Concentration-dependent redistribution of arsenic in silicon during thermal oxidation

Thin Solid Films 258 (1995) 336-340

ELSEVIER

Concentration-dependent redistribution of arsenic in silicon during thermal oxidation Seong S. Choi, M. J. Park*, W. K. Chut Department of Physics, Sun Moon University, Ah San, Chung Nam 337-840,

South Korea

Received 23 February 1994; accepted 14 September 1994

Abstract The redistribution phenomena (such as pile-up, push-back) of arsenic impurities in silicon during thermal oxidation are dependent upon the oxidation rate, the diffusivities of arsenic in silicon and SiO,, and the segregation rate of arsenic impurities at the interface between the oxide and silicon. The diffusivity of arsenic in SiO, is known to be negligible compared with the diffusivity of arsenic in silicon and the oxidation rate of silicon. The diffusivity of arsenic in silicon is also dependent on the arsenic concentration. The pile-up at the Si-SiO, interface as a result of the concentration dependence of arsenic, has not reported so far. For silicon samples implanted with low fluences (1 x 10” or 3 x lOI err?) of arsenic at 100 keV, a pile-up of arsenic was observed during thermal oxidation at 1050 “C, using Rutherford backscattering spectroscopy. For silicon samples implanted with fluences greater than 3 x lOI cm-*, push-back phenomena were observed. These phenomena can be explained only by the diffusivity of arsenic, dependent upon the concentration of arsenic in the silicon. Keywords:

Diffusion; Interfaces; Oxidation;

Rutherford

backscattering

1. Introduction Redistribution phenomena during the oxidation of impurities in silicon is dependent upon the ratio of the oxidation rate to the diffusion rate of the impurities. A theoretical model for the redistribution of arsenic impurities in silicon has been presented by Grove et al. [ 11. Experimental results, such as the pile-up of arsenic at the Si-SiOz interface during thermal oxidation of silicon, also have been described [2,31. The oxidation rate can be varied by increasing the oxygen pressure during thermal oxidation, while diffusion of arsenic impurities can be enhanced either by increasing the oxidation temperature or the concentration of the impurity. The redistribution phenomena obtained by varying the oxidation temperatures and the

*Department of Physics, Korean Military Academy, Nowon-ku, Seoul, South Korea. tSuperconductivity Center, University of Houston, Science and Research One, Houston, TX 77204-5506,USA. 0040-6090/95/$9.50

0

1995 -

SSDI 0040-6090(94)06374-5

Elsevier Science S.A. All rights reserved

spectroscopy

oxidation pressure have been reported previously [4]. Arsenic pile-up at the Si-SiOz interface during oxidation of arsenic ion-implanted silicon at 1050 “C has been investigated in terms of the diffusion rate of arsenic, dependent on the impurity concentration in the silicon.

2. Experimental

procedure

Samples were prepared by implantation arsenic ions of energy of 100 keV at fluences of 1 x 10157 x lOI As + cm2 on Si( 100) wafers. Thermal dry oxidations with and without a 4.5% HCI ambient, along with steam oxidation, were performed at 1050, 950 and 850 “C. All the samples were cleaned prior to oxidation, using the RCA cleaning method [S] followed by dipping in HF for 5 s. The thermal oxidations in previous reports [4, 51 were carried out to change the ratio BID'12, by varying the oxidation temperature or changing the dry oxygen pressure. The oxide thickness was measured using a

331

S. S. Choi et al. / Thin Solid Films 258 (1995) 336-340

Nanospec/AFT 010.0180 model. The depth profile of arsenic was examined by Rutherford backscattering spectroscopy (RBS) with helium ions of energy 2 MeV and by secondary ion mass spectroscopy (SIMS) using a primary beam of 0: ions of energy 15 keV. The differences between the arsenic profiles obtained by RBS and SIMS were also compared. The SIMS measurements were more accurate in depth, as a result of better resolution. The profiles of arsenic obtained by RBS were qualitatively agreeable with the SIMS data and were acceptable for our experimental purposes. About 200 8, of gold was evaporated on the surfaces of the same SiOz samples to avoid charging effects of the Si02 during SIMS measurements. In this report, only the arsenic profiles obtained by RBS of the samples with fluences of 1 x 1015, 3 x lOI and 3 x lOI As+ cm-* during thermal oxidation at 1050 “C were compared. The effect of the concentration-dependent diffusivity of arsenic was examined.

3. Discussion

and results

3. I. D@ision

during oxidation

When the oxide thickness is great enough for the oxidation rate to be controlled by diffusion of oxygen through the oxide, and not by the reaction rate at the Si-SiO, interface, the oxide thickness X will be determined by x = &‘I*

(1)

where B is the parabolic growth rate constant, proportional to exp( -E,/kT) at a given temperature for an oxidation time t, and E,, is the activation energy. During oxidation periods, the diffusion length X,, for arsenic in silicon is given by X,, = 2(Dt) I”

(2)

where D is the diffusivity of arsenic in silicon, proportional to exp( - E,/kT) during oxidation time t, and Ed is the activation energy for arsenic diffusivity. The diffusivity D will be given by [7] D = D,exp( -E,/kT)

The ratio of the Si-SiO, interface velocity (dX/dt) to the arsenic diffusion velocity in silicon (dX,,/dt) becomes proportional to the dimensionless quantity B/D’12. This ratio can be varied by changing either the oxidation rate B or the diffusivity D of arsenic in silicon. The dry oxygen pressure can be increased while keeping the diffusivity value constant, in order to change the oxidation rate [6]. Alternatively, the diffusivity value can be changed not only by variation of the oxidation temperature but also by increasing the arsenic concentration in the silicon. Details of the concentra-

tion-dependent diffusivity of impurities in silicon at a given temperature have been published by Fair [7]. In this paper, the redistribution phenomena of arsenic as a function of the concentration of arsenic in silicon during thermal dry oxygen oxidation at 1050 “C will be examined and explained in terms of the competitive relationship between the oxidation rate and the diffusion rate. The previous reports [4, 51 explain the pile-up and trapping phenomena dependent upon the ratio of the oxidation rate to the diffusivity, i.e. B/D”*. 3.2. Impurity

segregation

at Si-SiO,

interface

When silicon is thermally oxidized, a dopant impurity will redistribute at the interface until its chemical potential is equal on both sides of the interface, i.e. in silicon and SiO,. The ratio of the equilibrium concentration of the impurity dopant in silicon to that in SiO, near the interface is defined as the equilibrium segregation coefficient m. This segregation coefficient will be primarily determined by the chemical potential difference, the diffusivity of the impurity in the oxide, and the rate at which the interface moves with respect to the diffusion rate [ 1, 91. The redistribution phenomena, such as pile-up, depletion and push-back, of impurities in silicon near the Si-SiO, interface are dependent upon the ratio of the rates of oxidation and impurity diffusion in Si02 [ 1, 4, 10, 111. When the impurity segregation coefficient is less that unity (higher solubility in the SiO, than in silicon), as is the case for boron, the impurity will deplete into the SiO, [ 1, 121. However, for an impurity segregation coefficient larger than unity, impurities such as arsenic will pile up (snow plowing) in the silicon near the interface during oxidation. This is the case only when the diffusion rate is not greater than the Si-SiO, interface growth rate (oxidation rate). The diffusion of the impurity in the silicon will be dependent upon the temperature and concentration of the impurity in the silicon. In contrast, the oxidation rate will be dependent upon the temperature and the oxygen pressure. Thus, the oxidation rate was varied by increasing the pressure while keeping the temperature constant. However, by lowering the oxidation temperature, one can obtain an oxidation rate greater than the diffusion rate of the impurity in the silicon. This is because the diffusion rate decreases more rapidly with decreasing temperature than does the oxidation rate. The pile-up (snow-plow) phenomena dependent upon the B/D1/2 value less than 50 have been examined. When the temperature is decreased to a level of about 800 “C, the snow-plow phenomena at the interface increase. When the temperature becomes greater than 1000 “C, (i.e. the diffusion rate of the impurity in the silicon is greater than the oxidation rate), then the impurity would exhibit no pile-up at the interface,

S. S. Choi et al. 1 Thin Solid Films 258 (1995) 336-340

338

depending upon the concentration of the impurity in the silicon, while the impurity profile would be pushed back into the silicon substrate. This phenomenon can be called the “push-back phenomena without pile-up”. The relationship between the ratio of the oxidation rate to the diffusion rate (diffusivity) in silicon (B/D’/2), and the impurity pile-up in silicon or depletion at the Si-$0, interface has been observed before for both phosphorus and boron [ 1, 11- 141. The redistribution of phosphorus in silicon for values of B/Dli2 ranging from 0.1 to 10 was presented, with more pile-up found at the interface for greater values of B/D”‘. Impurity “snow plowing”, i.e. pile-up, at the interface also depends on the diffusivity of the impurity in the oxide. For example, for impurities such as gallium in silicon there is no snow plowing, only depletion of gallium near the silicon side of the interface, as a result of fast out-diffusion of gallium in the oxide to the SiO,-gas interface, even though the segregation ceofficient is larger than unity [l, 111.

3.3. Concentration-dependent

diflusivity

The diffusivity of the impurity is dependent not only upon the oxidation temperature but also upon the concentration of the impurity in the silicon. The depth profile of implanted arsenic ions will be approximated by a symmetric Gaussian distribution function [ 15, 161. The concentration of implanted arsenic atoms as a function of position is n(x) = n(R,) exp{ -(x2-?)zI

3.4. Results For 1 x 1015As+ cm-’ implantation with energy 100 keV in silicon, the peak concentration nP will be about 1.93 x 1020cmm3. For 3 x lOI As+ cm-* implantation with energy 100 keV, nP will be about 5.97 x 102’ cme3. The concentration of arsenic in silicon becomes O.ln, when x = R, + 2r, and becomes 0.61 nP when x = R, + rP, so that most of the implanted arsenic atoms will be in a region between the surface and x =R,+2r,. For our implantation energy of 100 keV, R, and rP are about 580 A [ 141. The concentration at x = R, + 2r,(about 994 A) for a fluence of 3 x lOI As+ cm2 is 5.97 x 1020cmm3. We also assume that most of implantation damage during ramp-up preoxidation annealing periods will be repaired and that, during this epitaxial regrowth, most of the arsenic atoms were placed into substitutional sites [ 17- 191. The electrically active arsenic concentration at 1050 “C is reported to be about 3.5 x 102’ cmP3. The sheet resistance of the 3 x 1016As’ cm-’ samples after rapid thermal annealing at 1050 “C for 10 s is about 45 R. In contrast, the sheet resistance for the samples with 5 x lOI cm-* after 30 min of ramp-up preoxidation annealing at 1050 “C is 30 Q. The detailed arsenic diffusion during the ramp-up annealing period was reported elsewhere [20, 211. The arsenic diffusivity at 1050 “C for silicon samples implanted with 3 x lOI As+ cme2 is about -2.5 x lo-l3 cm2 SK’, while the diffusivity for samples implanted with 1 x 10” and 3 x lOi As+ cm-’ becomes intrinsically about 4 x lo-l5 cm2 s-l from the graph published by Fair [7]. Two different phenomena were observed during thermal dry oxidation, depending on the concentration of the arsenic in the silicon: pile-up and push-back.

where the maximum concentration nP occurs at x = R,, and rP is the standard deviation. The diffusivity of the impurity will be given by

n

+ni,

where n is the extrinsic electron concentration and ni is the instrinsic electron concentration at the diffusion temperature. The factor of 2 represents the maximum enhancement of the diffusivity from the electric field effect. This formula for the arsenic diffusivity is from the multicharge state model, rather than the charge vacancy model of Hu and Schmidt [15]. In this report, the diffusivity of arsenic is taken from the published experimental data of Fair [7].

30

50

70

90

110 130 CHANNEL

150

170

190

210

Fig. 1. Arsenic profile obtained by RBS after 100 min of thermal dry oxidation at 1050 “C of arsenic-implanted silicon with fluence of 1 x 1Ol5 cm-’ at an energy of 100 keV. A pile-up phenomenon of arsenic at the Si-SiO, interface has been observed.

S. S. Choi et al.

I Thin Solid Films 258 (1995) 336-340 8000

8000

:; . 5.

.

-*.:

.

E,=

I.56

o=

MeV

I 561

MeV

.

6000

6000

..a,. , -..;-_.*.. . .- .

,” w 4000

9 w 4000 >

-. .. . .

. .

-1

c

2000

.

x5

2000

0

C 10

30

50

70

90

110

130

150

170

190

IO

210

30

50

70

3.4.1. Pile-up

Pile-up phonomena were observed by RBS, as shown in Figs. 1 and 2. The diffusion length X, is given by Eq. (2). The calculated minimum diffusion length X, during the oxidation procedure will be about 980 8, for a 100 min of oxidation at 1050 “C. Considering the molar ratios, the depths of silicon consumed for 2100 and 2000 A of oxide growth will be 924 and 880 A, respectively, i.e. d,i = 0.44d, where d is the thickness of SiO,. By considering the original peak distance R, (600 A) for 100 keV, As+ ion implantation, the arsenic pile-up peak at the interface does not result from the implantation peak but from arsenic segregation at the Si-SiOz interface. 3.4.2. Push -back A push-back phenomenon at the interface was served, as shown in Fig. 3, during 100 min of oxidation (with 4.5% HCl ambient at 1050 “C) of con samples implanted with 3 x 1016As+ cmp2. We

after thermal

oxidation

%

( x 1020 cmm3)

D (cm2 s-l)

;min)

1 3 3 3

1.93 5.79 51.9 51.9

4 x lo-‘5 4 x lo-‘5 2.5 x lo-‘s 2.5 x lo-t3

100 100 30 100

“See Fig. 1. %ee Fig. 2. “See Fig. 3.

obdry silialso

at 1050 “C of silicon

Dose (cm-‘) lOI 10’5 10’6 lOI6

110

Fig. 3. Pushback phenomenon of arsenic higher concentration-dependent diffusivity dation at 1050 “C of arsenic-implanted 3 x lOI cm-’ at an energy of 100 keV.

Fig. 2. Another pile-up phenomenon of arsenic during dry oxidation of arsenic-implanted silicon with fluence of 3 x 10’scmm2 at an energy of 100 keV.

Table 1 Redistribution phenomena energy 100 keV

90

130

I50

170

I90

210

CHANNEL

CHANNEL

x x x X

339

observed push-back phenomena during dry oxidations for 20, 30 and 40 min with and without a 4.5% HCl ambient. For dry oxidation of silicon implanted with 4 x 1016As+ cme2, for 100 min at 1050 “C, a push-back phenomenon of arsenic was also confirmed by RBS. In Table 1, the ratios of the oxidation rate to the diffusion rate of arsenic in silicon (B/D I”) for our experimental conditions are given. As our calculations indicate, when pile-up phenomena occur, the value of BID ‘I2 becomes about 4. For push-back phenomena, the value of B/D r’2 becomes 0.6. This is in agreement with our observations [5, 20, 211. The push-back phenomena were reported for B/D”2 of approximately unity during thermal oxidation of silicon implanted with very high fluences of arsenic [5]. 4. Conclusions Our previous results have exhibited trapping and pile-up of arsenic impurities at the Si-SiO, interface,

wafers

implanted

with

1 x 10t5, 3 x 10” and 3 x lOI6 As+ cm-*

d

980 980 4240 7700

is observed as a result of of arsenic during dry oxisilicon with fluence of

(A)

PB, s-“2)

2000 2100 1250 2266

25.8 27.1 29.5 29.3

B/D”’

Phenomenom

4.1 4.3 0.6 0.6

Pile-up” Pile-upb Push-back Push-back’

with

S. S. Choi et al. I Thin Solid Films 258 (1995) 336-340

340

depending upon the value of B/D"2.For a value of B greater than 50, trapping of arsenic in the oxide was exhibited, while pile-up at the interface was observed for values of B less than 50 [4,5]. Without the concentration-dependent diffusivity of arsenic in silicon, the experimental results about the arsenic profile in silicon cannot be explained. These observations reveal that the pile-up and push-back of arsenic depend on the concentration of arsenic in the silicon and on the value of B/D"2. (1) Pile-up phenomena at the Si-SiO, interface were observed as a result of low diffusivity of the arsenic impurities in silicon (about lo-” cm2 s-‘) during thermal dry oxidation at 1050 “C of silicon samples implanted with fluences of 1 x lOI and 3 x 1Or5As+ cmm2 at 100 keV. (2) Push-back phenomena at the Si-Si02 interface were observed as a result of high diffusivity (about lo-r3 cm* SK’) of the arsenic impurities in silicon during thermal dry oxidation at 1050 “C of silicon samples implanted with fluences greater than 3 x 1016As+ cmp2 at 100 keV. The ratio of the oxidation rate to the diffusion rate (B/D"*), has been found to be about 4 for pile-up becomes 0.6 for push-back phenomena, while BID '/* phenomena of arsenic. This result, along with our previous reports [5], will support a revised impurity redistribution model; that of a competitive relationship between the segregation rate, oxidation rate and diffusion rate.

References [l] A. S. Grove, 0. Leistiko, Jr. and C. T. Sah, .I. Appl. Phys., 35 (1964) 2695.

121H. Muller, J. Gyulai, W. K. Chu and J. W. Mayer, J. trochem. Sot.,

Elec-

122 (1975) 234.

[31 R. B. Fair and J. C. C. Tsai, J. Electrochem. Sot., 122 (1975) 1689.

[41 Seong S. Choi, M. Z. Numan, W. K. Chu, J. K. Srivastaba and E. A. Irene, Appl. Phys. Lett., 50 (11) (1987) 688. [51 Seong S. Choi, W. K. Chu and E. A. Irene, Proc. First Int. Conf on VLSI and CAD. Seoul, 1989, p. 108. [61 E. A. Irene, D. Dong and R. J. Zeto, J. Electrochem. Sot., 127 ( 1980) 396.

[71 R. B. Fair, Concentration profiles of diffused dopants in silicon, in F. F. Wang (ed). Impurity Doping Process in Silicon, North-Holland, New York, 1981, Ch. 7, p. 343. 181 W. Kern and D. A. Puotinen, RCA Rev., 31 (1973) 187. [91 C. D. Thurmond, in H. C. Gatos (ed.). Properties of Elemental and Compound Semiconductors, Interscience, New York, 1960, p. 121. [lOI E. C. Frey, N. R. Parikh, M. L. Swanson, M. Z. Numan and W. K. Chu, Mater. Res. Sot. Symp. Proc., 10.5 (1988) 277. 1111 B. E. Deal, A. S. Grove, E. M. Snow and C. T. Sah, J. Electrochem.

Sot.,

I12 (1965) 308.

1121 J. W. Coby and L. E. Katz, J. Electrochem. Sot., 123 (1976) 409.

1131 B. E. Deal and M. Sklar, J. Electrochem.

Sot., 112 (1965) 430. [I41 C. P. Ho, J. D. Plummer, J. D. Meindle and B. E. Deal, J. Electrochem. Sot., 125 (1978) 665. [I51 S. M. Hu and S. Schmidt, J. Appl. Phys., 39 (1968) 4272. 1161 T. E. Seidel, Implantation, in S. M. Sze (ed.), VLSI Technology, McGraw-Hill, New York, Ch. 6, p. 225. [I71 J. F. Gibbons, W. S. Johnson and S. W. Mylroie, Projected Range Statistics, Hutchinson St Ross, Dowden 2nd edn., 1975.

iI81 L. T. 1191 S. F. PO1 S.

Csepregi, E. F. Kennedy, T. J. Gallagher, J. W. Mayer and W. S&non, J. Appl. Phys., 48 (1977) 10. R. Wilson, W. M. Pauson, R. B. Gregory, A. H. Hami and D. McDaniel, J. Appl. Phys., 55 (1984) 4162. Choi and W. K. Chu, Proc. First Int. Conf on VLSI and CAD, Seoul, 1989, p. 100. WI S. S. Choi and M. J. Park, J. Korean Phys. Sot., 25 (3) 1992) 2266229.