Photoacoustic study of the effect of doping

PROOF COPY 03130SJOE

Photoacoustic study of the effect of doping

concentration on the transport properties of GaAs epitaxial layers

Sajan D. George S.Dilna

R. Prasanth

Abstract. We report a photoacoustic (PA) study of the thermal and transport properties of a GaAs epitaxial layer doped with SI at varying P. Radhakrishnan

C. P. G. Vallabhan V. P. N. Nampoori

Cochin University of Science and Technology

International School of Photonics Cochin-682 022, India

doping concentration, grown on GaAs substrate by molecular beam ep- itaxy. The data are analyzed on the basis of Rosencwaig and Ge!'sho's theory of the PA effect. The amplitude of the PA signal gives information about various heat generation mechanisms in semiconductors. The~·

perimental data obtained from the measurement of the PA signal as a function of modulation frequency in a heat transmission configuration

ilF' "1;

^{were fitted} with the phase of PA signal obtained from the theoretical E-mail: sajan@cusat.ac.in '~../i!1 model evaluated by considering four parameters-viz., thermal diffusiv·

':"';':i?~~ ity, diffusion coefficient, nonradiative recombination time, and surface 01 .. 4 recombination velocity-as adjustable parameters. It is seen from the

··;·~";;S7'· .. :.1i;, analysis that the photoacoustic technique is sensitive to the changes in

~'~, ~the surface states depend on the doping concentration. The study dem- ',' onstrates the effectiveness of the photoacoustic technique as a noninva-

'~6,and nondestructive method to measure and evaluate the thermal

;Hind li'ansport properties of epitaxial layers. © 2003 Sodety of Pfroto-Opttti

'0. ' . lion Engineers. [001: 10.1117/1.1564101) -.~~.

t~: photoacoustics; semioonductors; thermal and transport propel- .' ^~::.

~ .:-:

Paper

~286.~ived

Jul. 5, 2002; revised manuscript received Oct. 28, 2002;

accepted for pubJtCation Od. 28, 2002.

p.,<~--:~.z .

1 Introduction

In recent years, the laser-induced photoacoustic (PA) tech- nique has been effectively employed to characterize semi- conductor materials because of its versatility as a nonde- structive and noninvasive method fOT the evaluation of material parameters. HO All the photothermal methods are based on the detection, by one means or other, of thermal waves generated in the sample after excitation with modu- )ated optical radiation. In the simple and elegant PA tech- nique these thermal waves produce density fluctuations in the specimen and the surrounding medium, which can be detected either by a sensitive microphone or by a piezoelec- tric transducer.

In the past, much work has been done in the character- ization of both direct- and indirect-bandgap semiconductors using the PA technique.⁵-7 A detailed discussion of the con- tribution of various factors to the thermal flux in semicon- ductors under periodic optical excitation is given by Pinto Neto et a\.6 Dramicanin et al.⁷ gave an analytical solution for various factors contributing to heat generation in semi- conductors that has resulted in a major renaissance in the application of the PA etl'ect to the characterization of trans- port properties of semiconductors. However, not much work has been done to study the influence of doping con- centration on the thermal and transport properties of epi- taxially grown semiconductor layers. Some of the recent investigations show that doping can definitely influence the

OQt Eng. 42(5) 1-0 (May 2003)

PROOF COPV-03130SJOE 0091·328612003/$15.00

. fF'",.·.,

therm~l.piff~ivity and surface recombination velocity of compJ\:lfid semiconductors.⁹-12

In thiS!: ,,""" e present the results of our PA mea.swe- ial layer of GaAs doped with different i~. wn on a GaAs substrate by molecu-

< .' • Amplitude of the PA signal gives

a clear picture 0 . • OIlS heat generation mechanisms in semiconductors. ':; ~ of the PA signal is fitted with the theoretical model

ro--

w<'ihg the thermal diffusivity. dif·

fusion coefficient, surf'ac~:recqwbination velocity, and DOlI-

radiative recombination tU;nlf-"~iJdjustable parameters ^It) solve the heat diffusion equatjrin. -'''.-_'-~ .;-';"

''::-'

2 Experimental Setup ^{. .. {j/ ,}

A schematic representation of the ()pen photoacoustic ccU (Ope) used here is given in Fig. ). Optical radiation from an argon ion laser at 488 run (Liconix 5000) is used as die source of excitation, which is intensity-modulated using.

mechanical chopper (Stanford Research Systems SR 540) before it reaches the sample surface. Detection of the PA signal in the cavity is made using a sensitive electret mi·

crophone (Knowles BT 1754). Details of the PA cell are explained elsewhere.¹³ The cell has flat response in the fre·

quency range 40 to 4000 Hz. The phase of the photoacous- tic signal is measured using a dual-phase digital lock-in amplifier (Stanford Research Systems SR 830), which is highly sensitive and can read a change of 0.0) deg in pIwt angle, which corresponds to a very a small variation in 724

© 2003 Society of Photo-Optical Instrumentation Engineers

fa,30SJOE

Geofve et al.: Photoaooustic study ...

Incident Chopped Radiation

..

Sample Gas

1=1, ". -I,

1 AAceII geometry for th ~mission configuration.

#):~)

,frequency (-2Hz), so thit

IIta

obtained have degree of accuracy. The I po,i"'er used for the wdies is 50 mW with a Stabl ltY.of<r±O.5%. The

. II!e fixed on the OPe using vac@'m 'ase at the awl the illumination by periodically"m' ~ light

1111 the exposed portion of the sampl . "\

samples used for the present investigation are Si- GaAs epitaxiallayers grown on GaAs subs .""..

J

4OO,IIJTl by MBE. The epitaxiallayers hav 'thicS Ilf 10.25, 3, and 2 p.m, and the respective·

'005 are 2X 10¹⁴, 2X 10¹⁶, and 2X 10¹⁸ cm-

n properties of Ge-doped GaAs epitaxiallayers llready been treated using the monolayer rion.1O The differences between the two-layer ap- . and the monolayer method for photothermal

. IS are apparent only at high frequencies,14 viz., in iralreds of kilohertz. Hence our semiconductor can be explained in tenns of thennal piston model waig and Gersho,15 according to which, the pres- kIuaIions in the PA cell due to periodic heating of

are given by

(1)

PdTo) is the ambient pressure (temperature), Ig is kD!Ibofthe gas chamber, ug=(l+j)ag , where ag .':~/2= 11 IL_{g ,} with ILg the thennal diffusion length ps with thermal diffusivity a g' and

e

the sample e fluctuation at the sample-gas interface (x ,.!Jso, ^(J)= 2

'Trl,

where

I

is the modulation frequency.

iille remaining sections we are considering the PA cell for the heat tmnsmission configumtion shown . Iy in Fig. I. The temperature fluctuation e can itlioed from the solution of the thennal diffusion equa-

!l'Ien by ': I aT Q(x,t)

. : - - - - -

~ It, .J/ k, ⁽²⁾

~a, (k,) is the sample thennal diffusivity (conductiv-

.m

Q(x,t) is the heat power density generated in the

OpticajEngi'leering. Vol. 42 No. 5, May 2003 )'Y 031305JOE

sample due to absorption of the intensity-modulated laser radiation. In semiconductors, if the incident energy is greater than the bandgap of the semiconductor, then ther- mal power density Q(x,t) mainly arises from three differ- ent processes.

1. The thennalization component arises from fast non- mdiative intraband transitions in the conduction band of semiconductors. This occurs mainly due to the e1ectron-phonon interaction, which happens typically on the time scale of picoseconds. Hence this process can be taken as instantaneous for the modulation fre- quencies usually used in the photoacoustic experi- ment. The heat power density due to this process is denoted by

(3) where

fi

is the optical absorption coefficient for pho- tons having energy E, incident at x= -Is with an intensity 10 (W /crrh

2. The second component is due to the recombination of the photoexcited carriers in the bulk of the material after they travel a finite distance (D1") Ill, where D is the carrier diffusion coefficient and 1" is the recombi- nation time. The heat power density due to nonmdi- ative bulk recombination is given by

(4) .'~ n(x ,I) is the density of the photoexcited car-

"nrat:,,-";.~ -t.::," W

3. T~ dlfuadiative recombination of the photoexcited

CarTre

surface of the material also contributes to the . power density, and it is given by

where Vo is heating surface velocity at the sa From the above analysis,

(5) recombination velocity at the is the surface recombination

interface at x =

o.

to Eq. (2) depends on the de which obeys the carrier diffusion,

ious that the solution

" toexcited carriers, ion, namely,

an a

^{2n n fiIo} ~ ^.

-a =D-.;::ra - -

+

-h exp(x+I.) e'w/-vn (x,I)8(x)

t x T V

-Vane -1,,1)8(x+I.). (6)

For 488-nm mdiation from an argon ion laser we can assume that all the incident radiation is absorbed at the x

= -I, surface, so that we can replace ,BIa exp[,8(x+I,,)] in Eqs. (3) and (6) by Io(x

+

I,). Since the thennal conductiv- ity of the surrounding air is very small, we neglect the diffusion of heat into it. Then the solution of the coupled equations (2) and (6) leads to the expression for pressure

~5ctuations for the thennally thick sample as

PROOF copy 03130SJOE

George et a!.: Photoacoustic study ...

2e1oPo

[8-1

OP= T I k --exp( -Isu,) o gUg sUs 8

+ ;~~( U;~ ⁱ

^{+ ::)], (7)}

where u_s=(1 +j)a" a.=('TTf/a.)I12=(lIJL.) with JL. the thennal diffusion length of the sample, 1'=[(1 + jwr)IDr]l12 is the carrier diffusion coefficient, ⁸

=Eglhv, r=uIDy, ro=UoIDy, and

I .

(8)

--:i"

In the experimental frequency T, . - ";~ here, W T« 1, so that F, r, ro become real cons .o·';ependent of the modulation frequency. [t is reportCld. ".~ to Neto et al.⁶ that the

ope

signal for a semiconducf9JSJfnjl.!e in the ther- mally thick region is essentially detemifu~!J~Y"'" adiative recombination. Thus the expression for t'lie fluc- tuation in the experimental frequency range"' ilih w T

~1 is given by ,.,

2efoPoF

(I

^UT)

oP=

^-=r-2

+ - ,

Tolgk.DYTug ^{U. - Y-} u.

and the phase of the OPe signal is given by 4>= -+414> 'TT

2 '

where

(aDlv)(WTctl-+ 1) tan 414>= (aDlu)(1-wT_elT)-I-(wr_eff)2

with Ter7{(Dla.)-1]'

(I 0)

(11)

We took the thennal diffusivity, diffusion coefficient, surface recombination velocity, and relaxation time as ad- justable parameters, and then we fitted the variable part of

Eq. (10) to the experimentally obtained phase angle 414>.

4 Results and Discussion

Log-log plots of the amplitude of the PA signal against chopping frequency for the samples under investigation are given in Fig. 2. The three different heat generation mecha- nisms are evident from the figure. In the low chopping- frequency range, thennalization is the dominating proc.css in heat generation, followed by bulk and surface recombi- nation of photoexcited carriers, respectively. Figure 3 shows the best theoretical fit to the experimentally obtained phase of the photoacoustic signal. TIle values obtained as the best fitting parameters for the theoretical model is given in Table I. The fitting program fol1ows essentially the least- squares method developed using MATLAB. The fitting analysis resulted in the fol1owing accuracy of the fitted pa- rameters: thennal diffusivity ±2%, diffusion coefficient ± 5%, nonradiative recombination time ±3%, and surface re- combination velocity ±8%. It is seen from the figure that there is a minimum in the phase plot of all the specimens

PROOF COPY 03130SJOE

10

100 1000

Frequency (Hz)

Fig. 2 log-log plot of PA amplitude against chopping frequency.

under investigation. Many authors have attributed this change in shape as due to the change in heat generation mechanism in semiconductors from bulk nonradiative re- combination to surface recombination of photoexcited carriers.⁶ From the present studies, it is seen that the fre·

quenc9' at which the phase data show a minimum changes with the concentration of dopant. This may be due to the increase in recombination centers with increase in doping , ncentration, which in turn enhances heat generation due

ulk recombination.

t=

i:iS seen from Ta~le 1 ~t ?te thennal diffus~vilY of the s . n under conslderatton IS less than that of the earlier

" rted bulk GaAs sample.⁶ Thennal diffusivity is an im·

portaf\~; ophysical parameter, which detemlines the distri .',. 9..t,temperature in systems where heat How 0c-

curs. '¥Sr~orted earlier that the thennal diffusivity in semicondud'~orr~~ .. ,; s can deviate from the corresponding values in the. .. , l1terial.¹² It is seen clearly from Table I that the the . a . ivity of the epitaxial layer decreases with increase . :2c,.7

RiA

concentration. In semiconductoo heat is transporte4f1»);'""~th phonons and charge carriers.

;';~'1;';

48~---~~--~---~ ~~

~~~"::;~~~\

-49 -50

-- ^a.- _•

-51 ⁵²

"'0 - - -53

:

_111-54

.c D._

55

·57 300

7'~ :?

f~;~~[~:.'C.~J .•

400 500 600 100

Frequency (Hz)

Fig. 3 ope phase angle versus modulation frequency for !he samples under investigation. The solid lines represents the fits 01 r~ (10) to the data.

Optical Engineering, Vol. 42 No. 5, May 2003

tD31305JOE

George et al.: Photoacoustic study ...

I Thermal and transport properties of GaAs epitaxial layers . doping concentrations of Si.

2 3

1025 3 2

400 400 400

2 X 10¹⁴ 2x 10¹⁸ 2x 10¹⁸ 0.26 0.23 0.21

5.2 4.9 4.5

415 476 525

11.2 9.8 7

CODtribution to

thennal~ii:d~~~ivity

from phonons greater than that from cawet§~'c~peciaJ1y for car-

ions less than 10²⁰ 'i:qi:c³• lPe decrease in diffusivity can be explained iD, teri1ls of the domi-

contribution. Phonon scatteri'ini'ti'a)l:ey source

~llI:'ion processes and .Iimits theeyrforpance of me and optoelectromc devices, A'tldi®n of the which can be considered as point deteds, en- . ~e scattering of phonons, which results in a reduc- pIIonon mean free path and consequently a deCfe~k ihamal conductivity. It is shown in Ref 16 thal

the.

_aJ

conductivity k is governed by the i~ttjt(t resistivity W through the relation k= lIW= AT';',~.

K, n= 1.25 for GaAs, and A is a parameter that with increase in doping concentration. Since the diffusivity and thennal conductivity are directly re-

~I)Qcll other through a = k/ pc, where p is the density

kis the specific heat, the reduction in thennal conduc-

~lrilh increased doping concentration directly leads to . . value for the thermal diffusivity.

~ diffusion coefficient of a semiconductor is a very . . quantity, which detennines the distance traveled iI ~toexcited carriers before their recombination. It

D fiom the values obtained for the diffusion coeffi- IIiIaI it is not the ambipolar transport but the diffusion limt of minority carriers that essentially detennines l\ signal generation. This means that at an incident

~ of 50 mW, the photoinduced carrier population is iI!1llhe impurity concentration. It is also seen from the ,~the diffusion coefficient decreases with increase '08 concentration. The diffusion coefficient is di- Iltlaled to the mobility of carriers through the Ein- :dation D=kTp./e, where k is the Boltzmann con- T ~ the temperature, e is the carrier charge, and p. is

mer

mobility. At a constant temperature, the diffusion genl is es..~entially determined by the mobility of pho- ld carriers. The mobility of holes decreases with in-

: I1l doping concentration, wh ich results in a reduced ,f!he diffusion coefficient.

~itiOfJS of dopants have a strong influence on surface 'l)'. The dopanlS act as scattering cenlers, which ilctcrioration in the transport properties of the photo- J earners. Onc of the effects of incorporation of dop- me generation of macro steps (terraces), and the ol macrosteps give rise to striation. It was reported lbat the surface recombination velocity of the pho- t.! carners increases with increase in doping coneen-

~icai Engineering, Vol. 42 No, 5, May 2003 f03130SJOE

tration of Ge on an epitaxial layer of GaAs, 10 which agrees with our experimental result. It can be understood from the relation ^{j I =} uvrtli.1 (where U is the capture cross section for the photoexcited carriers, ^jlth is the thennal velocity of the photoexcited carriers, and N SI is the number of trapping centers per unit area) that the surface recombination veloc- ity is directly proportional to the density of surface trapping centers. The number of trapping eenters for the photoex- cited carriers at the surface of the epitaxial layer increases with doping, leading to an increase in the surface recombi- nation velocity, which is in agreement with our experimen- tal result.

The doping concentration influences the recombination time of the photoexcited carriers. It is important to point out that the photoacoustic signal is very sensitive to the carrier lifetime, so that the proper choice of this parameter is a significant step in the simulation process. The total carrier lifetime depends on various recombination pro- cesses. ]n the indirect-bandgap semiconductors like Si, nonradiative recombination is the dominant process, whereas in the direct-bandgap semiconductors like GaAs, radiative recombination dominates. Hence the evaluation of nonradiative recombination in GaAs and the study of varia- tion of the nonradiative recombination time with doping have great physical significance, especially with respect to design and fabrication of semiconductor light sources. It is

;' seen from our experiment that the recombination time de-

" -,,,reases with increase in doping concentration. This is be- :t;f'~1Se the recombination time is directly related to the mo- . ·<t.\;b111t)' of the photoexcited carriers. Since the mobility of

cam~ decreases with increase in doping concentration, t;pCtCcombination time also decreases with increase in dop- ing con~mration. Our values for the recombination time are ~Ii ,.Within the range of earlier reported values for doped'simples.⁶

]n co~(:luSion, we have demonstrated in this paper the capabili.yof t1l~:PA technique in general and OPe detec- tion in particular to~'study the thennal and transport proper- ties of photo~dted .carriers in layered semiconductor structures. We hiivejnv~tigated the influence of doping on the thermal and traitsp6ft pr()perties of the epitaxiallayer of GaAs doped with Si

C!f

w.nous concentrations, using ther- mal wave transmissioihlljd de!!;ction technique. From the analysis of experimental data;fit is obvious that the thennal diffusivity of epitaxial laye~Pdeil~ses with increase in doping concentration. It is 1iIt'~w~~)s<;en that the diffusion coefficient of the minority cameitj4~ses with increase in doping concentration, which fitl~\ie

fo

the reduction in the mobility of carriers with doping: Doping also influences the surface recombination velocity and the nonradiative re- combination time. The surface recombination velocity of the photoexcited carriers increases with increasing doping concentration, whereas the nonradiative recombination time decreases. This paper shows that the PA technique in the transmission detection configuration is a simple and effec- tive method for the study of thermal anti transport proper- ties in semiconductors.

Acknowledgments

This work is suppolted by Netherlands University Federa- tion for International Collaboralion (NUFFIC). The authors

~9h to thank Prof. 1. H. Wolter and Prof. J. E. M.

PROOF COPY 03130SJOE

Geofge et ill.: PhoIoacousIic study .

Haverkort (COBRA group, Technical University of Eiod·

hoven, the Netherlands) for the semiconductor samples. Sa·

jan D. George wishes to acknowledge the Council of Sci·

entific and Industrial Research, New Delhi for providing financial assistance. S. Dilna acknowledges the Department of Science and Technology, India, for her research fellow·

ship. V. P. N. Nampoori thanks the UGC for financial as·

sistance through a research award program.

References

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2.

,.

4.

S.

•

7.

S.

9.

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A. ~;~~:~'~i

.;";:Ed. ,

PholQUCQuslic and 17ttmnuJ w""" P~ ilt

~ Elxvier Scienti~c, North--Holland, New Yort.

" . ~=;~~_~~-::'- i"~tr.s'~!4~~~~,~~:r..;,;',;.~;;

(1999).

13. N. A. Gcort!e and Ymayaluishnan, .. Photoacoustic ewl..ation of!her- mal difYiuiviry of coo;onu( $hell:' J. P"y~.: COIJdrnJ. Malln" 14, 4S09-4SI3 (2002).

14. C. Cbri3lOfides, F. DiakOGOS, A. Seas, A. ChriSUlu, M. Nestoros, and A. M&lldel~ "Two-layer model for photomadullted thermorefIoc- tancc studies on semiconducton.," J. AppI. PIry3. 10(3), I7IS-lnS (19%).

IS. A. Rosc/lCWllig and A. Gcnbo, "Theory ofphotoa<::ousti<: cffect with solids," J. App!. PIryt. 47(1), &4-69 (1976).

16. S. Adachi, PhysiaJl P"'fWnia oflll-V Semiconduc:/Ot"

eo.r..--IJ,

^p.

59. John Wilcy and Sons., New Yort..

PROOF COPY 031305JDE

Slljlln D. G.orge, received tis MSc degree in physics with specialization WI electronics from the University of Keraia, India, in 1998. He is CUlTently a researth feIow wor1Ung towa/"ds his PhD degree al the II)- temational School of PhoIonic$, Cochin UniYBlSity 01 Sdenc.a and TBCtw"IoIogy, Ill- dla. His researdllnterests indude thennal and optical dliIroclerization 01 various ma-

lerials such as compound semicotldudots, supel1altices, liquid ay5tal$, and ceramics using photothermal techniques.

S. Dllna received her MSc degree In ~

k:s -Mth spedaUation in Quanlum eIecta\- k:s from Cochin University 01 SciMce an!

TedtooIogy, India. in 2000. She is tuIIrtr a research fellow working toward$ her PNl d8gnMt 8t the International School 0/ f'W.

tonics, Cochin University 01 ScienoI n Technology, India. H8f research inlerISI i'I- dudes laser-prtl(luced pla_, 1IsIr·

induced ablation in materials. and pIICb

!henna! ima!jng.

R. Prannth received his MSc ~ n physics with specialization In eIectJtrics from !ha Uniwfsily 01 KenIIa. India. n

1995. and his MTech degree in DJItOeIIC-

Ironies and laser tBdvlology at Codlin I.ft.

versify 01 Scienca and Toctlnoiogy,lncia.iI 1998. Presently, he is wor1ting towards his PhD in a joint projed between Ihe TI!Id6 cal University of Eindhoven and blnW·

national School 01 Photor»cs. His rfleIWd1 interest indud8s S8I'l1icooductor IWIfIOSIM.

ItM"8S and 1as8f-matt8f il'\l"8faCtion$.

P. RIodhakrishnan leceived hi$ MSI; de- gree in physics from the UniYtrsily cl Kerala In , 9n, and his PhD degffle frtn Cochin Univefsity 01 Science and TectnoI- ogt in '986. He has been a ieclurw ath Cochin College from 1979 to 1988. Pres- ently he is a professor at the tn\wllalilnl School 01 PhoIonics, Cochin ~ cl Science and Technology. He Is a fIIII'IW

or

the executille c:ommittee 0I1he I'1"Iom , liIS8I" spectroscopy. and libel" optic ....

70 journal papetS III these . . .

C. P. GlrljavaUabhan reaIived ~ ~

and PhD degrees in 1965 and 1971, It- spvdiveIy. from l.IniYersity 01 KenU, nil.

and did his postdodoral resea-ct\.

Southampton L.JrWversity in Un!ted Iq- . He was also a visiting proIessor;l\

1/\SliMe. Freiberg, Germa'lJ

Is the dean of !he

.

FaoAy cl

^...

v. P . !" NN'~,~::;~,

M S UnIvefSty. ^received tU MSc'" ~

respediveIy'. He Is CU"

at the lnterIIaIiIN

""""" U .... ' " " , , I

renlly a

...

^~

....,~

general secretary of

01 India. His resean;h intBfesl$

photothermill methods. nuorescence SI*"

trosoopy, oonIinear optics. fibBr optics, n ias8l"-ptOduced pla$ffi3s. He has ~ more lhan 200 joumal papers in these areas.

728

Optical Enginearing. VOl. 42 No. 5. May 2003