Universal expressions for average projected range and average damage depth in ion-implanted substrates

42

Nuclear

Instruments

and Methods

in Physics

Research

B15 (1986) 42-46

North-Holland.

UNIVERSAL EXPRESSIONS DEPTH IN ION-IMPLANTED

FOR AVERAGE SUBSTRATES

PROJECTED

Y. KIDO, I. KONOMI, M. KAKENO, K. YAMADA, Toyota Central Research and Development Aichi-ken, 480-I I, Japan

Laboratories,

RANGE AND AVERAGE

Amsterdam

DAMAGE

K. DOHMAE, and J. KAWAMOTO

Inc., 41-1, Aza Yokomichi,

Oura Magukute,

Nagakute-rho,

Aichi-gun,

Substrates of Al, Si, LiF. AI,O,, GaP. and GaAs were implanted with 45 to 420 keV N, Al. Ar, Mn. Ni, Zn, Te, and Xe ions. The reduced energies cover the range from 0.1 lo 5. Depth distributions of implanted ions and displaced host atoms were determined by means of backscattering (including channeling) and nuclear resonance reaction measurements followed by computer-simulated spectrum analyses. The results are compared with other experimental data and theoretical predictions given by Gibbons et al. (GJM) and Winterbon et al. (WSS). For the latter theory, optimum WSS parameters are determined to give a good fit to the experimental data. It is concluded that reduced projected range and reduced damage depth are proportional to reduced energy but cannot be expressed by unified relations for all ion-substrate combinations. However, systematic investigation reveals that introduction of a new scaling coefficient gives two universal expressions for modified reduced projected range and modified reduced damage depth as a function of average reduced energy.

1. Introduction

and damage depth versus reduced gated for a variety of ion-substrate

Ion implantation has been widely utilized to form p-n junctions and trapping levels at desired depths within various semiconductors. Needless to say, precise information on depth distributions of implanted ions and displaced host atoms is indispensable for the fabrication of actual devices. Up to now, a number of theoretical and experimental investigations [l-4] have been performed over a wide range of implantation energies. Winterbon et al. (WSS) [5] proposed the power approximation and predict a universal relation between reduced projected range and reduced energy. Kalbitzer and Oetzmann [6] reported a universal range curve similar to the WSS prediction by experimental data analysis for monatomic substrates. In the present work, projected range and damage distributions were determined by random an channeling backscattering analysis. For 15N and 27Al ions, nuclear resonance reactions of “N(p, ay)“C and 27Al(p, y)‘sSi were used to derive their depth profiles. In order to obtain accurate depth distributions, we have developed three types of computer codes to simulate random and channeling backscattering spectra and excitation curves of y-ray yield. Both experimental system resolution and effect of energy straggling are taken into account in the spectrum simulation and a joined half-Gaussian is assumed as a depth distribution. The results obtained are compared with other experimental [1,2] and theoretical ones [5,7]. For WSS theory using power potentials, optimum WSS parameters are determined from the present experimental results. Furthermore, universal relations of reduced projected range 0168-583X/86/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

energy are investicombinations.

2. Experiment We prepared mirror-finished, n-type (1 ll)-oriented GaP, p-type, (lOO)-oriented GaAs with thickness 400 pm, (OOOl)-oriented Al,O, with thickness 800 pm as the targets. Thick polycrystals of Al and LiF were also used for ion-range measurements. During implantation, the targets were cooled to about 100 K with liquid nitrogen to suppress epitaxial recovery of the damaged regions and migration of the implanted ions and induced defects. The implantation energy was calibrated using the nuclear resonance reaction of 19F(p, cyy)lhO at 340 keV with a fwhm of 2.5 keV. A LiF film with thickness 0.5 pm evaporated onto a Si-wafer was used for this purpose. Ion beams impinged on the targets about 5” off from the major crystal axis to avoid channeling. In order to suppress electrical charging of insulator targets, we made the irradiation area as small as possible, typically 3 x 6 mm2 and used relatively low-current ion beams. As analyzing beams, 2.0 MeV 4He and 0.85 to 1 .O MeV H ions were used for backscattering and channelrespectively. The ing and for 15N and 27Al detections, resonance reactions used are 15N(p, ay)“C at 898 keV and 27Al(p, y)28Si at 992 keV. To obtain a definite random spectrum, the specimen mounted on a goniometer was rotated slowly around the major crystal axis tilted about 5’ from the incident beam axis.

Y. Kido et al. / Average projected range und damage depth

43

3. Data analysis

D(ion

The method to simulate random and channeling backscattering spectra was reported in detail in the previous work [8]. To synthesize a channeling spectrum. ue used the multiple scattering model. As a typical example, simulated random and channeling backscattering spectra from (Ill)-oriented GaP substrates are shown in figs. I(a) and (b). For the ZOO-keV Ar’-imp anted GaP, two half-Gaussian shapes, joined at a n odal damage depth, are assumed as the defect profile. In this section, we explain briefly how to simulate an e?.citation curve of y-ray yield obtained by a nuclear resonance reaction. Firstly, we assume the depth distrib Ition of implanted ions to be a joined half-Gaussian:

of the imwhere C,,, is the maximum concentration planted ions, R m is the modal range, and I’, and r, are the fwhm’s of the joined half-Gaussians. The average projected range R, and the standard deviation IJ~ are evaluated from the following relations:

C (x)=C,,,,exp

I-y(x-R”,)2 I )

=r,

forx
and

r,=r,

forxzR,,

(1)

(2)

R,=R”,+$$.

(31

nn

1 0 =p p 4&X?

(r,+r2)2+(3-~)(r_-r,)2_

(4)

The substrate consists of n elements and the atomic concentration of the ith element is denoted by C, (i = 1. 2,. , n). After ion implantation, the elemental composition is changed and expressed as follows:

C,(x) =

I

r

dose) =jC,(x)dx,

c, - Cr(x)/n.

(5)

Next, we subdivide the target into many thin slabs with constant thickness At (atoms/cm2). Immediately before impinging on the pth slab counted from the top surface, the energy distribution of the analysing beam is expressed by 2vK7 = J+

F(E-5)

-+EJ ;‘:

exp I

I

,’

E,,=E,,,-

1

1,

S(E,)Ar.

(6)

h=l

where E,, is the incident analysing beam energy, r,f is the total energy spreading of the analysing beam at the pth slab and S(E) is the corresponding stopping power of the ion-implanted substrate. The values of (r,f)’ is the sum of the energy straggling r,’ and the initial energy spreading r,” owing to the experimental system resolution. We used Bohr energy straggling and the semiempirical formula proposed by Andersen and Ziegler [9] as Hi stopping power. No significant difference is seen between Bohr’s (free electron model) and Chu’s (Hartree-Fock model) [lo] energy straggling values in the spectrum simulation. Linear additivity of stopping power and energy straggling values for constituent elements are postulated for compound substrates. Finally, the total y-ray yield for the incident energy E,,, is given by

800

LiO Channel

Number

b “0 7

26

0

I

I

I

.

L50

100 Channel

)

I

F( E-

800

E,)C,(x,,)ArdE,

Number

Fig 1 (a) Random and (111) channeling spectra from the unimplanted GaP crystal. The solid curves drawn are the corresponding simulated spectra. (b) Observed and simulated (11 I) channeling spectra from the 200-kev Ar+-implanted GaP wth a dose of 3 x 10”/cm2 at 100 K. The fitting parameters used are C,,, = 0.43, D,,, (modal damage depth) = 6.0~ 10’~,/cm2, r, = 4.5 x 10”/cm2, and Tz = 6.5 x lO”/cm*.

x,, = (p - 1)At.

(7)

where E, is the resonance energy and r corresponds to the fwhm of the resonance. An appropriate constant C, is determined by the relation (2). The best fitted curve is obtained by adopting the appropriate fitting parameters such as C,,;,,. R “,, r,. and 1; to make the deviation II. RANGE AND DAMAGE PROFILES

Y. Kido et al. / Average projected range and damage depth

44

following relation approximation:

aa

GaP

“N+ 1x10’6/cm2

“Ni

-kl0

9s)p

9io

9io

Tnr,Aem+

C-,.r-..

at

A

75

keV

6

100

keV

C

125

keV

P.aY

9;o /

I,,.\,

IOOK

1°C

9io

\

Fig 2 (a) y-ray fields plotted as a function of incident H energy for 75-. loo-, and 12%keV 15N+-implanted Gap. The solid curves drawn are the best fitted excitation curves. The resonance reaction used is ” N(p, ay)‘*C at 898 keV with the fwhm of 2.2 keV.

1 x 1 016/cm2

at 100 K

B

100

keV

C

125

keV

between

p, and

e using the power

(l-m)p?t

p (c)P

hm

(8)

’

where p,(c)= CpRp, C,,= Nna’y. The notation used here follows the LSS description [3]. For the WSS parameters m and h, it is suggested that the case M = l/3 is an excellent approximation at small e, whereas m = l/2 is a reasonable over-all approximation. In this case, the scattering potential is V(r) = c n,XY-I/n1 (Cmh is an appropriate constant). Kalbitzer and Oetzmann [6] reported the universal expression of p,(r) = 1.63 e2/? at 0.01 < c < 0.3 and 2.26 at 0.3
00)

cc/z;.

(11)

Fig. 4 shows the relation of the average projected range versus the average reduced energy for “N, 27Al, and

0

0:1

0.3

0.i Depth

1 pm

0.i

0,'s

1

Fig. 2 (b) Depth distributions of the implanted t5N atoms derived from the best fitting conditions shown in fig. 2(a).

6-

.

Zn’,

Al+,

Te+ -

A Mn’, Td

-

SI

.’

Al

Al+

%5-

from the experimental data as small as possible. Fig. 2(a) shows the experimental excitation curves together with the best fitted ones for 75-, loo-, and 125keV I5 N +-implanted Gap. From the optimum fitting parameters, the depth distributions of 15N implanted into GaP are generated as shown in fig. 2(b).

4. Results and discussion In the present study, we tried to get simple expressions for both reduced projected range p, and reduced damage depth pd as a function of reduced energy c. For ion range distributions, Winterbon et al. derived the

5 Lz

+ /

cp = 2.20E

PL

As+ /’

ii

,p’o

‘0‘3 -

P’

c; %2U < nU ’

-

O/ 0

l

.f

Projected

Range

o

Crowder

&Tltle

Present

work

/

/

A.. 1 Reduced

2 Energy

3

Fig. 3. Reduced projected range versus reduced energy for Mn and Te implanted into Al and Al, Zn, and Te implanted into Si. The open circles correspond to the experimental data reported by Crowder and Title.

Pro)ected

N: Al:

A;

Range Mn: NI:

Kr'Te+, Xe’

Theory --1

OO

Average

2 Reduced

Winterbon et 01 lm=0.5 h=O.LZl Gibbons

et al i.

3 Energy

F g. 4. Average reduced projected range versus average reduced er~ergy for “N. “Al. and “‘Te implanted into GaAs. The solid lil.es and dashed curves denote the WSS (m = l/2. h = 0.42) ar d CrJM predictions.

12‘Te implanted into GaAs. As clearly seen, the theorerical estimate by Gibbons et al. (GJM) [7] agrees with our experimental data for “N and lZXTe but gives much lower values for Al than the present result. The WSS parameters m = i and h = 0.42 are a reasonable overall approximation for GaAs substrates. The optimum WSS parameters derived from the present experiment for Si, LiF, Al,O,, GaP. and GaAs are listed in table 1. As can be seen in fig. 4. the average reduced projected range is pr,lportional to the average reduced energy but not expressed by a unified relation for the various ion! implanted into GaAs. The present result for GaP is almost the same as that for GaAs, whereas the general relation p, = 1.20 c,, has been obtained for LiF and Al 20, substrates consisting of low Z elements In order to derive a universal relation between reduced projected range and average reduced energy for all ion-substrate combinations, we introduce a modificd scaling coefficient defined by ,1

c,,,= nCc,cu;c;, (Y; = ( Z,/Zp)().‘”

= 1.0

Table

for Z, < Z, , for Z, 2 Z, .

1

WSS parameters

available

for Si, LiF. AI,O,,

GaP. and GaAs

substrates. Substrate

Projected

Si Ga4s GaP Al 70, LiF’

we = 0.5. II? = 0.5, m =0.5, m=0.5, M = 0.5.

range h = 0.4OkO.02 X = 0.42kO.02 X=O.42kO.O2 h=0.35*0.02 h = 0.37 * 0.02

Damage

depth

m m M m

X = 0.4OkO.02 h = 0.42kO.02 h=0.35*0.02 x=0.35*0.02

= 0.5. = 0.5. =OS. =os,

I/”

OO

1

2 Average

3 Reduced

L

5

Energy

Fig. 5. Modified reduced projected range versus average reduced energy for N. Al. Ar. Mn. Ni. Te. and Xe ions implanted into LiF. Al ,O,. GaP, and GaAs. The open circles correspond to the experimental data for “Kr and “?Xe implanted into Al,O, reported by Jespersgard and Davies.

where Z, and Z, correspond to the atomic numbers of the constituent target atoms and the implanted ions, respectively. Thus, the modified reduced projected range LiF. Al,O,. GaP, Pmp (= C,npRp) fo r ion-implanted and GaAs are plotted as a function of the average reduced energy in fig. 5. As clearly seen, the experimental data are well described by the universal relation n,p = 2.35~,,. This expression is consistent with that P proposed by Kalbitzer and Oetzmann and with the WSS prediction. 4.2.

Dumuge

depth

We have found out the generalized scaling law in the relation between the modified reduced projected range and the average reduced energy. It is natural to expect another universal expression for the modified reduced damage depth versus the average reduced energy. Fig. 6 shows the linear relation of the reduced damage depth versus the reduced energy for Al+. Zn+. and Te+-implanted Si substrates. Except for the data points for P+-implanted Si reported by Crowder and Title [2]. experimental data are expressed by the relation p,, (6 ) = 1.8Oc. The average reduced damage depth p,, for ‘“N +, 27Al+. and 4”Arf-implanted GaAs are plotted as a function of 6.1V in fig. 7. For “Al’ and 4”Ar+-implanted GaAs. the WSS parameters no = l/2 and X = 0.42 give good agreement with the present experimental data. On the other hand, the WSS values for “N+-implanted GaAs are 25% lower than the experimental data. A general relation cannot be seen also for the Ar”. and Mn ‘-implanted GaP. However, the relation pJ = 1.05~.,, applies to the Mn+, Ni’, and Te’-implanted AlJO, substrates. As described in sect. 4.1. we introduce the modified 11. RANGE

AND

DAMAGE

PROFILES

Y. Kido et al. / Averqe

projected

r

reduced damage depth defined by prnd = C&R,. Here, R, is the average damage depth. The experimental values of prnd for ion-implanted GaAs are plotted as a function of rsV in fig. 8. The similar universal relation to polyatomic media and P”,d = 1.9OF,,, is applicable consistent with the result obtained for ion-implanted Si. The optimum WSS parameters for ion-implanted Si, Al 20,. GaP, and GaAs substrates are listed in table 1,

Al+, Zn’, Te’ + SI .

l

“d = 1.80E _j__ +

0 P+

/ lO AS’ 0

/

Damage

P+

Depth

o Crowder l

2

1 Reduced

g Title

Present

work

3

Energy

Fig 6. Reduced damage depth versus reduced energy for Al+, Si. The open circles are the experizn+, and Te+-implanted mental data for P+ and As+-implanted Si given by Crowder and Title.

2’

1.5 GaAs

i

/

---

/ OO

1 Average

2 Reduced

3

WInterban et 01 m=05. h=O.LZ m=os.

X=056 L

Energy

Fig. 7. Average reduced damage depth versus average reduced GaAs. The solid energy for “N+, “Al+, and 40Ari-implanted lines denote the WSS predictions (m = I, X = 0.42)

Average

Reduced

range and dumuge deprh

Energy

Fig. 8. Modified reduced damage depth versus average reduced energy for N +, Al+, Ar+. Mn+. Ni+, Te+. and Xe+-implanted Al 2O,. GaP, and GaAs.

5. Conclusion Depth distributions of implanted ions and displaced host atoms ar.: determined by means of backscattering, nuclear resonance reaction, and channeling measurements followed by computer simulation analysis. The present results certify the availability of the power approximation proposed by Winterbon et al. The optimum WSS parameters derived from the present experiment are m = i and X ranging from 0.34 to 0.44. The universal expressions of the average projected range and average damage depth available for any ion-substrate combination have been derived from systematic data analysis. In fact, introduction of the new scaling coefficient gives two universal relations of P,,,, = 2.356,” and Pm‘1= 1.9Or,, for ion range and damage depth, respectively. The physical meaning of this scaling is not yet clarified but these scaling laws are very useful in device fabrication by ion implantation. The authors would like to thank H. Doi, S. Noda, and T. Hioki for valuable discussions. The technical support of A. Itoh and M. Ohkubo is also gratefully acknowledged.

References [l] P. Jespersgard and J.A. Davies, Can. J. Phys. 45 (1967) 2983. [2] B.L. Crowder and R.S. Title, Ion Implantation (Gordon and Breach, New York, 1971) p. X7. 13) J. Lindhard, M. Scharff and H.E. Schiott, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 33 (1963) no. 14. Range [41 D.K. Brice and K.B. Winterbon. Ion Implantation and Energy Deposition Distributions, (IFI/Plenum, New York, 1975). [51 K.B. Winterbon, P. Sigmund and J.B. Sanders, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 37 (1970) no. 14. [61 S. Kalbitzer and H. Oetzmann, Radiat. Eff. 47 (1980) 57. [71 J.F. Gibbons, W.S. Johnson and SW. Mylroie, Projected Range Statistics, (Halstead Press, New York, 1970). VI Y. Kido and Y. Oso. Nucl. Instr. and Meth. B9 (1985) 291. and J.F. Ziegler, Hydrogen Stopping [91 H.H. Andersen Powers and Ranges in All Elements, (Pergamon Press. New York, 1977). IlO1 W.K. Chu, Phys. Rev. Al3 (1976) 2057.