Concentration, Solubility, and Equilibrium Distribution Coefficient of

Concentration, Solubility, and Equilibrium Distribution Coefficient of Nitrogen and Oxygen in Semiconductor Silicon Y. Yatsurugi, N. Akiyama, and Y. Endo Komatsu Electronic Metab Company, Hiratsuka, Japan

and T. Nozaki Institute o~ Physical and Chemical Research, Wako-shi, Saitama, Japan

ABSTRACT The concentration of nitrogen and oxygen in semiconductor silicon and their solubilities in silicon at its melting point have been measured by charged particle activation analysis and infrared spectrophotometry. It has been found that: (i) commercial semiconductor silicon contains less t h a n 1 • 1015 a t o m s / cm 3 of nitrogen in the un-ionized state; (ii) the solubility in solid silicon is 4.5 • 1.0 X 10i5 a t o m s / c m 3 for nitrogen and 2.75 +_ 0.15 X l0 is a t o m s / c m ~ for oxygen; and (iii) the solubility in liquid silicon is about 6 X l0 is a t o m s / c m 3 for nitrogen a n d 2.20 __. 0.15 • l0 is atoms/cma for oxygen. Thus, the equil i b r i u m distribution coefficient has been d e t e r m i n e d to be about 7 X 10 -4 for n i t r o g e n a n d 1.25 +_ 0.17 for oxygen. The solubilities of the two elements are compared with those of other elements, especially carbon, and are discussed thermochemically. After m a x i m u m purification of a n y semiconductor material or metal, carbon, nitrogen, or oxygen almost always constitutes a m a j o r portion of the r e m a i n i n g impurity. These light elements are a b u n d a n t in nature, b u t a reliable d e t e r m i n a t i o n of their s u b - p p m level cannot be carried out with ease. We reported previously o n the concentration and behavior of carbon in semiconductor silicon as studied b y charged particle activation analysis (1). Similar studies have been made for nitrogen and oxygen. I n f r a r e d spectrophotometry was also used for oxygen, after calibration by activation analysis. As is well known, the activation analysis gives the total oxygen concentration, but the spectrophotometry is sensitive only to oxygen forming the Si-O-Si bonding in silicon crystal. I n this paper, (i) the concentration range for n i t r o g e n and oxygen in commercial semiconductor silicon is presented, (ii) the solubilities of the two elements in solid and liquid silicon at its m e l t i n g point are given, (iii) the physical states of the two elements in solid silicon are discussed, and (iv) the solubilities of carbon, nitrogen, and oxygen i n silicon are treated thermochemically.

SisN4 powder was kept just above its melting point in an evacuated quartz ampoule and was then suddenly cooled to give silicon grains (2-4 m m d i a m e t e r ) . For the oxygen doping, the result of Kaiser and Breslin was used (2). In an atmosphere of oxygen, a m o l t e n zone was made, kept immobile for 10 min, and t h e n caused to t r a v e l i n a part of a silicon rod. Several parts of the same rod were zone melted with various velocities to provide the sample for solubility measurements. Also, the molten zone was cooled s u d d e n l y for the m e a s u r e m e n t of the solubility of oxygen in liquid silicon; the solidification rate was of the order of 100 mm/min. Activation analysis.--The reactions of 14N(p,~)liC and i60 (3He,p)lSF were used for the activation analysis of nitrogen and oxygen, respectively. Detailed descriptions of the charged particle activation analysis for carbon, nitrogen, and oxygen in semiconductor silicon are given in a separate paper (3). Careful e x a m i n a t i o n of the accuracy in the o:r determination, however, showed that the result of the given method involving the chemical separation of 18F should be corrected by a factor of 1.19 ~ 0.03. This correction is d u e m a i n l y to the coprecipitation of PbC12 with PblSFC1, which results in a n overestimation of carrier recovery and thus an u n d e r e s t i m a t i o n of oxygen content (4). I n the present study, oxygen concentrations over 2 • 1017 a t o m s / cm 3 were u s u a l l y determined nondestructively, and the correction was applied to the results of the separationinvolving method. This activation analysis has as its lower limit of sensitivity 1 • 1014 a t o m s / c m 3 for nitrogen and 5 X 1014 atoms/cm 3 for oxygen. U n c e r t a i n t y in the d e t e r m i n a tion of nitrogen is estimated to be 10 and 30% for concentrations of 1 X 1017 a n d 1 • 1015 atoms/cm3, respectively. For oxygen, the accuracy is slightly better t h a n for nitrogen in concentrations over 5 • 10i5 a t o m s / c m 3 b u t is poorer in those u n d e r 2 • 1015 a t o m s / c m 3. For g r a n u l a r samples a technique different from that described in Ref. (3) should be used in the charged particle b o m b a r d m e n t . A cavity (30 X 20 • 3 m m ) was made in an a l u m i n u m block and was covered b y a pure silicon plate (200 ~m thick). The sample grains were put in the cavity and b o m b a r d e d by the charged particles t h r o u g h the plate. After the removal of the surface c o n t a m i n a t i o n by etching u n d e r controlled conditions, the induced a n n i h i l a t i o n activity was measured nondestructively and its decay followed. This

Experimental Sample

preparation.--Commercial

semiconductor silicon of various origins and specifications was collected as the sample. I n order to obtain polycrystalline silicon rods of anomalous n i t r o g e n contents, m o n o silane was decomposed t h e r m a l l y in the presence of ammonia. Also, e l e m e n t a r y silicon in various stages of the monosilane process at Komatsu Electronic Metals C o m p a n y was t a k e n to be analyzed. For the meas u r e m e n t of the m a x i m u m solubility of the two elements, pure silicon was doped with each of t h e m up to the saturation concentration at the m e l t i n g point of silicon. For the m e a s u r e m e n t of the solid solubility of nitrogen, a silicon rod (30 m m diameter) was cut into hemicylinders and a sufficient q u a n t i t y of Si3N4 was sandwiched b e t w e e n them. A m o l t e n zone (10 m m in length) with various velocities was then passed through several parts of the sandwich, in an atmosphere of argon containing several per cent of n i t r o gen. I n the zone-melting, the melt was always covered with small particles of silicon nitride. To determine the solubility of n i t r o g e n in liquid silicon, silicon with K e y words: solubility, equilibrium distribution coet~cient, i n f r a r e d spectrophotometry of O, p h a s e d i a g r a m of N-Si, p h a s e diagram of O-Si, concentration of N and O in Si.

975 Downloaded on 2014-12-20 to IP 129.219.247.33 address. Redistribution subject to ECS terms of use (see ecsdl.org/site/terms_use) unless CC License in place (see abstract).

J. Electrochem. Soc.: S O L I D - S T A T E S C I E N C E A N D T E C H N O L O G Y

976

(~} (E) (I

t e c h n i q u e gives slightly poorer accuracies t h a n t h e v a l u e described above.

Infrared ~pectrophotometry oi oxygen.~The absorbarme of t h e o x y g e n a b s o r p t i o n p e a k at 1108 c m - 1 was m e a s u r e d at room t e m p e r a t u r e b y a p o p u l a r spectrop h o t o m e t e r of g r a t i n g t y p e ( J a p a n Spectroscopic Comp a n y Model I R - G ) . A f t e r e x a m i n a t i o n of m e a s u r e m e n t conditions, t h e s p e c t r o p h o t o m e t e r was s e t as follows: b e a m cross section, 10 X 5 mm; scanning velocity, 600 c m - ~ / h r ; m e c h a n i c a l slit width, 0.6 m m (observed spectral half-width, 38 c m - 1 ) . The sample thickness a f t e r a m i r r o r - p o l i s h i n g w i t h the a i d of diam o n d p a s t e w a s selected to be 2, 5, or 10 m m w i t h unc e r t a i n t y of ___5 ~m. A n u l t r a p u r e silicon, after being a s c e r t a i n e d b y activation analysis not to contain m o r e t h a n 3 X 10 ~ a t o m s / c m ~ of oxygen, was used as the reference sample. T h r o u g h o u t t h e p r e s e n t study, care was t a k e n to the possible inhomogeneous d i s t r i b u t i o n of oxygen w i t h i n a single silicon slice (5). Since a n u m b e r of different values h a v e b e e n rep o r t e d for the a b s o r p t i v i t y of o x y g e n in silicon (5-11), we first e x a m i n e d it using various silicon samples of k n o w n histories. Their absorbances w e r e m e a s u r e d and then t h e y w e r e a n a I y z e d b y activation analysis. [The a b s o r p t i v i t y is defined b y the r e l a t i o n of 10 -abe 1 0 - a = T/To, w h e r e a is the absorptivity, b is t h e samp l e thickness, c is the concentration, and T and To are the t r a n s m i t t a n c e for the s a m p l e a n d for the p u r e m a t r i x itself, respectively, after the correction of m u l t i ple reflection. Thus, t h e absorption coefficient is equal to (ln 10) ac.] The results for a s - g r o w n samples a r e shown in Fig. 1 (for l o w e r o x y g e n concentration r a n g e ) and Fig. 2 (for higher o x y g e n concentration r a n g e ) , t o g e t h e r w i t h t h e calibration curve used in the p r e s e n t study. Two o t h e r c a l i b r a t i o n curves a r e also shown in Fig. 2. The e v e r - r e p o r t e d results for the comparison b e t w e e n inf r a r e d absorption and activation analysis (6,9-11), v a c u u m fusion (5, 7, 8) of the lithium-diffusion m e t h o d (9) can be g r o u p e d into two categories, one corresponding to an a b s o r p t i v i t y of 0.073 • 0.010 (cm 9 atomic p p m ) - ~ (5-7) and the o t h e r giving c o n s i d e r a b l y l o w e r absorptivities. O u r c a l i b r a t i o n curve belongs to the former, M a n y of our e x p e r i m e n t a l plots in Fig. 2 lie in t h e u p p e r side of our own calibration curve, w h i c h is t h e e x t r a p o l a t i o n from the e x p e r i m e n t a l plots in Fig. 1. A discussion for the justification of our c u r v e a n d for the e x p l a n a t i o n of the u p w a r d d e v i a t i o n of t h e exp e r i m e n t a l plots in Fig. 2 is given in a l a t e r section. As low as 5 X 10 ~ a t o m s / c m ~ of o x y g e n can be det e c t e d b y this s p e c t r o p h o t o m e t r y at r o o m t e m p e r a t u r e , w h e n a r e l i a b l e reference s a m p l e is available. Its p r e cision is b e t t e r t h a n activation analysis for concentrations over 2 X 10 ~ a t o m s / c m ~. The effect of surface

4-8

3 2-4

1-21

./

/

3-6o

=

/

% 2C-40 g 20

I

/ -/5/

w ~=-a~t ~ ~ IC120 lC -To

,,

4

'

1'o

IR absorption by the oxygen Fig. 2. Infrared absorption vs. total oxygen concentration in higher concentration range. Experimental plots: e , for ordinary as-grown crystal; O , for soddenly solidified crystal. Calibration curves: A, present work; B, by Kaiser et al. (for single-beam method) (5); C, by Baker (8). Units of the ordinate: I, weight ppm; II, atomic ppm; Ill, 1017 atoms/cm 3. Abscissa: i, absorbance for |cm sample; ii, absorption coefficient (cm-i).

o x y g e n was e x a m i n e d b y t r e a t i n g s a m p l e slices w i t h various r e a g e n t s u n d e r 200~ no n o t a b l e change of t h e absorbance has b e e n observed. Measurement o5 the e~ect of nitrogen on conductivi t y . ~ T h e r e s i s t i v i t y of semiconductor silicon crystals of v a r i o u s n i t r o g e n contents was m e a s u r e d b y t h e usual method. Nitrogen was then r e m o v e d from the crystals b y t h r e e zone passes, and the change in the r e s i s t i v i t y was measured. F u r t h e r , t h e concentration of phosp h o r u s and boron w e r e d e t e r m i n e d b y t h e m e l t - b a c k t e c h n i q u e (12), and t h e i r contribution to the r e s i s t i v i t y of the z o n e - m e l t e d s a m p l e was s u b t r a c t e d in o r d e r to d e t e r m i n e t h e effect of n i t r o g e n on the resistivity. Results and Discussion

Nitrogen and oxygen content oj semiconductor silic o n . ~ N i t r o g e n content of c o m m e r c i a l semiconductor silicon w a s found to be a l w a y s less t h a n I X 10 ~5 a t o m s / cm 3 and u s u a l l y in t h e r a n g e of 1 X 1014 and 5 • t014 a t o m s / c m ~. O x y g e n contents of various kinds of semiconductor silicon have a l r e a d y b e e n r e p o r t e d in our previous p a p e r t o g e t h e r w i t h the carbon content ( t ) . Most of the float-zone crystals c o n t a i n e d from 2 X 10 ~5 to 2 X 10 TM a t o m s / c m 3 and Czochralski c r y s t a l s u s u a l l y h a d f r o m 2 X 10 l~ to 1 X l0 TM a t o m s / c m ~ of oxygen. It is clear t h a t t h e o x y g e n content of the silicon single c r y s t a l depends on t h e condition of t h e c r y s t a l formation but scarcely on t h e s t a r t i n g material.

Solubility and equilibrium distribution coe~cient oJ nitrogen.--Nitrogen was found to b e d i s t r i b u t e d almost

(~)(1)(I) 0 .F 4~

July 1973

u n i f o r m l y t h r o u g h o u t the entire p a r t of the s a m p l e p r e p a r e d b y z o n e - m e l t i n g the Si3N4-inserted rod, except at its t a i l - e n d portion, as is shown in Fig. 3. I n the

./

1019

-~

10~e I017

/

w i

0:2

i

o'4~

i

i

)

o'.~ o'.81i~il

g 1016

-%

vo o~

Oo

oJ

IR absorption by the oxygen Fig. 1. Infrared absorption vs. total oxygen concentration in lower concentration range. Units of the ordinate I, weight ppm; II, atomic ppm; III, 1017 atoms/cm 3. Abscissa: i, absorbance for 1cm sample; if, absorption coefficient (cm-1).

Locetion I zone-length unit from the top) Fig. 3. Nitrogen distribution in a silicon rod after a passage of a nitrogen-saturated molten zone. Zone velocity: 0.4 ram/rain.

Downloaded on 2014-12-20 to IP 129.219.247.33 address. Redistribution subject to ECS terms of use (see ecsdl.org/site/terms_use) unless CC License in place (see abstract).

Vol. 120, No. 7

NITROGEN AND OXYGEN IN SEMICONDUCTOR Si

zone-melting, t h e liquid phase was a l w a y s s a t u r a t e d w i t h nitrogen. The r e s u l t a n t solid silicon, however, could contain a s l i g h t l y h i g h e r concentration of nitrogen t h a n its solid solubility at the m e l t i n g p o i n t of silicon, because the solid-liquid b o u n d a r y m i g h t have been dendritic a n d thus the g r o w i n g solid phase would have c a p t u r e d a small fraction of the liquid phase. In fact, the nitrogen concentration in the solid was found to d e p e n d on the z o n e - t r a v e l i n g velocity, as is shown in Fig. 4. The solid solubility at the m e l t i n g point of silicon can be obtained b y the e x t r a p o l a t i o n of the curve in Fig. 4 to zero velocity; it is 4.5 _ 1.0 • 10 TM a t o m s / c m s. N i t r o g e n solubility in liquid silicon at its m e l t i n g point was d e t e r m i n e d b y the use of the s u d d e n l y solidifled sample; it was found to be about 6 • 10 TM a t o m s / cm 3. This value agrees f a i r l y w e l l w i t h the v a l u e of a r o u n d 1019 a t o m s / c m 3 r e p o r t e d b y K a i s e r and Thurmond (13). A l m o s t the same nitrogen concentration was o b s e r v e d at the t a i l - e n d portion of the s a m p l e f r o m t h e SisN4-inserted rod w h e n this portion was solidified rapidly. The e q u i l i b r i u m distribution coefficient of nitrogen b e t w e e n solid and liquid silicon, which is e q u a l to the ratio of nitrogen solubility in solid silicon to t h a t in liquid silicon at its melting point, has thus been d e t e r m i n e d to be about 7 • 10-4. F r o m t h e above information, the phase d i a g r a m of the N-Si system in the e x t r e m e l y low nitrogen concent r a t i o n range can be drawn. It is shown in Fig. 5. The l o w e r i n g of the m e l t i n g point (AT) was calculated from the relation AT = x ( 1 -- Keq)RTm2/L [1] w h e r e x is t h e concentration of the solute in the liquid phase in mole fraction, Keq is its e q u i l i b r i u m distribution coefficient, R is the gas constant, and Tm and L are the m e l t i n g point and the m o l a r heat of fusion, respectively, of the solvent (for silicon, T m = 1683~ and L : 12.1 • 0.4 k c a l / m o l ) . This equation is an i n t e g r a t e d form of C l a p e y r o n ' s equation and is valid for dilute solutions obeying Raoult's law. A m o n g various silicon nitrides, Si3N4 is r e g a r d e d as the stable f o r m w h e n contacted w i t h silicon at its m e l t i n g point (13). In the single-crystal f o r m a t i o n of silicon, i m p u r i t y nitrogen is r e m o v e d v e r y easily, because not only

(D

~D

~4-g

0

'

1:o

'

2:o

Zone velocity (mm/min) Fig. 4. Nitrogen concentration in silicon solidified from nitrogensaturated melt with various rates.

o~0

0.02 n.

:~ 0.04

% 0.06

_~o.os

?

4

LicL.

3.0

o 0

~

Suddenly cooled

2.0

0

0

Zone velocity (rnm/rnin) Fig. 6. Oxygen concentration in silicon solidified from oxygensaturated melt with various rates. r Result of activation analysis with standard deviation. FI: Result of infrared spectrophotometry.

is its d i s t r i b u t i o n coefficient so small but also it evaporates so r e a d i l y from a silicon m e l t (14).

Solubility and equilibrium distribution coeI~cient oS oxygen.--The total o x y g e n concentration in silicon crystals obtained b y solidification of t h e o x y g e n - s a t u r ated melt at various rates is shown in Fig. 6. F o r each rate, from 4 to 11 wafers w e r e cut out of the zone-melted rods and analyzed by activation; the m e a n value of the r e s u l t is indicated in Fig. 6 with s t a n d a r d deviation. The i n f r a r e d - s e n s i t i v e o x y g e n concentration is also shown in Fig. 6, although only the total concentration is necessary for the d e t e r m i n a t i o n of the solubility. The solubility of o x y g e n in solid silicon a n d liquid silicon at its m e l t i n g point can be given as the total o x y g e n concentration for the crystals solidified from the o x y g e n - s a t u r a t e d m e l t at an infinitely low rate and an infinitely high rate, respectively. Thus, although some a r b i t r a r i n e s s m a y be seen in d r a w i n g the smooth curve in Fig. 6, the following constants have been obtained: (i) solubility of o x y g e n in solid silicon at its m e l t i n g point, 2.75 • 0.15 • 1018 atoms/cm3; (ii) solubility of o x y g e n in liquid silicon at its m e l t i n g point, 2.20 • 0.15 • 1018 atoms/cm3; and (iii) e q u i l i b r i u m distribution coefficient of oxygen in silicon, 1.25 __ 0.17. The phase d i a g r a m of the O-Si system in the ext r e m e l y low o x y g e n concentration r a n g e is shown in Fig. 7. The raising of the m e l t i n g point was calculated b y Eq. [1] for Keq equal to 1.25. The stable oxygen silicide in contact w i t h silicon is k n o w n to be SiO at the melting point of silicon b u t to be SiO2 at s o m e w h a t l o w e r t e m p e r a t u r e s (15). O x y g e n in silicon forms a peritectic m i x t u r e and cannot be r e m o v e d b y segregation. Oxygen, however, e v a p o r a t e s easily from a silicon m e l t as SiO, and t h e oxygen content of the usual floatzone crystals is h i g h l y d e p e n d e n t on the conditions of a t m o s p h e r e in t h e zone-melting. Infrared-insensitive oxygen.--As is seen in Fig. 6, silicon crystals m a d e from o x y g e n - s a t u r a t e d m e l t u s u a l l y contained i n f r a r e d - i n s e n s i t i v e oxygen, w i t h its q u a n t i t y increasing w i t h the decrease of the solidification rate. The u p w a r d deviation of the e x p e r i m e n t a l

/ Lie[i+ Si3N4

Liq.

O9

n-

0.006 0.0O4

~ 0.002 f

Si + Si3N4

2

977

S

i

+

Li%+ SiO L

i

Si

~

/

Si+SiO

0

4

'

&

'

10~8at./cm3 Nitrogen concentration

1015 Qt./cm 3

Fig. 5. Phase diagram of N-Si system in extremely low nitrogen concentrations.

cJ

0

Oxygen concentration (1018 et./cm3) Fig. 7. Phase diagram of O-Si system in extremely low oxygen concentrations.


978

J. EIectrochem. Soc.: S O L I D - S T A T E S C I E N C E A N D T E C H N O L O G Y

plots in Fig. 2 can be explained also by the presence of infrared-insensitive oxygen. The n a t u r e of this infrared-insensitive oxygen is thought to be aggregates of oxygen (16). The aggregation process and the solid solubility of oxygen in silicon have been studied by m a n y workers (16-18). It has been reported that the aggregation proceeds fairly rapidly over 1000~ and that oxygen in heat-treated silicon is partly aggregated w h e n its concentration is relatively high. Also from our observation on the change of the infrared absorbance in heat-treatment, it can be guessed that the aggregation proceeds to a notable extent after a melt of a relatively high oxygen content is solidified at a usual rate in industrial zone-melting or Czochralski process. Although the rate of aggregation depends on m a n y factors, it is quite n a t u r a l that the lower the solidification rate and the higher the total oxygen concentration, the larger the aggregated fraction, when other factors are the same. A t e n d e n c y of the concenration dependence can be observed in Fig. 2. The e x p e r i m e n t a l relationship b e t w e e n the total and infrared-sensitive oxygen concentration in Fig. 1 is denoted b y a straight line, indicating the absence of a n y notable a m o u n t of oxygen aggregate in this low concentration range. This gives a justification of our calibration curve, although m a n y e x p e r i m e n t a l plots in Fig. 2 lie on the upper side of it. The i n f r a r e d - i n s e n sitive fraction, however, has been found mostly to be less than 20% of the total oxygen i n as-grown silicon crystals.

E~ect ol nitrogen on semiconductor property.-- The resistivity of an N-type crystal c o n t a i n i n g nitrogen up to the saturation concentration at the melting point 4.5 • 10z5 a t o m s / c m 3, was found to be 37 ohm-cm, showing the existence of 1.4 • 1014/cm3 of free electrons. By the melt-back technique, boron content was found to be about 2 • 1012 a t o m s / c m 3. Thus, even w h e n the free electrons were entirely due to the nitrogen, the ionization degree of nitrogen should be less than 4%. The phosphorus content of the original crystal was calculated from the measured resistivity of the zone-melted crystal by the use of its reported effective distribution coefficient which was regarded as 0.35 for our solidification rate of about 0.5 m m / m i n ; it was 1.1 • 1014 a t o m s / c m 3. Therefore, the n u m b e r of free electrons i n the silicon crystal excluding those derived from the phosphorus atoms a m o u n t s to only about 1% of the n u m b e r of nitrogen atoms. W h e n the evaporation of phosphorus in zone-melting is taken into account, the ionization degree of nitrogen should be less t h a n 1%. A still higher resistivity (7000 ohm-cm) was reported by Kaiser and T h u r m o n d for silicon crystals grown from a nitrogen-saturated melt (13). They calculated the distribution coefficient of nitrogen to be less t h a n 10 -7 on the assumption that the nitrogen was totally ionized in silicon, although they did not rule out the possibility of the presence of un-ionized nitrogen. Now the existence of un-ionized nitrogen has been proved, and the distribution coefficient of less than 10 -7 has been shown to be incorrect.

J u l y 1973

Comparison o] the solubility and distribution coe~icient.--A s u m m a r y of the solubilities of carbon, nitrogen, and oxygen in solid and liquid silicon at its m e l t i n g point (or more correctly at the eutectic or peritectic point) and their e q u i l i b r i u m distribution coefficients is given in Table I. The solubilities of the three elements in liquid silicon are of the same order and are considerably lower than those of m a n y metallic elements, which are soluble up to 102~ atoms/cm 3 (19). The solubility in solid silicon, on the other hand, is m a r k e d l y different among the three elements. Oxygen is more soluble t h a n m a n y refractory metals in solid silicon but less soluble t h a n m a n y metals of low m e l t i n g points (with a few exceptions such as zinc), and nitrogen is one of the least soluble elements (19). The distribution coefficients of elements within a given group of the Periodic Table have been k n o w n to increase with the decrease of atomic n u m b e r (19). This rule, however, does not hold true for carbon and nitrogen, which have smaller distribution coefficients t h a n silicon and phosphorus.

Explanation o] the low solubilities and the small distribution coefficients.--The low solubilities can be explained by the following two properties of the three elements: (i) they form stable silicides of vast dissociation energies (SIC, SiaN~, a n d SiO), and (if) they are significantly smaller than silicon in atomic size. The small distribution coefficients of carbon and nitrogen can also be explained by the latter. As is well known, the solubility in general can be given by the relation of [M] = exp[hS/R] exp[--AH/RT]

[2]

where [M] is the solubility of a solute M in mole fraction, S is the entropy of solution, R is the gas constant, A H is the heat of solution, and T is the absolute temperature. Since H for a solid solution implies the energy necessary for the rupture of its crystal lattice, the following tendency is regarded as existing naturally and has actually been observed (19): the larger the heat of vaporization of the solute substance, the higher its A H and consequently the lower its solubility. For the present three elements w h e n dissolved in the atomic state, the heat of dissociation of the stable silicide into silicon bulk, and monatomic gas of carbon, nitrogen, or oxygen should be regarded as equivalent to the heat of vaporization for a usual metallic solute substance. The heats of dissociation calculated by the use of thermochemical tables (15, 20) are shown in Table I. They are as large as the heat of vaporization of a refractory metal (e.g., Zr, 146; Nb, 172; W, 203; Re, 186 kcal/mol at 25~ and this can be the m a j o r reason for the low solubilities. Oxygen in liquid silicon m a y be in the molecular state of SiO, because its heat of vaporization is about 70 kcal/mol (15). However, this molecule is so different from silicon in atomic size and shape that its solubility should be low, as is shown by the elastic model theory cited just below. The replacement of an atom in its own crystal by a foreign atom of a different size introduces a strain

Table I. Solubilities of carbon, nitrogen, and oxygen in silicon at its melting point and their equilibrium distribution coefficients and some related values

S o l u b i l i t y i n solid Atoms/cma Atomic fraction Solubility in liquid Atoms/cm3 Atomic fraction E q u i l i b r i u m distribution coet~cient H e a t of dissociation,* K e a l / m o l Atomic radius, A Tetrahedral radius, A

Carbon

Nitrogen

3.2 • 0.3 x 10 zT 6.5 ~- 0.5 x 10 "~

4.5 • 1.0 x 10 TM 9 --4-2 • 10-8

2.75 • 0.15 • 10 TM 5.6 + 0.3 • 10 -~

4.5 • 0.5 • 10~s 9 - 1 x 10 -~ 0.07 + 0.01 1.9 X 102 0.77 0.77

6 x l 0 ss 1.2 • 10-~ 7 x 10 -4 1.6 • 103 0.53 0.70

2.20 -----0.15 • 10 TM 4.5--+ 0.3 x 10 -~ 1.25 "4- 0.17 1.6 x l 0 s 0.60 0.66

* T h e h e a t of reaction for S i C = S i + C, V4Si~N4 = % S i C, N , or O.

Oxygen

+ N o r S i O = S i + O, w i t h t h e p r o d u c t s b e i n g s o l i d S i a n d m o n a t o m i c

g a s of


Vol. 120, No. 7

N I T R O G E N A N D O X Y G E N I N S E M I C O N D U C T O R Si

e n e r g y into the crystal, w h i c h is a component of AH. The strain e n e r g y ( [ E st] ) for a substitutional i m p u r i t y in silicon has been shown to be given b y the r e l a t i o n of [E st] : 22 X 1020 (At) 2 c a l / m o l

[3]

w h e r e Ar is the d i s p a r i t y of t e t r a h e d r a l r a d i u s (in angstroms) b e t w e e n silicon and the i m p u r i t y (21). A m o n g various theories t r e a t i n g the solubility or alloy formation, t h e elastic model t h e o r y emphasizes the role p l a y e d b y the d i s p a r i t y of atomic size (22). This t h e o r y shows that: the g r e a t e r the disparity, the less the m u t u a l solubility both in liquid and solid solution and also t h e less the distribution coefficient. The t e t r a h e d r a l r a d i i and atomic radii of the t h r e e elements are shown in Table I. F o r silicon t h e y a r e both 1.17A. Since even thallium, lead, and b i s m u t h a r e l a r g e r t h a n silicon b y only about 3A in t e t r a h e d r a l radius, the disp a r i t y b e t w e e n silicon a n d t h e t h r e e e l e m e n t s should be considered to be r e m a r k a b l e . A l t h o u g h this t h e o r y is r e g a r d e d as not a l w a y s reasonable (22), it can explain the small solubilities of t h e t h r e e e l e m e n t s and also t h e small d i s t r i b u t i o n coefficients of c a r b o n and nitrogen. Since n i t r o g e n in solid silicon is not ionized, it is p r o b a b l y not substitutional. The much higher ionization potential of n i t r o g e n (14.54 eV) t h a n the ionization potentials of other G r o u p V e l e m e n t s (P, 11.0; As, about 10; Sb, 8.46; Bi, about 8 eV) can be an additional cause of the u n d e t e c t a b l y low concentration of ionized substitutional nitrogen.

Numerical value of AH and h S . - - I t w o u l d be w o r t h w h i l e calculating AS in Eq. [2] b y t h e use of the solub i l i t y in Table I a n d of t h e r e p o r t e d a l l . F o r carbon in liquid silicon, Scace gave 59 k c a l / m o l for 5H (23); thus AS is obtained as about 17 cal tool -1 deg -1. F o r carbon in solid silicon, t h e v a l u e of AH r e p o r t e d b y Bean and N e w m a n (18) agrees closely w i t h our result (24), the l a t t e r being 55 ___ 4 k c a l / m o l . It thus follows t h a t AS : 88 __ 2.6 cal m o l - 1 d e g - L Two different values h a v e been r e p o r t e d for AH of o x y g e n in solid silicon: 22 _.+ 2 k c a l / m o l b y Hrostowski (17) and 38 ___ 4 k c a l / m o l b y Bean a n d N e w m a n (18). The f o r m e r and the l a t t e r give --6.4 +_ 1.5 cal tool -1 d e g - 1 and 3.0 _+ 2.5 cal tool -1 deg -1, respectively, for AS. W e followed t h e i r e x p e r i m e n t ; our result is closer to the f o r m e r t h a n to the latter. The s m a l l e r hH of o x y g e n t h a n t h a t of carbon m a k e s o x y g e n m o r e soluble in solid silicon t h a n carbon in spite of its v e r y small AS. Anomalous distribution coefficient of oxygen.--Oxygen in solid silicon is k n o w n to be interstitial, f o r m i n g a S i - - O - - S i bonding. The small size a n d the b i v a l e n t n a t u r e w i t h its o w n b o n d angle of o x y g e n a t o m are considered f a v o r a b l e for o x y g e n to be in this state. This can be the reason for the h i g h e r solid solubility of o x y g e n t h a n t h a t of carbon and n i t r o g e n and also of

979

its anomalous distribution coefficient. F r o m the electronic configuration of n i t r o g e n atom, the f o r m a t i o n of a S i - - N - - S i bonding in silicon c r y s t a l is r e g a r d e d as the least probable.

Acknowledgment The a u t h o r s w o u l d like to e x p r e s s t h e i r t h a n k s to the Cyclotron G r o u p of the I n s t i t u t e of P h y s i c a l a n d Chemical Research for t h e i r b o m b a r d m e n t services in the activation analysis. M a n u s c r i p t s u b m i t t e d Sept. 28, 1972 revised m a n u script received Jan. 30, 1973. A n y discussion of this p a p e r will a p p e a r in a Discussion Section to b e published in the D e c e m b e r 1973 JOURNAL. REFERENCES 1. T. Nozaki, Y. Yatsurugi, and N. A k i y a m a , Th/s Journal, 117, 1566 (1970). 2. W. K a i s e r and J. Breslin, J. Appl. Phys., 29, 1292 (1958). 3. T. Nozaki, Y. Yatsurugi, and N. A k i y a m a , J. Radioanal. Chem., 4, 87 (1970). 4. T. Nozaki, Y. Yatsurugi, N. A k i y a m a , Y. Endo, a n d Y. Makide, ibid., To be published. 5. W. K a i s e r a n d P. H. Keck, J. Appl. Phys., 28, 882 (1957). 6. E. A. S c h w e i k e r t and H. L. Rook, Anal Chem., 42, 1525 (1970). 7. K. Graft, E. Grallath, S. Ades, G. Goldbach, and G. TSlg, Solid-State Electron., To b e published. 8. J. A. Baker, ibid., 13, 1431 (1970). 9. B. Pajot, ibid., 12, 923 (1969). 10. C. K. Kimm, Radiochem. Radioanal. Letters, 2, 25 (1969). 11. C. Gross, G. Gaetano, T. N. Tucker, and J. A. Baker, This Journal, 119, 926 (1972). 12. F. H. Horn, ibid., 114, 1307 (1967). 13. W. K a i s e r and C. D. T h u r m o n d , J. Appl. Phys., 30, 427 (1959). 14. T. Nozaki, Y. Makide, Y. Yatsurugi, N, A k i y a m a , and Y. Endo, Int. J. Appl. Radiat, Isotopes, 22, 607 (1971). 15. O. Kubaschewski, E. L1. Evans, a n d C. B. Alc0ck, "Metallurgical T h e r m o c h e m i s t r y , " p. 226, P e r gamon, O x f o r d (1967). 16. W. Kaiser, H. L. Frich, and H. Reiss, Phys. Rev,~ 112, 1546 (1958). 17. H. J. H r o s t o w s k i and R. H. Kaiser, J. Phys, Che~, Solids, 9, 214 (1959). 18. A. R. Bean and R. C. Newman, ib~d,, 32~ 1211 (1971). 19. F. A. Trumbore, Bell System Tech. J,~ 39, 205 (1960). 20. E.G., Ref. (15), p. 304; a n d " J A N A F T h e r m o c h e m i cal Tables," compiled b y D. R. S t u l l et al., dist r i b u t e d f r o m Clearinghouse, U.S.A. (1965-1967). 21. K. Weiser, J. Phys. Chem. Solids, 7, 118 (1958). 22. R. A. Oriani, ibid., 22, 335 (1957). 23. R. I. Scace a n d G. A. Slack, J. Chem. Phys., 30, 1551 (1959). 24. Y. Endo, Y. Yatsurugi, N. A k i y a m a , and T. Nozaki, Anal. Chem., 44, 2258 (1972).
