Determination of the complex refractive index profiles in P+31 ion implanted silicon by ellipsometry

Surface Science 49 (1975) 441-458 0 North-Holland Publishing Company

DETERMINATION

OF THE COMPLEX REFRACTIVE

INDEX PROFILES

IN Pi1 ION IMPLANTED SILICON BY ELLIPSOMETRY J.R. ADAMS* and N.M. BASHARA** Electrical Materials Laboratory, College of Engineering, Lincoln, Nebraska 68508, U.S.A.

Received

29 November

1974; revised manuscript

received

University of Nebraska,

15 January

1975

Ellipsometry was used to determine the complex refractive index profiles in silicon implanted with PJ1 ions with energies of 35, 52,5 and 70 keV. The profiles were determined both by anodization-stripping of the implanted layer and by numerical fitting of multiple-angle-of-incidence ellipsometer data taken on the as-implanted surface, assuming that the implantation would exhibit a Gaussian distribution. Good correlation was obtained between the two types of profiles, indicating that the non-destructive measurements on the as-implanted surface may be useful in process control. Good agreement with published results was also obtained on the increase in depth with energy of both the damage and the implanted species.

1. Introduction

The increasing importance of ion implantation as a method for inducing changes in the electrical and optical properties of semiconductors, glasses and ceramics has motivated extensive study into many aspects of the implantation process [ 11. Because the implantation process introduces a large number of defects into the implanted region, almost as much effort has been devoted to the determination of the nature and the effects of the damage as to the desired effects of the implanted ions [?I. Depending on the ion species, total dose, and implantation energy, the density of defects can be sufficient to drive the surface layer of a crystalline specimen amorphous thereby negating or seriously affecting the properties desired unless the specimen is annealed to a high temperature [2b]. In certain case, such as radiation tolerant transistors, it may be advantageous to retain some of the effects of the damage, provided these effects are defined. Regardless of the end result, it is necessary to characterize the damage region. To accomplish this a number of techniques have been used including helium ion back* Currently a member of the Technical Staff, Sandia Laboratories, Albuquerque, This work was supported by the United States Atomic Energy Commision. ** Work supported by the National Science Foundation.

New Mexico.

442

J.H. 4dams, N.M. Busharu/Conzplex re.fructive index profiles

scattering [ 1,3], electron diffraction [4-6,101 , electron microscopy [7,9], electron spin resonance [lo- 121, electron paramagnetic resonance [ 121 , electron channeling patterns [ 141, visual observation [ 1,101 and optical reflection and transmission spectroscopy [ 10, 15-241. Ellipsometry has also been shown to be a valuable tool for the analysis of refractive index changes in Si [25] and fused siluca [26:27]. To investigate the effects of implantation on the optical properties, visual observation and retlection and transmission spectroscopy leave much to be desired because of the inhomogeneous nature of the implanted region. Consequently, an accurate quantitative characterization cannot be obtained solely from the reflection or transmission spectrum. In contrast multiple-angle-of-incidence ellipsometry [28,29], at a judiciously chosen wavelength [29], coupled with an appropriate optical model and removal of succesive layers of implanted material is well suited to a quantitative analysis of the effects of the ion implantation on the optical properties and a determination of the spatial extent and profile of the implantation. In this paper we report the results of ellipsometric measurements of the complex refractive index profiles produced in high resistivity 5 R cm (111) silicon by implantation of PiI ions at energies of 35, 52.5, and 70 keV, and to doses of 2.0 X lOI and 1.O X 1016 ions/cm2. A comparison o f the results of multi-angle-of-incidence ellipsometer- measurements con the as-implanted surface with the results of ellipsometric measurements and anodization-stripping of the implanted region is given.

2. Experimental

procedure

2. I. Inn irnplan tatio yl Samples for these experiments were cut from (Ill) orientation* high resistivity, z 5 a cm. boron-doped silicon wafers using a YAG laser scriber to 0.250 in. X 0.500 in (6.3 mm X 12.6 mm) dimensions. The samples were then etched in a 1 : 10 solution of 49% HF acid in deionized water, cleaned ultrasonically in trichloroethylene, acetone, and methyl alcohol and jet dried using high purity dry nitrogen. Implantation of the phosphorous ions was carried out at room temperature, -23 “C, in a Lintott ** high-tluence ion accelerator using phosphorous trichloride for the source of P$t ions. The beam (approx. 1 cm dia.) was mass analyzed and slowly scanned over the samples. The background pressure in the implantation chamber was approximately 2 X 1O-6 torr. Samples were implanted at ion energies of 35, 52.5, and 70 keV, to fluences of 2.0 X 1014 ions/cm2 and 1.O X 1016 io%/cm2 and the total dose was controlled to + 1% at a dose rate of approximately 3.5 X 1013 ions/cm2 sec. The samples were misoriented by 7” with respect to the incident beam to minimize channeling of the implanted ions. * This orientations was found to be accurate to within 1” as determined from optical orientation measurements on unimplanted specimens cut from the same wafers according to ASTM Method F26--66. ** Manufactured by Lintott Engineering Co. Ltd., Horsham, England.

J.R. Adami

N.M. GasharalComplex

refractive index profiles

443

2. I. .4nodic oxidation and stripping In order to measure the refractive index profiles induced by the ion implantation, layers of implanted material were removed by anodic oxidation and stripping [30,31]. Samples were mounted in a Teflon fixture which allowed the sample to be anodized, etched, and ellipsometric measurements to be taken without removing the sample from the holder. Electrical contact to the specimen was through a polished stainless steel slug against which the specimen was pressed by the Teflon fixture. Samples were anodized at a constant-current density of 5 mA/cm2 in an electrolyte solution consisting of 1.O g KNO,, 25.0 ml deionized H,O, and 225.0 ml ethylene glycol. The electrolyte was stirred constantly during the anodization and the sample was illuminated with a 60 W incandescent bulb 10 cm from the sample. The cathode for the anodization cell was a 1.O cm X 2.0 cm platinum foil. The anodic oxide was removed in a 1 : 10 solution of 49% HF acid in deionized water. The sample, in its holder, was then rinsed in deionized water, acetone, and methyl alcohol, and dried by a jet of high-purity dry nitrogen. This cleaning procedure was used throughout these experiments. Following each anodization, the thickness and refractive index of the anodic oxide was measured by ellipsometry. In order to obtain an accurate value for the oxide film thickness and refractive index at each step, it was necessary to account for the underlying implanted layer in the calculations because the refractive index of the implanted layer differed from that of the Si substrate [32]. The implanted layer was taken into account by using the effective optical constants for the surface after removal of the anodic axode. These constants were used for the substrate values when computing the oxide thickness and refractive index. To simplify the model, the oxide layer was assumed to be uniform and homogeneous. The average ratio of anodic oxide to phosphorus-implanted Si removed was determined after all of the implanted layer was removed. This ratio was then used to estimate the amount of phosphorus-implanted Si removed by each stripping step. The exact spatial point of onset of the unimplanted substrate could only be determined within the resolution capability of each stripping step. For exact determination of the onset of the unimplanted substrate, an infinite (large) number of stripping steps would be required; a patently impractical procedure. The total amount of phosphorus-implanted Si removed was determined by measuring the depth of the stripped region using multiple-beam interferometry [33]. Knowing the total thickness of the phosphorus-implanted Si removed and the total thickness of anodic oxide removed (thicknesses of oxide at each step multiplied by the number of steps) the ratio of the total amount of phosphorus-implanted Si to total amount of anodic oxide (tSi/t,,) is then known. Furthermore, since the total number of layers stripped is known, the amount of phosphorus-implanted Si removed by each stripping is then determined. The results summarized in table 1 are in good agreement with values published by others [3,31].

___ 100 100 50

___,_ A-l A-2 A-3

___~__._ 8 24 20

Number of anod~zati~~ns

1.406 .i 0.014 1.411 IO.014 1.415 2 Ml27

_I~__._^I___

Average oxide refractive index (computedfa

39.5 +. 1.9 41.5 t 2.3 20.1 * 1.4

Average oxide thi~kness/la~er (computed) (nrn) ___l__ .~ .___...

.~___

15.9 + 1.5 15.8 + 0.6 8.1 + 1.0

0.403 0.380 0.403

thickness Ratiob of Si removed per ‘Siltox anodization Inn0 -____._ ____^_~._.I-_-.. ..__ -..-_-AVenge

,._,., “.--_-.__~^^_^__~-~.~

a In the computer program used to evaluate the refractive index and thickness of the Si0, film, the extinction coefficient could also be computed. The extinction coefficient for these films was found to be zero to at least 4 decimal places and is therefore reported here ta be equal to zero. b Total thickness of talented Si itSi) to total anodic oxide thickness (fox).

,_______

Anodization voltage W)

Sample nunlber

Table 1 A summary of the anodic oxidation and stripping experiments described in this paper _______.-----___*-_.~_._---_--^. --.-~.

% P

44s

2.3. b‘llipsometric measurements The ellipsometcr /34] used for this work was a manual Gaertner L-l 19X conf!gured in the polarizer, compensator. sample, analyzer (PCSA) arrangement with fixed-compensator nulling [32] and a He Ne 632.8 nm laser light source. The compensator was a quartz Babinet Soleil type and the polarizer and analyzer were calcite Glan air-spaced prisms. The ellipsometcr was aligned using the techniques described by Zeidler et al. [35]. Four alignment marks. each more than 2.0 m from the sample, were established during the initial alignment. and these points were used to check the slignment of the sample each time the sample was reinserted following an anodijr.ation and/or stripping step. A clip-in holder f’or the anodization sample holder was designed for the cllipsometer sample table and after the initial alignment it was seldom necessary to adjust the sample table. It was found that the sample could be repositioned to within +O.OlS” as determined from repeated measurements on the same sample surface which was removed from and replaced in the ellipsometer sample fixture. The angle-of-incidence scale was checked periodically by setting the ellipsometer to the straight-through position several times. The absolute error in the angle of incidence, which is dependent on the beam deviation and the azimuth of the polarizer prism [36], was found to be less than approximately 0.06” for our il~s(rument. The relative error in the setting of the angle-(of-incidence sc& was less than 0.01”. The ellipsometer divided circles were calibrated while taking two-zone measurcmenrs on the initial samples using techniques developed in this Laboratory 1371. The uncertainty in the calibration constants was found to be less than approximately 0.06”. (See the Discussion section.) Once the divided circle calibration constants were established, rlleasurert?eI~ts were t:*Set: in only one ellips~)r~letric zone and the ellipsometric parameters Ij and A were computed using the equations given by Azlam and Hashara [38]. 2.4. Data reduction The refractive index profiles were computed from ellipsorllcter rlleasurcillents taken in air at four angles of incidence (57.5”, 60.0’. 62.5”. 65.0’) on the asimplanted surface after etching in 1 : IO t1F and rinsing and drying as described above, and on the sample surface immediately following each anodization-stripping step.

For reduction of the data on the as-implanted surface a Fortran IV computer program was developed based on the nonlinear least-squares numerical inversion of the exact Drude equations for a multiple-filmed surface as described by Schueler [28]. In the program, the ion-implanted surface could be modeled as being composed of one or two independent refractive index profiles. Their parameters were adjusted

SO that the values of Q and A fit the obscrvcd 4 and A taken refractive

at multiple

index

profile

values of the ellipsometer

angles of incidclicc. from

an expression

The program

involving

up to eight

eters. l‘hc profile is nlodclcd as a scrics of ten assumed whi& values of + and A may be computed. For the work

rcportcci

tu the refractive index

change

index caused

refractive

index

deviations

were

squares

by the implanted

adjusted

to oht3iu

of the observed

species.

coefficient values

independent

were used

to that

described

provides a numerical used in dctcrmining

by Schroeder

one applicable to the refractive

The magnitudes

01‘ the peaks in the depth

their

spatial

A which

values

were

of Q and

and Dieselman

[26]

and standard

a nonlinear

refractive

index

Icast-

A at all angles

of in-

were required This approach

. except

that

tit to the experimcrltal the

from

(k).

cidence. Mcasurcmcnts al ;I minimum of four angles of incidence adjust all eight paramctcrs of the two independent distributions. similar

;I

param-

films

and one applicable

of 3 and

(tncasul-cd)

determined

homogeneous

distributions

due to the damage

end extinction

(II)

estimate

two Gausian

here,

change

parameters

explicitly

data and a slightly different profile which is more applicable

to is

the program model was to the

actual physical situation *. It should be pointed out that this method is restricted to samples whwe cxtinstion cocfficicnt (k). even in the implrlntcd layer. is sufficicntly small at the measuring wavelength to allow the lifiit wave to pcnctr:ite the entire inlloriiogcnco\Is region. Also. it is not possible to tinaiiibiquouslS,)llsl}/ determine a coniplex rct‘ractivc index profile 1‘1.oni nmsurcniciits on the surface only, unless a rela. tivcly ;iccuI-ate cstiliiatc‘ of the pt-ofilu (typically within 20%) is known beforch;lr,d.

analysis

Although

could

was used. We knew section

then

of the data obtained

have been done by the method 1. ‘fhc

the avc~agc thickness

avtmgc

be computed

refractive

the optical

from

multiple-aligl~-of

” Schrwdrr

and Diewlman

[ 261

tivc index prot’ilc .ind .illhough

a simpler,

of each composite

and extinction ric measurcmcnts.

at the surt‘aze until the .:--implanted of the rct’ractivc index and extinction calculated

the anodi/.ation-stripping above.

constants

layer

experiments

more

direct

method

as described

in

coefficient of the layer could WC wcrc then able to determine

index

I‘rcmi cllipsomot

the profile in two ways. In the first WC clctcrniincd

from

described

of each successive

layer.

starting

substrate was reached using the averegc cocfficicnt of the composite underlying

incidence

measurements.

used a sum of ten (;auswn

rhcy .~llowed the ret‘rclrtivr

Secondly.

distributions

values layers

we followed

10 compute the refrrlc-

indict\ to he complex.

the mq2nitude

and 111~\jn of the c‘l~~ngcin the c<)mplcx rct’r:lctivc index was fixed lor A yivcn Ckusrrlin hution. yxcics

In our m~dcl. one or tlw IUO (Lussian distribution.

and the other to thr damage distribution.

the chanpec in the refractive distrihutmnz. within

distributions

index of) and extinction

The magnirudes and the signs of

coct’ficicnts tk) bare independent

fhc Jcplh and \tandard deviation of rhc perturbations

LL (;.~ua\~.~r:di\trihution.

dccrcawlg ivhilc maintainins

distri-

WI\ assigned to the implanted

on II and k wrc

for both

the wmc

Our procedure allo\vs )I to increaw at the sxne rime 3s !i is ti (;aussidn

prolile

of the s~n,c depth

and standard deviation.

J.R. Adams, N.M. BasharalComplex

refractive index profiles

441

procedure of Bayley and Townsend [27] in their studies on silica glass by working backwards starting with the unimplanted substrate. The Fortran IV computer program used for this substrate-to-surface analysis involved only a minor modification of the method described by Schueler [28]. The results of the two procedures were nearly identical. The results of the second procedure were used in plotting the data discussed in section 3.

3. Results and discussion 3.1.

Complex refractive index anodized-stripped

profiles

Dose 2.0 X 10’4ions/cm2 Figs. l-4 show the results of the experimental measurement of the refractive index (n) and extinction coefficient (k) profiles in P,,’ ion-implanted Si for incident energies of 35, 52.5 and 70 keV, respectively. The figures clearly show that the peak of the refractive index and extinction coefficient profiles moves deeper into the specimen with increasing ion energy. Within the depth resolution (see table 1 for the values of materials stripped), the initial peaks of both the n and k profiles for both the 35 and 52.5 keV specimens are in good agreement with the position of the damage peaks predicted from the theory of Sigmund and Sanders [39]. The general shape of the profiles is also in good agreement with the damage profiles predicted by Brice 1401. For reference, the location of the peaks of the implanted species distributions as predicted by the LSS [41] theory (Rpr) and the peaks of the damage distributions as predicted by Sigmund and Sanders [39] (RpD) are shown. To illustrate the correlation between the structure in the profiles and the theoretical distributions, the depth of the secondary peak in the refractive index profile (P,) labeled E, F, and G in fig. 2) and the depth of the primary peak in the extinction coefficient (Pk) labeled A in figs. la, 1b and 1c were plotted as a function of incident ion energy. These results are illustrated in fig. 3. The secondary peak in the refractive index was taken as the location of the maximum point immediately preceding a consistent (and usually rapid) downward trend in the refractive index. The solid lines show the depth of the peak of the damage (RpD) and ion (RpI) distributions and the standard deviation of the distributions (ARpD and ARpI) as predicted by Sigmund and Sanders [39] and the LSS [41] theories, respectively. At spatial depths beyong the initial peak there is considerable “tailing” of the complex refractive index profile for all three implantation energies. In each case there is structure particularly in the extinction coefficients profile, which suggests that in unannealed specimens both the damage and the implanted species contribute to the changes in the optical properties of Si. This structure is evident in the second peak in the extinction coefficient labeled B in fig. 1 (particularly in the 52.5 keV specimen fig. lb), the rounding and broadening of the profiles in the vicinity of the LSS peak (RpI), and a third peak labeled C which appears in all three specimens

448

n

-

I

ABSOLUTE

3.9

4.0

la)

DEPTH,nm

128.0

f 3 64.0

F

(b)

DEPTH,

nm

128.0

f

I

192.0

RELATIVE

ABSOLUTE

n

3.E

3.9

4.c

4.1

4.2

4.3

64.0

Cc)

DEPTH,

nm

128.0

I

I RELATIVE

ABSOLUTE

Fig. 2. The refractive index profiles of the specimens of fig. 1. (a). (b) and (c) are for the 35, 52.5 and 70 keV implantation energies, respectively. The points marked E. F and C in the figures approxi~te~y correspond to the peak of the ion distribution predicted by the LSS theory 1411 and are the locations of the “secondary” peak in the refractive profile as discussed in fig. 3. The absolute and rdative uncertainties discussed in section 2 are indicated by the vertical error bars in the upper right of the figures.

64.0

3.7

n

4.1

4.2

4.3

37..

192.0

I RELATIVE

1u--

E

3.e

--+--e--t----

I

3.6-

3%

4.0..

4.1..

4.2..

4.37-

I

450

J.R. Adams, NM Bashava/Complex refractive index profiles

d

ENERGY,

KeV

Fig. 3. Depth of the primary peak in the extinction coefficeint (Q) and the secondary peak in the refrative index (P,) determined from figs. 1 and 2 as a function of incident ion energy. The secondary peak in the refractive index was taken as the location of the maximum point immediately preceeding a consistent (and usually rapid) downward trend in the refractive index. The solid lines show the depth of the peaks of the damage (R& and ion (RPI) distributions and the standard deviation of the distributions (AR~J, and ARpl) as predicted by Sigmund and Sanders [39] and the LSS theory [41].

prominent at 35 keV) near the end of the tail of the distributions. The third peak (C) is probably associated with moderatel~channeled ions which introduce interstitial atoms (atoms which are not incorporated on a lattice site or are associated with vacancy groups) which cause a localized stress and electric field perturbation of the optical constants of the lattice. Also, a stress field at the interface between the disordered and ordered regions might produce similar effects. We are sure these structural features in the profiles are physically significant because the majority of the errors discussed in the section 3 affect only the quantitative values of the complex refractive index at all points in the profile. The qualitative structure in the profiles is inaffected. From an analysis of the possible ellipsornetric errors, discussed previously, and from the results of the computer reduction of the data* we have estimated the absolute and relative errors in the determination of the refractive index profiles caused by the ~In~ertainty in the determinatiol~ of the complex refractive index (both n and k) from point to point within the profile. The magnitudes of these errors are shown by the error bars on the profiles. The absolute error will only shift an entire pr-ofile up or down on the vertical axis, it will not affect the general shape of a profile (271.

(particularly

* The program

computes

the 95% confidence

intervals

for each of the computed

parameters

(n, k).

J. R. Adams, N.M, BasharajComplex

refractive index profiles

451

0.190-

I

Q180--

RELATIVE

0.170-.

0.160--

K 0.150-

-

0.140--

0.130--

0.120

1

64 DEPTH,

128 nm

Fig. 4. Extinction coefficient profile of specimen A-4 implanted at 35 keV, dose = 2.0 X 1Ol4 ions/cm’. Annealed at 650 “C for 2 hr. Note the expanded vertical scale as compared with fig. 1. The relative uncertainty in the extinction coefficient in each layer is shown by the vertical error bar in the upper right of the figure.

The magnitude of the refractive index change (both n and k) for the 35 keV implanted specimen is 50% larger than changes in the 52.5 and 70 keV implanted specimens. This is consistent with the damage theories of Brice [40]. Even after annealing for 2 hr at 650 “C samples implanted at 35 keV exhibit structure in the extinction coefficient profile (see fig. 4). This may correspond to the residual damage observed by Tamura in electronmicroscopy studies [7]. From these results it is obvious that ellipsometry can detect even very small amounts of damage in Si, as was seen by Ibrahim and Bashara [25]. Within experimental uncertainties, no structure was observed in the refractive index (n) profile on the annealed specimen. A brief comment is in order on unaided visual effects. Among the low dose samples, only the specimen implanted at a dose of 2.0 X 1014 ions/cm2 at 35 keV exhibited a milky appearance on the as-implanted surface. This was not evident on the asimplanted surface of the 52.5 or 70 keV specimens. However, all of the high-dose specimens (1 .O X 1016 ions/cm2) exhibited a milky appearance on the as-implanted surface. The milky appearance was definitely not associated with contamination;

J.R. Adams,

452

N.M. Bashara/Complex

refractive

index p-ofiles

many authors have reported it to be associated with disorder. Our observations indicate the disordered region in the 35 keV specimen, (dose = 2.0 X 1014 ions/cm*), was sufficiently close to the surface to be observable. 3.2. Complex refractive index on as-implanted surface In order to evaluate the usefulness of ellipsometric determination of the complex refractive index profile solely from measurements on the as-implanted surface, the data on the as-implanted surfaces of the specimens in figs. 1 and 2 was analyzed using the procedure described in section 2.4.1. Fig. 5 shows the computer-determined profile for the specimen implanted at 35 keV. Similar results were obtained at the higher implantation energies; in general, good agreement was obtained between the profile determined from measurements on the as-implanted surface, and the profile determined from the anodization-stripping experiments*. Several dominant * Since the computer-generated profiles are not perfect duplicates of the true profiles it is not unexpected that the second peaks should be depressed. The major features of the profiles remain in good qualitative

if not quantitative

agreement.

4.5r

0.60

I

II

1

J

140.0

70.0 DEPTH,

r

nm

DEPTH,

“m

(b)

Fig. 5. Refractive index and extinction coefficient profiles - (a) and (b), respectively - in PiI ion-implanted Si as determined by multiple-angle-of-incidence ellipsometry on the as-implanted surface. Implantation energy = 35 keV; dose = 2.0 X lOI ions/cm’.

J.H. Adams. R-M. Baslrara/Complex

wfracrise index profiles

453

features were noted in the computer solutions for the refractive index profile. These are discussed in more detail in the following section.

Ellipsometric measurements on the samples implanted to a dose of I X lO’6 ions/cm* were restricted to four angles of incidence on the as-implanted surface, and the cwnplcx refractive index profile was computed using the techniques described in section 2.4.1. Multiple-angle-of-incidence measurements (at 55.0, 60.0, 65.0 and 70.0”) were made on at least two specimens at each of the three implantation energies. The values of I$ and A at all angles of incidence for different specimens implanted at a given energy were in agreement to within 0.1’. The variation (at ;I given angle of incidence) in $ and A between specimens implanted at the different energies was between lo and 7”. Figs. 6 and 7 show the computer-determined profiles for the specimens implanted at 35 keV and 53. 5 keV, respectively. The 70 keV profile is not shown because is is similar and contributes no new information which is pertinent to the discussion. To find a minimum least-squares solution for the profile. the initial starting guess for ea
4.30r

4.20-

4 io-

n 4.00

3.90.

3.80

3 70 -

1J L-J

L.-.

L _

--

70.0

DEPTH, (a)

140.0

nm

.1400

7To_AL-

D’PTH.

nm

(b)

Fig. 6. Refractive index and extinction coefficient profiles (a) and (b), respectively in I’;, ions-implanted Si as determined by multiple-angle-of-incidence ellipsomctry on the as-implanted surface. Implantation energy = 35 keV; dose = I.0 x IO’” ions/cm’.

J.R. Adams, NM

454

BasharalComplex

refractive index profiles

4.2Or

410-

4.00

-

0.60

-

0.40

-

0.30

-

_

n 310.

k 3.60

-

3.70

-

3.60

I

I

1

70.0 DEPTH,

140.0 nm

(a)

Fig. 7. Refractive index and extinction determined tion energy

70.0

140.0 DEPTH,

nm

@I

coefficeint profiles - (a) and (b), respectively by multiple-angle-of-incidence ellipsometry on the as-implanted surface. = 52.5 keV; dose = 1 .O X lOI ions/cm2.

- as Implanta-

overlapping distributions had to be within approximately 20% of the “true” solution for the program to converge. If the initial starting guess was in error by more than approximately 20% (particularly in the magnitude parameters) the program would diverge, or stop before a reasonably small sum-of-squares had been obtained. On occasion a “reasonable” minimum sum-of-squares was obtained, but one or more of the parameters of the distributions at this “solution” would be in violent disagreement with the known physical situation. (Usually the standard deviation of the refractive index profile would be several hundred nm, giving a very deep, flat profile). This requirement was determined primarily from the data on the specimens implanted to a dose of 2 X 1014 ions/cm. The “best” (minimum sum-of-squares) solution was always obtained by allowing all eight parameters to be adjusted simultaneously, but on occasion it was desirable to hold one or more of the parameters constant in order to obtain a better estimate for the other parameters or to examine the effects of variations in the parameters of the distributions. The “best” solution was used for the profiles of figs. 5-7. In the process of obtaining the computer-generated profiles, several important features of the distributions were noted. First, the magnitude of the peak of the refractive index profile of the Gaussian distribution always fell between 114 and 116% of the substrate refractive index. The most typical value (for 4 out of the

J.R. Adams, N.M. Bashara/Complex

refractive index profiles

455

6 specimens analyzed in this manner), for the peak in the refractive index, was 115% of the substrate refractive index. The magnitude of the refractive index peak of the first Gaussian distribution was the most accurately determined parameter of all the parameters of both distributions. This result is in good agreement with the magnitude of the peak of the refractive index obtained from the anodization-stripping experiments. Second, the profiles determined for the specimens implanted to a total dose of 1 X lOI ions/cm2 were all definitely broader than the profiles of the specimens implanted to a dose of 2 X 1014 ions/cm *. This is consistent with the damage theories of Sigmund and Sanders [39]. Third, in order to obtain a convergent solution, it was necessary to allow the second (deepest) Gaussian distribution to have a negative effect on the refractive index profile. The effect on the overall refractive index profile was to force a relatively narrow dip in the refractive index usually causing y1to go below the refractive index of the substrate. The depth of the minimum in the refractive index profile (not necessarily the depth of the maximum negative effect) always occured at a depth of approximately 70nm. If the positions (depth) of the Gaussian distributions were forced to occur away from the optimum solution (by holding the depth parameters constant at a value 5510 nm from the optimum solution) the magnitudes and standard deviations of the distributions were adjusted by the program to force the negative dip in the overall refractive index profile to occur at the same depth. The depth of this negative peak appeared to move somewhat deeper into the specimen with increasing implantation energy, although within the resolution of these profiles, making a firm statement to this effect is not possible. Finally, the magnitude of the peak of the extinction coefficient profile was the least acc.uately determined parameter of all the parameters of the distributions. The magnitude of the peak of the extinction coefficient profile could be held anywhere between 400% and 600% (300-500% increase) of the substrate extinction coefficient with only a small effect on the sum of the squares. However, the shape of the extinction coefficient profile (depth, standard deviation) remained unchanged when the magnitude of the peak was forced away from the optimum solution. 3.3. Properties of the damage region jhm a simplified model In order to assess the usefulness of ellipsometry for measuring the extent of the residual damage following annealing, the initial multiple-angle-of-incidence ellipsometer measurments of Specimen A-4, both before and after annealing to 650 “C for 2 hr, were used to compute the properties of the surface by assuming simplified one-layer and two-layer models. For the unannealed specimen, neither the one-film model nor the two-film model were adequate enough representations of the refractive index profile to allow the computer program to converge to a satisfactory solution for an average complex refractive index for the damage region; the convergence was extremely slow and the refractive index and extinction coefficeints for the films in

456 Table 2 Kcsults

of nlultiplc-angle-of-incidence

refractive

two ways shown. consistine complex refractive following

complete stripping and k 0.140)

One-film

model

3.920

i 0.204

10.040

*Cl.040

d,.= 77,s

of the phosphorus-implalltcd

1 he

? lI).O’-

wrface

15.3 ? 5.0

model

were

model

film

unreasonably

thicknesses of the

mately

74 nm.

guesses

f01 tl,

74 nm

and

For

the

and

this

the

would

value

by

program.

as the

the found

used

(in

+ d2

of the (The

to be approxiwere

in the

found

models.

two-layer rapidly

Starting

inodel) converge

program

two-

the individual

could to about

adjusted

the

corn-

solutions model

of‘ the in lmtcr

expcrimcnrs.

‘I‘llc

were

provided

found

refractive

index

qrecment

wirh

values

~OI- both

;I slightly

better

and for

the

one-layer

to the

extinction

the values

wmputed

the fit

and

coel‘ficicnr

obtained two

two-

experimental fbr the

by the anodim

models

are shown

in

3.

Although

the

in the

one-film

two-tilm

annealed

model damage

n~~~clcl is in better

of the

damage

Overall.

on

results

;I

was

the

the

profile

;mtl from

cst imate of the

the values

of the film

complcs

refractive

computed

computed

for

the

by

the

thickness

studies.

good

the

3 better thickness

with

unannraled

are in very

computed

Gaussian

provides region.

q,reement

experiments.

which

assuming

region

these

tion-stripping index

about

spccimcn.

were

cl,

sum while

thicknesses

guesses

thicknesses

the

layer(s).

two-film

magnitudes

n~xfcl

lion-stripping

index

oscillate ofrhc

and

the

10.003

76 nm was

computed

starting

-i 0.16(1

that

adjusted

llfll

1.fl + 12.0nm

noted

model

These

initial

and

being

one-layer

model)

00 nm

then index

the

one-layer

it was

were

later.)

10 the

and

the

3.864 to.003

at approximately

the

be discussed

the

nnncalcd

two-layer t:1hlc

for

would

models;

data

indices

computed

ml

refractive

Isyer

refractive

film

(in

50

However.

constant

and

insentitive

be between plex

large.

relatively

3s will

to be relatively

=

cII.1 + d1.2 = 6

remained

thickness

j
near

wbstratc

at the value obtained

region; )I was found to

,111

._ the

Si was modeled in the

in the calculations

Region

layer

on specimen A-4 (the comples

of either one or two layers; the unimplantcd

indcs was held constant

bc 3.863

‘if=

measurements

index and thickness of the I~hosl)h’)rus-iruplantcd

agreement

location

me;lsurements

for the unannealed

with

of the

the

negative

on the

results dip

as-implanted

specimens.

of the

in the

anodiza-

refractive surface

hq

457

4. Conclusions

We have den~onstrated that it is possible to use e~lipsom~try to dctcrrl~inc the complex refractive index profiles of high energy ion-implanted silicon surfaces both by anodization-stripping of the implanted surface and from analysis of multiplcangle-of-incidence measurements on the as-implanted surface assuming the implantation distribution was Gaussian. The complex refractive index profiles generated from the measurements on the as-implanted surface are in good agreernent with those obtained by aItodiZati(~n-stripping. As expected. the depth of the peaks of the profiles increase with increasing energy of the implanted ions. Annealed specimens show effects (evident in the extinction coefficient profiles) of residual damage even after a treatment of 650 “C for 2 hr. The properties of the annealed surface may also be approximated by using a simplified one-layer or two-layer model; the overall depth of the damage region determined from these simplified ~mxlels are in good agreement with results obtained by anodi~atiorl-stripping and/or the use of the more sophisticated Gaussian model. The reasons for the negative dip observed in the refractive index (H) profiles for the unannealed specimens which occur at approximately 70.0 nm below the surface. will be reported elsewhere.

Acknowledgement

The authors are grateful to Dr. W. Beezhold for discussions regarding ion implantation and advice and assistance in fabricating the ion-implanted samples.

References

Ill

See for example: J.W. Mayer, L. Eriksson and J.A. Davies, Ion Impiantalion in Semiconductors (Ac;ldcmic Press, New York, 1970); R.C. Wilson and G.R. Brewer, Ion Beams, with Application to Ion Implantation (Wiley, New York, 1973). (a) J.F. Gibbons, Proc. IEEE 60 (1972) 1062, and refcrcnces therem; tb) J.F. Gibbons, Proc. IEEE 56 (I 968) 295. 131 Y. Akasaka. K. Horie, K. Yoneda, T. Sakurdi, H. Nishi, S. Kawabe and A. Tohi. J. Appl. Phys. 44 f 1973) 220. 141 R.L. Jacobsen and G.K. Wehner, J. Appi. Phyc. 36 (1965) 2674. [51 H.E. Farnsworth and H. Hayek, Surface Sci. 8 (1967) 35. 161 M. Hen&r, Surface Sci. 22 (1970) 12. [‘I M. Tamura, Appl. Phys. Letters 23 (1973) 651: and refercncer therein. Phyc. Rev. Lcttcrc 27 (1971) 1794. 181 T.M. Donovan and K. Hcinemann, 191 D.J. Nelson, R.S. Mazey and R.S. Barns, Phil. Msg. 17 (1968) 1145. 1101 R.L. Crowder, R.S. Title, Y.H. Rrodsky and G.D. Pettit, Appl. Phys. Letters 16 (1970) 205.

458

J.R. Adams. N.M. Bashara/Complex

[ 111 N.N. Gerasimenko, [ 121 [ 131 [14] [l51 [l61 1171 1181 [l91 (201 [2ll [221 ~231 1241 [251 [261 1271 1281 [291

[301 [3ll [321 [331 [341

[351 L361 1371 [381 1391

[401 1411 [421 [431

refractive

index profiles

A.V. Dvurechenskii, S.I. Romanov and L.S. Smirnov, Soviet Phys.Semiconductors 6 (1973) 1692. S. Hasegawa, K. Ichida and T. Shimizu, Japan. J. Appl. Phys. 12 (1973) 1181; and references therein. K.L. Brower and W. Beezhold, J. Appl. Phys. 43 (1972) 3499. S.M. Davidson and G.R. Booker. in: Proc. First Intern. Conf. on Ion Implantation, Eds. L. Chadderton and F. Eisen (Gordon and Breach, New York, 197 1) p. 81. D.J. Bilekno, V.M. Evdokimov, N.P. Kaganova, G.P. Kostyunina, A.A. Kukharshii al:d V.K. Subaskiev, Soviet Phys.-Semiconductors 5 (1972) 1247. L.N. Strel’tsov and LB. Khaibullin, Soviet Phys:Semiconductors 5 (1972) 2083. T.C. McGill, S.L. Kurtin and G.A. Shifrin, J. Appl. Phys. 41 (1970) 246; Appl. Phys. Letters 14 (1969) 223. H.J. Stein, F.L. Vook and J.A. Borders, Appl. Phys. Letters 14 (1969) 328. C.S. Chen and J.C. Corelli, J. Appl. Phys. 44 (1973) 2483. R.R. Hart and O.J. Marsh, Appl. Phys. Letters 14 (1969) 225. V.M. Evdokimov, A.A. Kukharshii, L.N. Strel’tsov, V.B. Titav and LB. Khaibullin, Soviet Phys-Semiconductors 4 (1970) 797. J.C. Dyment, J.C. North and L.A. D’Asaro, J. Appl. Phys. 44 (1973) 207. S.M. Spitzer and J.C. North, J. Appl. Phys. 44 (1973) 214. D.D. Shell and A.U. MacRae, J. Appl. Phys. 41 (1970) 4929. M.M. lbrahim and N.M. Bashara, Surface Sci. 30 (1972) 632.Damage induced by 200~-400 eV ions is discussed. J.B. Schroeder and H.D. Dieselman, J. Appl. Phys. 40 (1969) 2559. Only the real part (n) of refractive index is determined. A.R. Bayley and P.D. Townsend, J. Phys. D (Appl. Phys.) 6 (1973) 1115. D.G. Schueler, Surface Sci. 16 (1969) 104. M.M. Ibrahim and N.M. Bashara, J. Opt. Sot. Am. 61 (1971) 1622. This paper shows that a necessary condition for use of multiple-angle ellipsometry is independence of the optical parameters with respect to an ellipsometric parameters. Because of dispersion effects this constraint is wavelength dependent. K.M. Bunsen and R. Linzey, Trans. Met. Sot. AIME 236 (1966) 306. W. Przyborski, J. Roed, J. Lippert and L. Sarholt-Kristensen, Radiation Effects 1 (1969) 33. J.R. Adams and N.M. Bashara, Surface Sci. 47 (1975) 655. B.J. Stern, Rev. Sci. Instr. 34 (1963) 152. For a general discussion of ellipsometry see for example, N.M. Bashara, A.C. Hall and A.B. Buckman, in: Physical Methods of Chemistry, Vol. I, Part IIIC, Eds. A. Weissberger and B. Rossiter (Wiley, New York, 1972) p. 453. J.R. Zeidler, R.B. Kohles and N.M. Bashara, Appl. Opt. 13 (1974) 1115. J.R. Zeidler, R.B. Kohles and N.M. Bashara, Appl. Opt. 13 (1974) 1591. A. procedure for in-process calibration of the ellipsometer divided circles is being reported elsewhere. R.M.A. Azzam andN.M. Bashdra, J. Opt. Sot. Am. 61 (1971) 600; J. Opt. Sot. Am. 61 (1971) 1118. P. Sigmund and J.B. Sanders, in: Proc. Intern. Conf. on Applications of Ion Beams to Semiconductor Techniques, Grenoble, France, 1967 Ed. P. Glotin (Editions OPHRYS) p. 215. D.K. Brice, Radiation Effects 6 (1970) 77. J. Lindhard, M. Scharff and H. Schiott, Kgl. Danske Videnskab, Selskab, Mat. Fys. Medd. 33 (1963) 1. J.M. Morabito and J.C. Tsai, Surface Sci. 33 (1972) 422. G. Dearnaley, J.H. Freeman, G.A. Gard and M.A. Wilkins, Can. J. Phys. 46 (1968) 587.