FREQUENCY CHARACTERISTICS: A SOURCE OF INFORMATION IN PHOTOACOUSTICS Mirosław Maliński Department...

FREQUENCY CHARACTERISTICS: A SOURCE OF INFORMATION IN

PHOTOACOUSTICS

Mirosław MalińskiDepartment of Electronics and Computer

StudiesTechnical Univeristy of Koszalin, Poland

Contents

IntroductionMultilayer optically opaque systemsOptically semitransparent systemsDetermination of thermal parametersDetermination of recombination parametersAir-tightness measurements of packagings

Introduction

Photoacoustics uses frequency amplitude and phase characteristics of the FA signal for determination of several parameters of samples such as:

thermal diffusivity and effusivity of the material,thickness of thin films, detection of delaminations or voids in layer systems, determination of recombination parameters of carriers, air-tightness of packagings and others.

This presentation is limited to the analysis of frequency domain FA characteristics measured with a microphone or piezoelectric methods

Temperature spatial distribution

),,,,,(),,,,,())2exp(1(2

0),,,,,( RlfxNRlfxMlR

IRlfxT

))exp(())exp(()exp()exp()2exp(

))exp(())exp(()exp()exp(),,,,,(

lxxxlR

lxxxRlfxM

))exp((1)2exp()exp(

))exp((1)2exp()exp(),,,,,(

xxlRx

xxlRxRlfxN

2/1/)1(),( fif

Photoacoustic signals

Microphone detection

Piezoelectric detection

),(

,,,,,02

f

RlfxTSF

ll

dxRlfxTxl

ldxRlfxT

lS

0

2

0

),,,,,(2

6),,,,,(

1

),(

,,,,,2

f

RlflxTSR

Experimental set-up

SAMPLE

DRIVER

PHOTOACOUSTIC CHAMBER

MICROPHONE

LOCK-IN AMPLIFIER

MODULATOR

SOURCE OF LIGHT

LENS

MONOCHROMATOR

LENS

PREAMPLIFIER

PC

Multilayer optically opaque systems

TF TR

1 2 3


4321

4321

11

0

MMMM

LLLLITF

4321

132312

11

0 )1)(1)(1(

MMMM

RRRITR

)cosh()cosh()cosh(111 3322111323121 lllRRRL

)cosh()sinh()sinh(111 3322111323122 lllRRRL

)sinh()sinh()cosh(111 3322111323123 lllRRRL

)sinh()cosh()sinh(111 3322111323124 lllRRRL

)cosh()cosh()sinh(111 3322111323121 lllRRRM

)cosh()sinh()cosh(111 3322111323122 lllRRRM

)sinh()sinh()sinh(111 3322111323123 lllRRRM

)sinh()cosh()cosh(111 3322111323124 lllRRRM


Theoretical frequency domain dependencies of a phase of a photoacoustic signal for a transistor structure of a thickness l1=230 m, a lead frame of the thickness l3=350 m for different values of air delaminations: 1– 0.025 m, 2– 0.05 m, 3– 0.075 m, 4– 0.1 m, 5– 0.15 m, 6– 0.2 m.

6 5

4

3

2

1

10 100 1 10 3 110

100

90

80

FREQUENCY [Hz]

PH

AS

E [

deg]


Correlation of the phase of the PA signal and the force of detachment of the transistor structure from a lead frame. Solid line is a theoretical curve, circles are experimental points, BC 237 transistor structures

Phase(S) = (180/)arg (S1( d2 = 0 m)p + S2(d2 = 0.1 m)(1-p) )Force necessary for detachment is proportional to the parameter p

PHASE [deg] -70 -75 -80 -85 -90 -95 -100

FO

RC

E [

N]

12

10

8

6

4

2


Frequency characteristics of water on an aluminum plate of the thickness 40 m. Description: line 1 – R = 1(air), line 2 – R = 0.905 (water), line 3 – R = 0.75, circles and boxes are experimental results. Frequency characteristics of ethanol on an aluminum plate of the thickness 40 m. Description: line 1 – R = 1 (air), line 2 – R = 0.95 (ethanol), line 3 – R = 0.75, circles and boxes are experimental results.

FREQUENCY [Hz]

10 15 20 25 30

5.2

3.9

2.6

1.3

0

AM

PLIT

UD

E [a

.u.]

1

2

3

FREQUENCY [Hz]

10 15 20 25 30

5.2

3.9

2.6

1.3

0

AM

PLIT

UD

E [a

.u.]

1

2

3

Optically semitransparent systems

Schematic diagram of a thin semitransparent layer on the semitransparent backing Application – characterization of thin semiconductor films on semiconductor thick substrates

l2 l1 X 0

TF

I0


2222111211

122110

11

1111112

11

111

111211

01

)(

)()(

)(

)(

)(

)(

)(

)exp()exp(1exp

exp12exp

exp1

2exp1

hlRlRhlI

h

lhlR

h

lh

lR

IhTF


Amplitude and phase photoacoustic frequency characteristics of a l1= 10 m thick layer on the thick substrate. Parameters taken for computations: 1=0 cm-1 , 2=10000 cm-1 (solid line), 1=104 cm-1, 2=103 cm-1 ( dash line), 1=0.3 cm2/s, 2=0.9 cm2/s, GaAs/Si

100 200 300 400 5000

0.1

0.2

0.3

0.4

FREQUENCY [Hz]

AM

PL

ITU

DE

[a.

u]

100 200 300 400 500100

80

60

40

FREQUENCY [Hz}

PH

AS

E [

degs

]


Application of the frequency characteristics for detection of the thickness SCL in semiconductorsComparison of the amplitude spectra and frequency characteristicsSCL- is the subsurface layer of the semiconductor where light is absorbed but does not give the contribution to the FA signal


Theoretical characteristics presenting the predicted influence of a SCL on the photoacoustic amplitude and phase characteristics in the front configuration. Parameters: =0.01 cm2/s, thickness of the layer l1=5 m – dash line, l1=10 m – dotted line, l1=15 m – solid line, 1=0 cm-1, 2=1000 cm-1, R12=0.

0 500 10000.2

0.4

0.6

0.8

FREQUENCY [Hz]

AM

PL

ITU

DE

RA

TIO

[1]

0 200 400 600 800 1000

40

20

0

FREQUENCY [Hz]

PH

AS

E S

HIF

T [

degs

]


The phase frequency characteristics of the PS/Si structure in the reflection configuration. Diamonds and circles are for exc=514 nm and exc=670 nm. Parameters of PS layer =0.016cm2/s, kc=0.0042 cal(cmKs)-1, 1(514nm)=1900 cm-1, 1(670nm)=903 cm-1.M.Maliński, L.Bychto, A.Patryn, J.Gibkes, B.K.Bein, J.Pelzl ‘Investigations of the optical and thermal parameters of porous silicon layers with the two wavelength photoacoustic method’ J.de Physique IV France (2005) accepted.

1 10 100 1 10 3

1 10 4 150

100

50

FREQUENCY [Hz]

PHA

SE [

DE

G]

Determination of thermal parameters

R

lRlRl

1

)exp()exp(),sinRh(

R

lRlRl

1

)exp()exp(),cosRh(

),sinRh(

,,,2 Rl

IRflS r

r

1

),(sin

)),(cos1(3)1/()1(2),,,(

2 RlRhl

RlRhRR

l

IRflPr


ZnSe crystal l = 0.081 cm =0.01 cm2/s ( solid line), = 0.05 cm2/s, 0.1 cm2/s , 0.2 cm2/s.Zn0.83Be0.17Se l=0.1161 cm =0.05 cm2/s, =0.01 cm2/s, =0.1 cm2/s and = 0.2 cm2/sM.Maliński, J.Zakrzewski ‘Advances in photoacoustics and photothermal spectroscopy of semiconductors’ OSA’ 04 Conference Sobieszewo Poland

20 40 60 80 100 120 140 0

20

40

60

80

100

FREQUENCY [Hz]

PHA

SE [

deg]

20 40 60 80 100 120 140 0

20

40

60

80

100

FREQUENCY [Hz]

PHA

SE [d

eg]


Si sample l=240m and =0.6 cm2/s. Description of lines: line 1 – R = 1, line 2 – R = 0.9, line 3 – R = 0.76, line 4 – R = 0.5. Circles and diamonds are experimental lines, lines are theoretical curves.

0 50 100 150 150

140

130

120

110

100

FREQUENCY [Hz]

PHA

SE [

degs

]

1

2

3

4


Dependance of the thermal conductivity of SiGe on the composition

CONCENTRATION of Si in SiGe

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

100

80

60

40

20

0

TH

ER

MA

L C

ON

DU

CT

IVIT

Y

[W

/mK

]

Determination of recombination parameters in TWI-PW model

bggSRbggNRR

bggTbgg

VVfDlEExVVfDlEEx

VVfDlEExVVfDlEEx

,,,,,,,,,,,,,,,,,,

,,,,,,,,,,,,,,,,,,

d

x

xg

T dzxzWzdzxzWzdE

IEEx ,exp,exp

2exp12 20

1

0

d

x

xg

NRR dzxzWzndzxzWznd

IEx ,,

2exp1 20

1

0

xdWdnVxWnVd

IEx bg

g

SR ,,002exp1 21

0

xzdxzxzdzxxzW 2expexp2expexp,1

xzdxzdxzxzxzW 2exp2expexpexp,2

Determination of recombination parameters

Computations of Ge samples: = 0.4 cm2/s, l = 0.1 cm, = 2010-6 s, D = 44 cm2/s, V = 500 cm/s a) = 0.110-6 s and D = 22 cm2/s b).

Rys 1

10 100 1 103

1 104

1 105

1 104

1 103

0.01

0.1

1

FREQUENCY [Hz]

AM

PL

ITU

DE

[a.

u.]

Rys 1

10 100 1 103

1 104

1 106

1 105

1 104

1 103

0.01

0.1

1

FREQUENCY [Hz]

AM

PL

ITU

DE

[a.

u.]

Determination of recombination parameters

Si: =0.37 cm2/s, L=0.1 cm, E1=2.0 eV, E2=1.4 eV, Eg=1.1 eV, D=44 cm2/s, V=800 cm/s, = 100 s

10 100 1 1030.5

1

1.5

2

2.5

3

3.5

FREQUENCY [Hz]

AM

PL

ITU

DE

R

AT

IO

[a.u

.]

10 100 1 10350

0

50

100

FREQUENCY [Hz]P

HA

SE

S

HIF

T [

degs

]

Air-tightness measurements

S

C

T2

T1 V1

V2 M C - chip S - substrate H - hole M - microphone

H

Power Generator

Preamplifier

PC

Lockin MC500

PA Chamber


Parameters taken for computation: = 1710-6 [Ns/m2], L = 6-4 [m], M = 2810-3 [kg/mole], V2 = 2.1610-6 [m3], V2/V1 = 3.19, r = 20 m...60 m, = 1.3 [kg/m3], Na = 610-23 [mole-1], T = 300 K, k = 1.3810-23 [J/K].

E

-UZ +UZ +UZ

+ _

-UZ

U2

TC

MIC

OA

RCCiCC

CC

)(U

(R)URAm

21

2

21

21

2

2

)(

)(

0)(

4

8

r

LR

TkN

VMC

a

i

i


1) r = 108m; 2) r = 91m;3) r = 78m; 4) r = 69m; 5) r = 42m; 6) r =24m;1) r = 115m; 2) r = 86m; 3) r = 83m; 4) r = 71m; 5) r = 50m; 6) r = 24m;

10 100 log (f)

1

2

4

5

3

6

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

AM

PL

ITU

DE

R

AT

IO

[1]

10 100 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

log (f) A

MP

LIT

UD

E

RA

TIO

[1

]

5

4

3

1

2

6

L.Majchrzak, M.Maliński ‘Analysis of a Thermoacoustic Approach for the Evaluation of Hermeticity of Packaging of Electronic Devices’ XXIV IMAPS Poland Conf 2005

Air-tightness measurements - theory

211

2

21

1121

2

1)(

CCRCCi

CRiGGU

21

11

11 A

APT

21

12

1

APT 2/1

11 )()( iTG 2/1

22 )()( iTG

)cosh()sinh(

)sinh(1

)cosh()(

iiiiii

ii

ii

iii

dd

ddA

Silicon Chip

A(1)

Substrate

A(2) T1 P1 T2

G1T1

(i)1/2 G2

T2(i)1/2

C1 C2 R1 U2

21 AAA

L.Bychto, M.Maliński ‘Determination of air-tightness of the packagings’ submited to AAuA 2005


Silicon layer: d1=0.08[cm], 1=1.2[W/cmK],=0.6[cm2/s]

Substrate (copper): d2=0.2[cm], 2=3.9[W/cmK],=1.1[cm2/s]

Radius of holes: 1- 50m, 2- 30m, 3- 10m, 4- 5m, 5- 1m

10 100 1 1031 10

9

1 108

1 107

1 106

1 105

1 104

1 103

0.01

0.1

1

Frequency [Hz]

Nor

mal

ized

Am

plit

ude

[a.u

.]

1 2

3

4

5

0 5 10 15 20400

300

200

100

0

Frequency [Hz]

Nor

mal

ized

Pha

se [

deg]

1 2 3

4

Conclusions

Frequency FA characteristics are a useful tool bringing information about:Multilayer optically opaque systemsOptically semitransparent systemsThermal parametersRecombination parameters of carriersAir-tightness of packagings

Thank You for Your attention

FREQUENCY CHARACTERISTICS: A SOURCE OF INFORMATION IN PHOTOACOUSTICS Mirosław Maliński Department...

Documents

Transcript of FREQUENCY CHARACTERISTICS: A SOURCE OF INFORMATION IN PHOTOACOUSTICS Mirosław Maliński Department...