Abstract:
To analyze an electric component in depth, provision is made to submit the aforementioned component to focused laser radiation. It is shown that by modifying the altitude of the focus in the component, some internal parts of the aforementioned component can be characterized more easily.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is the National Stage of International Application No. PCT/FR2007/051130 International Filing Date, 18 Apr. 2007, which designated the United States of America, and which International Application was published under PCT Article 21 (s) as WO Publication 2007/119030 A3 and which claims priority from, and the benefit of, French Application No. 0651382 filed on 19 Apr. 2006. 
     BACKGROUND 
     The object of the disclosed embodiment is a method and device for measuring energy interactions in an electronic component. The purpose of the disclosed embodiment is to improve the characterization of electronic components with respect to attacks of this nature. 
     SUMMARY 
     Naturally or artificially radiant environments (neutrons, protons, heavy ions, flash X or gamma rays) can interfere with the function of electronic components. These attacks are caused by interactions between the material and the particles of the radiant environment. One of the consequences of this is the creation of parasitic currents in the component. Such parasitic currents vary in strength according to the site of the interactions between the material and the particles. This expresses the presence of isolated charge collection zones within the component. 
     Interference of this kind by heavy ions and protons and is typically encountered in space, by satellites and space shuttles. At the lower altitudes used by aircraft, neutrons occur most frequently. Attacks of this nature may also be encountered at ground level, where they can affect electronic components fitted in portable devices or cars. 
     It is very important to know the shape and position of the charge collection zones inside the components in order to be able to research the sensitivity of the component to radiant environments, and indeed to any kind of phenomenon caused by the creation of parasitic charges in electronic components, due to electrostatic discharges (ESD), for example. 
     In order to be able to predict the behaviour of components when they are exposed to heavy ions, neutrons and protons, particularly for space and aeronautical applications, it is necessary to know not only the dimensions of the charge collection zones in terms of surface area, but also their characteristics in depth, which requires the ability to create maps in three dimensions. 
     The conventional method of analyzing the sensitivity of an electronic component to radiation is to bombard the component with a stream of particles and record the interference events that occur. Since this type of test involves radiating the entire component, it cannot be used to identify the location of the charge collection zones. Moreover, these tests are rather costly, because there are relatively few facilities in the world that are capable of generating the requisite particle streams. Finally, even if the particles used in a particle accelerator are the same as those present in the radiant environment, their energy levels may be different. This can result in serious errors, particularly with regard to the depth to which the particles penetrate the component. 
     Narrow beams can be obtained from the outputs of particle accelerators. It is then possible to use these microbeams to map the sensitivity zones of a component. This mapping is carried out in one plane and can only be used to show the location of these charge collection zones on the surface. This type of test does not yield any information about the depth to which the sensitive zone extends. 
     Previously, the laser was used primarily as a tool for preliminary characterization tool of the sensitivity of components to radiation. Like the particles in the radiant environment, at the appropriate wavelength the laser can generate parasitic currents inside components. 
     The laser has one very significant advantage for the purposes of studying the effects of radiation. Since the spatial resolution of the laser is able to achieve relatively small dimensions with respect to the elementary structures in electronic components, it is possible to create a map of an electronic component, as with a microbeam, and to identify its charge collection zones. Until now, it has suffered from the same limitation as the microbeam, namely it has not been possible to obtain detailed information about the location at depth of the sensitive zone inside the component, nor about its thickness. 
     A method based on non-linear absorption (using two photons) is known that addresses this drawback. However, the laser source used is non-industrial and the method is extremely difficult to perform outside of a laboratory. 
     The object of the disclosed embodiment is a method that enables the position at depth and the thickness of the charge collection zones to be determined in any electronic component, using a laser probe of fixed wavelength within the absorption band of the semiconductor. Essentially, the laser radiation of the disclosed embodiment is focused. In order to explore the thickness of the component, the laser radiation focus is moved inside the component thickness. This movement may be effected by translation or by more or less convergent focusing. The description that follows is based on the method using translation. For the variation using convergence, it is necessary to select different calculation methods, which are however within the capabilities of one skilled in the art, and are no more than simple optical constructions. 
     The method of the disclosed embodiment may be used to determine the sensitivity of electronic components to radiation on the basis of laser tests: the information about the geometry of the charge collection zones in the components are then used as input parameters in error prediction simulations with regard to the particles (heavy ions, neutrons, protons, etc.). 
     Finally, the method of the disclosed embodiment is able to reveal the weaknesses of a technology in terms of resistance to radiation, which is important information for the development of new components in terms of the methods of manufacturing them. 
     It should be noted that the laser sources used in the disclosed embodiment are inexpensive, very reliable, and available commercially, and therefore fitting for an industrial environment. 
     Accordingly, a further object of the disclosed embodiment is a method for characterizing sensitivity to energy interactions in an electronic component, in which,
         the electronic component is activated,   the electronic component thus activated is excited using laser radiation,   a malfunction of the activated electronic component corresponding to this excitation is measured, and   a map is created of the locations of interest in the component where these interactions are strongest,
 
wherein,
   the laser radiation is focused to various depths in the component and   the energy interactions for these different depths are measured.       

    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The disclosed embodiment will be understood more clearly if the following description is read with reference to the accompanying figures. The figures are for exemplary purposes only, and are not limiting of the disclosed embodiment in any way. The figures show: 
         FIG. 1 : A schematic representation of a device that may be used to perform the method according to the disclosed embodiment; 
         FIG. 2 : A graphical representation of the effects of offsetting the focus of the laser according to the disclosed embodiment; 
         FIG. 3 : In a zone of interest, the map of critical energy for which interactions are critical depending on the focusing depth; 
         FIG. 4 : A schematic representation of three examples in an known zone of interest, in which the explanation of defocusing the laser bears out the results of  FIG. 3 ; 
         FIGS. 5 to 7 : The representation of the various zones of interest on a component, with their correspondences,  FIGS. 6 and 7  in the signals detected; 
         FIG. 8 : A map of critical power depending on the defocusing depth for a second type of component; 
         FIG. 9 : The schematic representation of the simulation procedure showing how knowledge of the location of the sensitive zones measured with the disclosed embodiments is used to evaluate the component&#39;s sensitivity to heavy ions or neutrons or protons. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  shows a device that may be used to perform the method according to the disclosed embodiment. The objective of the disclosed embodiment is to measure the effects of energy interactions in an electronic component  1 . A semiconductor crystal  2  furnished with various implants is therefore attached in known manner and as described overleaf to electronic component  1 : such implants may include casings such as  3 , wells such as  4  in such a casing  3 , and zones that have been embedded by impurities such as  5  to  8 . While such may not be construed as limiting of the disclosed embodiment, semiconductor crystal  2  is a p-type silicon crystal in which casing  3  is implanted with N+ type impurities, well  4  is implanted with P+ type impurities, zones  5  to  8  are implanted with impurities of various kinds depending on the electronic functions and connections that must be created in order to produce the electronic component. Concentrations of impurities in components of this kind are usually in the order of between 1015 and 1023. The implanted zones  5  and  6  as well as the casings  3  and wells  4  are separated from each other by silicon oxide barriers such as  9 . Connections such as  10 , which are typically metallic and created by vaporization of the connections, are created in known manner and end at an interface  11  with electronic component  1 . Base surface  12  of semiconductor wafer  2  typically rests on a protection element  13 , preferably a metallization. In some cases, protection element  13  is made from an extremely hard material, for example cobalt. Protection element  13  is located on a face of crystal  2  opposite the one in which implants  5  to  8  are located. 
     According to the disclosed embodiment, the electronic component that is likely to be exposed to energy interactions is excited with a laser source  14  so that the malfunctions in the component may be measured. This laser source  14  emits radiation  15  which attacks electronic component  2 . In order to optimize the effects of such an attack, component  1  is preferably exposed to the attack at its base  12 . In order to optimize the effects of such attack, a window  16  is preferably opened in protection element  13  (particularly by a chemical or mechanical process), through which radiation  15  from laser  14  may reach the component. 
     During testing, electronic component  1  is connected to a power supply and control device  17  via its interface  11 . As shown schematically, device  17  includes a microprocessor  18 , which is connected via a data, address and control bus  19  to a program memory  20 , a data memory  21 , interface  11  with laser source  14 , and a laser energy attenuation system  35 . Device  17  also includes a comparator  22 , also shown schematically, receiving both an expected electrical value via a preset input  23  and electrical signals recorded by interface  11  in component  1  via a measurement input  24  while the component is exposed to interactions and excitations from laser  14 . 
     Comparator  22  may be replaced by a subroutine for measuring the coherence of the signal received from electronic component  1  with an expected signal. The measurement function may be static: in this case, only the values of voltages and currents present at the contact points on interface  11  are tested. It may also be dynamic. In this case, microprocessor  18  is also equipped with a clock that times certain operations, the sequence of which must conform to a known journal, and measurements are taken to determine whether this journal is reproduced in the expected manner, or there are anomalies. 
     Particularly with microprocessor  18 , it is known conventionally to move source  14  in directions XY relative to surface  12  of crystal  2 . When making this move, it is possible to register the locations of interest, where measurements have shown that the interactions between radiation  14  and semiconductor  1  are strongest, and are indeed becoming critical. However, this knowledge is not sufficient. It still provides no information about depth. 
     The hole formed by window  16  is smaller than the dimension of wafer  2  in component  1 . Hole  16  is small because, if it is made too large, the conditions of electrical operation of component  1  way be altered. In particular, it is essential to ensure that the electrical connection of layer  13  can be maintained. This being the case, the trace of the impact of radiation  15  on surface  12  is naturally smaller than hole  16 , otherwise it would serve no purpose to displace window  16  in directions X and Y. Moreover, despite all the precautions taken, the dimensions of the implantation zones such as  5  to  8  are much smaller than the trace of the impact from laser radiation  15 . This is not shown fully in  FIG. 1  for reasons of clarity. In practice, however, the trace of the impact is significantly larger than the size of an elementary function in the electronic component. For example, with regard to a static type memory cell, the area of the impact trace is significantly greater than that of a memory cell of this static memory. 
     Using this technique, it is known to identify the zones of interest in component  1  in the sense that these zones are the sites of interactions that are harmful to the functioning of component  1 . The objective of the disclosed embodiment is to determine the exact part of the component that is the site of such harmful interaction. Typically, the question to be answered is whether the area concerned is that of the bottom  26  of casing  3 , the bottom  27  of well  4 , or the interface area  28  of one of the implanted zones  5  to  8 . Knowing this depth may lead to changes being made to the level at which impurities are implanted in the various zones, to strengthen the component with regard to these interactions. 
     In order to achieve this result, provisions have been made in the disclosed embodiment to focus laser radiation  15  using a focusing device, represented schematically here by a lens  29 , and to use this lens  29  to vary a focusing depth Z of a focus  30  of the radiation  15  focused thereby. For example, a depth  31 , as illustrated, in this case is located below surface  12  but above the surface of the bottom  26  of casing  3 . A height  32  of the crystal of semiconductor  2  is generally in the order of 300 micrometres, whereas the height used for separation oxides  9  may be in the order of 600 micrometres. Of course, account is also taken of the fact that the refractive index of crystal  2  is different from the refractive index of air. This is not shown in  FIG. 1 , where the focused radiation is indicated by straight beams  34 . According to the disclosed embodiment, the energy interactions of the radiation on component  1  are measured for each focusing depth. This measurement is taken according to the following principle. 
     Once laser source  14  has been positioned with respect to a zone of interest (measured as described previously), for a first given focusing operation, e.g., on surface  12 , commands are transmitted to attenuator  35  using microprocessor  18  and bus  19  to adjust the attenuation level of the laser energy, and microprocessor  18  and bus  19  are also used to command source  14  to emit a laser pulse. Reducing the attenuation level of attenuator  30  causes the laser energy to increase. As a result of this increase, the laser power that is dissipated in component  1  increases. In practice, this application of energy excitations may be pulsed (particularly to prevent the component from being heated excessively by continuous illumination). In addition, power may be adjusted incrementally, though this is a preference and not obligatory. Experimentally, the energy (power) value is highest at the start, and is reduced until the critical value is obtained (but the reverse is also possible: starting with the lowest energy value and increasing the value progressively). The coherence of the signal read in component  1  with an expected signal is measured at the end of each pulse. If this coherence is good, the attenuation is reduced. At a certain point, a critical power is reached, the power for which, for the first time, the electronic response from component  1  is not what is expected. The value of this critical power is noted. 
     Then the focusing position of the laser source is changed, for example by moving lens  29  towards component  1  (or possibly by using a lens with variable focal length), such that focus  30  is advanced farther inside crystal  2 . The process of increasing (or decreasing as desired) the power is repeated for this new position at depth of this focus  30 , and a new value for the critical power is obtained. By proceeding in this manner, it is possible to record a map in depth, not simply of the surface, of the malfunctioning of electronic component  1 . 
     In fact, the spatial distribution of a laser beam at the focal point of an objective is ideally modeled by Gaussian curve in a plane, and by a decreasing exponential in depth. In two dimensions, the energy density llaser of the beam propagating in a medium with index n is expressed by: 
     
       
         
           
             
               I 
               laser 
             
             = 
             
               
                 Io 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ⅇ 
                   
                     
                       
                         - 
                         2 
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             x 
                             + 
                             y 
                           
                           ) 
                         
                         2 
                       
                     
                     
                       
                           
                       
                       ⁢ 
                       
                         
                           ω 
                           ⁡ 
                           
                             ( 
                             z 
                             ) 
                           
                         
                         2 
                       
                     
                   
                 
                 ⁢ 
                 
                   ⅇ 
                   
                     
                       - 
                       α 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     z 
                   
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 and 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ω 
                   ⁡ 
                   
                     ( 
                     z 
                     ) 
                   
                 
               
               = 
               
                 
                   ω 
                   0 
                   2 
                 
                 ⁡ 
                 
                   ( 
                   
                     1 
                     + 
                     
                       
                         ( 
                         
                           
                             λ 
                             ⁡ 
                             
                               ( 
                               
                                 z 
                                 - 
                                 
                                   z 
                                   0 
                                 
                               
                               ) 
                             
                           
                           
                             pn 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ω 
                               0 
                               2 
                             
                           
                         
                         ) 
                       
                       2 
                     
                   
                   ) 
                 
               
             
           
         
       
     
     where: ? 0=width of the beam at the focusing point (in this case at z=z 0 ). 
     n=index of the propagation medium. 
     lo=density of incident laser energy before it penetrates the semiconductor in J/cm2) 
     After focusing, the beam widens again rapidly as soon as it passes the focusing point. When the beam penetrates a semiconductor, made from silicon for example, the refractive properties due to the difference between the indices of air (nair=1) and silicon (nsi=3.5) have the effect that, in the absence of an air/silicon interface at position z=0, the beam would be focused on z=z 0 ′, but with the interface present, the focusing point would be advanced to depth z=z 0 , with the parameter ? oSi as the characteristic beam defined at 1/e2 of maximum intensity. This parameter is called the “beam waist” in English. 
     Using the properties of Gaussian beams and their transmission at interfaces, it may be shown that:
 
ω osi =ω oair =ω 0 z 0 =n si xz 0 ′
 
     The beam is focused at a depth zo in the silicon with a characteristic beam defined at 1/e2 of maximum intensity identical to that which it would have had without the interface. A variation of dz in the normal identification point therefore translates to a variation of nsi.dz in silicon. 
       FIG. 2  shows two schematic examples of propagation in silicon with focusing points at different depths. If the energy h? of the laser beam photons is greater than the potential barrier in crystal  2 , these photons are able to create free charges within the semiconductor along the length of their passage. 
     It can be shown that the volume density of charges (e.g., the electrons symbolised by n) introduced by a laser beam having incident energy density lo as far as depth z in the semiconductor is: 
     
       
         
           
             
               n 
               ⁡ 
               
                 ( 
                 
                   x 
                   , 
                   y 
                   , 
                   z 
                 
                 ) 
               
             
             = 
             
               · 
               η 
               · 
               
                 ( 
                 
                   1 
                   - 
                   R 
                 
                 ) 
               
               · 
               
                 λ 
                 hc 
               
               · 
               α 
               · 
               
                 
                   I 
                   laser 
                 
                 ⁡ 
                 
                   ( 
                   
                     x 
                     , 
                     y 
                     , 
                     z 
                   
                   ) 
                 
               
             
           
         
       
     
     where: 
     h=Planck&#39;s constant. 
     c=speed of light. 
     λ=laser wavelength. 
     (1−R) llaser=density of laser energy penetrating the semiconductor. 
     α=coefficient of absorption of the semiconductor. 
     ?=quantum efficiency ˜1. 
     Suppose that the sensitive charge collection zone is represented physically by the rectangle and is located at a depth of z=zs. The laser beam will create more charges in the collection zone when it is focused on zo=z 1 =zs than when it is focused on zo=z 2  (where z 2  is different from z 1 ). Charge collection will therefore be more efficient in the first case, and the laser energy required to obtain a given quantity of collected charges (hereinafter called the critical energy) will be reduced. This critical energy corresponds to a critical power for a given pulse duration. If the curve of the critical energy, also called threshold energy, plotted against focusing depth zo, is traced in the configuration of  FIG. 2 , it will have the shape shown in  FIG. 3 . It is the application of this curve (study of minimum) that provides the depth of the sensitive collection zone (in this case zs). In fact, more laser power is required at z 2  (&lt;z 1 ) to disrupt the operation of component  1 . Less power is required at z 1 . Therefore, height zone z 1  is more sensitive than height zone z 2 . 
     If one considers the other two directions X and Y, it will be noted that this does not happen in all cases under review. In fact,  FIG. 4  shows three more examples, A, B and C. In example A, the collection zone is smaller than the laser beam (represented by a disc on the figure) at z 2  and larger than the beam at z 1 . Therefore, the critical threshold will be lower at height zone z 1  than at height zone z 2 . In example B, since the sensitive zone is considerably larger than the width of the laser beam, the critical threshold will be the same everywhere. The experiment is not conclusive, except to show that a much shorter focal length must be used to achieve the conditions of example A. In example C, for which the sensitive zone is of the same type as for example B, (for a given focusing convergence), it is observed that the method enables the heights of the edges of the sensitive area to be detected (particularly due to neutralization of a portion of the laser radiation that reaches a zone where it does not produce parasitic currents in the component). In this case, the critical power is greater. Therefore, the edge of the zone corresponds precisely with the position in X and Y of source  14  for which the power that is useful for revealing the phenomenon starts to become greater than for an adjacent location. 
     It is therefore not necessary to position the focus of the exploration in a zone of interest that has been defined beforehand on the surface, or more generally in X and Y, before starting to explore in depth, in Z. Typically, exploration may begin anywhere, and the X, Y and Z coordinates of the various focuses may be determined according to any strategy, even randomly, both in terms of depth and on the XY plane. In the same way, in order to change the depth of focusing inside the component, one may decide to alter the wavelength of the laser radiation, in fixed increments for example, rather than moving lens  29  relative to the component. 
     It is essential to use a laser for which the material under investigation is not transparent. The energy of the laser photon must be greater than the potential barrier, the energy gap of the semiconductor. In the case of silicon, the wavelength of the laser must be shorter than 1.1 micrometre. On the other hand, it must be ensured that the laser is able to penetrate far enough into the silicon to be able to excite zones that are buried at depth. 
     The duration of the laser pulse has no real significance for this method since the pulse duration only affects the threshold for triggering the phenomenon. Provided the laser has sufficient energy, the choice of pulse duration is not critical. 
     The smaller the size of the laser trace, or spot, the more sensitive the method becomes. For example, we have succeeded in showing that a spot size of 4 micrometres is ideally suited to the method with a wavelength of 1.06 micrometres. 
     The laser beam may be incident on the front face of the component (electrode side) or the rear face (substrate  2 ). Since the laser beam does not penetrate metallizations, irradiation via the rear face is preferable for revealing all sensitive zones. However, the method may be applied in either direction. 
     Threshold energy is defined as the laser energy required in order to obtain a given quantity of collected charges, called the critical charge. Without in any way limiting the effects that may be studied, for analogue components that may be reflected by a given transient current level at output or by triggering of a destructive failure. For SRAM memories, it may be reflected as the energy or critical charge that enables a bit state change or triggering of a parasitic phenomenon known as latchup. 
     Accordingly, the first step is to create a laser map in two dimensions, in directions X and Y of the component. The entire surface of the component is scanned by the laser. For each scan position, the laser energy at which the observed phenomenon is triggered is recorded. An example of laser mapping showing two clear sensitive zones is shown in  FIG. 5 . Investigation in depth is then carried out according to the principle described previously on a given number of points of interest. It is typically carried out for points  1  to  4  in one case and points  5  to  11  in the other. 
     Here, the method is applied to an electronic component of the comparator type. Two charge collection zones have been identified by the laser mapping procedure. Sensitivity studies in depth have been conducted at different points, at the centre and edges of these charge collection zones for each of these two-dimensional zones. 
     As was explained previously, and will be confirmed in the following text discussing the theoretical aspect of the method, the minimum of the curve Ethreshold=f(focusing depth) corresponds to the position at depth of the sensitive zone. 
     With the curve associated with point  4  of the first case,  FIG. 6  shows above all that it is easier to determine the position in depth at the edge of the sensitive zone. For points  1  to  3 , detection of the minimum is not as obvious, since the gradient is shallower. With reference to the zone containing points  5  to  11 , shown in  FIG. 7 , the conclusions are the same. Point  7  enables the height of the sensitivity to be determined as 130 micrometres. If the distance of 60 micrometres between lens  29  and surface  12  is deducted, a height of 70 micrometres is obtained. Then, applying the ratio of the air-silicon refractive index, yields a final result of about 240 micrometres for the depth of the sensitive zone. 
     Taking into account the refractive index of silicon and the offset of the abscissa of the curve, the position of the minimum shows that that sensitive zone is located at a depth of about 340 micrometres measured from the rear face of the component (air silicon interface) for the zone of points  1  to  4 , and at a depth of 240 micrometres for the zone of points  5  to  11 . 
     In the case of static RAM-SRAM-type components, the width of the laser beam is such that ω(z) is larger than the dimensions of the memory point regardless of the position of the laser relative to the memory point. Accordingly, variations in ω(z) will entail variations in the threshold energy. Consequently, as shown in  FIG. 8 , a detection along the lines of example C of  FIG. 4  is obtained. The method works as it should. 
     In theoretical terms, the sensitive zone having thickness h and sides a, b is located at (xs, ys, zs). The laser beam is focused on (xo,yo,zo) in the silicon. 
     Basing ones assumptions on the Rectangular Parallelepiped (RPP) model, that is to say that the charge collection zone is contained in a rectangular parallelepiped, it is possible to calculate the number of charges generated in this rectangular parallelepiped having sides a, b and h and located at depth zs in xs, ys, by a Gaussian beam focused on xo=0, yo=0, zo). 
     
       
         
           
             
               η 
               charge 
             
             = 
             
               η 
               · 
               
                 
                   λ 
                   · 
                   
                     ( 
                     
                       1 
                       - 
                       R 
                     
                     ) 
                   
                   · 
                   α 
                 
                 
                   h 
                   · 
                   c 
                 
               
               · 
               
                 I 
                 0 
               
               · 
               
                 
                   ∫ 
                   
                     
                       z 
                       
                         s 
                         - 
                       
                     
                     ⁢ 
                     
                       h 
                       2 
                     
                   
                   
                     
                       z 
                       s 
                     
                     + 
                     
                       h 
                       2 
                     
                   
                 
                 ⁢ 
                 
                   · 
                   
                     ⅇ 
                     
                       
                         - 
                         α 
                       
                       · 
                       z 
                     
                   
                   · 
                   
                     
                       ω 
                       0 
                       2 
                     
                     
                       
                         ω 
                         ⁡ 
                         
                           ( 
                           z 
                           ) 
                         
                       
                       2 
                     
                   
                   · 
                   
                     
                       ∫ 
                       
                         
                           x 
                           s 
                         
                         - 
                         
                           a 
                           2 
                         
                       
                       
                         
                           x 
                           s 
                         
                         + 
                         
                           a 
                           2 
                         
                       
                     
                     ⁢ 
                     
                       · 
                       
                         ⅇ 
                         
                           - 
                           
                             
                               2 
                               ⁢ 
                               
                                 x 
                                 2 
                               
                             
                             
                               
                                 ω 
                                 ⁡ 
                                 
                                   ( 
                                   z 
                                   ) 
                                 
                               
                               2 
                             
                           
                         
                       
                       · 
                       
                         
                           ∫ 
                           
                             ys 
                             - 
                             
                               b 
                               2 
                             
                           
                           
                             ys 
                             + 
                             
                               b 
                               2 
                             
                           
                         
                         ⁢ 
                         
                           · 
                           
                             ⅇ 
                             
                               - 
                               
                                 
                                   2 
                                   ⁢ 
                                   
                                     y 
                                     2 
                                   
                                 
                                 
                                   
                                     ω 
                                     ⁡ 
                                     
                                       ( 
                                       z 
                                       ) 
                                     
                                   
                                   2 
                                 
                               
                             
                           
                           · 
                           
                               
                           
                           ⁢ 
                           
                             ⅆ 
                             x 
                           
                           · 
                           
                               
                           
                           ⁢ 
                           
                             ⅆ 
                             y 
                           
                           · 
                           
                               
                           
                           ⁢ 
                           
                             ⅆ 
                             z 
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
     where 
     
       
         
           
             
               I 
               0 
             
             = 
             
               
                 2 
                 · 
                 
                   E 
                   0 
                 
               
               
                 π 
                 · 
                 
                   ω 
                   0 
                   2 
                 
               
             
           
         
       
     
     and Eo, incident laser energy at z=0. 
     Integrating the preceding expression yields: 
     
       
         
           
             
               η 
               charge 
             
             = 
             
               η 
               ⁢ 
               
                 
                   
                     4 
                     · 
                     λ 
                     · 
                     
                       ( 
                       
                         1 
                         - 
                         R 
                       
                       ) 
                     
                     · 
                     α 
                   
                   
                     h 
                     · 
                     c 
                   
                 
                 · 
                 
                   E 
                   0 
                 
                 · 
                 
                   
                     ∫ 
                     
                       
                         z 
                         s 
                       
                       - 
                       
                         h 
                         2 
                       
                     
                     
                       
                         z 
                         s 
                       
                       + 
                       
                         h 
                         2 
                       
                     
                   
                   ⁢ 
                   
                     · 
                     
                       ⅇ 
                       
                         
                           - 
                           α 
                         
                         · 
                         z 
                       
                     
                     · 
                     
                       [ 
                       
                         
                           erf 
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   2 
                                 
                                 
                                   ω 
                                   ⁡ 
                                   
                                     ( 
                                     z 
                                     ) 
                                   
                                 
                               
                               · 
                               
                                 ( 
                                 
                                   
                                     a 
                                     2 
                                   
                                   - 
                                   xs 
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                         - 
                         
                           erf 
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   2 
                                 
                                 
                                   ω 
                                   ⁡ 
                                   
                                     ( 
                                     z 
                                     ) 
                                   
                                 
                               
                               · 
                               
                                 ( 
                                 
                                   
                                     
                                       - 
                                       a 
                                     
                                     2 
                                   
                                   - 
                                   
                                     x 
                                     s 
                                   
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                       ] 
                     
                     · 
                     
                       [ 
                       
                           
                       
                       ⁢ 
                       
                         erf 
                         ( 
                         
                             
                         
                         ⁢ 
                         
                           
                             
                               2 
                             
                             
                               ω 
                               ⁡ 
                               
                                 ( 
                                 z 
                                 ) 
                               
                             
                           
                           · 
                           
                             ( 
                             
                               
                                 
                                   - 
                                   b 
                                 
                                 2 
                               
                               - 
                               ys 
                             
                             ) 
                           
                         
                         ) 
                       
                       ] 
                     
                     · 
                     
                       ⅆ 
                       z 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               ω 
               ⁡ 
               
                 ( 
                 z 
                 ) 
               
             
             = 
             
               
                 ω 
                 0 
                 2 
               
               · 
               
                 
                   [ 
                   
                     1 
                     + 
                     
                       
                         
                           λ 
                           ⁡ 
                           
                             ( 
                             
                               z 
                               - 
                               zo 
                             
                             ) 
                           
                         
                         2 
                       
                       
                         π 
                         · 
                         n 
                         · 
                         
                             
                         
                         ⁢ 
                         
                           ω 
                           0 
                           2 
                         
                       
                     
                   
                   ] 
                 
                 2 
               
             
           
         
       
     
     For the threshold laser energy Eo=Ethreshold corresponding to the critical charge ncharge=Qcrit, the following applies: 
     
       
         
           
             
               E 
               threshold 
             
             = 
             
               
                 Q 
                 critique 
               
               
                 
                   
                     
                       η 
                       · 
                       
                         
                           4 
                           · 
                           
                             λ 
                             ⁡ 
                             
                               ( 
                               
                                 1 
                                 - 
                                 R 
                               
                               ) 
                             
                           
                           · 
                           α 
                         
                         
                           h 
                           · 
                           c 
                         
                       
                       · 
                       
                         
                           ∫ 
                           
                             
                               z 
                               s 
                             
                             - 
                             
                               h 
                               2 
                             
                           
                           
                             
                               z 
                               s 
                             
                             + 
                             
                               h 
                               2 
                             
                           
                         
                         ⁢ 
                         
                           · 
                           
                             ⅇ 
                             
                               α 
                               · 
                               z 
                             
                           
                           · 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         [ 
                         
                           
                             erf 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     2 
                                   
                                   
                                     ω 
                                     ⁡ 
                                     
                                       ( 
                                       z 
                                       ) 
                                     
                                   
                                 
                                 · 
                                 
                                   ( 
                                   
                                     
                                       a 
                                       2 
                                     
                                     - 
                                     
                                       x 
                                       x 
                                     
                                   
                                   ) 
                                 
                               
                               ) 
                             
                           
                           - 
                           
                             erf 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     2 
                                   
                                   
                                     ω 
                                     ⁡ 
                                     
                                       ( 
                                       z 
                                       ) 
                                     
                                   
                                 
                                 · 
                                 
                                   ( 
                                   
                                     
                                       
                                         - 
                                         a 
                                       
                                       2 
                                     
                                     - 
                                     
                                       x 
                                       s 
                                     
                                   
                                   ) 
                                 
                               
                               ) 
                             
                           
                         
                         ] 
                       
                       · 
                     
                   
                 
                 
                   
                     
                       
                         [ 
                         
                             
                         
                         ⁢ 
                         
                           
                             erf 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     2 
                                   
                                   
                                     ω 
                                     ⁡ 
                                     
                                       ( 
                                       z 
                                       ) 
                                     
                                   
                                 
                                 · 
                                 
                                   ( 
                                   
                                     
                                       b 
                                       2 
                                     
                                     - 
                                     
                                       y 
                                       s 
                                     
                                   
                                   ) 
                                 
                               
                               ) 
                             
                           
                           - 
                           
                             erf 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     2 
                                   
                                   
                                     ω 
                                     ⁡ 
                                     
                                       ( 
                                       z 
                                       ) 
                                     
                                   
                                 
                                 · 
                                 
                                   ( 
                                   
                                     
                                       
                                         - 
                                         b 
                                       
                                       2 
                                     
                                     - 
                                     
                                       y 
                                       s 
                                     
                                   
                                   ) 
                                 
                               
                               ) 
                             
                           
                         
                         ] 
                       
                       ⁢ 
                       
                         ⅆ 
                         z 
                       
                     
                   
                 
               
             
           
         
       
     
     The integral is calculated for example by the trapezoid method. This function describes the trend of the threshold energy as a function of the focusing depth. The profile of this expression yields the curve of  FIG. 3 , for example. 
     Function Erf(x) tends towards  1  when its argument is large. Therefore, in order to observe variations in threshold energy Ethreshold, the ratios: 
               (         2       ω   ⁡     (   z   )         ·     (       a   2     -     x   s       )       )     ⁢           ⁢   and   ⁢           ⁢     (         2       ω   ⁡     (   z   )         ·     (       b   2     -     y   s       )       )           
must vary, which is effective in examples A and C of  FIG. 4 , but not in B.
 
     Accordingly, in the case of a sensitive zone for which dimensions a and b are significantly larger than ω(z) (regardless of the depth) (example B), the threshold energy will not vary. 
     Conversely, for identical ω(z), if the laser beam is fired at the edge of the sensitive zone, the threshold energy will vary because in this case 
               (         2       ω   ⁡     (   z   )         ·     (       a   2     -     x   s       )       )     ⁢           ⁢   and   ⁢           ⁢     (         2       ω   ⁡     (   z   )         ·     (       b   2     -     y   s       )       )           
do vary.
 
     Suppose that there is only one sensitive zone, which is located at a depth of z s  and has a thickness h (see also  FIG. 8 ). If the expression of E threshold  as a function of z is derived, the result is: 
     
       
         
           
             
               
                 ∂ 
                 Ethreshold 
               
               
                 ∂ 
                 z 
               
             
             = 
             
               
                 
                   Q 
                   crit 
                 
                 × 
                 
                   
                     
                       ∂ 
                       
                         n 
                         charge 
                       
                     
                     
                       ∂ 
                       z 
                     
                   
                   
                     n 
                     charge 
                     2 
                   
                 
               
               = 
               
                 
                   Q 
                   crit 
                 
                 × 
                 
                   
                     
                       
                         ∂ 
                         
                           n 
                           charge 
                         
                       
                       
                         ∂ 
                         
                           z 
                           s 
                         
                       
                     
                     × 
                     
                       
                         ∂ 
                         
                           z 
                           s 
                         
                       
                       
                         ∂ 
                         z 
                       
                     
                   
                   
                     n 
                     charge 
                     2 
                   
                 
               
             
           
         
       
     
     As was explained in 2.1.1, 
     
       
         
           
             
               
                 ∂ 
                 
                   z 
                   s 
                 
               
               
                 ∂ 
                 z 
               
             
             = 
             
               
                 n 
                 si 
               
               . 
             
           
         
       
     
     The derivative of the curve representing the trend of the charge generated as a function of the depth thus enables the extremum of the function to be characterized. The expression of this derivative is given below (for the sake of clarity, the values of xs, ys, a and b are such that: xs=ys=0 and a=b, but the general calculation would yield identical results: 
                 ∂   ncharge       ∂   z       =       n   si     ×     η   ·       λ   ·     (     1   -   R     )     ·   α       h   ·   c       ·     E   o     ·     [               ⅇ       -   α     ·     (       z   x     +     h   2       )         ·       [     erf   (         2       ω   ⁡     (       z   s     +     h   2       )         ·     (     a   2     )       )     ]     2       -                 ⅇ       -   α     ·     (       z   s     -     h   2       )         ·       [     erf   (         2       ω   ⁡     (       z   s     -     h   2       )         ·     (     a   2     )       )     ]     2             ]               
and zs=nsi*z.
 
     The extremum is given by: 
                   ∂     n   charge         ∂   z       =   0     ,         
or:
 
     
       
         
           
             
               
                 ⅇ 
                 
                   
                     - 
                     α 
                   
                   · 
                   h 
                 
               
               · 
               
                 
                   [ 
                   
                     erf 
                     ( 
                     
                       
                         
                           2 
                         
                         
                           ω 
                           ⁡ 
                           
                             ( 
                             
                               
                                 z 
                                 s 
                               
                               + 
                               
                                 h 
                                 2 
                               
                             
                             ) 
                           
                         
                       
                       · 
                       
                         ( 
                         
                           a 
                           2 
                         
                         ) 
                       
                     
                     ) 
                   
                   ] 
                 
                 2 
               
             
             = 
             
               
                 [ 
                 
                   erf 
                   ( 
                   
                     
                       
                         2 
                       
                       
                         ω 
                         ⁡ 
                         
                           ( 
                           
                             
                               z 
                               s 
                             
                             - 
                             
                               h 
                               2 
                             
                           
                           ) 
                         
                       
                     
                     · 
                     
                       ( 
                       
                         a 
                         2 
                       
                       ) 
                     
                   
                   ) 
                 
                 ] 
               
               2 
             
           
         
       
     
     Since the product α.h tends towards 0 (α≈20 cm−1 for silicon and a level of doping less than 1017 cm3 and with a wavelength of 1.06 micrometres, z is in the order of a few to a few tens of micrometres), equality is achieved when zs, centre of the sensitive zone at depth, is equal to the focusing point of the laser zo, because then ω(z 0 +h/2)=ω(z 0 −h/2). 
     Thus, the minimum of the experimental curve characterizing the trend of the threshold energy as a function of the focusing depth does indeed correspond, based on the assumptions of the RPP model, to the depth at which the sensitive zone is buried. 
       FIG. 9  is a schematic representation of a simulation of attacks by heavy ions or other particles. With the disclosed embodiment, we have succeeded in defining positions of sensitive zones  36  and  37  in X, Y and Z in a component  1 . For the sake of simplicity, it is convenient to consider that zones  36  and  37  are sensitive, and that the rest of the component is not sensitive. More generally, a coefficient of sensitivity may be assigned to each zone. Once this three-dimensional map has been created, component  1  is virtually bombarded with heavy ions, neutrons, protons, or other particles along various trajectories  38  and  39 . The correlation between the results obtained with the laser and the results obtained in an accelerator is not direct because the mechanisms of interaction with the material are different. But theories are known that may serve as the basis for making these correlations. This means that it is possible to deduce the zones that are sensitive to particles from the zones that are sensitive to laser radiation. 
     In the example, beam  38  passes beside sensitive zone  36 , while beam  39  is directed straight into the centre of zone  37 . The occurrence or non-occurrence of a failure is measured depending on the direction and power of each beam. A sensitivity score is prepared for component  1  for a statistically relevant level of simulated bombardment activities.