficiently far apart that they may be treated as single point charges, as opposed to a line of charges. 
         [0057]    For an EO material  402  in the form of a trigonal EO crystal, the refractive index n z (x′) depends on the field E x (x′) as follows: 
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         [0000]    where n 0  is the refractive index of the material for ordinary rays (i.e., rays directed along the crystal axis C of the EO material  402  shown in  FIG. 4A ) and r 51  is the relevant electro optic coefficient for photons traveling in the direction of the crystal axis C. 
         [0058]    For radiation R of vacuum wavelength λ, the accumulated phase change φ is given by 
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                     . 
                   
                 
               
             
           
         
       
     
         [0059]    By way of numerical example, assume that the EO material is Potassium Tantalum Lithium Niobate (KTaLiNbO 3 ), for which r 51 =42 pm/V and r 33 =1400 pm/V, n 0 =2.312, n e =2.273. Further assume a=5 μm, λ=532 nm. The phase shift induced by a single free electron is therefore ˜0.8 μrad 
         [0060]    Also assume monitoring of the dark port, where I dark ˜φ 2  I laser  and P laser =10 W, or 5×10 4  photons/optical cycle and the laser has a beam waist ω 0 =5 μm. For a 10 keV electron (υ˜0.2c) the transit time is ˜8 fs or about 4.5 optical cycles. This equates to ˜1.4×10−7 signal photons per electron event. The effect is therefore probably too small to detect single electrons with a CW laser beam. 
         [0061]    According to certain aspects of the present disclosure, however, the signal may be increased dramatically if the laser radiation R is directed along the surface of the EO material closest to the charged particle beam  401  in a direction more or less parallel to the direction of travel of the charged particles that make up the beam.  FIG. 4B  schematically illustrates an arrangement similar to that shown in  FIG. 4A , except that the laser beam radiation R is directed along the surface of the EO medium  402  along a direction parallel to the direction of travel of the charged particle beam  401 . The phase change φ for the radiation R passing through the EO medium  402  in the direction shown in  FIG. 4B  may be calculated from the electric field for a non-relativistic charged particle and the material properties and dimensions of the EO medium. 
         [0062]    The electric field from free non-relativistic electron is again given by: 
         [0000]    
       
         
           
             
               
                 
                   E 
                   x 
                 
                  
                 
                   ( 
                   
                     x 
                     ′ 
                   
                   ) 
                 
               
               = 
               
                 e 
                 
                   4 
                    
                   
                     
                       
                         πɛ 
                         0 
                       
                        
                       
                         ( 
                         
                           x 
                           - 
                           
                             x 
                             ′ 
                           
                         
                         ) 
                       
                     
                     2 
                   
                 
               
             
             , 
           
         
       
     
         [0063]    For radiation traversing a trigonal crystal perpendicular to the crystal axis C in the manner shown in  FIG. 4B , the index change n x (x′) is given by: 
         [0000]    
       
         
           
             
               
                 
                   n 
                   x 
                 
                  
                 
                   ( 
                   
                     x 
                     ′ 
                   
                   ) 
                 
               
               = 
               
                 
                   n 
                   e 
                 
                 - 
                 
                   
                     1 
                     2 
                   
                    
                   
                     n 
                     e 
                     3 
                   
                    
                   
                     r 
                     33 
                   
                    
                   
                     
                       E 
                       x 
                     
                      
                     
                       ( 
                       
                         x 
                         ′ 
                       
                       ) 
                     
                   
                 
               
             
             , 
           
         
       
     
         [0064]    where n 0  is the refractive index of the material for ordinary rays (i.e., rays directed perpendicular to the crystal axis C of the EO material  402  shown in  FIG. 4A ) and r 33  is the relevant electro optic coefficient for photons traveling in the EO material in this direction. The accumulated phase change φ is given by: 
         [0000]    
       
         
           
             
               
                 
                   φ 
                   = 
                     
                    
                   
                     
                       
                         2 
                          
                         π 
                       
                       λ 
                     
                      
                     
                       
                         ∫ 
                         0 
                         l 
                       
                        
                       
                         
                           ( 
                           
                             
                               
                                 n 
                                 y 
                               
                                
                               
                                 ( 
                                 
                                   x 
                                   ′ 
                                 
                                 ) 
                               
                             
                             - 
                             
                               n 
                               e 
                             
                           
                           ) 
                         
                          
                         
                             
                         
                          
                         
                            
                           
                             x 
                             ′ 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     - 
                     
                       
                         ∫ 
                         0 
                         l 
                       
                        
                       
                         
                           
                             
                               n 
                               e 
                               3 
                             
                              
                             
                               r 
                               33 
                             
                              
                             e 
                           
                           
                             4 
                              
                             
                               
                                 
                                   λɛ 
                                   0 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       x 
                                       ′ 
                                     
                                     - 
                                     x 
                                   
                                   ) 
                                 
                               
                               2 
                             
                           
                         
                          
                         
                             
                         
                          
                         
                            
                           
                             z 
                             ′ 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       
                         
                           n 
                           e 
                           3 
                         
                          
                         
                           r 
                           33 
                         
                          
                         el 
                       
                       
                         4 
                          
                         
                           
                             
                               λɛ 
                               0 
                             
                              
                             
                               ( 
                               
                                 
                                   x 
                                   ′ 
                                 
                                 - 
                                 x 
                               
                               ) 
                             
                           
                           2 
                         
                       
                     
                     . 
                   
                 
               
             
           
         
       
     
         [0000]    where l is the length of the EO material  402  along the path of the charged particle beam  401 . 
         [0065]    Assume again that the EO material  402  is KTaLiNbO 3 , for which r 33 =1400 pm/V, and n e =2.273. By way of numerical example, assume a=5 μm, l=1 mm, λ=532 nm, P laser =10 W, or 5×10 4  photons/optical cycle. Also assume monitoring of the dark port, where I dark ˜φ 2  I laser    
         [0066]    The phase shift induced by a single free electron is therefore φ˜5.5 mrad. The length of the laser pulse having a maximum interaction with an electron in the beam  401  is ˜2a or 10 μm. This corresponds to a transit time 2a/v g ˜166 fsec or 62 opt. cycles, where v g  is the group velocity of the radiation R in the EO material  402 . This equates to about 93 signal photons per electron event. Though the effect is small, it allows for detection of single electrons with a CW laser beam. 
         [0067]    Aspects of the present disclosure include implementations based on the principle of operation illustrated in  FIG. 4B . Specifically,  FIG. 5  depicts an example of an interferometer-based charged particle beam measurement system  500  somewhat similar to the system  200  depicted in  FIG. 2 . In the system  500  charged particles  501  of a charged particle beam travel in a vacuum channel a distance w proximate a dielectric slab waveguide WG. The channel is wide enough to permit passage of a beam of the charged particles  501  without interrupting (e.g., clipping) it. The waveguide WG includes a slab of EO material  502  sandwiched between a substrate S that acts as a cladding and a resistive coating  503 . The resistive coating  503  dissipates charge from stray charged particles that hit the walls of the EO-monitor so that electrostatic charge does not accumulate on the walls. The substrate S has a different refractive index than the EO material  502 . By way of example, and not by way of limitation, the substrate S may be made of silicon dioxide (SiO 2 ) and the EO material  502  may be Potassium Tantalum Niobate (KTaNbO 3 ). The waveguide WG forms a probe arm of an interferometer, e.g., a Mach-Zehnder interferometer. In the example depicted in  FIG. 5 , the interferometer is implemented partly with optical fiber. Alternative implementations may use free-space optical components. 
         [0068]    Radiation R from a source such as a laser L may be coupled into the waveguide WG using free space optics  505 . By way of example, and not by way of limitation, the laser L may be a continuous wave (CW) laser that produces a beam of radiation R characterized by a vacuum wavelength of 532 nm. Commercially available examples of suitable lasers include a Verdi 20 W optically pumped semiconductor laser (OPSL) lasers from Coherent, Inc. of Santa Clara, Calif. and 100 W fiber lasers available from IPG Photonics of Oxford, Mass. 
         [0069]    An optical isolator  507  may be placed between the laser L and the optics  505  to prevent back coupling of radiation. A first beamsplitter  506  divides the radiation R into a probe beam that is coupled into the waveguide WG and a reference beam that is coupled into a reference arm of the interferometer. By way of example, and not by way of limitation, the probe beam may be coupled into the waveguide using a second set of free space optics  509  and a first grating coupler G 1 . The probe beam may be coupled out of the waveguide WG in a similar manner, e.g., using a second grating coupler G 2  and a third set of free space optics  511 . The probe beam travels through the EO material  502  of the waveguide WG in a direction more or less parallel to the direction of travel of the portion of the intended charged particle trajectory that is proximate the waveguide. The wavelength of the radiation R and the properties of the waveguide WG are chosen so that the group velocity of the probe beam in the EO material  502  is approximately equal to the velocity of nearby charged particles  501 , to within a range of adjustment of the charged particle velocity. The charged particle velocity may be closely matched to the group velocity of the probe beam, e.g., by adjusting an appropriate voltage in the system that produces the beam of charged particles. 
         [0070]    After the probe beam is coupled out of the waveguide WG, a second beamsplitter  510  combines the reference beam and probe beam. Part of the combined beam is coupled (e.g., by optical fiber) to a dark port detector  514  and part of the combined beam may optionally be coupled to a bright port detector  516 . The reference arm may optionally include variable attenuator VA, a coarse delay (e.g., a length of optical fiber), and a variable phase control VP to optimize signal at the dark port detector  514 . The variable phase control VP may use a suitable nonlinear optical material, e.g., lithium niobate (LiNbO3). Phase adjustment may be implemented by adjusting the temperature of the nonlinear optical material. Operation of the system  500  is similar to the operation of the system  200  described above, but with greater sensitivity as a result of the waveguide arrangement in the probe arm of the interferometer. 
         [0071]    The performance of a system of the type shown in  FIG. 5  may be appreciated by referring to  FIG. 6  and  FIG. 7 . The graph depicted in  FIG. 6  shows an expected pulse profile from detection of a single electron in a waveguide electron detector of the type shown in  FIG. 5 . The expected pulse is about 200 fs in duration. The graph shown in  FIG. 7  estimates the number of photons per electron as a function of the wavelength of the probing radiation using KTaNbO 3  as the EO material. From the graph, one may determine that the expected number of photons per electron at 532 nm is ˜170 photons/electron 
         [0072]    The waveguide design illustrated in  FIG. 5  may also be applied to the type of detector architecture depicted  FIG. 3 .  FIG. 8  illustrates an example of such a system  800 . In this system  800  a beam of charged particles  801  travels in a vacuum channel proximate a dielectric slab waveguide WG. In the waveguide WG a slab of EO material  802  is sandwiched between a substrate S that acts as a cladding and a resistive coating  803 . The substrate and cladding have different refractive indices than the EO material  802 , e.g., as described above with respect to  FIG. 5 . Radiation R from a source such as a laser L may be coupled into a polarization maintaining fiber F, e.g., using free space optics  805  and an optical isolator  807 . A second set of free space optics  809  and a first grating G 1  couple at least some of the radiation R into the waveguide WG as a probe beam. The incident polarization of the radiation R entering the waveguide WG may be controlled, e.g., by a waveplate W. The probe beam may be coupled out of the waveguide WG, e.g., using a second grating coupler G 2  and a third set of free space optics  811 . The wavelength of the radiation R and the properties of the waveguide WG may be chosen so that the group velocity of the probe beam in the EO material  802  is approximately equal to the velocity of nearby charged particles  801 , to within a range of adjustment of the charged particle velocity. The charged particle velocity may be closely matched to the group velocity of the probe beam, e.g., by adjusting an appropriate voltage in the system that produces the beam of charged particles. 
         [0073]    As the probe beam travels through the EO material  802  of the waveguide WG in a direction more or less parallel to the direction of travel of the portion of the intended charged particle trajectory that is proximate the waveguide EO interaction between the probe beam and charged particles  801  cause a change of polarization of the probe beam. 
         [0074]    After the probe beam is coupled out of the waveguide WG, a polarizing beamsplitter  810  directs probe beam radiation having a polarization orthogonal to the initial polarization to a dark port detector  814 . Probe beam radiation having the same polarization as the incident polarization may be coupled to a bright port detector  816 . combines the reference beam and probe beam. Operation of the system  800  is similar to the operation of the system  300  described above with respect to  FIG. 3 , but with greater sensitivity as a result of the waveguide arrangement in which the probe radiation travels parallel to the charged particles and at a group velocity that matches the velocity of the charged particles. 
         [0075]      FIG. 9A  and  FIG. 9B  illustrate an example of a charged particle beam system  900  that incorporates certain aspects of the present disclosure. In this non-limiting example, the system  900  is configured as a scanning electron microscope (SEM) having charged particle optical column  902  with an electron source  915 , beam optics elements  935 , an immersion lens  904 , which may be an electrostatic or magnetic lens. The optical column  902  may be controlled by electronics  936 , referred to herein as a beam driver. The beam driver  936  may control the electron source  915 , beam optics elements  935  and immersion lens  904 . In this example, the beam optics  935  include two or more electrically conductive cylinders maintained at voltages that produce electric fields to extract electrons from the source  915  and form them into a primary beam  903  that travels in the direction of a target  901 . The immersion lens  904  focuses the primary beam into a narrow spot at the surface of the target. 
         [0076]    A electro optic beam detection apparatus  940  is placed proximate a waist of the primary beam  903 , e.g., between the elements of the beam optics  935 . By way of example, and not by way of limitation, the apparatus  940  may include an interferometer of the type shown in  FIG. 5  in which the probe arm includes an optical waveguide formed in a slab of electro optical material proximate the beam waist. A laser L may provide the probe beam and reference beam to the apparatus  940 . The probe beam travels in the waveguide more or less parallel to the primary beam  903  and is combined with the reference beam. The combined beam is coupled to a photon detector  942 , which may be coupled to a dark port of the apparatus  940 . In such a case, the photon detector  942  produces a signal A that is proportional to the dark port interference signal of the interferometer. 
         [0077]    In alternative implementations, the apparatus  940  may include a polarization sensing apparatus of the type illustrated in  FIG. 8 . Furthermore, aspects of the present disclosure include implementations in which two or more EO detector apparatus  940  are placed proximate the primary beam  903 , for reasons discussed below. 
         [0078]    Electrons from the electron beam column  902  are focused onto a surface of the target  901 , which may be an integrated circuit wafer or a test wafer. The target  901  is supported by a stage  918 . The electrons may be scanned across the surface of the target  901 , e.g., by deflecting fields provided by one or more electrostatic deflector plates  906 . Voltages are provided to the deflector plates  906  via a beam scanner driver  908 . In some implementations, the beam scanner driver  908  may apply currents to magnetic coils to scan the electron beam across the target  901 . Alternatively, the stage  918  may include a stage scanning mechanism  911  and stage scanner driver  919  configured to move the target along X-Y plane parallel to the surface of the target  901  in one or more directions relative to the optical column  902 . In some implementations the stage scanning mechanism  911  and stage scanner driver  919  may move the stage in one direction (e.g., the X direction) as the beam scanner driver  908  scans the beam in a different direction (e.g., the Y direction). Alternatively, the stage scanner driver  919  may drive the stage in both the X and Y directions relative to the optical column  902  to scan the beam across the target while the beam remains fixed relative to the optical column. 
         [0079]    Electrons striking the target  901  are either backscattered or initiate secondary emission. The electron beam column collects a portion of such backscattered or secondary electrons  917  (or other secondary particles) that emerge from the surface of the target  901 . The collected electrons  917  impinge on a secondary particle detector  910 , which generates a secondary signal B that is proportional to the amount of backscattering or secondary emission. The signal may be amplified by an amplifier  912 . The amplified signal and a signal from the beam scanner driver  908  and/or stage scanner driver  919  are combined by an image generator  914  to produce a magnified image of the surface of the target  901 . Images generated by the image generator  914  may be analyzed by the image analyzer  916 , e.g., to determine a measure of quality of the modified surface or shape and size of resulting formed structures. 
         [0080]    In accordance with aspects of the disclosure, the secondary signal B from the secondary particle detector  910  (or amplifier  912 ) and the photon signal A from the photon detector  942  may be coupled to a signal processor  944  to cancel out the effect of noise in the primary beam  903 . By way of example, and not by way of limitation, the signal processor  944  may produce an output proportional to a ratio of the secondary particle signal B to the photon signal A. 
         [0081]    In alternative implementations, sources of energetic particles other than electrons (e.g., ions, neutrons, ultraviolet radiation, or X-rays) may be used as alternatives to the electron source  915 , depending on the nature of the system. In addition, the energetic particle source may be separate from and/or located outside of the charged particle optical column  902 . For example, in X-ray photoelectron spectroscopy (XPS) the primary energetic particles may be X-rays that initiate emission of secondary electrons from the target. In ultraviolet photoelectron spectroscopy (UPS) the primary energetic particles may be ultraviolet photons that similarly initiate emission of secondary electrons from the target. Also, in alternative implementations, other types of charged particles (e.g., positive or negative ions) may backscatter from or be emitted by the target and pass back up through the optical column  902  to impinge on the secondary particle detector  910 . For example, in secondary ion mass spectroscopy (SIMS) the primary particles are energetic ions and the secondary charged particles are ionized atoms of the target material that are knocked off of the target as a result of energetic impact by the primary ions. 
         [0082]    Some charged particle systems include a charged particle energy analyzer (e.g., a cylindrical mirror analyzer, Bessel box, parallel plate analyzer) as part of the optical column  902  between the immersion lens  904  and the secondary particle detector  910 . Such spectrometers are used for energy selection of secondary electrons, e.g., as in Auger electron spectroscopy (AES) for chemical analysis of the target  901 . Other systems include a mass spectrometer (e.g., a magnetic sector, RF quadrupole, or Wien filter to select secondary charged particles by mass, e.g., as in SIMS systems. 
         [0083]    By way of example, and not by way of limitation, images may be generated by driving the beam scanner in a raster pattern in which the primary beam scans across the sample  901  in one direction with the beam scanner driver  908  and beam deflector plates  906  (or scanner coils) and the detector signal as a function of beam position is converted into a line of the image as is well known in the art. At an end of the scan of the beam in one direction (e.g., the X-direction), the beam location may be adjusted by a small amount (e.g., an amount comparable to a size of the beam spot on the sample) in a different direction (e.g., the Y-direction) and another scan may be performed to generate another line of the image. By repeating this process an image of part of the sample may be generated. 
         [0084]    In alternative implementations, images may be generated by scanning the primary beam across the sample  901  in one direction (e.g., the X-direction) and converting the detector signal as a function of beam position into a line of the image. The stage scanner driver  919  and stage scanning mechanism may translate the sample  901  by a small amount in a different direction (e.g., the Y-direction) at the end of each line scan. 
         [0085]    Secondary detector  910  may be a diode device with a junction and depletion region. By way of example and not by way of limitation, detector  910  can be a PN junction, a PIN junction. In alternative implementations, the detector  910  may be a CMOS detector (e.g., CCD), silicon-based or III-V detector, multi-channel plate, photodiode array, avalanche photodiode and/or Schottky diode. In one example, the detector  910  is PN junction diode that includes a positively doped P region and a negatively doped N region. A depletion region, an area of neutral charge, exists between the P and N regions. When a photon enters the device, electrons in the crystalline structure become excited. If the energy of the photon is greater than the bandgap energy of the material, electrons will move into the conduction band crating holes in the valence band where the electrons were. These electron-hole pairs are created throughout the device. Those generated in the depletion region drift to their respective electrons. This results in a positive charge buildup in the P layer and a negative one in the N layer. The amount of charge is directly proportional to the amount of light falling on the detector. 
         [0086]    It should be noted that in addition to SEM systems, many other charged particle systems may employ the secondary charged particle detection device according to the present disclosure. Examples of systems may include, but are not limited to, systems configured to implement focused ion beam (FIB), ultraviolet photoelectron spectroscopy (UPS), X-ray photoelectron spectroscopy (XPS), Auger electron spectroscopy (AES), and Secondary Ion Mass Spectroscopy (SIMS). 
         [0087]    As shown in the block diagram of  FIG. 9B , the image generator  914  and image analyzer may be part of a controller  920 . The controller  920  may be a self-contained microcontroller. Alternatively, the controller  920  may be a general purpose computer configured to include a central processor unit (CPU)  922 , memory  924  (e.g., RAM, DRAM, ROM, and the like) and well-known support circuits  928  such as power supplies  921 , input/output (I/O) functions  923 , clock  926 , cache  934 , and the like, coupled to a control system bus  930 . The memory  924  may contain instructions that the CPU  922  executes to facilitate the performance of the system  900 . The instructions in the memory  924  may be in the form of the program code  925 . The code  925  may control, e.g., the electron beam voltage and current produced by the source  915 , the focusing of the beam with the beam optics  935  and the immersion lens  904 , the scanning of the electron beam by the coils  906 , the scanning of the stage  918  by the stage scanner  911  and the formation of images with the signal from the detector  110  in a conventional fashion. The code  925  may also implement analysis of the images. 
         [0088]    The code  925  may conform to any one of a number of different programming languages such as Assembly, C++, JAVA or a number of other languages. The controller  920  may also include an optional mass storage device,  932 , e.g., CD-ROM hard disk and/or removable storage, flash memory, and the like, which may be coupled to the control system bus  930 . The controller  920  may optionally include a user interface  927 , such as a keyboard, mouse, or light pen, coupled to the CPU  922  to provide for the receipt of inputs from an operator (not shown). The controller  920  may also optionally include a display unit  929  to provide information to the operator in the form of graphical displays and/or alphanumeric characters under control of the processor unit  922 . The display unit  929  may be, e.g., a cathode ray tube (CRT) or flat screen monitor. 
         [0089]    The controller  920  may exchange signals with the imaging device scanner driver  908 , the e-beam driver  935  and the detector  910  or amplifier  912  through the I/O functions  923  in response to data and program code instructions stored and retrieved by the memory  924 . Depending on the configuration or selection of controller  920 , the scanner driver  908 , detector  910 , amplifier  912 , photon detector  942 , and/or signal processor  944  may interface with the I/O functions  923  via conditioning circuits. The conditioning circuits may be implemented in hardware or software form, e.g., within code  925 . Also, in some implementations, the functions of the signal processor  944  may be implemented in software within the code  925 . 
         [0090]    It is desirable that the EO waveguide of the EO detector  940  be placed as close as possible to the beam waist in the primary beam  903  without clipping the beam.  FIG. 9C  illustrates a numerical example for determining the aperture size and the waveguide and the length of the waveguide for a given beam geometry in an axial plane. The numerical example assumes a 10 kV primary electron beam  903  with reduced brightness of 10 8  A/m 2 /sr/V, and 10 nA beam current. 
         [0091]    The normalized transverse emittance of the beam ε N  is given by: 
         [0000]    
       
         
           
             
               ɛ 
               N 
             
             = 
             
               
                 
                   
                     I 
                     
                       B 
                       r 
                     
                   
                   × 
                   
                     ( 
                     
                       
                         2 
                          
                         
                             
                         
                          
                         e 
                       
                       
                         
                           π 
                           2 
                         
                          
                         
                           m 
                           e 
                         
                          
                         
                           c 
                           2 
                         
                       
                     
                     ) 
                   
                 
               
               ∼ 
               
                 6.3 
                 × 
                 
                   10 
                   
                     - 
                     4 
                   
                 
                  
                 
                   
                     I 
                     / 
                     
                       B 
                       r 
                     
                   
                 
               
               ∼ 
               
                 6.3 
                 × 
                 
                   10 
                   
                     - 
                     12 
                   
                 
                  
                 m 
                  
                 
                   - 
                 
                  
                 rad 
               
             
           
         
       
     
         [0092]    The geometric transverse beam emittance is 
         [0000]    
       
         
           
             
               ɛ 
               G 
             
             = 
             
               
                 
                   ɛ 
                   N 
                 
                 
                   β 
                   γ 
                 
               
               ∼ 
               
                 3.5 
                 × 
                 
                   10 
                   
                     - 
                     11 
                   
                 
                  
                 m 
                  
                 
                   - 
                 
                  
                 rad 
               
             
           
         
       
     
         [0093]    The growth of the beam beta function with drift down the z-axis (focus at z=0) is β(z)=β 0 +z 2 /β 0    
         [0094]    Growth of the beam envelope in the transverse (X) direction as a function of axial position z follows the following equation X(z)=√{square root over (ε G β(z))}=X 0 √{square root over (1+(ε G   2 /X 0   2 )×z 2 /X 0   2 )} 
         [0095]    The depth of focus is Z depth ≡β*=X 0   2 /ε G    
         [0096]    The divergence angle is α=ε G /X 0    
         [0097]    For a X 0 =1 μm focus β*=28 mm and a=35 μrad. 
         [0098]    Hence a waveguide 1 mm long and 10 μm aperture will not interfere with (clip) the primary beam  903  in this example. 
         [0099]    As mentioned above, there are a number of different configurations for the EO detector  940 . A few of this are described below with respect to  FIG. 10A  and  FIG. 10B  and  FIG. 11  though  FIG. 13 .  FIG. 10A  shows a top down view of an apparatus  1000  in which a pair of interferometer EO detectors  1040  of the type shown in  FIG. 5  are configured to detect the x-axis position of the center of a charged particle beam  1001  traveling parallel to the z-axis direction. In an alternative implementation, the EO detectors  1040  may be polarization detectors of the type shown in  FIG. 8 . Each EO detector  1040  includes an EO waveguide WG oriented parallel to a path of the beam  1001 . The two waveguides are separated by a gap through which the beam  1001  can pass. Photon detectors  1014  are coupled to the dark ports of the EO detectors  1040  (or polarization detectors). Signals from the photon detectors  1014  may be coupled to signal processors  1024 . A sum of the signals from the left and right photon detectors is proportional to the beam current. A difference between the signals from the left and right photon detectors is proportional to the position of the center of the beam  1001  along to the x-axis. This difference may be calibrated to be zero when the beam is perfectly centered. 
         [0100]    As shown in  FIG. 10B , the apparatus  1000  may optionally include a second pair of EO waveguide detectors  1040  with their waveguides WG oriented to sense the position of the center of the beam  1001  relative to the y-axis. In  FIG. 10B , the Z-direction is directed out of the plane of the drawing. 
         [0101]    According to another aspect of the present disclosure, EO detectors as described herein may be configured to measure a charged particle beam energy spectrum.  FIG. 11  depicts a top down view of a possible design of an energy spectrometer  1100  in which eighth EO detectors are arranged around the axis of a charged particle beam  1101  to capture the energy spectrum of the beam. Each EO detector includes a waveguide that is group-velocity-matched to a different beam energy setting. For simplicity, only the waveguide portions WG a , WG b , WG c , WG d , WG e , WG f , WG g , and WG H  of the detectors are shown. The detectors may be configured to operate, e.g., as shown in  FIG. 5  or  FIG. 8 . Some alternative implementations may implement a combination of beam position sensing and energy spectrometry, e.g., by using waveguides WG a  and WG e  for the x position sensor and waveguides WG c  and WG g  for the y position sensor, while using the remaining waveguides WG b , WG d , WG f , and WG h  as energy detectors. The energy-sensing waveguides WG b , WG d , WG f , and WG h  may have different cross-sectional dimensions configured such that the group velocity of optical probe beams in those waveguides are matched to the velocities of charged particles of different corresponding energies. Alternatively, different frequencies of radiation may be used to adjust the group velocities. 
         [0102]    In some implementations, the charged particle beam may be spatially separated into different beams according to particle energy and the current of the separate beams may be measured. By way of example,  FIG. 12  illustrates a system  1200  in which a charged particle beam  1201  is disperse using a chicane  1202 . In the chicane, a first magnetic sector  1204  bends and spatially disperses the charged particle beam  1201  into different paths according to their velocities. A second magnetic sector  1206  bends the dispersed paths of the particles to make them parallel at a dispersion plane. EO detectors are arranged with an array  1207  of EO waveguides WG parallel to the paths of the particles in the dispersion plane. After the particles pass through the waveguide array  1207 , two additional magnetic sectors  1208 , 1210  bend the dispersed paths of the particles and converge them back into a narrow beam. 
         [0103]    Each waveguide WG in the array  1207  may be configured so that the group velocity of an optical probe beam in that waveguide is matched to the velocity of charged particles having the kinetic energy corresponding to its location in the dispersion plane. The energy resolution of the system  1200  is set by the spacing of the waveguides in the array and the dispersion value at the dispersion plane. 
         [0104]    Aspects of the present disclosure also include implementations in which an electro optic apparatus is configured to operate as a beam profile monitor. For higher beam current or longer signal integration an imaging scheme that measures the spatial beam profile by imaging of the phase shift of a probe beam in an EO material is envisioned. By way of example, and not by way of limitation, as illustrated in  FIG. 13 , in an electro optic apparatus  1300  a charged particle beam  1301  traverses a gap g between two EO crystals  1302  in the z direction and a polarized collimated optical probe beam of radiation R travels through both crystals  1302  and across the gap in an orthogonal direction (e.g., the x direction, as shown in  FIG. 13 ). In  FIG. 13 , the z-direction is perpendicular to the plane of the drawing towards the viewer. The collimated probe beam R is transported to a detector array via optics  1303  that image the face of one of the EO crystals  1302  through a polarizing beam splitter  1304  onto a detector array  1314 , e.g., a charge-coupled device (CCD) array or similar device. An image intensifier  1305  may be placed between the beam splitter  1304  and the detector array  1314 . By way of example and not by way of limitation, the image intensifier  1305  may be some kind of electron amplifier. Examples of electron amplifiers include MCP and PMT devices, both of which operate via an electron avalanche that creates an amplified electron signal. The beam splitter  1304  may be configured to act as an analyzer in a polarizer-analyzer mode so that the detector array  1314  is at a dark-port. The beam current density near the crystal face generates a spatially dependent polarization rotation that is proportional to the beam current density. This spatially dependent polarization rotation at the crystal face is the imaged onto the photo-detector array  1314 , which produces an output A. In the example shown, the probe beam is dispersed in the z direction so that the output A can be interpreted as a plot of beam current density has a function of axial (z) position. In alternative implementations, the probe beam R may be collimated in a way that it is dispersed in the y direction (i.e., along a plane perpendicular to the x-z plane containing the beam  1301 ) and the output A may be interpreted as a plot of beam current density as a function of transverse (y) position. 
         [0105]    To allow for a shallow depth-of-focus for the probe beam and to image the beam profile a line-focusing (e.g., quadrupole) beam transport scheme may be used for the charged particle beam  1301 . In other alternative implementations, a detector apparatus that uses an array of parallel EO waveguides such as those described above with respect to  FIG. 12  could accomplish the same beam profile monitoring function. 
         [0106]    Those skilled in the art will recognize that two or more the functions of apparatus of the type described above, e.g., beam current monitoring, beam position monitoring, beam energy spectrometry, or beam profile monitoring may be implemented in a multi-function monitor that uses one or more EO or other wakefield charged particle detectors. 
         [0107]    The implementations described above are configured to monitor the non-radiative field component of the free electron by means of a second-order effect in a crystal. However, aspects of the present disclosure are not limited to such implementations. In some alternative implementations, wakefield beam interaction mechanisms other than electro optic interactions may be used. By way of example, and not by way of limitation, radiative mechanisms that may be employed include generation of radiation by an undulator in which a charged particle beam (e.g., an electron beam) passes between arrays of magnets that produce transverse magnetic fields of alternating direction. Other alternative implementations may utilize the Cerenkov effect, in which electromagnetic radiation is emitted when a charged particle (such as an electron) passes through a homogeneous dielectric medium at a speed greater than the phase velocity of light in that medium. Still other alternative implementations may be based on generation of transition radiation by passing charged particles through an inhomogeneous medium, such as a boundary between two different media. Yet other alternative implementations may be based on generation of radiation by the Smith-Purcell effect by passing an energetic beam of charged particles near a grating or other photonic structure. Of the aforementioned mechanisms, Smith-Purcell is perhaps the most efficient mechanism and has been observed from a non-relativistic electron beam. The main problem for the radiative schemes is the efficiency for the free-electron to radiate a photon, as for even the most efficient photonic structures the coupling coefficient is orders of magnitude smaller than 1. Therefore for a typical SEM beam current and any reasonably-sized photonic structure (e.g. gratings) that would probe it the resulting photon current and signal will be relatively small. 
         [0108]    By way of further example, radiative probing of a charged particle beam with a laser beam could also done by Compton scattering instead of the electro optic effect or other wakefield effect if the probing laser beam has a sufficiently large amount of power. Compton scattering refers to an inelastic scattering of a photon by a quasi-free charged particle, e.g., an electron. Such scatter decreases the energy of the photon (which may be an X-ray or gamma ray photon). The increase in energy may be observed as an increase in wavelength) 
         [0109]    For example, the low-energy limit of the Klein-Nishia formula for photon-electron scattering cross-section is given by: 
         [0000]    
       
         
           
             
               
                  
                 σ 
               
               
                  
                 Ω 
               
             
             ∼ 
             
               r 
               e 
               2 
             
             ∼ 
             
               7.8 
               × 
               
                 10 
                 
                   - 
                   30 
                 
               
                
               
                 m 
                 2 
               
             
           
         
       
     
         [0110]    The transit time t of a free electron through the focus of a laser beam with waist w 0  is approximately ½ μm, 1=532 nm; assume an electron kinetic energy of ˜4 kV, the electron velocity is about 0.2c, where c is the speed of light in vacuum. 
         [0111]    Therefore, 
         [0000]    
       
         
           
             t 
             = 
             
               
                 c 
                 
                   ω 
                   0 
                   2 
                 
               
               ∼ 
               
                 2 
                 × 
                 
                   10 
                   
                     - 
                     15 
                   
                 
                  
                 sec 
               
             
           
         
       
     
         [0112]    The probability T for a photon scattering event for this laser beam is ratio of the electron cross-section and the laser focus area probing it is given approximately by: 
         [0000]    
       
         
           
             T 
             ∼ 
             
               
                 4 
                  
                 π 
                  
                 
                     
                 
                  
                 
                   r 
                   e 
                   2 
                 
               
               
                 ω 
                 0 
                 2 
               
             
             ∼ 
             
               4 
               × 
               
                 10 
                 
                   - 
                   16 
                 
               
             
           
         
       
     
         [0113]    The required CW power to generate 1 scattered photon per free electron is therefore 
         [0000]    
       
         
           
             P 
             ∼ 
             
               hc 
               
                 Tt 
                  
                 
                     
                 
                  
                 λ 
               
             
             ∼ 
             
               5 
               × 
               
                 10 
                 11 
               
                
               W 
             
           
         
       
     
         [0114]    While the above includes a complete description of the preferred embodiment of the present invention, it is possible to use various alternatives, modifications and equivalents. Therefore, the scope of the present invention should be determined not with reference to the above description but should, instead, be determined with reference to the appended claims, along with their full scope of equivalents. 
         [0115]    The appended claims are not to be interpreted as including means-plus-function limitations, unless such a limitation is explicitly recited in a given claim using the phrase “means for.” Any element in a claim that does not explicitly state “means for” performing a specified function, is not to be interpreted as a “means” or “step” clause as specified in 35 USC §112, ¶6. In particular, the use of “step of” in the claims herein is not intended to invoke the provisions of 35 USC §112, ¶6.