Detection and resolution enhancement of laser induced fault localization techniques 2

Chapter _ Chapter 5: Pulsed Laser with Lock-In Detection In this chapter, an analytical model based on the heat transport mechanism is developed to describe the pulsed laser induced phenomena of a biased metal line structure with ac-coupled and dc-coupled detection systems The model is validated with experimental results of pulsed-TIVA and pulsed-DReM signal response It is then applied to understand the sensitivity of pulsed laser with narrowband (NB) and wideband (WB) lock-in detection and its dependence on pulsing frequency and sample thermal time constant Narrowband lock-in and wideband lock-in detections are implemented on ac-coupled and dc-coupled detection systems NB lock-in is implemented with a commercial lock-in amplifier while WB lock-in is implemented with a software digital algorithm developed to provide robust scan time and detection sensitivity enhancement The experimental results correlate with the theoretical understanding Significant detection sensitivity enhancement factors between 15 – 20 times have been achieved with NB lock-in detection and between – times with WB lock-in detection at pulsing frequency range between 200 Hz to kHz on an Al metal line with a thermal time constant of 30 μs This significant sensitivity enhancement is demonstrated in the following chapter on the localization of Cu/Lowk interconnect reliability defects which are otherwise not detectable with conventional laser induced techniques 5.1 Pulsed Laser Induced Signal Response Model In this section, an analytical model based on the heat transport mechanism to describe the pulsed laser induced signal response of a single metal line structure using ac- 99 Chapter _ coupled and dc-coupled detection systems is developed The model is then validated with experimental results from pulsed-TIVA and pulsed-DReM response on an Al line structure 5.1.1 DC-Coupled Pulsed Laser Induced Signal Reponse Fig 5.1 illustrates the cross-section view of the line structure used in the model The metal line structure with 2.5 μm width and 0.5 μm thickness is embedded in μm thick silicon dioxide on silicon substrate As the laser scans across the biased metal, the thermal stimulation results in an instantaneous increase in temperature of the metal line This results in a power change due to increased resistance if the structure is biased Fig 5.1 Cross-section view of a metal line with 2.5 μm width and 0.5 μm thickness During laser heating on the metal, uniform heating is assumed at the metal surface Thus, the analytical temperature solution T ( z, t ) that describes the heat diffusion of plane thermal wave into the depth, z of a semi-infinite, homogeneous and isotropic 100 Chapter _ sample due to harmonically oscillating heating and cooling events from a pulsed laser at frequency,  on the sample surface is [88]:  z z  T ( z , t )  Am exp  d  exp i t  d   th  th       , (5.1) where t is time, Am is the amplitude of the oscillating temperature signal which is dependent on the heat flux at the surface, z  , and d th describes the thermal diffusion length which is a function of the oscillating frequency,  , and thermal properties of the sample as follows [88]: d th  2c  m c p , (5.2) where c is the heat conductivity,  m and c p represent the density of mass and the specific heat capacity of the metal According to eqn (5.2), for an Al or Cu line, which is used as the metallization interconnects in semiconductor ICs, the thermal diffusion length at a heating oscillating frequency from 10 Hz to 10 kHz would reduce from 1.76 mm to less than 60 μm Since the metal thickness is much smaller than the thermal diffusion length, which is usually the case for integrated circuits, the metal line is considered as a thermally thin sample, i.e the temperature of the top metal surface is equal to the bottom surface during heating and cooling The averaged temperature of the metal line of mass, m , with constant heating laser power, P , at t  can be expressed as [88]: mc p T  Ts T  P t Rth , (5.3) 101 Chapter _ where Ts is the starting temperature and Rth represents the thermal resistance The above differential equation is solved with the following boundary conditions: T (0)  Ts , Laser " ON" T (To 2)  Ts  T , Laser " OFF" (5.4a) , (5.4b) , to yield average temperature, Tavg (t ) , for a single laser pulse as follows:    t   Ts  T 1  exp    ,     ON     T   Tavg (t )    t o   ,  Ts  T exp   OFF        Laser " ON" , (5.5) Laser " OFF" where T  PRth and  ON   OFF  mc p Rth The change in average temperature ( Tavg (t )  Tavg (t )  Ts ) is then converted to the pulsed laser induced voltage pulsed change vdc (t ) as follows:    T t  , t  o v d 1  exp        DUT     pulsed T   v dc (t )    t o     v exp  To   d v d exp    2 DUT  DUT         ,   , To  t  To (5.6a) pulsed pulsed v dc (t )  Av v dc (t ) (5.6b) Assuming  ON   OFF   DUT , eqn (5.6a) thus models the dc-coupled laser induced voltage change of a metal line under the pulsed period, To of 50% duty cycle assuming that thermal rise time,  ON during laser “ON” and thermal fall time,  OFF during laser “OFF” of the DUT is the same and is represented by  DUT Figs 5.2 (a) 102 Chapter _ and (b) show the dc-coupled signal response at unity gain Av , according to eqn (5.6b), for 500 Hz and kHz pulsing frequencies respectively with 50% duty cycle with vd  1V and  DUT  30s  DUT  30s was experimentally found to be a representative time constant of an Al line which will be shown in the later section (a) f o  500 Hz , To /   DUT (b) f o  5kHz , To / ~ 3 DUT Fig 5.2 DC-Coupled laser induced voltage change at (a) 500 Hz and (b) kHz with vd Av  1V and  DUT  30s These waveforms clearly indicate that the dc-coupled signal response attenuates with increasing pulsing frequency Due to the DUT thermal time constant, a finite time is required for the DUT to respond to the temperature change Fig 5.2(a) illustrates that at a low pulsing frequency, when laser beam ON/OFF time is much greater than DUT 103 Chapter _ thermal time constant, To /   DUT , maximum signal amplitude is achieved during the laser irradiation as there is sufficient time for the DUT to be heated up to the maximum temperature However, with increasing pulsing frequency such that beam ON/OFF time is comparable to 3 DUT , Fig 5.2(b) shows that the signal amplitude is attenuated due to insufficient time for laser heating Further increasing the pulsing frequency would result in greater attenuation of the signal response Thus, these results indicate that sample thermal time constant plays an important role in determining the pulsing frequency for maximum signal sensitivity pulsed pulsed In the frequency domain, Fourier transform of vdc (t ) would yield vdc ( ) expressed as follows: pulsed vdc ( )  vd s    sTo  1  exp     vd DUT  s DUT  T   1  exp  o  2  DUT    sTo  1  exp       T   exp  o   2 DUT   T    exp  o  2   DUT     exp sTo         T   1  exp  o   2 DUT        exp sTo      , (5.7) where s  j The term in eqn (5.7) illustrates the effect of  DUT as a  s DUT single pole low pass filter with a time constant of  DUT Thus, at high pulsing frequency, signal is attenuated 104 Chapter _ 5.1.2 AC-Coupled Pulsed Laser Induced Signal Response Assuming that the low pass corner of the amplifier bandwidth is large enough to have insignificant distortion of the signal response, the ac-coupled pulsed laser induced pulsed pulsed signal response, v ac ( ) , is then derived by multiplying vdc ( ) with the 2nd order high pass ac-coupled amplifier response as follows:  s  s   s   s   pulsed pulsed v ac ( )  v dc ( )  Av       , (5.8) Eqn (5.8) shows that at low pulsing frequency, the ac-coupled signal is distorted by amplifier high pass response dependent on  and  , while at high pulsing frequency, the signal is suppressed by the low pass effects from  DUT The time domain pulsed expression, v ac (t ) , is shown in Appendix A With vd  1V , Av  1V / V ,  DUT  30s ,   2.2ms and   10ms , Fig 5.3 shows the comparison between dc-coupled response described by eqn (5.6) and the accoupled response described by eqn (5.8) with increasing laser pulsing frequencies from 100 Hz to kHz at 50% duty cycle 105 Chapter _ (a) f o  100 Hz , To /   DUT (b) f o  500 Hz , To /   DUT (c) f o  5kHz , To / ~ 3 DUT Fig 5.3 Laser induced voltage change for ac-coupled and dc-coupled detection systems at varying pulsing frequencies with vd Av  1V ,  DUT  30s ,   2.2ms and   10ms 106 Chapter _ For To /   DUT , Figs 5.3(a) and (b) illustrate that during the beam “ON” time, the dc-coupled response saturates upon reaching the maximum signal amplitude while the ac-coupled response starts to decay upon reaching the signal peak This is due to the differentiating effect of the high pass filtering The same effect also results in the reverse signal peak observed in the ac-coupled response during beam “OFF” time which is commonly known as the “tail” Fig 5.3(c) shows that when the beam ON/OFF time is closer to  DUT , the dc-coupled and ac-coupled responses have similar attenuated waveforms except at different average voltage levels, as the high pass eliminates the average voltage in the ac-coupled response 5.1.3 Experimental Verification of Model The pulsed laser induced response on the Al line structure from Fig 3.4 is used to verify the theoretical model A square wave control signal at 50% duty cycle was fed into the laser control unit to pulse the laser The laser was programmed to remain focused and perform stationary pulsing on the line structure The dc-coupled pulsedDReM and ac-coupled pulsed-TIVA signal response after the voltage amplification was then monitored and captured by a digital oscilloscope Fig 5.4 Control signal and pulsed-DReM signal with DUT biased at 30.8 mV, 26.4 mW laser power, voltage gain of 10 kV/V and bandpass settings DC-10 kHz 107 Chapter _ Fig 5.4 shows the control and pulsed-DReM signal waveforms  DUT is measured to be approximately 30 μs from the time taken for voltage change to reach 63% of its final asymptotic value Figs 5.5(a) and (b) show the pulsed-DReM and pulsed-TIVA laser induced voltage changes of the DUT at increasing pulsing frequency For both setups, the DUT was biased at an equivalent quiescent voltage of 30.8mV and a laser power of 26.4 mW was used for irradiation Both sets of waveforms were captured at the same amplification of 10 kV/V Band pass filter settings of dc-10 kHz was used for pulsedDReM at F  45 for dc-coupled detection and 0.03 Hz - 10 kHz was used for pulsedTIVA for ac-coupled detection The waveforms were then overlaid with the simulated dc-coupled and ac-coupled signal response modeled by eqn (5.6) and eqn (5.8), respectively with vd Av  1.9V ,  DUT  30s ,   2.2ms and   10ms Fig 5.5 shows that the simulated waveforms demonstrate good correlations to the experimental waveforms at a pulsing frequency range from 10 Hz – kHz The double differentiating effects of the ac-coupled detection mode which includes signal decay after reaching its peak signal amplitude, undershoot/overshoot signature during beam “ON/OFF” at a low frequency and “tail” peak during beam “OFF” are also well described by the theoretical model as shown in Figs 5.5 b(i) - b(iii) At low pulsing frequencies from 10 Hz – 100 Hz, Figs 5.5 a(i) and a(ii) show that the dc-coupled simulated waveforms underestimate the experimental waveforms During beam “ON” time, instead of saturating to a constant voltage, pulsed-DReM signal voltage continues to increase in a gentle slope This additional signal is attributed to 108 Chapter _ A second frequency generator producing a reference signal, VR , at frequency, f , where f  f1 , is connected to the first to produce an overall frequency modulated square wave control signal, VR' , to pulse the laser T1 refers to the period of the square wave reference VR1 Fig 9.2 Principle waveforms describing pulsed-DReM with double lock-n detection assuming T1 /   DUT Fig 9.2 shows the expected waveforms from the double lock-in setup Assuming that pulsed T1 /   DUT , the pulsed-DReM signal response, vdc (t ) with signal amplitude, v d would then be modulated similarly to VR' as shown in Fig 9.2 The st lock-in amplifier operates at f1 Its signal output f NB (t ; f1 ) dc measures the first harmonic pulsed signal of vdc (t ) with a signal amplitude of vd /  for  t  T2 / For T2 /  t  T2 , f NB (t ; f1 ) dc  as vdc (t )  Thus, f NB (t ; f1 ) dc would produce a signal output at frequency f The nd stage lock-in amplifier takes in f NB (t ; f1 ) dc and 194 Chapter _ operates at lock-in frequency f It is during 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013703-013703-10, 2009 Ramsay E, Pleynet N, Xiao D, Warburton RJ, Reid DT, “Two-Photon Optical-Beam-Induced Current Solid-Immersion Imaging of a Silicon Flip Chip with a Resolution of 325 nm”, Opt Lett, Vol 30, No 1, pg 26-28, 2005 Goh SH, Quah ACT, Sheppard CJR, Chua CM, Koh LS, Phang JCH, "Effect of Refractive Solid Immersion Lens Parameters on the Enhancement of Laser Induced Fault Localization Techniques", Proc Int Symp Physical & Failure Analysis of Integrated Circuits (IPFA 2008), 7-11 Jul 07, Singapore, pg 2025, 2008 Goh SH, Quah ACT, Sheppard CJR, Chua CM, Koh LS, Phang JCH, "Effect of Refractive Solid Immersion Lens Parameters on the Enhancement of Laser Induced Fault Localization Techniques", Int Symp Testing & Failure Analysis (ISTFA 2008), 2-6 Nov 08, Portland, Oregon, USA, pg 1-6, 2008 Quah ACT, Goh SH, Ravikumar VK, Phoa SL, Narang V, Chin JM, Chua CM, Phang JCH, “Combining Refractive Solid Immersion Lens and Pulsed Laser Induced techniques for Effective Defect 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Techniques for Integrated Circuit Failure Analysis”, Proc Int Symp Physical & Failure Analysis of Integrated Circuits (IPFA 2009), 6-10 Jul 09, Singapore, pg 11-18, 2009 Phang JCH, Chua CM, Quah ACT, Goh SH, “Scanning Optical Microscope System for Design Debug and Failure Analysis of Advanced Integrated Circuits”, Singapore President‟s Technology Award, 28 th Sep 2009 www.astar.edu.sg/AwardsScholarships/PresidentsScienceandTechnologyAwards/Pre sidentsTechnologyAward/WinnerCitationNUSandSemicaps/tabid/839/Defaul t.aspx Goree J, “Double Lock-In Detection for Recovering Weak Coherent Radio Frequency Signals”, Rev Sci Instru, Vol 56, No 8, pg 1662-1664, 1985 Ho HW, Zheng XH, Phang JCH, Balk LJ, “Reliable and Accurate Temperature Measurement using Scanning Thermal Microscopy with Double Lock-In Amplification”, Proc Int Rel Phys Symp (IRPS 2009), 26-30 Apr 09, Montreal, Canada, pg 804-807, 2009 203 Award & Patents _ Appendix A From chapter 5, the dc-coupled laser induced voltage change of a metal line under pulsed period, To of 50% duty cycle with a sample thermal time constant,  DUT is expressed as follows:    T t  , t  o v d 1  exp        DUT     pulsed T   v dc (t )    t o     v exp  To   d v d exp    2 DUT  DUT         ,   , To  t  To (A.1) Fourier transform of vdc (t ) would yield vdc ( ) expressed as follows: pulsed pulsed pulsed vdc ( )  vdc ( ) A  vdc ( ) B For t  (A.2) To , pulsed vdc ( ) A  vd s   sTo 1  exp     vd DUT     s DUT   To exp   2 DUT     sT    exp  o   1      (A.3) For To  t  To , pulsed vdc ( ) B   vd DUT   To exp   2  s DUT   DUT   vd T exp  o  2 s DUT    sT  exp sTo   exp  o      sT  exp sTo   exp  o          (A.4) , 204 Award & Patents _ pulsed where s  j The ac-coupled signal response, v ac ( ) is derived as follows:  s  s        s   s  pulsed pulsed vac ( )  vdc ( )  Av   , (A.5) pulsed vac ( )  s  s pulsed  vdc ( ) A Av    s   s      s  s pulsed   v dc ( ) B Av     s   s         (A.6) pulsed Therefore, from eqn (A.6), v ac ( ) A is expressed as follows: pulsed vac ( ) A  v A  v A    sT   d v  d v 1  exp  o   s   s         To A B C    vd Av DUT     exp   2 DUT 1  s DUT  s 1  s      sT    exp  o   1      (A.7) pulsed v ac ( ) B is expressed as follows: pulsed vac ( ) B  To A B C    vd Av DUT     exp   2 DUT 1  s DUT  s 1  s     T  vd Av exp  o  2 DUT    sT  exp sTo   exp  o     1   sTo     s   s  exp sTo   exp           , (A.8) where      1 1 , A , B  DUT   1  1    DUT  1     DUT  1 , C  By using    1  the properties of the inverse Fourier Transform function expressed as follows: 205 Award & Patents _   F 1   exp at u (t ) a  s  (A.9) , g (t  t o )  G( f ) exp jt o  (A.10) , where u (t ) is a unit step function The time domain expression for ac-coupled signal pulsed response, v ac (t ) is derived as follows: pulsed pulsed pulsed vac (t )  F 1 vac ( ) A  vac ( ) B  , (A.11) pulsed v ac (t )   1   t   t  v d Av   T  To   exp  o  v d Av  exp    exp    1  exp          2   2   DUT     1         A   t  C  t  T t  B  v A    exp    exp   , exp  0t o d v DUT              2  1    DUT   DUT     T  T      t o   t  o       exp    v A  1  exp  To   exp    d v  2      1     DUT                    T  T  T      t o   t o   t o  A   To     B exp    C exp    v A     1  exp  d v DUT exp       DUT     2 DUT    DUT 1   2                  v A    T  To  To  exp  o  ,  t  To  d v 1  exp   2   2    DUT       (A.12) pulsed where a dc scaling factor derived from the average value of v dc (t ) , pulsed vdc (t ) expressed in eqn (A.13) is inserted to approximate the effects of the shift in the dc-level when To is close to  DUT  To  vd Av    2  pulsed vdc (t ) exp     To 1  exp   2 DUT     T   exp  o   2      (A.13) 206 ,       Award & Patents _ List of Publications Quah ACT, Koh LS, Chua CM, Palaniappan M, Chin JM, Phang JCH, "DCCoupled Laser Induced Detection System for Fault Localization in Microelectronic Failure Analysis", Proc Int Symp Physical & Failure Analysis of Integrated Circuits (IPFA 2006), 3-7 Jul 06, Singapore, pg 327332, 2006 Quah ACT, Koh LS, Tan SH, Chua CM, Phang JCH, “Enhanced detection sensitivity with pulsed laser digital signal integration algorithm”, Proc Intl Symp Testing & Failure Analysis (ISTFA 2006), pg 234-238, 2006 Tan TL, Quah ACT, Gan CL, Phang JCH, Chua CM, Ng CM, Du AY, “Localization of Cu/Low-k Interconnect Reliability Defects by Pulsed Laser Induced Technique”, Proc Int Symp Testing & Failure Analysis (ISTFA 2007), 4-8 Nov 07, San Jose, California, USA, pg 156-160, 2007 Quah ACT, Chua CM, Tan SH, Koh LS, Phang JCH, Tan TL, Gan CL, "Laser-Induced Detection Sensitivity Enhancement with Laser Pulsing", Electronic Device Failure Analysis, Vol 10, Issue 3, pg 18-26, 2008 Goh SH, Sheppard CJR, Quah ACT, Chua CM, Koh LS and Phang JCH, “Design considerations for refractive solid immersion lens: Application to subsurface integrated circuit fault localization using laser induced techniques”, Rev Sci Instru, Vol 80, Issue 1, pg 013703-013703-10, 2009 Goh SH, Quah ACT, Sheppard CJR, Chua CM, Koh LS, Phang JCH, "Effect of Refractive Solid Immersion Lens Parameters on the Enhancement of Laser Induced Fault Localization Techniques", Proc Int Symp Physical & Failure Analysis of Integrated Circuits (IPFA 2008), 7-11 Jul 07, Singapore, pg 2025, 2008 Goh SH, Quah ACT, Sheppard CJR, Chua CM, Koh LS, Phang JCH, "Effect of Refractive Solid Immersion Lens Parameters on the Enhancement of Laser Induced Fault Localization Techniques", Int Symp Testing & Failure Analysis (ISTFA 2008), 2-6 Nov 08, Portland, Oregon, USA, pg 1-6, 2008 Quah ACT, Goh SH, Ravikumar VK, Phoa SL, Narang V, Chin JM, Chua CM, Phang JCH, “Combining Refractive Solid Immersion Lens and Pulsed Laser Induced techniques for Effective Defect Localization on Microprocessors”, Proc Int Symp Testing & Failure Analysis (ISTFA 2008), 2-6 Nov 08, Portland, Oregon, USA, pg 402-406, 2008 Phang JCH, Goh SH, Quah ACT, Chua CM, Koh LS, Tan SH, Chua WP, “Resolution and Sensitivity Enhancements of Scanning Optical Microscopy Techniques for Integrated Circuit Failure Analysis”, Proc Int Symp Physical & Failure Analysis of Integrated Circuits (IPFA 2009), 6-10 Jul 09, Singapore, pg 11-18, 2009 207 Award & Patents _ Award & Patents Chua CM, Ng HY, Koh LS, Phang JCH, Tan SH, “Method and System For Measuring Laser Induced Phenomena Changes in a Semiconductor Device”, Patent No US 7,456,032 B2, 25th Nov, 2008 Chua CM, Quah ACT, Tan SH, Koh LS, Phang JCH, “Method of Testing an Electronic Circuit and Apparatus Thereof”, Patent No US 7,623,982 B2, 24th Nov, 2009 Phang JCH, Chua CM, Quah ACT, Goh SH, “Scanning Optical Microscope System for Design Debug and Failure Analysis of Advanced Integrated Circuits”, Singapore President‟s Technology Award, 28th Sep 2009 www.astar.edu.sg/AwardsScholarships/PresidentsScienceandTechnologyAwards/Pr esidentsTechnologyAward/WinnerCitationNUSandSemicaps/tabid/839/Defa ult.aspx 208 ... ac   2? ??v d Av (2  x)  sin (2n  1) o t d  1 y 1 z    2 2   (To  2t d ) n 1 2n  1  (2n  1) (2? ?? )  (2n  1) (2? ?? )    A(1  x)   2 1  (2n  1) (2? ?? )   2? ??v d Av... 1  (2n  1) (2? ?? )      B (1  y ) ? ?2  x  , 2   (2n  1) (2? ?? )     C (1  z )  2    (2n  1) (2? ?? )  (5.17a) ac b2 n 1 ( o )    (2n  1)(1  y )  2 4vd Av ? ?2 ... (To  2t d )  b2 n1 (o ) 1  cos[(2n  1)otd ]    2n    n1  (5 .22 a) (5 .22 b) Substituting eqn (5.14a) and eqn (5.14b) into eqn (5 .22 b) results in the in-phase WB lock-in detection