Detection and resolution enhancement of laser induced fault localization techniques 2

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 cons

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 3 – 8 times with

WB lock-in detection at pulsing frequency range between 200 Hz to 1 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/Low-

k 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-

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 2 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 ( t z, ) that describes the heat diffusion of plane thermal wave into the depth, zof a semi-infinite, homogeneous and isotropic

sample due to harmonically oscillating heating and cooling events from a pulsed laser

at frequency, on the sample surface is [88]:

,exp

exp)

m

d

z t i d

z A

t

z

where t is time, A is the amplitude of the oscillating temperature signal which is m

dependent on the heat flux at the surface, z0 , and d describes the thermal th

diffusion length which is a function of the oscillating frequency, , and thermal properties of the sample as follows [88]:

c th

c

where c is the heat conductivity, m and c represent the density of mass and the p

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 0 can be expressed as [88]:

,

th

s p

R

T T P t

where T is the starting temperature and s R represents the thermal resistance The th

above differential equation is solved with the following boundary conditions:

,ON"

"

Laser ,

"

Laser ,)

"

Laser ,

2exp

ON"

"

Laser ,exp

1)

t T

T

t T

,2

,2exp2

exp

2,

exp1)

DUT

o d

pulsed

dc

T t T T

v

T t v

T t

t v

t v







(5.6a)

)()

and (b) show the dc-coupled signal response at unity gain A , according to eqn (5.6b), v

for 500 Hz and 5 kHz pulsing frequencies respectively with 50% duty cycle with

V A

v d v 1

 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

thermal time constant, T o /2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

In the frequency domain, Fourier transform of v pulsed (t)

exp12

exp2

exp1

1

exp2

exp2

exp12exp

o

DUT

o o

DUT

DUT

d

o DUT

o

DUT

o o

d

sT T

T sT

s

v

sT T

T sT

1 term in eqn (5.7) illustrates the effect of DUT as a

single pole low pass filter with a time constant of DUT Thus, at high pulsing frequency, signal is attenuated

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

signal response,  pulsed()

,1

1)

()

(

2 2 1

s A v

Eqn (5.8) shows that at low pulsing frequency, the ac-coupled signal is distorted by amplifier high pass response dependent on 1 and 2, while at high pulsing frequency, the signal is suppressed by the low pass effects from DUT The time domain expression, v ac pulsed (t), is shown in Appendix A

With v d 1V , A v 1V/V, DUT 30s, 1 2.2ms and 2 10ms, Fig 5.3 shows the comparison between dc-coupled response described by eqn (5.6) and the ac-coupled response described by eqn (5.8) with increasing laser pulsing frequencies from 100 Hz to 5 kHz at 50% duty cycle

(a) f o 100Hz,T o /2DUT

(b) f o 500Hz,T o /2DUT

(c) f o 5kHz,T o /2~3DUTFig 5.3 Laser induced voltage change for ac-coupled and dc-coupled detection systems at varying pulsing frequencies with v d A v 1V , DUT 30s,

ms

2.2

1 

 and 1 10ms

For T o /2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 pulsed-DReM 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

Fig 5.4 shows the control and pulsed-DReM signal waveforms DUTis 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 pulsed-DReM at F45 for dc-coupled detection and 0.03 Hz - 10 kHz was used for pulsed-TIVA 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 v d A v 1 V.9 , DUT 30s, 1 2.2msand 2 10ms

Fig 5.5 shows that the simulated waveforms demonstrate good correlations to the experimental waveforms at a pulsing frequency range from 10 Hz – 5 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

the continual increase in DUT resistance as heat diffuses away from the irradiated spot to the rest of the metal line This effect shows up as higher reverse “tail” peaks for pulsed-TIVA waveforms shown in Figs 5.5 b(i) and b(ii)

With increasing pulsing frequency from 1 kHz to 5 kHz, signal attenuation was observed for both pulsed-DReM and pulsed-TIVA waveforms in Figs 5.5 a(v) and b(v) respectively It can also be observed at a higher frequency that the laser induced signal lags the control signal transition by approximately 45 µs This is due to the time delay from the triggering of the “ON/OFF” control signal to the actual turning on

of the laser

a(i) Pulsed DReM response at 10Hz b(i) Pulsed TIVA response at 10Hz

a(ii) Pulsed DReM response at 100 Hz b(ii) Pulsed TIVA response at 100 Hz

a(iii) Pulsed DReM response at 500 Hz b(iii) Pulsed TIVA response at 500 Hz

a(iv) Pulsed DReM response at 1 kHz b(iv) Pulsed TIVA response at 1 kHz

a(v) Pulsed DReM response at 5 kHz b(v) Pulsed TIVA response at 5 kHz Fig 5.5 (a) DC-coupled pulsed-DReM and (b) ac-coupled pulsed-TIVA signal response at varying pulsing frequency overlaid with simulated dc-coupled and ac-coupled response

In summary, an analytical model has been developed based on the heat transport mechanism, to describe the laser induced voltage change under the irradiation of a pulsed laser for both dc-coupled and ac-coupled detection systems The model has shown good correlation with experimental results extracted from pulsed-DReM and pulsed-TIVA signals of an Al metal line The model will then be used in subsequent sections to study the signal sensitivity of pulsed laser with lock-in detection

5.2 Lock-In Detection

Lock-in detection methodology has been extensively applied in scientific research and industrial applications to improve detection sensitivity It enhances signal to noise measurement by using bandwidth narrowing to reduce broadband noise in order to recover the embedded weak signal [89-91] The implementation of lock-in measurement of a periodic input signal, f (t) modulated at a frequency of o is summarized in Fig 5.6 It consists of three essential blocks, namely the input signal amplifier, the phase sensitive detection (PSD) or multiplier and the low pass filter In the input signal channel, an amplifier is necessary to amplify the signal to a level sufficient to overcome the self-noise of the multiplier The PSD offers synchronous detection through the multiplication of f (t) with a correlation reference input, e (t)of the same fundamental frequency The output of the mixer, f i (t) is introduced to a low pass filtering stage with a time constant, LIA The filter time constant determines the effective bandwidth of the lock-in detection and the SNR obtained is proportional

to LIA at a frequency of o [92]

Fig 5.6 Block diagram of a lock-in amplifier [89]

The periodic input transient f (t)at a fundamental frequency of ocan be expanded in Fourier Series as

.,

)]

sin(

)cos(

[2

1)

o n

The Fourier coefficients are expressed by,

.)sin(

)(

2)(

,)cos(

)(

2)(

T

o o

o

n

T

o o

o

n

dt t n t f T b

dt t n t f T a

1)(

1)

T dt t f T t

where LIA T o for the lock-in measurement output to be time independent Eqn (5.11) thus shows that the aperiodic lock-in output, f OT (t), truncated over a time interval is actually the time average measurement of the intermediate stage, f i (t), over the pulse period [93]

Generally there are two types of lock-in detection, namely narrowband (NB) lock-in detection and wideband (WB) lock-in detection [88] Narrowband lock-in detection

uses a harmonic sine/cosine function as the correlation function while wideband

lock-in uses a square wave correlation function as shown lock-in Fig 5.7 Dual phase measurements can be achieved for each type of lock-in detection by using in-phase and quadrature-phase correlation functions which are at 90o phase difference as shown in Figs 5.7a(i) and a(ii), respectively for NB lock-in detection, and Figs 5.7b(i) and b(ii), respectively for WB lock-in detection Both types of detection can be implemented in analogue and digital lock-in amplifiers using sinusoidal/square references or a set of weighted waveforms representing the harmonic/square functions

a(i) Narrowband in-phase b(i) Wideband in-phase

a(ii) Narrowband quadrature-phase b(ii) Wideband quadrature-Phase Fig 5.7 Narrowband a(i) in-phase and a(ii) quadrature-phase correlation functions and

wideband b(i) in-phase and b(ii) quadrature-phase correlation functions

From eqn (5.11), the in-phase, f NB IP(o) and quadrature-phase, f NB QP(o) narrowband lock-in detection outputs of a periodic input, f (t), are expressed as follow [93]:

,2

)()

o IP

)()

o QP

NB

b

where a1(o) and b1(o) represent the Fourier coefficients of the fundamental harmonic The in-phase, f WB IP(o), and quadrature-phase, f WB QP(o) , of wideband lock-in detection outputs of f (t) are expressed as follows [93]:

,)(12

12

)(

1

1 2

12

)(

1

1 2

In this section, the voltage sensitivities of ac-coupled and dc-coupled detection systems with NB and WB lock-in detection and their dependence on pulsing frequency and sample thermal time constant are studied It will be shown that lock-in detection on ac-coupled systems has a narrower pulsing frequency range than dc-coupled systems for optimum output signal due to its dependence on both sample thermal time constant and the high pass effects of ac-coupled detection mode It will also be shown that WB lock-in detection acquired a greater signal magnitude than NB lock-in However, this does not translate to higher detection sensitivity as it will be

shown from the experimental results that NB lock-in offers a greater SNR enhancement factor than WB lock-in

5.2.1 Narrowband Lock-In Detection

5.2.1.1 DC-Coupled Detection Systems

Substituting v dc pulsed (t) expressed in eqn (5.6b) into eqn (5.10) would arrive with the Fourier coefficients for the odd harmonics of the dc-coupled pulsed laser induced signal response as follows:

,)1()2()12(1

4)

o dc

)12(8)1()12(

2)

2 1

n

A v n

x n

A v

o dc

T x

(5.14a) and eqn (5.14b) into eqn (5.12a) and eqn (5.12b), respectively with n1yields the in-phase, f NB IP(o)dc , and quadrature-phase, f NB QP(o)dc , NB lock-in detection outputs of pulsed laser induced voltage change for dc-coupled detection systems as follows:

,)1()2(1

2)

dc o IP

4)1()

2

x A v x

A v

Eqn (5.15a) and (5.15b) are illustrated in Fig 5.8 with v d A v 1V and

s

 30 for varying pulsing frequency The signal magnitude output is computed

with the expression described as follows:

.)()( IP 2 QP 2

mag

f f

Fig 5.8 Narrowband lock-in detection output for dc-coupled detection systems with

V A

v d v 1

Fig 5.8 shows that the output signal magnitude remains constant at low frequency and begins to decay when f o 1kHz At f o 1kHz, the dc-coupled waveform resembles that of a square wave function as shown in Fig 5.5a(ii) Thus, the lock-in output resides mainly in the quadrature-phase channel which uses a sine correlation function As the dc-coupled waveforms begin to experience distortion with increasing pulsing frequency, the phase difference between input and quadrature-phase channel results in the output signal residing in both in-phase and quadrature-phase channels

At high pulsing frequency, f o 1kHz , the attenuation of dc-coupled waveforms results in decreasing signal magnitude These results show that maximum NB lock-in signal sensitivity can be achieved at f o 1kHz forDUT 30s

5.2.1.2 AC-Coupled Detection Systems

Similarly, substituting  pulsed()

ac

v expressed in eqn (5.8) into eqn (5.10) would arrive with the Fourier coefficients for the odd harmonics of the ac-coupled pulsed laser induced signal response as follows:

)2()12(1

)1(

)2()12(1

)1(

)2()12(1

)1(

22

)2()12(1

1

)2()12(1

12

2

)(

2 2

2 2

2 2

2 2

2 2

y B n

x A

x T

A v

n z n y

x T

o

v d

o ac

n

(5.17a)

,)1()12(2

)1()2()12(1

)12(

)1()2()12(1

)12(

)1()2()12(1

)12(

)2(4

)2()12(1

)1)(

12(

)2()12(1

)1)(

12(2

4

)(

2 2

2 2

2 2

2 2

2 2

y A v

z n

n C

y n

n B

x n

n A

x A

v

n

z n

n

y n

T

x A

v

b

v d v

d

o

v d

o ac

2 1

quadrature- 

)2(1)1()2(1)1()2(12

)1()2(1

1)

1()2(1

12

)(

2 2

2

2 2

B x

A x

A v

z y

x T

A

v

f

v d

o

v

d

ac o IP

)1()2(1

)1()2(1

)1()2(1)2(2

)1()2(1)1()2(122

)(

2 2 2

2 2

x y A v

z C

y B

x A

x A

v

z y

x T

A v

f

v d v

d

o

v d

ac o QP

s

 30 , 1 2.2msand 2 10ms Fig 5.9(b) shows the comparison of the

narrowband lock-in signal magnitude between dc-coupled and ac-coupled detection systems

Fig 5.9 (a) Narrowband lock-in detection output for ac-coupled detection systems

withv d A v 1V , DUT 30s, 1 2.2msand 2 10ms

Fig 5.9 (b) Narrowband lock-in magnitude output for dc-coupled and ac-coupled

detection systems

Fig 5.9(a) shows similarly with Fig 5.8 that lock-in output for ac-coupled detection systems resides dominantly at the quadrature-phase channel Fig 5.9(b) shows that the magnitude of the output signal for ac-coupled systems increases with increasing pulsing frequency, peaks at around 1 kHz and decays with further increasing frequency When f o 1kHz, while the lock-in output for dc-coupled systems remains relatively constant, the output for ac-coupled systems suffers signal attenuation This

is due to the loss of the fundamental harmonic signal as a result of the high pass response of the ac-coupled detection mode When f o 1kHz , the output signal magnitude for ac-coupled systems also decays with increasing pulsing frequency due

to the signal loss from insufficient dwell time for laser heating These results show that maximum NB lock-in signal sensitivity for ac-coupled detection system can be achieved at f o 1kHz for DUT 30s

5.2.2 Wideband Lock-In Detection

5.2.2.1 DC-Coupled Detection Systems

Substituting eqn (5.14) into eqn (5.13) would arrive with the WB lock-in detection outputs for the in-phase, f WB IP(o)dc, and quadrature-phase, f WB QP(o)dc, channels of dc-coupled detection systems expressed as follows:

,)2()12(1

)1(16

2

)1()

(

1

2 2

d dc o IP

WB

n

x A

v x

A v f





.)2()12(1

11

2

1)1(

8)(

1

2 2

o QP

WB

n n

x A v f







Fig 5.10 Wideband lock-in detection output for dc-coupled detection systems

withv d A v 1V andDUT 30s

Fig 5.10 illustrates eqn (5.19) withv d A v 1V andDUT 30s It shows that WB lock-in output for dc-coupled detection systems occurs only in the in-phase channel The signal magnitude variation with pulsing frequency behaves similarly with the NB results for dc-coupled detection systems shown in Fig 5.8 Maximum signal sensitivity can also be achieved at f o 1kHz

5.2.2.2 AC-Coupled Detection Systems

Similarly, the wideband lock-in detection output for the in-phase, f WB IP(o)ac, and quadrature-phase, f WB QP(o)ac, channels of ac-coupled detection systems are derived

by substituting eqn (5.17) into eqn (5.13) and they are expressed as follows:

,)1(2)

12()2(1

)1(

)12()2(1

)1(

)12()2(1

)1(

)2(8

)12()2(1

)1()

12()2(1

)1()

2(8

)(

1

2 2

2 2

2 2

1

2 2

1

2 2

x y A v

n

z C

n

y B

n

x A

x A

v

n

z n

y T

x A

v

f

v d

n v

d

n n

o

v d

ac o IP

)1(

)2()12(1

)1(

)2()12(1

)1(

12

1)

2(4

)2()12(1

1)

2()12(1

11

2

1)

2(4

)(

1

2 2

2 2

2 2

1

2 2

2 2

n o

v d

ac o QP

WB

n

z C n

y B n

x A

n

x A

v

n

z n

y n

T

x A

Fig 5.11 Wideband lock-in detection output for ac-coupled detection systems

withv d A v 1V , DUT 30s, 1 2.2msand 2 10ms Fig 5.11 illustrates eqn (5.20) with v d A v 1V , DUT 30s , 1 2.2ms and

5.2.2.3 DC-Coupled and AC-Coupled Comparison

Fig 5.12 Narrowband and wideband lock-in detection magnitude output for dc-coupled and ac-coupled detection systems withv d A v 1V ,10sDUT 30s, 1 2.2msand

ms

10

2 

Fig 5.12 summarizes this section by comparing the NB and WB lock-in detection magnitude output for both dc-coupled and ac-coupled detection systems with

V

A

v d v 1

 , 10sDUT 30s , 1 2.2ms and 2 10ms It shows that for a

periodic input signal with 1V amplitude (i.e v d A v 1V ), the time averaged lock-in measures a lower output signal magnitude (i.e < 1V) The signal magnitude of WB is higher than NB lock-in detection as it measures the sum of the odd harmonics of the periodic input instead of the single fundamental harmonic

It also shows similar frequency dependence for both NB and WB lock-in on coupled and dc-coupled detection systems Lock-in signal sensitivity peaks at 1 kHz for ac-coupled detection systems while it saturates at f o 1kHz for dc-coupled detection systems forDUT 30s Lock-in detection on ac-coupled detection systems has narrower pulsing frequency range due to the effects from both the sample thermal time constant, which limits the pulsing frequency in the higher frequency regime, and the high pass filtering in ac-coupled detection mode which limits the pulsing frequency in the lower frequency regime For devices with smaller thermal time constant, e.g Cu interconnects where DUT 10s has been reported [94], the saturation frequency for dc-coupled systems and the peak frequency for ac-coupled systems would increase from 1 kHz to around 3 kHz

ac-5.3 Experimental Results

A series of experiments were conducted using NB and WB lock-in detection with pulsed-DReM and pulsed-TIVA on a single Al line structure shown in Fig 3.4, to compare their detection sensitivities at varying pulsing frequency It will be shown

that the experimental measurement correlates with the analytical results on the lock-in signal sensitivity discussed in section 5.2 NB lock-in is implemented with a commercial lock-in amplifier while WB lock-in is implemented with a software digital algorithm developed for greater ease of use and a more robust scan time It will

be shown that NB lock-in detection is more sensitive than WB lock-in detection due

to greater noise reduction A detection sensitivity enhancement factor between 15 - 20 times can be achieved with NB lock-in detection

5.3.1 Narrowband Lock-In Detection

The use of a pulsed laser with a NB lock-in amplifier to enhance detection sensitivity was first introduced in 2001 [53] for fault localization Detection sensitivity is enhanced by a pulsed laser at a specific frequency where the noise level is low together with a lock-in amplifier for signal processing However, the implementation

of the lock-in methodology is complex and there is little understanding on the interaction between lock-in parameters, like lock-in time constant and phase difference, with laser scan parameters, like scan speed and pulsing frequency The difficulty of setting the appropriate parameter values has posed a limitation for the application of lock-in as a routine enhancement method for fault localization In this section, critical parameters of NB lock-in detection for fault localization are studied

By optimizing these parameters, localization precision is achieved with enhanced detection sensitivity

5.3.1.1 Experimental Setup

Pulsed-TIVA with NB lock-in detection was implemented using Perkin Elmer 7280 DSP Lock-In Amplifier (LIA) and the experimental setup is shown in Fig 5.15 A frequency generator is used to generate a square wave control signal, V , to R

simultaneously pulse the laser and also supply a reference signal to the LIA The LIA senses the frequency of V and generates internal sine/cosine functions for NB lock-in R

detection [91] It takes in the amplified pulsed-TIVA signal, v ac pulsed (t), from the DL

1201 voltage preamplifier operating in ac-coupled mode and its output, f NB(o)ac, is connected to the analogue input of the SOM 1005 for digitization and signal processing

Fig 5.13 Pulsed-TIVA with narrowband lock-in detection experimental setup

5.3.1.2 Laser Scan Speed

Laser scan speed is determined by the laser dwell time per pixel Figs 5.14 a(i) and b(i) show the frontside reflected- pulsed-TIVA overlay at a dwell time of 1.5 ms/pix and 250 μs/pix, respectively at 2 kHz pulsing frequency and a lock-in time constant

s

 500 It is evident from these overlay images that localization accuracy is

compromised at a shorter dwell time of 250 μs/pix Fig 5.14 b(i) shows from the overlay image that the signal from the metal line is right shifted Furthermore, Fig 5.14 b(ii) shows that the pulsed-TIVA signal is distorted and has weaker signal intensity, as compared with the signal at a longer dwell time in Fig 5.14 a(ii) This is because at a particular LIA, the lock-in output has a “memory” effect lasting around about 3 – 4 LIA[92] Thus, it is critical to calibrate dwell time against LIA for the lock-in output to accurately reflect the input and also for precise fault localization

a(i) Overlay image

dwell time : 1.5 ms/pix

b(i) Overlay image dwell time : 250 μs/pix

a (ii) Pulsed-TIVA image

dwell time: 1.5 ms/pix

b(ii) Pulsed-TIVA image dwell time: 250 μs/pix Fig 5.14 Frontside reflected- pulsed-TIVA overlay and pulsed-TIVA images with dwell time of (a) 1.5 ms/pix and (b) 250 μs/pix at f o 2kHzand LIA500s

Fig 5.15 shows the tabulated pulsed-TIVA voltage sensitivity with dwell time normalized against LIA for 2 kHz and 200 Hz pulsing frequencies LIA 500s is used with 2 kHz pulsing frequency and LIA 5ms is used with 200 Hz pulsing

frequency The line profiles across AA‟ on the pulsed-TIVA images for 2 kHz and

200 Hz are shown in Fig 5.16 (a) and (b) respectively These results show that

although the voltage sensitivity saturates at a dwell time greater than 2LIA /pix, the

line profiles show that a dwell time greater than 3LIA /pix is necessary for precision

localization within 1 pixel (~1.1 μm) variation

Fig 5.15 Pulsed-TIVA with NB lock-in detection with normalized scan speed,

pix

LIA /

 at 200 Hz pulsing frequency with LIA = 5 ms and 2 kHz pulsing frequency

with LIA = 500 μs

(a) Line profile across AA‟ for 2 kHz (b) Line profile across AA‟ for 200 Hz Fig 5.16 Line profiles across AA‟ of pulsed-TIVA images at (a) 2 kHz withLIAof 500 μs and (b)

200 Hz withLIAof 5 ms at same laser power, pre-amplifier settings and biasing condition

5.3.1.3 Lock-In Time Constant

The output of the lock-in amplifier at frequency f is a constant dc voltage measuring o

the r.m.s value of the input fundamental harmonic centered at f The o LIA parameter determines the cut-off frequency of the low pass filter in the output stage It reflects how slowly the output responds, the degree of output smoothing and thus determines the lock-in detection sensitivity Fig 5.17(a) shows the pulsed-TIVA detection sensitivity at 500 Hz plotted against the lock-in time constant normalized against pulsing period, i.e.LIA T o The increase in dwell time, which is set 3LIA/ pix(based

on section 5.3.1.2) for precise localization, with LIA T o is also illustrated in Fig 5.17(a) Fig 5.17(b) shows the corresponding signal and noise variations withLIA T o

Fig 5.17 (a) Detection sensitivity and dwell time of pulsed-TIVA with normalized

lock-in time constant,LIA T o at 500 Hz pulsing frequency

Fig 5.17 (b) Voltage sensitivity and noise standard deviation of pulsed-TIVA with normalized lock-in time constant,LIA T o at 500 Hz pulsing frequency

Fig 5.17(a) and (b) show that increasing LIA improves the SNR by a factor of

LIA

 by noise reduction The pulsed-TIVA voltage sensitivity remains relatively

constant forLIA T o 1 However, there is always a tradeoff between lock-in detection sensitivity and scan time Doubling LIA would require doubled scan time for precise fault localization Thus, for practical NB lock-in application LIA T o is recommended to optimize experimental scan time

(a) Reflected-pulsed TIVA overlay (b) Pulsed TIVA signal

Fig 5.18 Frontside (a) reflected- pulsed-TIVA overlay and (b) pulsed-TIVA images

at f o 50Hz with LIA 500s(LIA 0.025T o) and 1.5ms / pix dwell time

Fig 5.18 (a) and (b) show the reflected- pulsed-TIVA overlay and pulsed-TIVA images at 50 Hz with LIA 500sand dwell time of 1.5ms / pix This illustrates that when LIA<< T , inadequate suppression of o 2f o signal component from the multiplier stage results in time dependent lock-in output which shows up as discontinuous signals Note that the localization precision is not compromised as shown in Fig 5.18(a) since dwell time 3LIA /pix

in Fig 5.5 b(v) , there exists a phase difference between the reference signal and input signal This results in signal outputs in both in-phase and quadrature-phase channels

as shown in Figs 5.19 a(i) and a(ii), respectively To optimize the voltage sensitivity

of the in-phase channel, a phase offset of 43o is set in the lock-in amplifier to compensate for the phase difference between the fundamental harmonic signal component and the in-phase correlation function This optimized the signal output in the in-phase channel as shown in Fig 5.19 b(i) and its magnitude can be described by eqn (5.16)

a(i) In-phase output

without phase offset

a(ii) Quadrature-phase output without phase offset

b(i) In-phase output

with 43o phase offset

b(ii) Quadrature-phase output with 43o phase offset Fig 5.19 Narrowband pulsed-TIVA in-phase and quadrature-phase output at

kHz

f o 2 ,LIA 500s (a)without phase offset and with (b) 43o phase offset

5.3.1.5 Detection Sensitivity Variation with Pulsing Frequency

A series of experiments were conducted to compare the detection sensitivities of pulsed-TIVA and pulsed-DReM with NB lock-in detection at varying pulsing frequency The experimental setup for pulsed-DReM is shown in Fig 5.20 and DReM

is operated at F45for optimum sensitivity It is similar with pulsed-TIVA setup except that the voltage pre-amplifier is operating in a dc-coupled mode

Fig 5.20 Pulsed-DReM with narrowband lock-in detection experimental setup

The experimental conditions are illustrated in Table 5.1 Based on the understanding

of the parameters from the previous sections, at each pulsing frequency, f , o LIA T o

and the dwell time is set to 3LIA/ pix for precise localization Phase offset is also adjusted to maximize the signal output magnitude at the in-phase channel

Table 5.1 Experimental settings for pulsed-TIVA and pulsed-DReM with narrowband

Pre-Amplifier Settings

(input coupling HPF at 72 Hz) DC

Lock-In Amplifier Settings

Fig 5.21(a) shows the detection sensitivity of pulsed-TIVA and pulsed-DReM with

NB lock-in detection at varying pulsing frequencies The corresponding voltage sensitivities and noise standard deviation variations with pulsing frequency are shown

in Figs 5.21(b) and (c), respectively They are normalized with the lock-in amplifier gain and converted to lock-in voltage output at a pre-amplifier gain of 10 kV/V The voltage sensitivity plot in Fig 5.21(b) is also fitted with the lock-in magnitude simulation results discussed in Fig 5.9(b) with v d A v 0.26 , DUT 30s ,

(a) Detection sensitivity

The noise level between pulsed-DReM and pulsed-TIVA are generally comparable across the frequency range except that at close to 50 Hz, higher noise was observed in the pulsed-DReM system This could be due to the extended detection bandwidth into the lower frequency regime in dc-coupled operating mode that allows the 50 Hz power supply noise to couple into the detection system For pulsed-TIVA, this noise

is likely suppressed by the high pass filters For f o 500kHz, the 1/ f noise could have dominated which limits the noise reduction even when LIA is increased to give stronger noise rejection with decreasing frequency For 500kHz f o 4kHz, the slight increase in noise with increasing frequency could be due to increased broadband noise from larger output detection bandwidth as LIA reduces with increasing frequency

Combining the signal and noise, results in the detection sensitivity variation with pulsing frequency for NB pulsed-TIVA and pulsed-DReM shown in Fig 5.21(a) At

Hz

f o 500 , the drop in detection sensitivity for pulsed-DReM is due to stronger noise coupling while the drop in detection sensitivity for pulsed-TIVA is due to the signal loss For both detection systems, optimum detection sensitivities are achieved

at 200Hz f o 1kHz with maximum signal and lowest noise Within this range, significant SNR enhancement of between 15 - 20 times is achieved by comparing with the detection sensitivities of conventional TIVA and DReM setups with SNR of 6.7 and 6.9, respectively at the same laser power and biasing conditions

5.3.2 Wideband Lock-In Detection

Wideband lock-in detection is implemented by a digital algorithm that was developed and incorporated in the SEMICAPS SOM system for pulsed laser applications The algorithm was designed for in-phase WB lock-in measurement since the lock-in signal output is dominated by the in-phase channel for both dc-coupled and ac-coupled detection systems as shown in Figs 5.10 and 5.11, respectively The algorithm simplifies the lock-in detection by eliminating the need for a commercial lock -in amplifier and a function generator for synchronous detection, and the need to calibrate lock-in and scan parameters for optimal performance It shortens the minimum scan time by allowing precise lock-in measurement to be done within a single pulse period

5.3.2.1 Experimental Setup

The wideband experimental setups for pulsed-DReM and pulsed-TIVA are shown in Figs 5.22(a) and (b), respectively

(a) Pulsed-DReM

(b) Pulsed-TIVA Fig 5.22 Experimental setups of (a) pulsed-DReM and (b) pulsed-TIVA with digital

wideband lock-in algorithm

A software-generated square wave control signal, V , at 50% duty cycle is used to R

pulse the laser Instead of connecting to a lock-in amplifier, the SOM system receives the amplified pulsed laser induced voltage change from the preamplifier and the digital algorithm performs the WB lock-in measurements

Fig 5.23 Waveforms describing the principles of software digital wideband lock-in

algorithm

Fig 5.23 illustrates the implementation of the digital algorithm Within the beam

“ON” and “OFF” duration of each pulse period, T , the system waits for time delay, o

d

t , before sampling at 20 MHz sampling frequency The overhead time, t OH, is due to time delay for subsequent data processing steps after digital sampling The lock -in output signal is obtained by subtracting the sum of the digitized signals during beam

“ON” with the sum of the digitized signals during beam “OFF” expressed as follows:

,)()

()

m

pulsed ON m o

where M is the sampling size and t is the sampling period This method is thus s

analogous to WB lock-in detection with in-phase correlation function described in Fig 5.7b(i) The algorithm is repeated pixel by pixel over the preset scan frame It provides a simpler implementation of lock-in detection with a minimum scan speed of

pix

T o / It also allows averaging of N pulses for greater noise rejection

5.3.2.2 Averaging of N Pulses

Fig 5.24 shows the noise variation of pulsed-TIVA with WB lock-in detection with

averaging over N pulses at 142 Hz and 1.8 kHz pulsing frequencies They are

curve-fitted with trend lines to show a noise reduction factor close to N with averaging over N pulses This translates to a detection sensitivity increment factor of N with averaging over N pulses