DETERMINATION OF THE OPTICAL PROPERTIES OF GaAs AND InP BY MULTIPLE ANGLE OF INCIDENCE ELLIPSOMETRY

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DETERMINATION OF THE OPTICAL PROPERTIES OF GaAs AND InP BY MULTIPLE ANGLE OF

INCIDENCE ELLIPSOMETRY

H. Dinges

To cite this version:

H. Dinges. DETERMINATION OF THE OPTICAL PROPERTIES OF GaAs AND InP BY MUL-

TIPLE ANGLE OF INCIDENCE ELLIPSOMETRY. Journal de Physique Colloques, 1983, 44 (C10),

pp.C10-39-C10-43. �10.1051/jphyscol:19831007�. �jpa-00223456�

DETERMINATION OF THE OPTICAL PROPERTIES OF GaAs AND InP BY MULTIPLE ANGLE OF INCIDENCE ELLIPSOMETRY

H.W. D i n g e s

F o r s c h m g s i n s t i t u t der Detltschen Bmdespost beim F T Z , 6100 Dannstadt, F.R.G.

R6sumh

-

~~&llipsom&trie plusieurs angles dtincidence 9 a 6t6 u t i l i s 6 e p o u r d 6 t e r m i n e r l e s constantesoptiquesde GaAs etde InP. Cette mbthode n'a jusqulici 6th appliquhe ni 2 GaAs ni $

InP. Les quotients normalises des premidres dkrivhes de A par rapport aux constantes optiques sont calcul6s pour GaAs et InP. I1 est dhmontrh que c'gst seulement dans la gamme 6troite de 41 entre 7i0 et 77

,

pour des longueurs dtonde entre 436 et 870 nm, qu9il n'existe pas de corrblation entre les param8tres. Dans cette gamme dlangles, il n'y a, pourune longueur d70nde donnhe, que quelques solutions discr8tes pour les constantes optiques. Pour trouver la solution vraie, il faut effectuer des mesures A des longueurs d'onde differentes, en exigeant que no, et dox restent inchangks. Les rksultats obtenus pour GaAs et InP sont prgsentks.

Abstract

-

Multiple angle of incidence ellipsometry was used forthedetermination of the optical constants of GaAs and

InP. This method has not been applied to GaAs and InP so far.

The normalized ratios of the first derivatives of A with

respect to the optical constants are computed for GaAs and InP.

This computation shows that only in the small rangeof angles of incidence between 72O and 77O at wavelengths between 436 and 870 nm no correlation of parameters occurs. In this range of angles only a few discrete solutions for the optical constants exist for a given wavelength. The physically true solution can be distinguished by measuring at several wavelengths. The solution is made unique by the demand that nox and do, must remain unchanged for the different wavelengths.

-

Experimental results for GaAs and InP are presented.

Introduction

The measured ellipsometrical angles of a surface, measured at one wavelength X and one angle of incidence

+,

are denoted as $ and AM.

The evaluation of the optical constants (n, k) of a semicon8uctor layer covered with its natural oxide (nox, kox, dox) from the values of $M and AM is done using the Fresnel-Drude formulae. This method yields an underdetermined set of equations, since there are only two measured quantities (QM, AM) against five unknown parameters

.. . -

(n, k , no,, do,, kox). Multiple angle of incidence ellipsometry is a possibility to create further equations from which the unknown parameters can be uniquely determined.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19831007

JOURNAL DE PHYSIQUE

Parameter correlation test

Ibrahim and Bashara /I/ have published, that absence of correlation between parameters, indicated by invariance of the normalized ratio of the first derivatives of A, makes it possible to make optimal use of the overdetermined set of equations, which are available from multiple angle measurements. Until 1981 this parameter correlation test had not been applied to GaAs and 1nP covered with their natural oxide layers. We could show /2/ that for @ between 45O and 71° and wavelengths between 436 and 870 nm parameter correlation exists, especially between k and d

.

The optical constants used in this computation were taken fr08~own measurements /3/, which are in very good agreement with those of Aspnes and Studna /4/.

Table 1 shows these correlations for GaAs at X = 633 nm. The nor-

a

^A

a

A

malized derivatives of

-

^{and ;jf;} have very simular values for @

adox

$lo ab/anOx aA/akox aAladox a ~ l a n aalak 4 5 0.1247 0.1885 0.1504 0.0505 0.1529 5 0 0.1672 0.2489 0.2003 0.0723 0.2039 55 0.2271 0.3302 0.2690 0.1076 0.2742 60 0.3207 0.4476 0.3724 0.1738 0.3796 65 0.4974 0.6384 0.555 0.3343 0.5638

70 1.0 1 .O 1 .O 1 .0 1 .O

72 1.603 1.163 1.422 2.11 1.392

7 3 2.201 1.075 1.739 3.499 1.661 74 3.148 0.3212 1.987 6.408 1.789 75 3.732 -2.368 1.227 10.77 0.7939 76 1.843 -4.733 -0.8583 9.425 -1.329 7 7 0.1864 -3.831 -1.465 4.818 -1.755 Table 1: The variation with angle of incidence of the normalized aerivatives of b for GaAs covered with its natural oxide. For computation we took kox 0: nox

-

^{ikox = 1.9}

-

^0.005i,

n

-

^{ik = 3.837}

-

^{0.216i / 3 / and dox = 23.1}

8

between 45O and 70°, but differ increasingly for angles @ between 72O and 77O. For InP we computed the same results. These

correlations also hold for the investigated wavelength range from 436 to 870 nm. For the determination of -k from

aA/adox

ak ⁺ aA/ak adox = 0 (1)

Table 2 yields

aA/adox

aAlak

⁼ 0.0085 between 45' and 70°.

This means, that k(633 nm) = 0.216

-

0.0085 (dox

-

23.1). The

Other values from Table 1.

computational results for both GaAs and InP are summarized in Table 3 for different wavelengths.

GaAs I nP

-

^{. . ..-Ap,} _aAladox

^r

_aA/adox

A/nm _k 131

r

^{k 131}

^a

^Alak

Table 3: Relationship between k and dox at different wavelengths.

The used oxide thicknesses in the computational example are 23.1

8

for GaAs and 18.0 for InP, respectively.

JOURNAL DE PHYSIQUE

From Table 2 we see that for measurements between 72O and 77O no parameter correlation exists with respect to

4.

When measuring at multiple angles in this region only few solutions for the over- determined set of equations should exist /I/.

In order to avoid errors from measurements (e.g. due to surface roughness) we have computed pseudo ellipsometric angles P p , Ap at

different @i using the optical constants of Ref. 131. For the following test these 9 and Ap were taken instead of the measured values. Now the deviation% of these pseudo angles from the theoretical angles 9 , A were computed by varying the values of n, k, and dox.

where the index i denotes different @i. The steps for variation (0.1

8

for dox, 0.0001 for n and k) were chosen so small, that the changes in

9 , A from step to step were smaller than 0.01 degrees. In the

evaluation are taken kox to be zero and nox to be independent of A because the natural oxide layers are very ^~ thin /5/.

In Table 4 we see, that at each wa elength several minima occur. How- ever, considering the sum of the Xq for four different wavelengths only one minimum exists at the supposed values (dox = 23.1

2)

^{for all}

.9 1.5 1.7 2.5 3.0 8.7

24.0 1.6 3.1 !L&? 2.5 8.1

Table 4: Determination of the minima of

x

2 (eq. (2)) as a function of dox for X = 680, 765, 800 and 850 nm. Each column comprises the sum over 5 values of 4 ( 72O

. . .

76O). The last column is the sum of

x2.

For each value of dox (varied from 10 to 30

8)

the values of n and k have been optimized to yield the minimum of X2.

Experimental Results

As the differences in the last column of Table 4 are not too large, this method requires a careful measurement of I $ ~ , $M, A M and high-

- . -

quality optical ~urfages. All measurements were performed at five values of I$ = 72

,

⁷³

. . .

76O. The complex refractive indices at four wavelengths of one GaAs and one InP sample are summarized in the Tables 5 and 6. Following the above described procedure the thick-

of oxide layers were found to be 17.6

8

for the GaAs and for the _{I n P} sample in that specific Case.

X /nm n-ik X /nm n-ik

546.1 4.046

-

^{0.305i 546.1 3.656}

-

^0.3751

765 3.671

-

^{0.118i 633 3.515}

-

^0.292i

780 3.659

-

^{0.112i 765 3.441}

-

^0.209i

800 3.646

-

^{0.104i 850 3.438}

-

^0.143i

820 3.636

-

^0.095i

Table 5: Complex refractive Table 6: Complex refractive index of a n-doped index of a p-doped

(2x10'~ ~ m - ~ ) GaAs bulk sample (2x10'~ ~ m - ~ ) ' InP bulk sample at five wavelengths. at four wavelengths.

For GaAs, these refractive indices are in very good agreement with earlier publications 13, 4/. For InP, the real parts of the

refractive indices agree well with /3, 41. The imaginary part at- X = 546 nm is one percent lower than published by Cardona /6/.

The author is indebted to K. Bambey for help with the computer code and H. Burkhard, E. Kuphal and G. Weimann for discussions.

Literature

/I/ M.M. Ibrahim and N.M. Bashara, J. Opt. Soc. Am.

61,

1622 (1971) /2/ H.W. Dinges, Ellipsometry-Conference (sponsered by Polytec)

Munich (1981), unpublished

/3/ H. Burkhard, H.W. Dinges, and E. Kuphal, J. Appl. Phys.

53,

655 (1982)

/4/ D.E. Aspnes and A.A. Studna, Phys. Rev.

B,

985 (1983) /5/ H.W. Dinges, Thin Solid Films

50,

L17 (1978)

/ 6 / M. Cardona, J. Appl. Phys. 36, 2181 (1965); 32, 958 (1961)