Calculation of ion implanted boron emitter profiles

Nuclear Instruments and Methods 209/210 (1983) 27-31 North-Holland Publishing Company

27

CALCULATION OF ION IMPLANTED B O R O N EMITTER PROFILES Aleksander B,SKOWSKI and Wac/aw J. B I A L K O W S K I Institute of Electron Technology, 02668 Warszawa, Poland

The diffusion of ion implanted boron in the emitter region of a microwave p-n-p bipolar transistor has been studied. Boron implantations were performed in the dose range 3 x 1015-1x 1016cm-2 and the annealing time at 900°C was changed from 30 to 120 min. The four stream diffusion model was applied to calculate electrically active and inactive boron profiles. Calculated profiles were compared to the experimental one obtained using secondary-ionmass spectrometryand the incremental sheet resistance method. The Boltzmann-Matano analysis technique was applied to the diffusion profiles obtained and the variation of the effectiveboron diffusion coefficient with implanted dose and annealing time was determined. Electrical activity was also determined for different boron doses and annealing times.

1. Introduction Over the past several years ion implantation with subsequent drive-in diffusion has frequently been used in semiconductor processing to produce precisely controlled vertical device structures. The technique appears to be particularly useful for microwave bipolar transistor fabrication. Microwave bipolar transistor parameters are very sensitive to the base width, so precise control of the diffusion depth is extremely important. Typical structures usually have base width in the range 0.1-0.3 /~m and it is strictly determined by the emitter diffusion process. During emitter annealing, which is necessary to remove crystal damage caused by the implantation and to bring boron ions to substitutional lattice sites, after high dose implantation, enhanced boron diffusion occurs. This anomalous diffusion effect plays a significant role especially during shallow (less than 0.5 #m), highly doped emitter region processing and determines the minimum emitter-base junction depth. The behaviour during annealing of a concentration profile obtained by ion implantation is affected by crystal damage and by a considerable fraction of boron at nonsubstitutional lattice sites. All these effects caused by ion implantation influence the boron diffusion rate and its electrical activity. Enhanced diffusion of ion implanted boron was reported in numerous papers [1-5]. The diffusion coefficient of boron at 900°C was estimated to

have a value in the range 1.4 x 10-14-2.6 x 10-14 cm2/s, i.e. an order of magnitude higher than the thermal diffusion coefficient. A fast diffusion effect is assumed to be due to the diffusion of boron interstitials [4] or to the diffusion of boron-vacancy pairs [6,7]. It has been suggested by Frank and Berry [9] that the nonsubstitutional boron present after room temperature implantation consists mostly of boron - vacancy complexes together with a relatively small number of boron interstitials. The boron interstitials anneal at 200-300°C without long range migration, whereas the B - V complexes are thermally stable. Annealing of B - V complexes may proceed either by the capture of silicon selfinterstitials [9] or by the dissociation of the complexes [8]. Chu and Gibbons [6] proposed that during the anneal, the B - V pairs break up spontaneously into their consistuents until thermodynamic equilibrium is reached. To extend their three species model to high dose implantation cases when the peak impurity concentration exceeds the solid solubility limit, boron precipitates were included [8]. A model containing four interacting species is capable of explaining the major features of the annealing behaviours. These species are: substitutional boron, boron-vacancy pairs, positively charged vacancies, and immobile boron. With these four species both the diffusive redistribution and the electrical activity of the implanted boron during annealing can be modeled. It is the purpose of this work to calculate, using this model, electrically active and inactive boron

0 1 6 7 / 5 0 8 7 / 8 3 / 0 0 0 0 - 0 0 0 0 / $ 0 3 . 0 0 © 1983 North-Holland

I. THEORY

28

A. Bqkowski, W.J. Biatkowski / Ion implanted B emitter profiles

profiles in the emitter region of a microwave p - n - p bipolar transistor. Calculated profiles were compared to the experimental one obtained using SIMS and the incremental sheet resistance method. Good agreement between the calculated and experimental results was achieved.

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2. Experimental details The samples used for the measurements were {111) oriented p-type wafers with a 6 # m thick, 3 J2 cm boron doped epitaxially grown layer. The wafers were implanted with arsenic at a dose of 2 x 1014 cm-2. Following the implantation arsenic was driven-in in dry N 2 / O 2 atmosphere for 40 min at temperature 1160°C. An N-type layer, typical for p - n - p transistor base, with depth 0.65-0.75 /~m and a sheet resistance of 300 g2/D was formed. Subsequently the wafers were implanted with boron. Boron implantations were performed through a 0.12 ffm thick oxide layer at an energy 60 keV, at doses of 3 x 10 ~5, 6 x 10 ~5 and 1 x 1016 c m - 2 . The oxide layer was used to reduce the boron projected range in silicon, to minimize silicon damage at the surface during implantation and to prevent evaporation of impurities during subsequent nitrogen drive-in. After boron implantations the wafers were annealed in an N 2 atmosphere at 900°C for 30-120 min.

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Fig. 1. Concentration profiles of boron ( O ) and corresponding charge carrier profiles (e) obtained after implantations with different doses. Annealing temperature 900°C, annealing time 60 min, implantation energy 60 keY. (a) Q = 3 x 1015 c m - 2, (b) Q = 6 x 1015 cm -2, (c) Q = 1 x 1016 cm -2. Solid lines represent the four stream diffusion model simulation.

3. Experimental results

3.1. Concentration profiles of ion implanted boron The concentration profiles of implanted boron were measured using secondary-ion mass spectrometry. The accompanying charge carrier profiles were determined by sheet resistivity measurements combined with layer removal by anodic oxidation and etching. Fig. 1 gives the concentration profiles of boron and the corresponding charge carrier profiles.

3.2. Emitter-base junction depth

fig. 2. Boron implantation was performed at a dose of 6 x 1015 c m - 2 and an energy of 60 keV. The xj versus ~/t data in fig. 2 have for annealing time less than 60 min a slope corresponding to a °7r

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The p - n junction depths were measured for each sample using groove and stain techniques. The emitter-base junction depth dependence on emitter annealing time at 900°C is presented in

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Fig, 2. Emitter-base junction depth versus square root of emitter annealing time at 900°C. Boron implanted at a dose of 6 x 1015 cm 2 at an energy of 60 keV. Junction depths calculated for two different diffusion coefficients are also shown.

A. Bqkowski, W.J. Biatkowski / Ion implanted B emitter profiles 50

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3.4. Boron electrical activity

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The integral relative electrical activity, defined as the integrated electrical charge related to the implanted ion dose was found. In fig. 3 electrical activity for b o r o n versus annealing time for three different doses is shown.

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Fig. 3. Electrical activity as a function of annealing time at 900°C for three different doses: (a) Q = 3 x l0 Is cm -2 (,~), (b) Q = 6x 1015 c m 2 ( m ) , (C) Q = 1 x 1016cm 2 (e). Lines represent the four stream diffusion model calculation results.

diffusion coefficient of 2.6 × 10-14 c m 2 / s and for annealing time greater than 60 min a slope corresponding to a diffusion coefficient of 2.5 × 10-is cm2/s. Therefore not until after about 60 min of annealing does a substitutional-type diffusion prevail. 3.3. Boron diffusion coefficient

In order to determine the effective diffusion coefficient of b o r o n in the emitter region concentration profiles of electrically active b o r o n were approximated by smooth spline functions and using the B o l t z m a n n - M a t a n o transformation b o r o n diffusion coefficients were determined [10]. In fig. 4 the effective diffusion coefficient of b o r o n for three different doses, 3 x 10 ]5, 6 x 10 Is and 1 × 1016 c m - 2 , after 30, 60 and 120 min of annealing is shown. The effective diffusion coefficient versus annealing time calculated from profiles obtained using the four stream diffusion model is also shown in fig. 4.

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20 4-0 60 80 100 TIME (rain) Fig. 4. Effective diffusion coefficient of boron as a function of annealing time at 900°C for three different doses: (a) 3 x 1015 cm 2 (O), (b) 6×1015 cm 2 (m), (c) l×1016 cm -2 (A). Lines represent the four stream diffusion model calculation results.

4. Discussion Implantation of b o r o n into silicon at r o o m temperature produces the same order of magnitude of substitutional and nonsubstitutional boron atoms. Most of the nonsubstitutional b o r o n atoms are involved in B - V complexes [9]. Enhanced diffusion of ion implanted b o r o n is attributed to mobile, fast diffusing b o r o n fraction. This is assumed to be due to the diffusion of electrically inactive b o r o n - v a c a n c y pairs [6,7]. U p o n annealing the B - V pairs diffuse and convert into substitutional boron. Electrically active substitutional b o r o n diffuses by means of r a n d o m encounters with neutral vacancies. The diffusion of b o r o n then becomes a weighted diffusion with contributions from a slow, electrically active fraction (substitutional boron) and fast electrically inactive fraction ( B - V pairs). At high doses (greater than 10 Is cm 2) an inactive b o r o n fraction consisting of b o r o n precipitates is also formed when the implanted boron concentration exceeds the solid solubility [12]. Due to the thermal diffusion of b o r o n from an area of high concentration, dissolution of the precipitates occurs. Thus four species are involved in diffusion process of ion implanted boron. This species are B - V pairs, positive vacancies, substitutional boron, and b o r o n precipitates. To model the redistribution and electrical activity of b o r o n the chemical reactions and the diffusion of B - V pairs, vacancies, and substitutional b o r o n atoms must be taken into account (see Appendix). A large fraction of B - V pairs results in low electrical activity and fast diffusion, and conversely a large fraction of substitutional b o r o n results in high electrical activity and slow diffusion. Annealing will proceed with the conversion of a large population of B - V pairs into substitutional boron, with dissolution of precipitates and with decreasing diffusion rate and increasing electrical activity. During annealing at 900°C the b o r o n diffusion coefficient changes from 7 x 10-14 I. THEORY

30

A. Bqkowski, W.J. Biatkowski / Ion implanted B emitter profiles

cm2/s (diffusion rate of B-V pairs [6]) to 2.5 × 10 ~5 cm2/s (diffusion rate of substitutional boron [11]). For annealing times between 30 and 60 min the diffusion rate changes from 2.6 × 10 14 cm2/s to 2.5 × 10 15 c m 2 / s (fig. 2). Because boron diffusion is a weighted diffusion of two species, substitutional boron - electrically active and slow diffusing and boron--vacancy pairs - electrically inactive and fast diffusing a relation between diffusion and electrical activity exists. Electrical activity should approach 100% as enhanced diffusion diminishes to the ordinary diffusion rate, but due to boron precipitates approaches only 43% for a dose of 3 × 1015 cm -2 and 21% for a dose of 1 × 1016 cm 2. The rate at which the precipitates are dissolved is determined by the thermal diffusion of boron from the area of high concentration. Increase of the electrical activity for prolonged annealing is only due to dissolution of the boron precipitates (fig. 3). As was mentioned above the diffusion coefficient of boron shows a dose dependency (fig. 4). It is well known that the diffusion rate is proportional to the point defect concentration. Increasing the implanted dose, the concentration of positive vacancies is increased. Consequently increased concentration of boron-vacancy pairs as compared to substitutional boron concentration causes diffusion enhancement.

Appendix The annealing behaviour of ion implanted boron is governed by spontaneous conversion of B V pairs into substitutional boron. This process can be treated by the following chemical reaction k~

B - V + ~ B + V +, k2

where k 1 and k 2 are respective rate constants. On the other hand, during the annealing the release of vacancies from vacancy clusters, the absorption of vacancies to restore the equilibrium vacancy concentration, and boron precipitate dissolution take place. Taking account of the chemical reactions and the diffusion of B - V pairs, vacancies, and substitutional boron atoms, the simultaneous differential equations of the diffusion may be written aC B

02CB

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-- reaction rate,

02C~v - D B va X- z

+ reaction rate - precipitation rate + dissolution rate, aCv+

at

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- Dv + - aX - 2

-reaction rate - dissolution rate + generation rate - attainment of 5. Conclusions Ion implanted boron shows anomalous diffusion effects in the emitter region of p - n - p transistors during annealing at 900°C. The effective diffusion of boron is the weighted diffusion of two species: fast diffusing boron-vacancy pairs and slow diffusing substitutional boron. The diffusion of boron and its relative electrical activity are strongly affected by annealing time and ion implanted dose. A four stream diffusion model, taking into account simultaneous diffusion of four species (boron-vacancy pairs, substitutional boron, positive vacancies, boron precipitates) is particularly useful for analysing and predicting ion implanted boron and corresponding charge carrier profiles in the emitter region of p - n - p transistors. All the anomalies in the boron diffusion are well explained.

equilibrium rate, aCBp at - precipitation rate - dissolution rate; where C B, C~v, Cv~, CBp are the concentrations of boron substitutional atoms, B-V pairs, positive vacancies, and boron precipitate and D~, DBv, Dv+ indicate the diffusion coefficients of substitutional boron, B-V pairs, and positively charged vacancies, D~ = 0.55 exp( - 3 . 4 2 / k T ) cm2/s DBv = 6.65 × 10 5 e x p ( - 2 . 0 9 / k T ) cm2/s,

D v . = 9 × 10 `5 e x p ( - 0 . 3 3 / k T ) cm2/s, Reaction rate = -

[11] [8]

[13]

CBv - koCBCv+ T

where k 0 = 4 × 10 -28 e x p ( 3 . 3 8 / k T ) cm 3 [8] equilibrium constant and r = 1.51 × 10 5

A. Bqkowski, W.J. Bialkowski / Ion implanted B emitter profiles exp(1.76/kT)

s [8] - r e a c t i o n t i m e c o n s t a n t .

Precipitation rate -

rp

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s o l v e d u n d e r the f o l l o w i n g initial c o n d i t i o n s C B ( X, 0) = 0,

CBv - C s s

CBv ( X, 0) = A s - i m p l a n t e d b o r o n p r o f i l e ,

w h e r e C s s - s o l i d s o l u b i l i t y limit, rp = 1 s (arbitrarily small) - p r e c i p i t a t i o n t i m e c o n s t a n t .

Dissolution _ rate

31

C s s - (CBV + C B )

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C v + ( X , 0 ) = Cv+eq(gF) , CBp(X,

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A full d e s c r i p t i o n of the m o d e l is g i v e n in ref. 8 to w h i c h the r e a d e r is referred.

References

w h e r e rd~ s = 106 S ( d o s e a n d t e m p e r a t u r e d e p e n d e n t ) - t i m e c o n s t a n t for the d i s s o l u t i o n of b o r o n precipitate. G e n e r a t i o n of v a c a n c y r a t e = A D a m a g e ( x )

Tdarn X exp(-//-rda m ), where A-constant, damage(x)-primary damage p r o f i l e c o m p u t e d f r o m the e n e r g y d e p o s i t e d i n t o n u c l e a r process, rda m = 40 S -- t i m e c o n s t a n t s for the release o f v a c a n c i e s f r o m v a c a n c y clusters R a t e for a t t a i n m e n t of v a c a n c y e q u i l i b r i u m Cv+- Cv,~q

TV w h e r e Cv+eq = Cv,, e x p [ ( E v + - E F ) / k T ] c m 3 is the e q u i l i b r i u m c o n c e n t r a t i o n for p o s i t i v e v a c a n cies; Cvo = 5.5 • 10 22 e x p ( - 2 . 6 / k T ) c m -3 [14] the e q u i l i b r i u m c o n c e n t r a t i o n for n e u t r a l v a c a n c i e s ; Ec-Ev+=0.8-2.8-10-4T eV [15] the e n e r g y level o f p o s i t i v e v a c a n c i e s in the b a n d gap; E v is t h e F e r m i level: % = 10 - 4 s is the l i f e t i m e of the vacancies. The simultaneous differential equations were

[1] K. Wittmaack, J. Maul and F. Schulz, Ion implantation in semiconductors and other materials (Plenum Press, New York, 1973) p. 81. [2] H. Ryssel, H. Muller, K. Schmid and 1. Runge, Ion implantation in semiconductors and other materials (Plenum Press, New York, 1973) p. 215. [3] B.Z. Crowder, J.E. Ziegler and G.W. Cole, Ion implantation in semiconductors and other materials (Plenum Press, New York, 1973) p. 257. [4] W.K. Hofker, H.W. Werner, D.P. Oosthoek and H.A.M. de Greffe, Appl. Phys. 2 (1973) 265. [5] A. B~kowski and W.J. Bialkowski, Proc. Int. Working Meeting on Ion implantation in semiconductors and other materials (Prague, 1981) p. 151. [6] A. Chu and J.F. Gibbons, Ion implantation in semiconductors (Plenum Press, New York, 1976) p. 711. [7] J.R. Anderson and J.F. Gibbons, Appl. Phys. Lett. 28 (1976) 184. [8] A. Chu, Stanford University Technical Report No 4969-2 (1977). [9] W.F. Frank and B.S. Berry, Rad. Effects 21 (1974) 105. [10] A. B~kowski, J. Electrochem. Soc. 127 (1980) 1645. [11] D.A. Antoniadis, A.G. Gonzalez and R.W. Dutton, J. Electrochem. Soc. 125 (1978) 813. [12] W.K. Hofker, H.W. Werner, D.P. Oosthoek and N.J. Koenan, Appl. Phys. 4 (1974) 125. [13] M. Yoshida, Jpn. J. Appl. Phys. 18 (1979) 479. [14] J.A. Van Vechten, Phys. Rev. BI0 (1974) 1482. [15] J.A. Van Vechten and C.D. Thurmond, Phys. Rev. BI4 (1976) 3539.

I. THEORY