Indian Journal of Pure & Applied Physics Vol. 42, Apri l 2004, pp. 258-264

Dual phase wide band lock-in amplifier for linear and non-linear photo-thermal signal processing

K Sreekumar & v K Vaidyan

Department of Phys ics, University of Kerala, Thiru vananthapuram 695 581

Received 29 .111/.1' 2003: revised 27 .la/lll{l/)' 2004; accepted 26 Febma ry 2004

A dual pl13se lock-in amplilier has been designed and developed for the processing of photo-thermal signals in I I-II. to

11 0 kH z frequency range. with automati c freque ncy tracki ng over the ent ire bandwidth. The low power consurn rllion of about 3.5 W of the unit ensures an erlicient su pport in experiments of long durat ion like photothermal mi cros:opy and subsurface imaging. The system accepts reference signal s of any wave shape and synt hesizes corresponding sirie wave for fundamental- on ly- response. Second harmonic detecti on scheme has been incorporated for appli cati ons in non- linea r photothermal experiments up to 55 kHz. At I kH z, the measured common mode rejection ratio of the differential front end

is about 70 dB, input voltage noise is about 25 /I VI .Jfu and cu rrent noise is about. I pil i Jl-h The sensiti vity :s 200 nV

and the max imum poss ible dynamic reserve is 54 dB . The ful l-scale sensitivity is adj ustable from 2 ~t V to 200 mV and

time constant from I ms to 50s. Optional notch fi lters arc included for line frequency and its second harmon ic. The phase stability, output offset drift and the total output error have been anal yzed. The unit has heen employed in laser-photO:lcousti c imag ing fo r detecti ng a subsurface hole in an alu minium block and phototherma l radiometry of a si li con wafer and the results have been presented . Though developed I'or photothermal applications, care has been taken to make it a low cost general-pu rpose instrulTlent.

[Keywords: Photo-thermal signal processing; lock- in amplifier] IPC Code: H 04 L 12/ 12

1 Introduction

Photothermal (PT) tec hni q ue s, based o n the

analys is of light induced thermal diffus ion waves in matte r, have paved the way for several nove l a nd

revo luti o na ry meas ure ment tec hni ques l. Whe n an

intens ity modulated light beam fa ll s o n a materi al , the

non-radi a ti ve de-excitation of mo lec ul es cau ses periodic hea ting of the sample. The a mplitude and phase of thi s temperature variation carry quantitative

information rega rdin g the e lec trical , thermal a nd

o pti ca l prope rti es of th e irradiate d sa mpl e.

Spectroscopy of thin film se mi conductors, opaq ue

sa mpl es and bi o log ica l s pec im e ns, s urface a nd

s ubsurface imagi ng, c ha racte ri za ti o n a nd quality con tro l of semiconductors for microelectronics applications are a few key areas illustrating how thi s unique technique leads to remarkable advances in the characterization and metrology of material s2

.

The signal f rom the transducer in a PT experiment

is usually obscured by noise and fo r the measurement

of its a mpl itude and phase shift , the se of a lock -in

amp l ifier (UA) has become a usual practi ce. However,

fo r experi ments of long duration ( like PT mic roscopy),

w ith battery back up, the use of commerc ia l UA units is not advisable fo r the ir excess ive power consumption .

The la rge physica l size of these systems is yet another

problem as far as the compactness of the experimental a rra ngeme nt is co nce rne d. In ad d iti o n , in ma ny occas ions, the expenditure for the experiment is hig h only due to the inclusion of a commerc ia l LIA, even

tho ugh the versat ility of such a syste m is not at all

necessary.

Thou g h a na log lock -in amp lifi e rs are be in g rep laced by the ir di g ital coun te rparts, th e maj o r

adva ntage of the present work is the s impli ci ty of des ign yie lding good performance with a hand full of eas ily ava il able and lo w cost components.

2 Principle of Lock-in Detection

In the lock-in detection techn ique, the PT signal

SREEKUMA R & VAIDYAN : DUAL PHASE WID E BAND LOCK-IN AMPLIFIER 259

Signal

Reference

Signal amplifier and notch filters

Quadrant phase shifter and 2f ge nerator

Sine wave synthes izers

In-phase PSD

Quadrature PSD

Fig. 1- Si mplified block schematic of a dual phase lock-in amplifier wi th fundamental -only response

is modulat ed at a suitabl e frequency by using a modulated laser beam and a reference is deri ved from th e so urce of mod ulati on. The s ignal , aft e r amplifi cati on and necessary filtering, is multiplied with the reference in a phase sensiti ve detector (PSD) whi ch is a multiplier followed by a low pass filter Fig. I. If the reference is, el/ = EI/ sin UJ I, and the signal , with a phase shift <1> , is e, = E, si n( UJ 1+ <1», then the output of the multiplier is:

e/R

= (E,E/2)(cos<l> - cos(2 UJ 1+ <1» .. . ( 1)

The component cos(2 UJ 1+ <1» is filtered off and th e output of the PSD becomes

. .. (2)

In a dual-phase LI A, ano ther PSD multiplies the signal with a reference el/ = ER COSUJ I yielding an output

... (3)

v x and V y represent the signal as vector whose resultant is given by

R = (V 2 + V ~)1 12 X Y

... (4)

and phase by

... (5)

V x and V yare called the in-phase and quadrature signal components respecti vely.

3 Noise Rejection in Lock-in Detection

J n case , if the signal and th e reference di ffer slightly in frequency by ~w, then the PSD output. Eo = (Es E/2) cos {(~w)t + <I>}. Thi s component fluctuates sinusoidally with a frequ ency that increases with the freq uency diffe rence ~w. The filter response effectively attenuates these fluctu ations sustaining a dc output for signals within a very narrow band around the reference frequency.

If the reference signal is a sym metri cal square

wave (th e simpl es t case), then th e output of th e multipli er will be a harmonic series making undesired noise acceptance windows and the total mean square noi se" at the output of the PSD increases by 23%.

4 Design of a Dual-Phase Lock-in Amplifier 4.1 Signal Channel

The signal is fi rst amplified to a suffi cient voltage leve l usin g a low noise, wide band, source coupled differenti al amplifier (Fig. 2). Q3, Q4, Zl , R4, R5 and R6 supply a constan t drain current of 270 !--LA to each of the two transistors Ql and Q2. Any input that would result in a differential between the drains of Ql and Q2 is amplified by U I by a factor-l approximately equal to:

. . . (6)

With U2, R 14, R 15 and R 16, the gain can be changed f rom 0.1 25 to 12.5. With two non-inverting, ac coupl ed, operational amplifiers around AD829A, each of gain 10 (not shown in figure) , maxi mum stable ac ga in up to 1250 is achieved and thus the full sca le sensitivity is adjustable from 2 !--LV to 200 mY. The input resistance is set to 100 MQ using R

I• This discrete

component front end offers higher slew rate of about 70 V IllS compared to monolithic instrumentati on amplifiers like INA Ill. The notch filter around U3 and U4 has a sharp band rejecti on (-70 dB ) at the frequency given by:

j .= (2n R C )01/2 Hz . /I 4 . .. (7)

and is used for suppress ing th e line frequency component in the signal. Another one is used fo r second harmonic (from full wave recti fier circuits) line notch.

The maximum input voltages are ±2 V fo r single ended and ± I 0 V for di fferential signals . The si mulated (using spice models) CMRR is 90 dB while th e measured value is about 70 dB at J kHz and it decreases

2GO INDIAN J PURE & APPL PI-IYS, VOL. 42, APRIL 2004

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+ O~~I:- -Ri

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R7 100K

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- 12V

Fig. 2- Circuit diagram of the signal channel

by 20 dB/decade approximately . The obse rved deteri orat ion may be due to the presence of grou nd loop, which may be minimized using floating guard technique and double shielded cables5

. The error in the gain linearity is less than 1% from 1 Hz to 110 kHz. The phase shift crosses 5° at 110 kHz. The

simulated input noise voltage at I kHz is 25 Il V /.,JH;.

and current noise is about , 1 pA/.JHz for the front end .

4.2 Refercnce Channel

The fundam ental -only-response of the system env isages the synthesis of a si ne wave whose phase is variable from 0 to 360° with respect to the reference input and another sine wave orthogonal to it3

.

For s ignal proce ss in g in no n-lin ea r PT ex periments, a frequency -doubler is incorporated for generating the second harmonic (2f) of the reference6

.

The linea r phase locked loop (PLL) around US and U6 form the 2f generator (Fig. 3). U8, with f and 2f signal s as the inputs, produces a squa re wave of frequency f shifted in phase by approximately 90°. C8 is used for eliminat ing the errors due to propagation delay (compared to f, 2f suffe rs more delay before reac hing U8) at higher frequencies. Us ing two such sections and an inverter, re ference phase can be sh ifted to any quadrant , prior to sine wave synthes is.

The phase-selected square wave is app lied to a sine wave synthes izer, around U 10, as show n in Fig. 4. The c ircuits around U9 , UIO, U ll , U12 , U 13 and Q5 const itute a PLL with triangle wave output. The reference voltage to U 11 can be varied using YR4 to produce a proportional phase shi ft o f th e output triangular wave from -10 to 70° with respect to the input square wave. The square wave at pin-number 10 of U 10 acts as the input to the second PLL generating the quadrature triangular wave. Up to 100 Hz, the integrating capac itor C 12 is 111 . 1 nF, it is reduced to 11.1 nF at 1 kHz, 1.1 nF at 10 kHz and. 0. 1 nF at 100 kH z. Automatic frequency tracking is ac hieved by controlling switches S4, S5, and S6 (Omron G6A-274P Relays havi ng inter-electrode capacitance less than 0. 1 pF) wi th the help of a freq uency (reference) to voltage co nve rte r around IC LM 33 1 an d leve l sens in g comparators 7.

The second PLL is si ll1i lar to the first one except that the reference input of the vo ltag ~ co mparator is grounded. A buffered sinusoidal vol tage with total harmonic di stortion less than 2% is avai lable at the output of U 15, to be app lied to the in-phase PSD. The reference phase is measured using a linear phase meter, around an excl usive-OR gate, with lead-lag indicacion.

The input res istance of the circuit is 500 kQ and has a signal se nsitivity o f 500 mY, prov ided the

14

6 ' "

SREEKUMAR & VAIDYAN : DUAL PHASE WIDE BAND LOCK-IN AMPLIFIER

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1/4 CD4093

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ClK

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-

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Fig. 4- Circuit diagram of the reference sine wave synthes izer w ith phase shifter

minimum pulse width is I /.ls. The acquisition time is 40 s at I Hz, 10 sat 100 Hz and 3 s at 10 kH z. The phase noise is less than O. I ° above 100 Hz and the error in the orthogonality is ± 1.5° over the complete operating frequency. The phase meter has a resolution of 0.1 °.

4.3 Phase Sensitive Detectors

As in Fig. 5, the suitably amplified signal and the sinusoidal in-phase reference are multi pi ied in U IS that is a four quadrant analog multiplier. U 19, C 19 (Cx)' C20 (C/2) and Rx constitute a second order low pass filt er whose noise bandwidth is. I/SRxCx . The

262 INDI AN J PURE & APPL PI-IYS, VOL. 42, APRIL 2004

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minimum value of T is l imited to I ms by the slew rate of U 19 and its upper l imit is 50 s. A t 50 s, the total output error due to the input bias current and offset voltage crosses I % of the full sca le. U20 is a chopper stabili zed dc amplifier with a gain of either 133.33 or 13.33.

5 Performance of the System 5.1 Dynam ic Reserve

Dynamic reserve (DR) is th e ratio of maximum allowed peak-to-pea k va lue of an asy nchronous voltage to the peak-to-peak value of the signal voltage for fu ll -sca le output, at the input of the mu l tipli er. Beyond these va lues , clipping effects occur. In the present design, the former is 24.00 V and the later is 25 mY , yi Iding a DR o f about 54 dB. The experimentally observed DR (an asynchronous vo ltage that causes 5% error in th e full sca le output is measured) is about 52 dB . The reducti on may be due to the higher non-linearity than that claimed by the manufacturer of the PSD and the error in the noise measurement (using CRO). I f and are the ac and dc gai ns respectively, then the dc output of the L1A is:

... (8)

The factor 10 in the denominator arises from the transfer f unction of U 18. Hence, a dc gain of 133.33 ensures a full sca le output of 2.000V in a 3.5 digit voltmeter. If the signal is amplified to 250 mY, then the de gain required for the same full scale is 13.33 and the DR reduces to 34 dB.

5.2 Output Stabil ity

The drift in the output of the multiplier is about 50 ~lV/oC and this contributes to about 0.33% of the

full sca le if the DR is 54 dB, neglecting the dril't in the filter and dc am pl i f ier. When the DR is 34 dB, the drift reduces to 0.02%. Larger DR can be achieved by reducing ac gain and increas ing dc gain ('eeping their product constant), i f the output drift is tolerable.

6. Total Output Er ror and Sensitivity of the System

The L1 A is set to 20 ~V full scale for a DR of 54 dB with ti me constant l Os at a signa! frequency of I kH z. The max imum error in the gain sett ing is 1%.

25 11 VI,fH;, input noise contributes about 4 nV (rms)

noise, after low pass fi l tering, to the output and the corresponding error is 0.02%. For a c ange of 5°C in the operating temperature, the error due to the dri ft in the PSD is 1.67%. The exponenti al convergence of the filter resul ts in 0.2% error for a sett l ing time of 60 s. Due to the cos ine relation, the phase shift errors are negligible. The rms value of these uncorrelated errors i s about 2% y ield i ng an inp ut se nsiti v i ty of about 400 nV. If the DR were 34 dB , the sensiti vi ty would then be 200 n V.

7 Resul ts and Discussion

The major source of error in thi s instrument is the drift in the analog mul tip lier output and it depends on the settings and the variations in operating temperaturc. In linear PT experiments, the unit can process signals of frequency up to 110 kH z and it is 55 kHz if second harmonic signal detect ion is requ ired. The power consumpt ion is about 3.5 W and the estimated cos t is around $ 100. Fig. 6 shows a typical surface plot of an aluminium sample (l x I xO.2 em) with a pit of depth 0. 17 cm and diamcter 0.15 cm, on the oppos ite side of th e surface i lIumi nated for photo-acoustic Imagll1g.

SREE KUMAR & VA IDYAN : DUAL PI-lASE WID E BAN D LOCK-I N AMPLI FIER 263

o Fig. 6- Surfacc plot of the alumin iulll salllpl e depi cting the subsurface hole, obtaincd by photoacousti c imaging. One step corresponds to I 00 ~1111 along the X-direc ti on and 250 ~lIn along the Y -direction

The pump is a (40± 1) mW , 660 nm di ode lase r foc ussed to about 50x40 ~lm ~, modul ated us ing a mechani cal chopper. The chopping frequency is 75 Hz for which the thermal di ffu sion length in aluminium is 587 ~lIn . The photoacousti c cell is pl aced on an automated X- Y translation stage run with a step size of I 00 ~lm along the X-direction and 250 ~m along the Y -directi on. The scanned area is 5x2 mm2. The increase in th e phase re fl ec ts th e tra nsiti on from thermall y thick to thin reg ion where co nstructi ve interference occurs between the thermal wave at the surface and th at re fl ected from th e aluminium -a ir interface. The result is comparable with that obtained in standard techniqu es with commerc ia l loc k- in ampli fierss.

Fig. 7 shows th e vari ati o n of ph oto th ermal radi ometri c (PTR) ampl i tude agai nst the choppi ng frequency for a front surface pol ished p-type si I icon wafer ( 10-1 5 Q cm, 6 inch, 480 ± 30 ~m thi ck) recorded at 300 K with an arrangement th at has bcen co rrec ted aga in s t las e r int ens it y and lock -in performance vari ations by sampling a part of the li ght beam1

. The beam size is about 5x4 mm 2 so th at one di mensional i ty of the semi-infinite model is val ids. The detector is an HgCdTe element of I mm2 acti ve area with spectral response in the 2-1 2 ~lm region. Data have been collected in the plasma wave dominating region2 and the best fit to the model yields minority

<ll

~ a. ~ 0:: f-0...

~ ~ z 0.1

lk 10k lOOk

Frequency (Hz)

Fig. 7- Experimenta l (0) and simulated (-) results of modulation frequency - PTR amplitude n.:sponse (measured using thc developed lock-in amplilicr) of a sil icon wakr. irrad ialcd with a (40± I) mW. 660 nm se mi co ndu ctor lasc r un de r direct square wave mod ul at ion (200 Hz - 100 kHz) with automatic power control (A PC)

ca rrI e r life tim e (1:) = (70±0 . 1 %) ~s, su rface reco mbinati on ve loc ity (s) = (78.8 ± I %) cm/s and photo-injected ca rri er diffusion coe ffi c ient (D ) =

" (8 .5± 1.5%) cm2/s. With a commerc ial lock- in , the dev iati on observed is within 1 % fo r the values of these parameters.

264 INDIAN J PURE & APPL PHYS, VOL. 42, APRIL 2004

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85 ( 1999) 7392. 3 Mcade M L, Lock-ill alllplifie rs: Prillciples alld applicatiolls

(Petcr Peregrinus Ltd ., London), 1st Edn, 1983, p.35. 4 Walt er G lung, Ie Op-Alllp cook book. (Howard W Saills

Indiana), 2nd Edn, 198 1, p.287. 5 Anton F P va n Putten , Electrollic lII easurelll ell t systellls:

Th eory aml practice (lOP Publi shing Ltd , l3ri stol), 2nd Edn, 1996, p.344.

6 Rajakarunanayake Y N & Wickrall1asi nghc ::-I K, Appl Ph),s Lell, 48 (1986) 210.

7 wlvw.llatiollal. colII

8 Sreekulllar K & Philip J, Advallces ill Ill stnrlllell talioll (New Age International , New-Delhi), 1st EdJl , 1996, p.8 16

9 Sheard S J, SOll1ekh M G & Hiller T, MOfer Sci Ellg. 135 (1990) 101