Modern Physics Lab-dimuthu

8/19/2019 Modern Physics Lab-dimuthu

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MODERN PHYSICS LAB

Electrical Characterization of

Semiconductor De ice!

D"C"B" O#e$!e%era&all '()*


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E+PERIMEN, I

Familiarization to the Lock-In Technique

In the first three sections of this experiment a lock-in amplifier is utilized to take the measurements.Therefore the primary objective of this section is to familiarize ourselves ith the techniques of thelock-in amplifier method.

Theory

! lock-in amplifier "also kno n as a phase-sensitive detector# is a type of amplifier that can extracta si$nal ith a kno n carrier ave from an extremely noisy environment. %asically it can lock outand separate out a sin$le si$nal ith a specific frequency. In our case the si$nal in question is a square

ave hich is a collection of sine aves at multiple frequencies and related amplitudes and phases. !&' pk-pk square ave is expressed as

(" t # ) *.&+,sin" ωt # ./&// sin", ωt # .&0/1 sin"0 ωt # .*2*3 sin"+ ωt # 4 "!#

The Lock-in amplifier ill lock in the first harmonic of the composite square ave. Therefore thesi$nal measured ill be the first part of the expression "!# and not &' pk-pk.

5rocedure

The Lock-in amplifier and the function $enerator ere connected as sho n in Fi$ure *. The Lock-inamplifier source as set to 67xternal8. ! /' "pk-pk# si$nal as applied "(ince the function $enerator $ives a /' pk-pk si$nal hen &' amplitude is $iven#. The frequency as set to * k9z. :sin$ the ;ref

phase< function of the (=20 lock in amplifier the in phase volta$e "' x# correspondin$ to harmonics *to + ere measured.

&i-ure ). The circuit for measurin$ harmonics of a square ave si$nal. =eference>In is the referencefrequency input and 6!-*8 is the si$nal in of the lock-in amplifier. 6?ut8 is the si$nal output of thefunction $enerator


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?bservations

The ' x values sho n here are r.ms. values as sho n belo in Table *.

Harmonicnumber Vx(rms)(V)

1 0.8796

2 0

3 0.2927

4 0

5 0.1753

6 0

7 0.1250,a#le ) @ The in-phase volta$e measurements

Aalculations

(ince the observed values are r.m.s. valuesB to convert them into pk-pk e have to multiply by &.2.!lso since the lock-in indicates the amplitude of each harmonicB accordin$ to equation "!# themaximum amplitude of each harmonic is the theoretical pk-pk value. (ince e have a /' pk-pk si$nalit is the ' max values in the equation multiplied by & as calculated belo in Table &.

Harmonicnumber Vx(rms)(V)

Vx(pp)(V)

Vx(pp)theoretical (V)

1 0.8796 2.4629 2.5460

2 0 0.0000 0.0000

3 0.2927 0.8196 0.8488

4 0 0.0000 0.0000

5 0.1753 0.4908 0.5092

6 0 0.0000 0.0000

7 0.125 0.3500 0.3638

,a#le ' @ The 7xperimental and Theoretical calculated values for pk-pk volta$es of differentharmonics

Ciscussion

The theoretical and experimental values are approximately matchin$. !nd since a square ave doesnot contain any odd numbered harmonics the zero values obtained for those are theoretically correct.

!s for the use of coaxial cablesB since e are measurin$ small ac si$nals that are part of a compositesi$nal it is important for noise and distortion effects to be isolated. (ince a coaxial cable reduceselectroma$netic interference drastically the reason for usin$ it in this experiment is self-evident.


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E+PERIMEN, II

Aapacitance Deasurement

In this section e ill use the lock-in technique to measure the capacitance and resistance of a device.In our case this this ill be an approximation of an equivalent circuit of a real capacitor.

Theory

The relationship bet een the apparent capacitance "A m# hich e measure experimentally and thereal capacitance "A# of the device is $iven by@

C mC

={(1 + Rl R )2

+ω 2 C 2 Rl2}

− 1

…….(B)

9ere ω is the an$ular frequency of the (IE7 ?:T volta$e from the lock in amplifier and Rl is the loadresistance.

If the series resistance Rl to the sample is small so that Rl R and ωCR l


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&i-ure ' @ The circuit for measurin$ the capacitance of a device. The shielded mixin$ box combines aCA si$nal from 6!:H ?:T *8 and an !A si$nal from 6(IE7 ?:T8. The contact resistance R s isi$nored in most cases.

5rocedure

The experiment as set up as sho n in Fi$ure & ith Rl at * and A set to .*JF. In the setup avariable resistance box and capacitance box ere used for = and A. For the Lock-in amplifier thesettin$s ere set as follo s@ 9armonic@*B =ef. (ource@ InternalB (IE7 ?:T" V s#@ . * 'B !:H ?:T@ *B!:H ?:T volta$e@ * ' and (IE7 ?:T frequency@ * k9z.

%y varyin$ the values of = from *k to 3D on a ran$e suitable for lo$ scaleB V y of the lock inamplifier as measured. Then frequency as set to *k9z and the above steps ere repeated andreadin$s ere taken.

Then in the system .*JF as replaced ith an unkno n capacitor and = as set to * k . Then(IE7 ?:T frequency as varied from * 9z to * k9z and V y as measured. Finally thecapacitance as measured usin$ LA= meter.

?bservations

Vs at 10kHz Vs at 1kHz

R (×10 3 Ω)Vy (×10 -

3 V) R (×10 3 Ω)Vy (×10 -

3 V)1 1.365 1 -0.281

2 1.409 2 -0.273

3 1.423 3 -0.269

4 1.431 4 -0.267

5 1.435 5 -0.266

6 1.437 6 -0.266

7 1.440 7 -0.265

8 1.442 8 -0.264

9 1.444 9 -0.26410 1.444 10 -0.264


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20 1.449 20 -0.263

30 1.451 30 -0.263

40 1.451 40 -0.262

50 1.451 50 -0.262

60 1.451 60 -0.262

70 1.451 70 -0.262

80 1.452 80 -0.262

90 1.452 90 -0.262

100 1.452 100 -0.262

200 1.452 200 -0.262

300 1.452 300 -0.262

400 1.452 400 -0.262

500 1.452 500 -0.262

600 1.452 600 -0.262

700 1.452 700 -0.262

800 1.452 800 -0.262

900 1.452 900 -0.262

1000 1.452 1000 -0.262

2000 1.452 2000 -0.262

3000 1.452 3000 -0.262

4000 1.452 4000 -0.262

5000 1.452 5000 -0.262

6000 1.452 6000 -0.262

7000 1.452 7000 -0.262

8000 1.452 8000 -0.262

9000 1.452 9000 -0.262

9999 1.452 9999 -0.262

,a#le * @ The 'y values for different loads at t o different frequencies

Aalculations

For the calculation the follo in$ equation as utilized.

C m= C = V y

ωV s Rl……(C )

9ere K ) & f here f ) *k9z and * k9z respectively. V s) . *' and Rl ) * . Therefore theequation is converted to

C m= C = V y

2 π × 1000 × 0.01 × 100

C m= C =

V y2000 π

……( E)


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Vs at 10kHz Vs at 1kHz

R(×10 3 Ω)

(×10 -!

")

R

(×103

Ω)

(×10 -!

")

1 0.2172 1

-

0.04472

2

2 0.2242 2

-

0.04344

9

3 0.2265

3

-

0.04281

3

4 0.2278 4

-

0.04249

4

5 0.2284 5

-

0.04233

5

6 0.2287 6

-

0.042335

7 0.2292 7

-

0.04217

6

8 0.2295 8

-

0.04201

7

9 0.2298 9-

0.04201

7

10 0.2298 10

-

0.04201

7

20 0.2306 20

-

0.04185

8

30 0.2309 30 -


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0.04185

8

40 0.2309 40

-

0.04169

8

50 0.2309 50

-

0.04169

8

60 0.2309 60

-

0.04169

8

70 0.2309

70

-

0.04169

8

80 0.2311 80

-

0.04169

8

90 0.2311 90

-

0.04169

8

100 0.2311 100

-

0.041698

200 0.2311 200

-

0.04169

8

300 0.2311 300

-

0.04169

8

400 0.2311 400-

0.04169

8

500 0.2311 500

-

0.04169

8

600 0.2311 600

-

0.04169

8

700 0.2311 700 -


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0.04169

8

800 0.2311 800

-

0.04169

8

900 0.2311 900

-

0.04169

8

1000 0.2311 1000

-

0.04169

8

2000 0.2311

2000

-

0.04169

8

3000 0.2311 3000

-

0.04169

8

4000 0.2311 4000

-

0.04169

8

5000 0.2311 5000

-

0.041698

6000 0.2311 6000

-

0.04169

8

7000 0.2311 7000

-

0.04169

8

8000 0.2311 8000-

0.04169

8

9000 0.2311 9000

-

0.04169

8

9999 0.2311 9999

-

0.04169

8

,a#le / @ The calculated apparent capacitance for the readin$s in table ,


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5lottin$ A vs = for both * k9z and *k9z frequenciesB e obtain the follo in$ $raphs.

0ra1h ) @Mraph of A vs. = at * k9z

5arameter 'alue 7rror ------------------------------------------------------------! .&*++, &. 21 07-/%* . &/ 1 1.,2&127-/%& - . *01& 1.&210&7-/%, . /, &.,,&,27-/%/ -/.&&+ ,7-/ &.201+/7-0------------------------------------------------------------

=-(quare"A?C# (C E 5------------------------------------------------------------

.33&30 &.,//,+7-/ ,+ . *


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------------------------------------------------------------

0ra1h ' @ Mraph of A vs. = at *k9z

5arameter 'alue 7rror ------------------------------------------------------------! - . //12 /.* &007-0%* . 0** *.&00&17-/

%& - . ,*+ *.&,1,07-/%, 2.,31&27-/ /.02+ &7-0%/ -2. &/,17-0 0.1*2&07-1------------------------------------------------------------=-(quare"A?C# (C E 5------------------------------------------------------------

.33/+/ /.1* 037-0 ,+ . *------------------------------------------------------------


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0ra1h *@ Mraph of A vs. =

Ciscussion@

Aalculations

#(Hz) Vy(mV) (×10 -!

")

100 -2.887 -4.59713200 -1.809 -1.44029

300 -1.207 -0.64066

400 -0.854 -0.33997

500 -0.614 -0.19554

600 -0.439 -0.11651

700 -0.299 -0.06802

800 -0.186 -0.03702

900 -0.085 -0.01504

1000 0.002 0.000318

2000 0.618 0.0492043000 1.070 0.056794


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4000 1.459 0.058081

5000 1.796 0.057197

6000 2.086 0.055361

7000 2.330 0.053003

8000 2.532 0.050398

9000 2.694 0.047665

10000 2.821 0.04492

20000 2.938 0.023392

30000 2.459 0.013052

40000 2.032 0.008089

50000 1.712 0.005452

60000 1.474 0.003912

70000 1.294 0.002944

80000 1.152 0.002293

90000 1.040 0.0018410000

0 0.952 0.001516

,a#le 2. Aapacitance vs. Frequency for unkno n capacitor

0ra1h / @ Mraph of A vs. f

!s sho n from the $raph the unkno n capacitor exhibits the same behavior as the kno n capacitor and its value is around 02 nF accordin$ to the $raph hich is conflict ith the measured value from


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&i-ure * @ The circuit for measurin$ the capacitance of a diode. ! diode can be consideredas a capacitor and a resistor in parallel. The equivalent circuit is $iven in expanded vie .

Aalculations

Vbias(V)

Vy(mV)

1$ % (×10 %%" -%)

0.30.016

32.37500244

6

0.20.045

20.30886052

2

0.10.042

50.34935053

3

0.00.037

80.44162705

4

-1.00.023

41.15241142

5

-1.50.021

01.43087165

5

-2.00.019

41.67662450

8

-2.50.018

21.90500664

2

-3.00.017

22.13295835

6

-3.50.016

52.31777557

4

-4.00.015

82.52769748

4

-4.50.015

32.69560596

4

-5.00.014

72.92014623

5

-5.5

0.014

4 3.04308642-6.0 0.013 3.26595103


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9 8

-6.50.013

63.41162629

8

-7.00.013

33.56727005

5

-7.50.013

13.67702581

4

-8.00.012

8 3.85140625

-8.50.012

5 4.03849216

-9.50.012

14.30991325

7

-10.00.011

94.45600169

5

,a#le 3. *NA& vs. ' bias for diode

0ra1h / @ Mraph of *NA& vs. ' bias

0ra1h 2 @ Mraph of *NA& vs. ' bias5arameter 'alue 7rror ------------------------------------------------------------! .31+** .*/+/,% - .,1/,+ . &+/*------------------------------------------------------------

= (C E 5------------------------------------------------------------


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0.618 2.382

0.593 1.407

0.572 0.928

0.538 0.462

0.442 0.058

0.000 0

,a#le 5. I vs. ' bias for positive biasVbias

(V)&((×10 -

! ' )-19.2 -1.97

-23.4 -2.44

-27.7 -2.97

-30.1 -3.31

-31.6 -3.56

-32.7 -3.77

-33.5 -3.95

-34.1 -4.11

-34.5 -4.25

-34.8 -4.38

-34.7 -4.47

,a#le 6. I vs. ' bias for ne$ative bias


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0ra1h 3 @ Mraph of I vs. ' bias

Ciscussion

(ince $ettin$ impedance matchin$ ith device and load resistor is an inte$ral part in currentmeasurementB the value of the load resistor should be comparable to the diode resistance. If the valueis too hi$h the resistor ill dominate and diode current ill not be seen in for ard bias. If the value istoo volta$e drop across load ill be too small to measure.

!dditional Aomments

In takin$ the volta$e readin$s hile varyin$ frequencyB e found that utilizin$ the Lock in amplifiers

built in frequency s eep function. It as much less time consumin$ than the manual method.9o ever one must take into consideration some important factors in the lock in settin$s. First is tochoose a $ood time constant so that the readin$ resolution is reportable. In our case e used & ms.!lso the sample rate should be comparably hi$h to $et a smoother $raph. Ge used ,& 9z. This is a

partial employment of the A-' measurement method utilized in the lab. Ge ere unable to locate a pro$rammable CA source to utilize the same methodolo$y for I-' measurement.

Modern Physics Lab-dimuthu

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