# Patent

## Title
Method for detecting heat generation points and device for detecting heat generate points

## Abstract

A heat generation point detection method comprises: step of stabilizing an average temperature of a surface of an integrated circuit S; steps of applying a bias voltage of a low frequency to the integrated circuit S and acquiring a heat generation detection signal detected from the integrated circuit S in response thereto; steps of supplying a bias voltage of a high frequency and acquiring a heat generation detection signal detected in response thereto; steps of detecting a phase shift between the bias voltage of the low frequency and the heat generation detection signal and a phase shift between the bias voltage of the high frequency and the heat generation detection signal; and step of calculating a change rate of the phase shift against a square root of the frequency of the bias voltage, and obtaining depth information of the heat generation point from the change rate.

## Background
TECHNICAL FIELD
The present invention relates to a heat generation point detection method and a heat generation point detection device for detecting a depth of a heat generation point in an integrated circuit.
BACKGROUND ART
A method of applying a periodic pulse voltage to an integrated circuit and detecting a thermal response is known as a conventional failure analysis method for integrated circuits such as LSI packages. For example, Non Patent Literature 1 below describes that a phase shift ΔΦ between electrical excitation and a local thermal response is detected and a depth of a defect is determined from the phase shift ΔΦ.
CITATION LIST
Non Patent Literature
Non Patent Literature 1: C. Schmidt et al., “Lock-in-Thermography for 3-dimensional localization of electrical defects inside complex packaged devices,” ISTFA2008: Proceedings from the 34th International Symposium for Testing and Failure Analysis, U.S.A., Nov. 2008, p. 102-107.
SUMMARY OF INVENTION
Technical Problem
In the above-described conventional analysis method, however, the phase shift ΔΦ is dependent on an amount of heat generation, a structure of an integrated circuit, and a position of a defect point, as well as the depth of the defect point, because the amount of heat generation varies depending upon the amplitude of an excitation signal and the condition of the defect point and because the heat capacity between the defect point and the surface of the integrated circuit varies depending upon the position of the defect point. This position dependency of the offset component of the phase shift arises from the fact that the heat transfer coefficient from the surface of the integrated circuit as sample to air is determined by temperature of the surface and the condition of convection at the surface.
A factor for error of the offset component of the phase shift is a temperature rise of the sample. Specifically, the temperature of the sample continuously rises during acquisition of the thermal response and a slope thereof due to the temperature rise is also detected as another wave, which has led to a tendency of failing to detect an accurate phase shift.
Under such circumstances, the present invention has been accomplished in view of the foregoing problem and it is an object of the present invention to provide a heat generation point detection method and a heat generation point detection device allowing accurate and stable detection of a depth of a heat generation point in an integrated circuit, independent of the position thereof.
Solution to Problem
In order to solve the above problem, a heat generation point detection method according to an aspect of the present invention is a heat generation point detection method for detecting a depth of a heat generation point in an integrated circuit, comprising: a first step of stabilizing an average temperature of a surface of the integrated circuit; a second step of supplying a periodic electric signal fluctuating at a first frequency, to the integrated circuit and acquiring a first detection signal indicative of a change of an amount of heat generation detected from the integrated circuit in response thereto; a third step of supplying a periodic electric signal fluctuating at a second frequency different from the first frequency, to the integrated circuit and acquiring a second detection signal indicative of a change of an amount of heat generation detected from the integrated circuit in response thereto; and a fourth step of obtaining depth information of the heat generation point, based on the first and second detection signals.
Furthermore, a heat generation point detection device according to another aspect of the present invention is a heat generation point detection device for detecting a depth of a heat generation point in an integrated circuit, comprising: an electric signal supply unit for supplying an electric signal to the integrated circuit; a control unit for controlling the electric signal supply unit so as to supply a periodic electric signal fluctuating at a first frequency and a periodic electric signal fluctuating at a second frequency different from the first frequency, to the integrated circuit; a detection unit for acquiring a first detection signal indicative of a change of an amount of heat generation detected from the integrated circuit in response to supply of the periodic electric signal of the first frequency and acquiring a second detection signal indicative of a change of an amount of heat generation detected from the integrated circuit in response to supply of the periodic electric signal of the second frequency; a calculation unit for obtaining depth information of the heat generation point, based on the first and second detection signals; and a temperature stabilization unit for stabilizing an average temperature of a surface of the integrated circuit.
The heat generation point detection method or the heat generation point detection device as described above is configured to detect the first detection signal indicative of the change of the amount of heat generation in response to the supply of the periodic electric signal of the first frequency and detect the second detection signal indicative of the change of the amount of heat generation in response to the supply of the periodic electric signal of the second frequency, from the integrated circuit in a state in which the average temperature of the surface of the integrated circuit is stabilized. Then the depth information of the heat generation point is obtained based on the first and second detection signals. This procedure is to calculate the depth information based on the thermal responses to the electric signals of the two frequencies detected while the average temperature of the surface of the integrated circuit is stabilized so as to be constant (or approximately constant); therefore, the depth information is obtained on a stable basis and with high accuracy, independent of the position of the heat generation point.
Advantageous Effect of Invention
The present invention allows accurate and stable detection of the depth of the heat generation point in the integrated circuit, independent of the position thereof.



BRIEF DESCRIPTION OF DRAWINGS
FIG. 1 is a block diagram showing a schematic configuration of an integrated circuit failure analysis device according to a preferred embodiment of the present invention.
FIG. 2 is a side view showing an example of a configuration of a temperature stabilization unit in FIG. 1.
FIG. 3 is a plan view showing a discharge state of gas to an integrated circuit by the temperature stabilization unit in FIG. 2.
FIG. 4 is a flowchart showing a procedure of a failure analysis operation for the integrated circuit S by the integrated circuit failure analysis device 1 in FIG. 1.
FIG. 5 is a drawing showing a temporal change of bias voltages applied by a voltage application unit 14 in FIG. 1.
FIG. 6 is a drawing wherein (a) shows a temporal change of a bias voltage, (b) a temporal change of a heat generation detection signal detected in an integrated circuit S comprised of a material with low heat capacity/low heat transfer coefficient, and (c) a temporal change of a heat generation detection signal detected in an integrated circuit S comprised of a material with high heat capacity/high heat transfer coefficient.
FIG. 7 is a drawing showing temporal changes of heat generation detection signals detected when a temperature rise occurs at a surface of the integrated circuit S.
FIG. 8 is a drawing showing temporal changes of heat generation detection signals detected in the target of the integrated circuit S.
FIG. 9 is a drawing wherein (a) shows a temporal change of a bias voltage applied at a low frequency, (b) a temporal change of a heat generation detection signal detected in the integrated circuit S, (c) a temporal change of a bias voltage applied at a high frequency, and (d) a temporal change of a heat generation detection signal detected in the integrated circuit S.
FIG. 10 is a graph showing a relationship between a square root of angular frequency of bias voltages applied to the integrated circuit S in the integrated circuit failure analysis device in FIG. 1, and observed phase delay bx.
FIG. 11 is a side view showing an example of the configuration of the temperature stabilization unit in a modification example of the present invention.
FIG. 12 is a plan view showing a discharge state of gas to the integrated circuit by the temperature stabilization unit in FIG. 11.
FIG. 13 is a side view showing an example of the configuration of the temperature stabilization unit in another modification example of the present invention.
FIG. 14 is a side view showing an example of the configuration of the temperature stabilization unit in another modification example of the present invention.



DESCRIPTION OF EMBODIMENTS
The preferred embodiments of the heat generation point detection device according to the present invention and the heat generation point detection method using the same will be described below in detail with reference to the drawings. Identical or equivalent portions will be denoted by the same reference signs in the description of the drawings, without redundant description.
FIG. 1 is a block diagram showing a schematic configuration of an integrated circuit failure analysis device which is a heat generation point detection device according to a preferred embodiment of the present invention. The integrated circuit failure analysis device 1 shown in the same drawing is a failure analysis device which detects a position of a heat generation point in an integrated circuit S such as LSI or IC and performs a failure analysis. This integrated circuit failure analysis device 1 is configured with a sample stage 10, a stage drive unit 12 to drive the sample stage 10, a voltage application unit (electric signal supply unit) 14, an imaging device 18, a control unit 20, an image processing unit 30, and a temperature stabilization unit 40.
The integrated circuit S as an analysis target is mounted on the sample stage 10 using X-, Y-, and Z-stages which can be driven in X-axis direction, Y-axis direction (horizontal direction), and Z-axis direction (vertical direction), respectively. This sample stage 10 is configured so that it can be driven in the X-, Y-, and Z-directions by the stage drive unit 12, thereby to carry out focusing in imaging, position alignment of imaging position, and so on for the integrated circuit S. The imaging device 18 as imaging means for acquiring a two-dimensional image of the integrated circuit S is installed above the sample stage 10. The imaging device 18 to be suitably used herein is an imaging device sensitive to a predetermined wavelength region, for acquiring an image based on a heat generation image on the surface of the integrated circuit S, e.g., an infrared imaging device sensitive to the infrared wavelength region. The surface of the integrated circuit S refers to an observation surface from which an image is taken by the imaging device 18.
A light-guide optical system 16 such as an objective lens for guiding the image on the surface of the integrated circuit S to the imaging device 18 is disposed on the optical axis between the sample stage 10 and the imaging device 18. The integrated circuit failure analysis device may be configured as follows: the light-guide optical system 16 is provided with a driving mechanism such as X-, Y-, and Z-stages and this driving mechanism allows the device to implement the focusing in imaging, the position alignment of imaging position, and so on for the integrated circuit S.
The integrated circuit failure analysis device is provided with the voltage application unit 14 for supplying a voltage signal to the integrated circuit S on the sample stage 10. The voltage application unit 14 is voltage application means for applying a necessary bias voltage to an electronic circuit in the integrated circuit S in carrying out a failure analysis based on detection of a heat generation point, and is configured including a power supply for application of voltage. Specifically, the voltage application unit 14 applies a voltage signal (periodic electric signal) of a rectangular wave fluctuating periodically, as a bias voltage. This operation results in applying a high voltage and a low voltage periodically to the integrated circuit S. The voltage application unit 14 is configured so that the frequency (repetition period) of the applied bias voltage can be changed by control of the control unit 20. The voltage application unit 14 is configured so that values of the high voltage and low voltage of the applied bias voltage can be changed by control of the control unit 20.
The imaging device 18 detects a plurality of analysis images in time series in a state in which the bias voltage is applied to the integrated circuit S by the voltage application unit 14. The analysis images acquired in this manner are images including the heat generation image on the surface of the integrated circuit S. The imaging frequency (frame rate) of the imaging device 18 may be set based on the frequency of the bias voltage applied to the integrated circuit S by the voltage application unit 14. For example, the imaging frequency of the imaging device 18 may be the same period as the frequency of the bias voltage applied to the integrated circuit S or may be set in proportion to the frequency of the bias voltage. This setting allows the device to capture heat generation images in relatively identical heat generation conditions, even at different frequencies of bias voltages.
Furthermore, for these sample stage 10, stage drive unit 12, voltage application unit 14, light-guide optical system 16, and imaging device 18, the integrated circuit failure analysis device 1 is provided with the control unit 20 for controlling operations thereof. This control unit 20 is configured with an imaging control unit 21, a stage control unit 22, and a synchronism control unit 23.
The imaging control unit 21 controls the bias voltage application operation by the voltage application unit 14 and the image acquisition operation by the imaging device 18, thereby to control the acquisition of analysis images of the integrated circuit S. The stage control unit 22 controls the operation of the sample stage 10 and the stage drive unit 12 (the moving operation of the integrated circuit S on the sample stage 10). The synchronism control unit 23 performs a control for achieving necessary synchronism of the imaging control unit 21 and the stage control unit 22 with the image processing unit 30 provided for the imaging device 18. Namely, the synchronism control unit 23 controls the stage control unit 22 to move the stage to a predetermined position for execution of a failure analysis of the integrated circuit S and thereafter controls the imaging control unit 21 to change frequencies of bias voltages at predetermined intervals in order. The synchronism control unit 23 also controls the value of the high voltage and the value of the low voltage in the bias voltage applied periodically. The synchronism control unit 23 controls the imaging control unit 21 to separately acquire the analysis images of the integrated circuit S in time with change timings of the frequencies of the bias voltages.
The image processing unit 30 is image processing means for performing image processing necessary for the failure analysis of the integrated circuit S, on the images acquired by the imaging device 18. The image processing unit 30 in the present embodiment is configured with an image storage unit 31, a heat generation signal acquisition unit (detection unit) 32, a voltage phase acquisition unit 33, a phase delay acquisition unit (detection unit or phase shift detection unit) 34, and a depth information calculation unit 35. The images of the integrated circuit S acquired by the imaging device 18 are fed to the image processing unit 30 and stored and accumulated in the image storage unit 31 as occasion may demand.
The heat generation signal acquisition unit 32 detects a heat generation detection signal indicative of a temporal change of an amount of heat generation detected at a plurality of points on the surface of the integrated circuit S, based on the plurality of analysis images acquired in time series.
The voltage phase acquisition unit 33 receives the waveform of the bias voltage applied by the voltage application unit 14, from the synchronism control unit 23, and acquires information of the phase of the bias voltage. The information of the phase of the bias voltage may be acquired by the voltage application unit 14 or by the control unit 20 and then supplied to the voltage phase acquisition unit 33 therefrom.
The phase delay acquisition unit 34 acquires information of the phase of the heat generation detection signal with respect to the information of the phase of the bias voltage applied by the voltage application unit 14, based on the heat generation detection signal indicative of the temporal change of the amount of heat generation acquired by the heat generation signal acquisition unit 32 and the phase information acquired by the voltage phase acquisition unit 33. This information of the phase of the heat generation detection signal corresponds to a phase shift between the bias voltage and the heat generation detection signal detected upon application of the bias voltage and, specifically, the phase delay acquisition unit 34 calculates a difference between the phase of the heat generation detection signal acquired by the heat generation signal acquisition unit 32 and the phase information acquired by the voltage phase acquisition unit 33. Here, the phase delay acquisition unit 34 detects the phase shift between the bias voltage and the heat generation detection signal, for each of the bias voltages changed to a plurality of frequencies. The phase delay acquisition unit 34 may directly acquire the phase shift by lock-in processing, from objects of the waveform of the heat generation detection signal and the waveform of the bias voltage. In this case, an output signal about the phase shift can be obtained by feeding the heat generation detection signal and the bias signal to a lock-in detector.
The depth information calculation unit 35 calculates the depth information of the heat generation point in the integrated circuit S, based on a plurality of phase shifts corresponding to the bias voltages of a plurality of frequencies, which were detected by the phase delay acquisition unit 34. Namely, the depth information calculation unit 35 calculates a change rate of the phase shift against a square root of the frequency which is a variable calculated from the frequency of the bias voltage, and calculates as the depth information the change rate or a value obtained by multiplying the change rate by a predetermined constant. This predetermined constant is preliminarily set as a coefficient about heat transfer dependent on physical properties of a material of the integrated circuit S. The depth information calculated in this manner indicates the depth of the heat generation point detected over a plurality of points on the integrated circuit S and is used for the failure analysis of the integrated circuit S.
The image processing unit 30 of this configuration is constructed, for example, using a computer. An input device 36 and a display device 37 are connected to this image processing unit 30. The input device 36 is composed, for example, of a keyboard, a mouse, and so on and is used, for example, to enter information and operation instructions necessary for execution of the image acquisition operation and the failure analysis operation in the integrated circuit failure analysis device 1. The display device 37 is composed, for example, of a CRT display, a liquid crystal display, or the like and is used, for example, to display various kinds of information such as the images and the depth information about the failure analysis in the integrated circuit failure analysis device 1.
The temperature stabilization unit 40 has a function to stabilize an average temperature of the surface of the integrated circuit S. FIG. 2 is a side view showing an example of a configuration of the temperature stabilization unit. As shown in the same drawing, the temperature stabilization unit 40 as a medium supply unit is configured including an air tank 41 reserving a gas (medium) such as air, a regulator (pressure regulating valve) 42 to regulate the pressure of the gas discharged from the air tank 41, an air hose 43 to guide the gas G discharged via the regulator 42 from the air tank 41, so as to flow the gas along the surface of the integrated circuit S, and a temperature control unit 44 to detect the temperature of the surface of the integrated circuit S and control the regulator 42 so as to keep the temperature constant. This air hose 43 is arranged so that a discharge outlet thereof is disposed at an end on the surface of the integrated circuit S and is directed toward a central part along the surface, and it is fixed to the sample stage 10 so as not to change its relative position to the integrated circuit S on the sample stage 10. The temperature control unit 44 includes a temperature detecting element (not shown) such as a thermistor arranged in the vicinity of the integrated circuit S, and controls the regulator 42 so as to keep constant values of temperature detected by the temperature detecting element, thereby increasing or decreasing the pressure of the gas G supplied from the air hose 43.
FIG. 3 is a plan view showing a discharge state of the gas to the integrated circuit S by the temperature stabilization unit 40. As shown in the same drawing, the air hose 43 of the temperature stabilization unit 40 has the size and shape suitable for discharging the gas G toward the other end S2 in a range wider than the width of one end S1 on the surface of the integrated circuit S. This allows the temperature stabilization unit 40 to generate a flow of the gas G along one direction at stable pressure over the entire surface covering a failure portion F in the integrated circuit S. As a result, the temperature stabilization unit 40 can stabilize the temperature of the entire surface of the integrated circuit S at a desired temperature.
This image processing unit 30 may be configured so that it, together with the control unit 20, is implemented as a single control device (e.g., a single computer). Concerning the input device 36 and the display device 37 connected to the image processing unit 30, they may also be configured similarly so as to function as input device and display device connected not only to the image processing unit 30 but also to the control unit 20.
The following will describe the procedure of the failure analysis operation about the integrated circuit S by the integrated circuit failure analysis device 1 and detail the heat generation point detection method according to the present embodiment. FIG. 4 is a flowchart showing the procedure of the failure analysis operation about the integrated circuit S by the integrated circuit failure analysis device 1, and FIGS. 5 to 9 are drawings showing temporal changes of signal waveforms processed in the failure analysis operation by the integrated circuit failure analysis device 1.
First, the temperature stabilization unit 40 is actuated to stabilize the average temperature of the surface of the integrated circuit S mounted on the sample stage 10 (step S01). After the temperature stabilization unit 40 detects that the average temperature of the surface of the integrated circuit S is stabilized by this temperature stabilization process, the synchronism control unit 23 controls the voltage application unit 14 to apply a bias voltage fluctuating at a low frequency (e.g., 1 Hz), to the integrated circuit S (step S02). This control causes a high voltage and a low voltage to be applied periodically to the integrated circuit S. In conjunction therewith, the imaging control unit 21 controls the imaging device 18 to separately acquire images according to the application timing of the low-frequency bias voltage. For example, the imaging control unit 21 controls the imaging device 18 to take images at the same frequency as the low frequency applied to the integrated circuit S or at an imaging frequency (frame rate) proportional to the low frequency. The images of the integrated circuit S acquired in this manner are stored once into the image storage unit 31 and thereafter processed by the heat generation signal acquisition unit 32, thereby to acquire a heat generation detection signal indicative of a temporal change of an amount of heat generation at a plurality of points (step S03).
Next, the synchronism control unit 23 controls the voltage application unit 14 to apply a bias voltage fluctuating at a high frequency (e.g., 2 Hz), to the integrated circuit S (step S04). This control causes a high voltage and a low voltage to be applied periodically to the integrated circuit S. In conjunction therewith, the imaging control unit 21 controls the imaging device 18 to separately acquire images according to the application timing of the high-frequency bias voltage. For example, the imaging control unit 21 controls the imaging device 18 to take images at the same frequency as the high frequency applied to the integrated circuit S or at an imaging frequency (frame rate) proportional to the high frequency. The images of the integrated circuit S acquired in this manner are stored once into the image storage unit 31 and thereafter processed by the heat generation signal acquisition unit 32, thereby to acquire a heat generation detection signal at a plurality of points (step S05). The frequencies of the bias voltages applied in steps S02, S04 may be suitably changed but are preferably set to not more than 10 Hz because too high frequencies must lead to place dependency of heat transference and amount of heat generation. The frequencies of the bias voltages changed do not always have to be limited to two types, but may be three or more types to acquire heat generation detection signals according thereto.
FIG. 5 shows a temporal change of the bias voltages applied in steps S02, S04. As shown in the same drawing, the synchronism control unit 23 controls the bias voltages so that a high-frequency period P2 follows a low-frequency period P1 in series and, a duration of acquisition of the heat generation detection signal in each of the period P1 and the period P2 is set so that a certain length of time passes after a start of application of the bias voltage in each of the periods P1, P2, in order to make the temperature in the integrated circuit S constant between those periods so as not to affect the amount of heat generation. It is also permissible to place a period without application of voltage between the period P1 and the period P2. The maximum voltages V1 and minimum voltages V2 of the bias voltages of rectangular waves are set at respective identical values between the frequencies so as to equalize conditions during heat generation in the integrated circuit S and the duty ratios of the bias voltages are also set at an identical value (e.g., 50%, 75%, . . . ) between the frequencies so as to equalize amounts of heat generation in the integrated circuit S. This is for the purpose of keeping an average temperature of a sample constant by making the amount of heat generation constant in the integrated circuit S. In this case, it is also possible to set the durations of acquisition of heat generation detection signals in the period P1 and in the period P2 continuous.
Referring back to FIG. 4, from targets of the waveforms of the low-frequency and high-frequency bias voltages applied to the integrated circuit S in steps S02, 04, the voltage phase acquisition unit 33 then acquires the phase information thereof (step S06).
Next, from processing targets of the heat generation detection signals corresponding to the application of the low-frequency and high-frequency bias voltages, which were acquired in steps S03, S05, the phase delay acquisition unit 34 acquires the phase information thereof with respect to the information of the phases of the bias voltages acquired in step S06 and detects phase shifts of the respective heat generation detection signals (steps S07, S08). Specifically, the phase delay acquisition unit 34 detects the phase shift from the heat generation detection signal about each of the low-frequency and high-frequency bias voltages, based on the heat generation detection signals corresponding to the application of the low-frequency and high-frequency bias voltages, which were acquired in steps S03 and S05, and based on the information of the phases of the waveforms of the low-frequency and high-frequency bias voltages applied to the integrated circuit S in steps S02 and 04. Next, the depth information calculation unit 35 calculates a change rate of the phase shift against the square root of the frequency, based on the phase shifts corresponding to the two frequencies, and multiplies the change rate by a predetermined constant to obtain the depth information (step S09). This depth information is calculated over a plurality of points on the surface of the integrated circuit S. Finally, the depth information thus calculated is processed as failure analysis information and displayed on the display device 37 (step S10).
The below will describe a mechanism of detection of the depth information of a heat generation point by the integrated circuit failure analysis device 1.
In FIG. 6, (a) shows a temporal change of a bias voltage applied at a certain frequency, (b) a temporal change of a heat generation detection signal detected in the integrated circuit S comprised of a material with low heat capacity/low heat transfer coefficient in response thereto, and (c) a temporal change of a heat generation detection signal detected in the integrated circuit S comprised of a material with high heat capacity/high heat transfer coefficient in response thereto. A phase shift calculated by the phase delay acquisition unit 34 in the integrated circuit failure analysis device 1 is D1 and this phase shift D1 includes a phase shift component D2 determined by a depth of a heat generation point in the integrated circuit S and a phase shift component D3 due to differences of delay of heat generation, heat capacity, and heat transfer rate. The shift component D3 in the phase shift D1 is significantly affected by a material of a heat transfer path in the integrated circuit S. In addition, the heat transfer coefficient of the integrated circuit S to air is determined by the temperature of the surface and convection based thereon, and therefore the shift component D3 is also significantly affected by the temperature of the surface of the integrated circuit S.
This difference of the phase shift D1 depending on the material can be explained as follows. A quantity Q of heat one-dimensionally transferred from the interior of the integrated circuit S is represented by Expression (1) below;
[Math 1]

Q=1+exp{−ax+i(wt−bx)}  (1).

In this expression, x represents a distance from a heat generation source to an observation point (surface) (=depth of the heat generation point), Q a quantity of heat passing the observation point, w the angular frequency (1⁄2π Hz), b a phase delay per unit length, and a an attenuation rate per unit length. A temperature T against this heat quantity Q is represented as changing quantity by Expression (2) below;




  
    
      
        [
        
          Math
          ⁢
          
            
          
          ⁢
          2
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        
          
            d
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        (
        2
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where q represents the specific heat and p the density.

Furthermore, from the thermal diffusion equation, where the heat transfer coefficient is denoted by κ, Expression (3) below is derived;




  
    
      
        [
        
          Math
          ⁢
          
            
          
          ⁢
          3
        
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        (
        3
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From Expression (1), Expression (4) below is derived herein as a second derivative with respect to x;





  
    
      
        [
        
          Math
          ⁢
          
            
          
          ⁢
          4
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        
          
            
              
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        (
        4
        )
      
    
  




and Expression (5) below is further derived from Expressions (2) and (3);





  
    
      
        [
        
          Math
          ⁢
          
            
          
          ⁢
          5
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        
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            -
            
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        (
        5
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From Expressions (4) and (5), we obtain Expression (6) below;





  
    
      
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          ⁢
          
            
          
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          6
        
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            (
            
              a
              +
              
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        =
        
          -
          
            
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                  κ
                
                )
              
            
            .
          
        
      
    
    
      
        (
        6
        )
      
    
  




By calculating the square root of imaginary i, we obtain Expression (7) below;





  
    
      
        [
        
          Math
          ⁢
          
            
          
          ⁢
          7
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        
          a
          +
          
            i
            ⁢
            
              
            
            ⁢
            b
          
        
        =
        
          
            ±
            
              
                1
                +
                i
              
              
                2
              
            
          
          ⁢
          
            
              
                ρ
                ⁢
                
                  
                
                ⁢
                qw
              
              κ
            
          
        
      
    
    
      
        (
        7
        )
      
    
  




From above Expression (7), a and b are expressed as Expression (8) below because the imaginary number and the real number are independent.





  
    
      
        [
        
          Math
          ⁢
          
            
          
          ⁢
          8
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        a
        =
        
          b
          =
          
            
              
                
                  ρ
                  ⁢
                  
                    
                  
                  ⁢
                  qw
                
                
                  2
                  ⁢
                  
                    
                  
                  ⁢
                  κ
                
              
            
            =
            
              
                f
              
              ⁢
              
                
                  
                    ρ
                    ⁢
                    
                      
                    
                    ⁢
                    q
                    ⁢
                    
                      
                    
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                    π
                  
                  κ
                
              
            
          
        
      
    
    
      
        (
        8
        )
      
    
  




The phase delay b is calculated as Expression (9) below.





  
    
      
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          Math
          ⁢
          
            
          
          ⁢
          9
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        b
        =
        
          
            
              
                
                  ρ
                  ⁢
                  
                    
                  
                  ⁢
                  qw
                
                
                  2
                  ⁢
                  
                    
                  
                  ⁢
                  κ
                
              
            
            -
            
              i
              ⁢
              
                
              
              ⁢
              a
            
          
          =
          
            
              
                f
              
              ⁢
              
                
                  
                    ρ
                    ⁢
                    
                      
                    
                    ⁢
                    q
                    ⁢
                    
                      
                    
                    ⁢
                    π
                  
                  κ
                
              
            
            -
            
              i
              ⁢
              
                
              
              ⁢
              a
            
          
        
      
    
    
      
        (
        9
        )
      
    
  




In Expressions (8) and (9), a and b have no imaginary component but in practical observation an offset which must not be originally observed is made in the phase delay b. As a matter of fact, the phase delay quantity can have an offset due to occurrence of distortion of waveform if there is a nonlinear factor such as transfer of heat through a plurality of paths, e.g., reflection from the sample edge, or slower heat transfer from the surface to the atmosphere than inside the sample, in actual measurement.

The conventional technology was to consider that the phase delay bx of heat generation observed at an observation point (surface) was proportional to the depth, and to simply calculate the depth of the heat generation source, based thereon. However, the offset can be produced in the actual delay quantity. This is dependent on the heat capacity inside the integrated circuit S, the amount of heat generation, the shape, the frequency of applied bias, and so on. For this reason, the phase offset varies depending upon where observation is conducted in the integrated circuit S, in the conventional technology, and it is difficult to always calculate an accurate depth of the heat generation source by the conventional technology. In contrast to it, the heat generation point detection method according to the present embodiment makes use of the finding that, as to the heat generation detection signals from the interior of the package of the integrated circuit S, the phase offset has little change against the square root of the frequency, at the low frequencies of the applied biases of not more than several Hz. The frequencies applicable herein have an upper limit value varying depending upon the integrated circuit S and are preferably approximately not more than 4 Hz.
Namely, the depth information detected in the heat generation point detection method according to the present embodiment is a slope of the phase delay bx against the square root of the frequency, and is a value represented by Expression (10) below;




  
    
      
        [
        
          Math
          ⁢
          
            
          
          ⁢
          10
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        
          
            d
            bx
          
          
            d
            
              f
            
          
        
        =
        
          x
          ⁢
          
            
              
                
                  ρ
                  ⁢
                  
                    
                  
                  ⁢
                  q
                  ⁢
                  
                    
                  
                  ⁢
                  π
                
                κ
              
            
            .
          
        
      
    
    
      
        (
        10
        )
      
    
  




This value is dependent on only the constants ρ, q, and κ determined by physical properties, and the constant π, successfully excluding the influence of the phase offset.

Here, the attenuation rate a also has a change caused by a change of heat transfer coefficient on the surface of the integrated circuit S. The heat transfer coefficient from the integrated circuit S to air varies depending on the temperature of the surface and convection based thereon. Then, in order to enhance the accuracy of the depth information calculated by Expression (10) above, the device has the temperature stabilization unit 40 to stabilize the temperature at the surface of the integrated circuit S.
Another factor for error in the depth information is a temporal change of temperature of the integrated circuit S. If the temperature of the integrated circuit S continuously rises during acquisition of data in the image processing unit 30, a slope of a waveform due to the temperature rise is also detected as another wave, separately from the original phase detection in measurement of phase. This situation is shown in FIG. 7. As shown in the same drawing, a temporal change of a heat generation detection signal detected in the integrated circuit S with occurrence of the temperature rise at the surface (FIG. 7(a)) is an addition of a temporal change of a heat generation detection signal with the slope corresponding to the temperature rise (FIG. 7(c)) to a temporal change of a heat generation detection signal detected in the integrated circuit S with the surface temperature being in a stable state (FIG. 7(b)). When the phase information is acquired from the target of the heat generation detection signal with occurrence of the temperature rise as described above, there is an error made in the depth information because the phase of the different wave as mixture of multiple waves is calculated. Therefore, the temperature stabilization unit 40 is provided for the purpose of also enabling acquisition of the heat generation detection signal in a state in which the surface temperature of the integrated circuit S is stabilized so as to keep the temporal change of surface temperature little.
FIG. 8(a) shows a temporal change of the heat generation detection signal acquired by the integrated circuit failure analysis device 1 without execution of the temperature stabilization process by the temperature stabilization unit 40, and FIG. 8(b) a temporal change of the heat generation detection signal acquired by the integrated circuit failure analysis device 1 with execution of the temperature stabilization process by the temperature stabilization unit 40. As shown, with execution of the temperature stabilization process, the heat generation detection signal excluding the slope due to the temperature change is started to detect after a lapse of a certain period of time, whereby variation of the phase shift acquired is reduced so as to enable stable calculation of the depth information with high accuracy.
In FIG. 9, (a) shows a temporal change of a bias voltage applied at a low frequency of 1 Hz, (b) a temporal change of a heat generation detection signal detected in the integrated circuit S in response thereto, (c) a temporal change of a bias voltage applied at a high frequency of 2 Hz, and (d) a temporal change of a heat generation detection signal detected in the integrated circuit S in response thereto. In the integrated circuit failure analysis device 1, a delay corresponding to the phase delay bx is observed as a delay quantity D1 at each frequency. This delay quantity D1 includes a phase shift component D2 determined by a depth of a heat generation point and a phase shift component D3 determined by the shape of the interior of a sample, the condition of the surface, and so on.
FIG. 10 shows a relationship between the square root of the angular frequency w of the bias voltage applied to the integrated circuit S and the observed phase delay bx, in the integrated circuit failure analysis device 1. As shown in the same drawing, each of the phase delays D1 observed at the low angular frequency w1 and at the high angular frequency w2 includes the shift component D2 and the shift component D3. When we calculate the slope of the phase delay bx against the square root of the angular frequency w, we can estimate the depth information independent of the heat capacity inside the integrated circuit S, the amount of heat generation, and the position, which is determined by the shift component D2 determined by the depth of the heat generation point, while eliminating the phase offset component D3.
The integrated circuit failure analysis device 1 and the heat generation point detection method using the same as described above include detecting the heat generation detection signal in response to the application of the low-frequency bias voltage and detecting the heat generation detection signal in response to the application of the high-frequency bias voltage, from the integrated circuit S. Then detected are the phase shift between the low-frequency bias voltage and the heat generation detection signal and the phase shift between the high-frequency bias voltage and the heat generation detection signal and, the depth information of the heat generation point is obtained from the change rate of the phase shift against the square root of the frequency. This procedure results in calculating the depth information while cancelling out the offset component in the temporal change of the amount of heat generation varying depending upon the position of the heat generation point, whereby the depth information is obtained with high accuracy, independent of the position of the heat generation point. Moreover, by obtaining the change rate of the phase shift against the variable calculated from the frequency of the bias voltage, we can also obtain the depth information independent of the amount of heat generation at the heat generation point, the internal structure of the integrated circuit, and the frequency of the bias voltage.
Namely, the phase delay bx between the bias voltage and the heat generation detection signal involves deformation of the heat generation detection waveform dependent on the quantity of heat from the heat generation source, the position of the heat generation point in the integrated circuit S, the internal structure and the heat capacity of the integrated circuit, and so on, and thus includes variation associated therewith. Therefore, direct evaluation of the phase delay bx leads to failure in calculating an accurate depth of the heat generation point. For example, even if a parameter is one allowing us to calculate an accurate depth as long as the measurement is carried out in the center of the integrated circuit S, a significant error is made by directly applying the parameter to the measurement at the sample edge. The error of this kind is made by a difference of heat transfer rate, a difference of the sum of heat capacity in a heat transferred range, and nonlinearity of heat transfer coefficient at the surface of the integrated circuit S. Specifically, it varies as shown in FIG. 6, with increase of heat capacity and with increase of heat transfer rate. In the phase delay bx, the shift component D3 due to the deformation of the response waveform is produced from the minimum 0° to the maximum 90°, in addition to the shift component D2 corresponding to the phase delay from the heat generation source. This component becomes an extra offset, which has made the calculation of accurate depth difficult heretofore. The present embodiment allows us to obtain the accurate depth information while removing such extra offset.
Since the amplitudes and duty ratios of the bias voltages of multiple frequencies applied to the integrated circuit S are set to be equal to each other, the amounts of heat generation at the heat generation point can be made more uniform and the dependency of the depth information on the frequency of the bias voltage can be reduced more. As a result, much more accurate depth information can be acquired.
Furthermore, the depth information is calculated based on the thermal responses to the electric signals of multiple frequencies detected while the average temperature of the entire surface of the integrated circuit S is stabilized at constant temperature. This can reduce the variation of the offset due to the change of heat transfer coefficient and the error of the phase shift due to the temporal change of temperature of the integrated circuit S, and thus the depth information is obtained on a stable basis and with high accuracy, independent of the position of the heat generation point. Particularly, since the irradiance intensity of infrared light increases with increase of temperature of the integrated circuit S, if the average temperature of the surface of the integrated circuit S is stabilized at temperature as high as possible without saturation of the imaging device 18, the amplitude of the detection signal can be increased even with the temperature amplitude of the integrated circuit S being constant, so as to increase S/N.
The present invention is by no means limited to the above-described embodiment. For example, the waveforms of the bias voltages applied to the integrated circuit S do not have to be limited to the rectangular waves, but may be other waveforms of voltages fluctuating periodically, like sinusoidal waves or triangular waves.
The maximum V1 and minimum V2 of the bias voltages may also be suitably changed according to a type of the integrated circuit S. However, when a plurality of frequencies are used as changed for one integrated circuit S, it is preferable to set the maximum V1 and minimum V2 constant.
Since an increase or a decrease of the frequency of the bias voltage leads to variation in amplitude of the heat generation detection signal, it is necessary to keep the amplitude at the lowest frequency to be measured, within a measurable range. Then, the integrated circuit failure analysis device 1 may be provided with a function to automatically detect an event of the amplitude of the heat generation detection signal exceeding the measurable range and output an error.
The temperature stabilization unit 40 for stabilizing the average temperature of the surface of the integrated circuit S may be configured as described below.
For example, as shown in FIGS. 11 and 12, the device may be configured by adopting a gas-circulating configuration capable of circulating the gas along the surface of the integrated circuit S, while adding an air hose 45 having an inhalation inlet opposed to the discharge outlet of the air hose 43 and inhaling the gas, in addition to the air hose 43 to discharge the gas. In this case, the air hose 43 and the air hose 45 are arranged so as to be opposed to each other on both sides of an area A1 on the surface certainly covering the failure portion F (FIG. 12). The temperature stabilization unit 40 of this configuration can keep the air current constant in the area A1 on the surface of the integrated circuit S to equalize the temperature of the entire surface of the integrated circuit S, thereby realizing stable detection of the depth information. The temperature stabilization unit 40 does not always have to be limited to the configuration to supply the cooled medium (heat medium for cooling), but it may be configured to supply a heated medium (heat medium for heating) as long as it enables stabilization of the surface temperature of the integrated circuit S.
Like the temperature stabilization unit 40A according to a modification example of the present invention shown in FIG. 13, the device may have a configuration wherein a highly thermal conductive plate (substrate) 46 of a flat plate shape is joined through a coating agent 47 with a high thermal conductivity such as oil, onto the surface of the integrated circuit S and wherein two cooling elements (temperature regulating members) 48, 49 are mounted at both ends on the surface of the highly thermal conductive plate 46. The highly thermal conductive plate 46 located in the vicinity of the integrated circuit S as described above has the size and shape enough to cover the entire surface of the integrated circuit S, and is comprised of a material which has a high thermal conductivity and is transparent to the infrared region, like diamond, Si, or SiC. The two cooling elements 48, 49 are cooling devices such as Peltier devices, each of which includes a temperature detecting element (not shown) such as a thermistor arranged in the vicinity of the surface of the integrated circuit S and which regulates the temperature so as to keep constant values of temperature detected by the temperature detecting element. These cooling elements 48, 49 may be replaced by heating elements such as heater devices or may be replaced by pipe conduits to circulate the heat medium along the surface of the integrated circuit S. The temperature stabilization unit 40A with the above-described cooling elements 48, 49 being arranged in the vicinity of the highly thermal conductive plate 46 can better stabilize the temperature of the entire surface of the integrated circuit S.
Like the temperature stabilization unit 40B according to a modification example of the present invention shown in FIG. 14, the device may have a configuration wherein the highly thermal conductive plate 46 of the flat plate shape is arranged through a predetermined gap on the surface of the integrated circuit S and wherein a pair of medium discharge unit 50 and medium inhalation unit 51 to supply a heat medium such as oil in one direction to the gap on the surface of the integrated circuit S are provided at both ends between the sample stage 10 and the highly thermal conductive plate 46. The temperature stabilization unit 40B with the above-described medium discharge unit 50 and medium inhalation unit 51 being arranged in the vicinity of the highly thermal conductive plate 46 can also better stabilize the temperature of the entire surface of the integrated circuit S.
Here, the aforementioned heat generation point detection method is preferably one further comprising a fifth step of detecting a first phase shift between the periodic electric signal of the first frequency and the first detection signal and a second phase shift between the periodic electric signal of the second frequency and the second detection signal, wherein the fourth step comprises obtaining the depth information of the heat generation point, based on the first and second phase shifts. Furthermore, the aforementioned heat generation point detection device is preferably one further comprising a phase shift detection unit for detecting the first phase shift between the periodic electric signal of the first frequency and the first detection signal and the second phase shift between the periodic electric signal of the second frequency and the second detection signal, wherein the calculation unit obtains the depth information of the heat generation point, based on the first and second phase shifts. This configuration is to calculate the depth information while cancelling out the offset component of the temporal change of the amount of heat generation varying depending upon the position of the heat generation point, and therefore the depth information is obtained with higher accuracy, independent of the position of the heat generation point.
Furthermore, the aforementioned heat generation point detection method is also preferably one wherein the fourth step comprises: calculating a change rate of the phase shift between the periodic electric signal and the detection signal against a variable calculated from the frequency of the periodic electric signal, based on the first and second phase shifts, and obtaining the depth information of the heat generation point from the change rate. Furthermore, the aforementioned heat generation point detection device is also preferably one wherein the calculation unit calculates a change rate of the phase shift between the periodic electric signal and the detection signal against a variable calculated from the frequency of the periodic electric signal, based on the first and second phase shifts, and obtains the depth information of the heat generation point from the change rate. In this case, the change rate of the phase shift is calculated against the variable calculated from the frequency of the periodic electric signal, whereby the depth information can also be obtained independent of the amount of heat generation at the heat generation point, the internal structure of the integrated circuit, and the frequency of the periodic electric signal.
Yet furthermore, preferably, the temperature stabilization unit has a medium supply unit for supplying a medium so as to keep the average temperature of the surface of the integrated circuit constant. When the device has such a temperature stabilization unit, the average temperature of the surface of the integrated circuit can be efficiently stabilized by the simple constituent unit.
Still furthermore, preferably, the temperature stabilization unit has: a substrate being transparent to the infrared region and arranged in the vicinity of the integrated circuit; and a temperature regulating member arranged in the vicinity of the substrate. When the device has such a configuration, the average temperature of the entire surface of the integrated circuit can be further stabilized.
INDUSTRIAL APPLICABILITY
The present invention is applicable to the heat generation point detection methods and heat generation point detection devices for detecting the depth of the heat generation point in the integrated circuit and allows accurate and stable detection of the depth of the heat generation point in the integrated circuit, independent of the position thereof.
REFERENCE SIGNS LIST
1 integrated circuit failure analysis device; 14 voltage application unit (electric signal supply unit); 18 imaging device; 20 control unit; 21 imaging control unit; 22 stage control unit; 23 synchronism control unit; 30 image processing unit; 31 image storage unit; 32 heat generation signal acquisition unit (detection unit); 33 voltage phase acquisition unit; 34 phase delay acquisition unit (detection unit or phase shift detection unit); 35 depth information calculation unit; 40, 40A, 40B temperature stabilization unit; 41 air tank; 42 regulator (medium supply unit); 43 air hose (medium supply unit); 44 temperature control unit (medium supply unit); 46 highly thermal conductive plate (substrate); 48, 49 cooling elements (temperature regulating member); 50 medium discharge unit (medium supply unit or temperature regulating member); 51 medium inhalation unit (temperature regulating member); S integrated circuit.

## Claims

1. A method for detecting a depth of a heat generation point in an integrated circuit, comprising steps of:
stabilizing physically an average temperature of a surface of the integrated circuit;
supplying a first electric signal at a first frequency to the integrated circuit;
detecting a first detection signal indicative of a change of an amount of heat generation detected from the integrated circuit in response to the first electric signal;
supplying a second electric signal at a second frequency different from the first frequency to the integrated circuit;
detecting a second detection signal indicative of a change of an amount of heat generation detected from the integrated circuit in response to the second electric signal; and
obtaining depth information of the heat generation point, based on the first and second detection signals.

2. The method of claim 1, further comprising step of: analyzing a first phase shift between the first electric signal and the first detection signal and a second phase shift between the second electric signal and the second detection signal to thereby
obtain the depth information of the heat generation point.

3. The method of claim 2, wherein the step of obtaining comprises: calculating a change rate of the phase shift between the electric signal and the detection signal against a variable calculated from the frequency of the electric signal, based on the first and second phase shifts, and obtaining the depth information of the heat generation point from the change rate.

4. A system for detecting a depth of a heat generation point in an integrated circuit, comprising:
an electric signal supply unit configured to supply an electric signal to the integrated circuit;
a control unit configured to control the electric signal supply unit so as to supply a first electric signal at a first frequency and a second electric signal at a second frequency different from the first frequency, to the integrated circuit;
a detection unit configured to detect a first detection signal indicative of a change of an amount of heat generation detected from the integrated circuit in response to supply of the first electric signal and configured to detect a second detection signal indicative of a change of an amount of heat generation detected from the integrated circuit in response to supply of the second electric signal;
a calculation unit configured to obtain depth information of the heat generation point, based on the first and second detection signals; and
a temperature stabilization unit configured to stabilize physically an average temperature of a surface of the integrated circuit.

5. A method for acquiring a depth of a heat generation point in an integrated circuit, comprising steps of:
stabilizing physically an average temperature of a surface of the integrated circuit;
supplying a plurality of electric signals to the integrated circuit;
acquiring a detection signal indicative of a change of an amount of heat generation detected from the integrated circuit in response each of the electric signals;
obtaining depth information of the heat generation point, based on the detection signals.

6. The system of claim 4, further comprising: a phase shift detection unit configured to analyze a first phase shift between the first electric signal and the first detection signal and a second phase shift between the second electric signal and the second detection signal, to thereby
obtain the depth information of the heat generation point.

7. The system of claim 6, wherein the calculation unit calculates a change rate of the phase shift between the electric signal and the detection signal against a variable calculated from the frequency of the electric signal, based on the first and second phase shifts, and obtains the depth information of the heat generation point from the change rate.

8. The system of claim 4,
wherein the temperature stabilization unit has a medium supply unit configured to supply a medium so as to keep the average temperature of the surface of the integrated circuit constant.

9. The system of claim 4,
wherein the temperature stabilization unit has:
a substrate being transparent to the infrared region and arranged in the vicinity of the integrated circuit; and
a temperature regulating member arranged in the vicinity of the substrate.

10. A system for acquiring a depth of a heat generation point in an integrated circuit, comprising:
an electric signal supply configured to supply a plurality of electric signals to the integrated circuit;
a detection unit configured to detect a detection signal indicative of a change of an amount of heat generation detected from the integrated circuit in response each of the electric signals;
a calculation unit configured to obtain depth information of the heat generation point on the basis of the detection signals; and
a temperature stabilization unit configured to stabilize physically an average temperature of a surface of the integrated circuit.