Diffusion and Oxidation of Silicon - ACS Publications - American

6 Diffusion and Oxidation of Silicon

Downloaded by CORNELL UNIV on May 10, 2012 | http://pubs.acs.org Publication Date: May 5, 1989 | doi: 10.1021/ba-1989-0221.ch006

Richard B . F a i r Microelectronics Center of North Carolina, Research Triangle Park, NC 27709, and Department of Electrical Engineering, Duke University, D u r h a m , N C 27706

Oxidation and diffusion in silicon are processes that significantly affect the fabrication of microelectronic devices. However, our knowledge of the fundamental principles governing these processes is inadequate, and this inadequacy affects our ability to understand and model submicrometer ultralarge-scale-integration technologies. These advanced processes require p-n junctions of 1000-Å depth and oxides of 100-Å thickness. The existing theories and models do not adequately describe the physical mechanisms that dominate diffusion and oxidation in these regimes. The theories, new ideas, issues, and unknowns about these processes are reviewed in this chapter.

S I L I C O N - P R O C E S S I N G T E C H N O L O G Y has d e p e n d e d h e a v i l y o n t h e r m a l oxidation a n d the diffusion of i m p u r i t i e s since the 1950s. T h e use of difiusion techniques to f o r m p - n j u n c t i o n s was disclosed i n a 1952 patent b y P f a n n (I). S i n c e t h e n , n u m e r o u s approaches have b e e n s t u d i e d o n h o w to i n t r o d u c e dopants into s i l i c o n w i t h the goal of c o n t r o l l i n g the electrical properties of the j u n c t i o n , concentrations of dopants, u n i f o r m i t y a n d r e p r o d u c i b i l i t y , a n d cost of manufacture. T h e r m a l oxides w e r e u s e d i n i t i a l l y to selectively mask dopants d u r i n g diffusion steps. A d d i t i o n a l research i n d i c a t e d that the passivation properties of t h e r m a l oxides may be u s e d to advantage i n devices. T w o v e r y i m p o r t a n t d e v e l o p m e n t s i n s e m i c o n d u c t o r technology g r e w out of research i n oxides: the planar process i n v e n t e d b y H o e r n i (2) a n d the M O S ( m e t a l - o x i d e - s e m i c o n d u c t o r ) transistor, w h i c h was first disclosed b y K a h n g and A t a l l a (3). O x i d a t i o n a n d diffusion c o n t i n u e to be i m p o r t a n t i n s u b m i c r o m e t e r V L S I (very-large-scale integration) technology. M o d e r n integrated devices r e q u i r e

0065-2393/89/0221-0265$14.85/0 © 1989 American Chemical Society

In Microelectronics Processing; Hess, D., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1989.

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MICROELECTRONICS PROCESSING: C H E M I C A L ENGINEERING ASPECTS

ultrashallow j u n c t i o n s of 1000-Â d e p t h a n d t h i n oxides of 100-A thickness. T h e s e r e q u i r e m e n t s make it necessary for s e m i c o n d u c t o r scientists a n d e n gineers to refine further the k n o w l e d g e base g o v e r n i n g these

processes.

S h o r t - t i m e or l o w - t e m p e r a t u r e steps are n e e d e d to p r o d u c e shallow j u n c t i o n s and t h i n oxides. T h e s e processing regimes have n e v e r b e e n e x p l o r e d before, and recent data have s h o w n that u n u s u a l transient effects occur d u r i n g dopant difiusion. T h e models based o n existing theories of oxidation do not a p p l y w e l l to oxides whose thicknesses are less t h a n 350 A . A l t h o u g h oxidation a n d diffusion are closely i n t e r r e l a t e d processes, they w i l l be discussed separately i n this chapter. H o w e v e r , the effects of oxidation


on diffusion a n d those of d o p i n g o n oxidation w i l l be c o v e r e d to emphasize the interrelationships that exist. T h e treatment o f the subject is not exhaustive; m y i n t e n t i o n is to give the reader a b a c k g r o u n d of the subject a n d to i n f o r m the reader about the issues a n d the gaps i n o u r k n o w l e d g e of these processes.

Diffusion T h i s section focuses on the diffusion of i m p u r i t i e s i n s i l i c o n . Because of the large solid s o l u b i l i t y i n s i l i c o n of group I I I a n d group V d o p i n g i m p u r i t i e s , difiusion proceeds b y interactions w i t h p o i n t defects: s i l i c o n vacancies and silicon self-interstitials. E a c h h i g h - t e m p e r a t u r e processing step can change the levels o f vacancies a n d self-interstitials a n d , therefore, the diffusion of i m p u r i t i e s . T h e s e effects c a n b e u n d e r s t o o d at two l e v e l s — t h e atomic l e v e l and the c o n t i n u u m l e v e l . A discussion o f diffusion from b o t h points of reference is p r o v i d e d i n the f o l l o w i n g sections. T h e process of i n t r o d u c i n g i m p u r i t i e s into silicon is c a l l e d

predeposition.

C h e m i c a l p r e d e p o s i t i o n is d e s c r i b e d i n terms of a solution to the diffusion equation. P r e d e p o s i t i o n b y i o n i m p l a n t a t i o n is d e s c r i b e d i n terms of i o n p e n e t r a t i o n i n t o s i l i c o n , d i s t r i b u t i o n s of i m p l a n t e d i m p u r i t i e s , lattice d a m age, etc.

Continuum Theory.

Solid-state difiusion is d e s c r i b e d i n terms of a

c o n t i n u i t y e q u a t i o n k n o w n as F i c k ' s second law:

(1)

E q u a t i o n 1 describes the rate of change o f the concentration of i m p u r i t y w i t h t i m e . T h e diffusion coefficient D is expressed i n square centimeters p e r second, a n d the concentration C is expressed usually i n n u m b e r of atoms per cubic centimeter.


6.

267

Diffusion and Oxidation of Silicon

FAIR

W h e n D is constant, the surface concentration of the diffusing i m p u r i t y is fixed, the concentration of the i m p u r i t y at χ = o°, C(«>, f), is 0 for a l l t i m e , a n d the concentration at any p o i n t i n the crystal at t = 0, C(x, 0), is 0. U n d e r these c o n d i t i o n s , the solution to e q u a t i o n 1 is g i v e n b y (4)

w h e r e erfc is the c o m p l e m e n t a r y e r r o r function. I f C(«>, t) = C

a n d C(x,

B

0) = C , w h e r e C

B

B

is the b a c k g r o u n d d o p i n g concentration i n the s e m i


conductor, t h e n

T h u s , for the b o u n d a r y conditions j u s t d e s c r i b e d , the concentration of i m p u r i t y as a function o f space a n d t i m e is g i v e n b y a c o m p l e m e n t a r y e r r o r function (erfc) whose a r g u m e n t is x / V D f . T h e c o m p l e m e n t a r y e r r o r f u n c t i o n is a tabulated f u n c t i o n . Diffusion processes that are p e r f o r m e d w i t h a constant surface c o n c e n tration are n o r m a l l y r e f e r r e d to as p r e d e p o s i t i o n steps. Predepositions are usually d o n e i n N furnace ambients w i t h a s m a l l percentage of 0 , a n d the 2

2

d o p i n g species is i n t r o d u c e d into the furnace i n gaseous f o r m . T h e dopant concentration i n the N

2

gas stream is v a r i e d to change the surface c o n c e n

tration i n the s i l i c o n . T y p i c a l p r e d e p o s i t i o n temperatures are 9 0 0 - 1 0 0 0 ° C , a n d t y p i c a l p r e d e p o s i t i o n periods are 3 0 - 6 0 m i n . T h e sources of dopants i n c l u d e l i q u i d s , solids, a n d gases. Boron.

F o r the p r e d e p o s i t i o n of b o r o n , the most p r e v a l e n t species i n

the gas phase i n the furnace is B 0 . O n c e B 0 2

3

2

3

is d e p o s i t e d o n the s i l i c o n

surface, the oxide reacts w i t h the silicon to b r i n g about d o p i n g , as s h o w n i n e q u a t i o n 4. B 0 2

B 0 2

3

(4)

+ - Si

3

m a y c o m e f r o m e i t h e r one of the reactions d e s c r i b e d i n equations 5

a n d 6. 2 H

3 ° 3 TS^S 2 ° 3 + B

4BN + 30

2

-H> 2 B 0 2

(5)

3H 0

B

2

3

+ 2N

2

(6)

T h e source of b o r o n n i t r i d e i n equation 6 may be the disks about the size of a s i l i c o n wafer that are p l a c e d next to the wafers i n the diffusion furnace.


268


B y v a r y i n g the partial pressure of the gas phase of the dopant i n the furnace, the concentration of i m p u r i t i e s i n the s i l i c o n can be changed. H e n ry's l a w relates the concentration of dopants that are i n t r o d u c e d i n the furnace to the surface concentration b y the r e l a t i o n C

0

where C

= Hp , s

0

is the

surface concentration o f dopant, H is H e n r y ' s constant, a n d p is the partial s

pressure of the dopant gas. F i g u r e 1 is a plot o f b o r o n concentration versus p that illustrates H e n r y ' s s

law. W h e n the s o l i d s o l u b i l i t y o f b o r o n i n s i l i c o n is r e a c h e d , H e n r y ' s l a w no l o n g e r applies. T h u s , most p r e d e p o s i t i o n steps are operated at a suffi c i e n t l y h i g h partial pressure i n the dopant gas phase to achieve s o l i d s o l u b i l i t y


of the dopant i n the s i l i c o n . T h i s r e q u i r e m e n t provides a natural c o n t r o l for r e p r o d u c i b l e difiusion results. F o r the p r e d e p o s i t i o n o f phosphorus, the p r e d o m i n a n t

Phosphorus.

species i n the gas phase is P 0 . T h e d o p i n g reaction w i t h P 0 2

5

2

5

is s h o w n

i n e q u a t i o n 7. P O 2

s

- Si0 2

+ - Si

Sources of P O vapor are s o l i d P O , N H H P 0 , or P N . 2

4

3 Χ 10

2

s

2

2

+ 2P

(7)

r e d phosphorus, P O C l ,

s

3

PBr , 3

4

Solid solubility of 20

1100

Β in Si at

°C / /

/ / Ε

/

ο ϋ

/

/ —

y%

Line corresponds to Henry's law. with Η = 2 Χ 10 atm/cm 25

/

I

I

0.5

3

I

1.5

2X

Ps (Torr) Figure 1. Surface concentration of boron as a function of the partial pressure of B 0 in the ambient at 1100 °C. (Reproduced with permisssion from ref erence 118. Copyright 1988 Noyes Publications.) 2

3


10

6.

FAIR


269

T h e goal o f the p r e d e p o s i t i o n step is to deposit some n u m b e r o f atoms p e r square c e n t i m e t e r , Q(t), i n the s i l i c o n substrate. T h a t n u m b e r is c a l c u l a t e d b y i n t e g r a t i n g the total concentration p e r c u b i c c e n t i m e t e r from 0 to °° as s h o w n i n e q u a t i o n 8.


(8)

O n c e the p r e d e p o s i t i o n is c o m p l e t e d w i t h Q atoms p e r square c e n t i m e t e r , the next step is to r e d i s t r i b u t e the atoms to give the d e s i r e d j u n c t i o n d e p t h . I f Q atoms p e r square c e n t i m e t e r are d e p o s i t e d o n the s e m i c o n d u c t o r surface w i t h the b o u n d a r y conditions C(x, t = 0) = Qb(x) a n d C(«>, t) =

0

(4), t h e n the d i s t r i b u t i o n o f i m p u r i t i e s after diffusion for a t i m e t is g i v e n b y a G a u s s i a n f u n c t i o n solution to e q u a t i o n 1 (equation 9).

(9)

T h e G a u s s i a n d i s t r i b u t i o n can b e u s e d to describe the i m p u r i t y profile that results f r o m a d r i v e - i n step w i t h no dopant gas i n the furnace. T h e d r i v e - i n step i t s e l f is p e r f o r m e d i n several types o f a m b i e n t s : d r y oxygen, steam, n i t r o g e n , o r argon. T h e d r i v e - i n temperatures range from 900 to 1200 °C. T h e analytical solutions to F i c k ' s c o n t i n u i t y equation represent special cases for w h i c h the diffusion coefficient, D , is constant. I n practice, this c o n d i t i o n is m e t o n l y w h e n the concentration of diffusing dopants is b e l o w a c e r t a i n l e v e l (~1 X 1 0 a t o m s / c m ) . A b o v e this d o p i n g d e n s i t y , D m a y d e p e n d o n local dopant concentration levels t h r o u g h electric field effects, F e r m i - l e v e l effects, strain, o r the presence o f o t h e r dopants. F o r these cases, e q u a t i o n 1 m u s t b e integrated w i t h a c o m p u t e r . T h e f o r m o f e q u a t i o n 1 is essentially the same for a w i d e range o f n o n l i n e a r diffusion effects. T h u s , the research emphasis has b e e n o n u n d e r s t a n d i n g the c o m p l e x b e h a v i o r o f the diffusion coefficient, D , w h i c h can b e a c c o m p l i s h e d b y s t u d y i n g diffusion at 1 9

3

the a t o m i c l e v e l .

Atomic Theory of Diffusion. Diffusion Mechanisms. T h e atomic theory of diffusion describes h o w an atom moves from one part of a crystal to another. T h e lattice sites i n a crystal are assumed to be fixed locations o f the atoms m a k i n g u p the crystal. T h e atoms oscillate a r o u n d these lattice sites, w h i c h are t h e i r e q u i l i b r i u m positions. T h e s e oscillations l e a d to finite In Microelectronics Processing; Hess, D., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1989.

270

MICROELECTRONICS PROCESSING: C H E M I C A L E N G I N E E R I N G ASPECTS

chances that an atom w i l l m o v e from its lattice site to another p o s i t i o n i n the crystal. A t o m s can m o v e from one site i n the crystal to another t h r o u g h the vacancy m e c h a n i s m , the interstitial m e c h a n i s m , a n d the interstitialcy m e c h a n i s m ( F i g u r e 2). O n the basis of t h e r m o d y n a m i c considerations, some of the lattice sites i n the crystal are vacant, a n d the n u m b e r of vacant lattice sites generally is a function of t e m p e r a t u r e . T h e m o v e m e n t of a lattice atom into an adjacent vacant site is c a l l e d vacancy diffusion. I n a d d i t i o n to o c c u p y i n g lattice sites, atoms can reside i n interstitial sites, the spaces b e t w e e n the lattice sites. T h e s e interstitial atoms can r e a d i l y m o v e to adjacent interstitial sites w i t h o u t


d i s p l a c i n g the lattice atoms. T h i s process is c a l l e d interstitial diffusion. T h e interstitial atoms may be i m p u r i t y atoms o r atoms of the host lattice, b u t i n e i t h e r case, interstitial atoms are generally present o n l y i n v e r y d i l u t e amounts. H o w e v e r , these atoms can be h i g h l y m o b i l e , a n d i n c e r t a i n cases, interstitial diffusion is the d o m i n a n t diffusion m e c h a n i s m . A m e c h a n i s m related to interstitial diffusion is the interstitialcy m e c h a n i s m . I n this process, an interstitial atom moves i n t o a lattice site b y d i s -

ooooo ο ο ο ο ooooo ο ο ο ο o o oo ooooo ο ο ο ο (a) T h e vacancy diffusion mechanism,

Ο

(b) T h e interstitial diffusion mechanism.

Ο

Ο

Ο

ο ο οοοο j

f

o

(c) T h e interstitialcy mechanism. Figure 2. Dominant diffusion mechanisms in silicon.


6.

271


FAIR

p l a c i n g the atom o n that site onto a n adjacent interstitial site. A l t h o u g h several other diffusion m e c h a n i s m s m a y exist i n semiconductors, the three mechanisms just d e s c r i b e d are d o m i n a n t i n s i l i c o n . The Flux Equation in Diffusivity.

T h e n u m b e r o f atoms that cross a

u n i t area i n u n i t t i m e is k n o w n as the flux. I n one d i m e n s i o n , the atoms o n l y m o v e to the r i g h t o r to the left w h e n they change p o s i t i o n along the χ axis ( F i g u r e 3). I n this s i m p l e case, the atoms are assumed to b e located i n planes at x a n d x 0

0

+ α

ω

as s h o w n i n the figure. T h e flux / is s i m p l y the


p r o d u c t o f the concentration C a n d the v e l o c i t y υ. χ =

(10)

CO

T h e net flux is the difference b e t w e e n the flux to the r i g h t a n d a n d that to the left.

(11)

where

C

XO

and

C

X O + T T O

are the concentrations at x a n d x + a , respectively. 0

0

0

T h e factor A i n e q u a t i o n 11 arises f r o m the fact that at any one p l a n e , h a l f l

ζ

Unit area

χ

Figure 3. Flux in the χ direction through the unit area in unit time. The planes of unit area are located at χ = x and χ = x + a . (Reproduced with permission from reference 118. Copyright 1988 Noyes Publications.) Q

Q

Q


272


of the atoms m o v e i n the + x d i r e c t i o n a n d other other h a l f m o v e i n the -x d i r e c t i o n . W h e n a approaches 0, 0

(12) \

a

/

0

ax

a n d e q u a t i o n 11 b e c o m e s


' • - - ϊ - f

( 1 3

»

F o r m o t i o n b y discrete j u m p s b e t w e e n planes a apart, the v e l o c i t y is the 0

p r o d u c t of the n u m b e r of j u m p s p e r second, Γ, a n d the distance a of each 0

j u m p . E q u a t i o n 13 may n o w b e w r i t t e n as

' • - - î ^ f a n d the q u a n t i t y ha^Y

Fermi energy; Ec, conduction band energy. (Reproduced with permission from reference 119. Copyright 1981 Academic Press.) v

F

c o n t r o l of the F e r m i l e v e l . W i t h e i t h e r m e t h o d of c o n t r o l , as the d o p i n g becomes m o r e η-type or m o r e p - t y p e , the total vacancy concentration i n creases as the p o p u l a t i o n o f i o n i z e d vacancies increases. Because i m p u r i t y a n d self-difiusion coefficients d e p e n d u p o n the concentration of vacancies, the diffusion coefficients w i l l also increase w i t h d o p i n g . S u c h c o n c e n t r a t i o n d e p e n d e n t diffusion can o c c u r w h e n the d o p i n g l e v e l exceeds the i n t r i n s i c e l e c t r o n c o n c e n t r a t i o n , n , at the diffusion t e m p e r a t u r e . A n illustration of c o n c e n t r a t i o n - d e p e n d e n t diffusion is s h o w n i n F i g u r e 7.

The Role of Point Defects in Silicon Processing.

The Balancing

Act in Silicon Processing. B o t h silicon oxidation a n d the diffusion of i m p u r i t i e s occur at h i g h temperatures a n d i n v o l v e p o i n t defects such as v a -


277

—

—


y

INTRINSIC DIFFUSION * ~

_ ^ EXTRINSIC DIFFUSION —

—

1 11Mill

1

1 1 1 (III

1

1 1 1 Mil]

.1

L_

LOG(n) ELECTRONS/cm3 Figure 7. Donor impurity diffusion coefficient (Di) vs. electron concentration (electrons per cm ) showing regions of intrinsic and extrinsic diffusion. (Reproduced with permisssion from reference 119. Copyright 1981 Academic Press). 3

cancies o r self-interstitials. T h e first l e v e l o f process d e s i g n involves t h e concept o f d o p i n g a n d j u n c t i o n formation, t h r e s h o l d voltage c o n t r o l , o r the gain c o n t r o l o f a transistor. A n o t h e r goal o f d o p i n g is l o w sheet resistance. T h e p r i m a r y goal o f oxidation is the c o n t r o l l e d g r o w t h o f S i 0

2

layers.

A critical c o n c e r n i n oxidation is the g r o w t h o f stable oxides w i t h e l e c t r i c a l integrity. T o create a nonplanar structure, i t is necessary t o consider t h e viscous flow characteristics o f the oxide a n d w h e t h e r t h e viscosity is l o w e n o u g h t o release stress. I n g e n e r a l , t h e process e n g i n e e r spends a l o t o f t i m e d e a l i n g w i t h these first-order r e q u i r e m e n t s , b u t the rest o f the t i m e is spent i n t r y i n g to balance factors that are generally not w e l l understood. T h e d i a g r a m o f the p o i n t defect balancing act is s h o w n i n F i g u r e 8. T h e arrows i n t h e figure indicate t h e directions o f interactions. F o r example, diffusion may change the concentration o f p o i n t defects, a n d point defects themselves can affect difiusion. O x i d a t i o n produces defects, a n d p o i n t defects can affect oxidation. T h e b a l a n c i n g act involves the generation of p o i n t defects a n d t h e effect o f this generation o n these major processes. D i f i u s i o n m a y i n t r o d u c e strain into t h e lattice that c a n affect surface q u a l i t y . A s these processes p r o d u c e p o i n t defects, e x t e n d e d structural defects may g r o w i n the s i l i c o n . P o i n t defects can also influence the p r e c i p i t a t i o n o f oxygen. O x y g e n is


278



Figure 8. The point defect balancing act in silicon processing. (Reproduced with permission from reference 118. Copyright 1988 Noyes Publications.)

i n c o r p o r a t e d i n t o the crystal d u r i n g crystal g r o w t h , a n d d u r i n g subsequent heat treatments, this oxygen may precipitate. T h e s e precipitates create good g e t t e r i n g sites for attracting m e t a l i m p u r i t i e s a n d , thus, r e m o v e t h e m f r o m active d e v i c e regions. S u c h i n t e r n a l g e t t e r i n g w o u l d have an i m p a c t o n junction quality.

Point Defects. P o i n t defects are d e f i n e d as atomic defects. A t o m i c defects such as m e t a l ions can diffuse t h r o u g h the lattice w i t h o u t i n v o l v i n g themselves w i t h lattice atoms or vacancies ( F i g u r e 9), i n contrast to atomic defects such as self-interstitials. T h e silicon self-interstitial is a silicon atom that is b o n d e d i n a t e t r a h e d r a l interstitial site. E x a m p l e s of p o i n t defects are s h o w n i n F i g u r e 9. O n e of the major controversies i n solid-state science is the nature of the d o m i n a n t native p o i n t defect i n silicon. Is the d o m i n a n t native p o i n t defect i n silicon the monovacancy or the silicon self-interstitial? W e l l - d e v e l o p e d arguments have b e e n p r o p o s e d for each t y p e , b u t the c u r r e n t consensus is that b o t h types are present a n d i m p o r t a n t .

Monovacancy. Statistical t h e r m o d y n a m i c s requires that i f a vacancy is f o r m e d b y r e m o v i n g an atom from the crystal a n d d e p o s i t i n g it o n the surface, t h e n the free e n e r g y of the crystal must decrease as the n u m b e r of created vacancies increases u n t i l a m i n i m u m i n this free energy is reached. Because a m i n i m u m i n the free energy exists for a c e r t a i n vacancy concentration i n the crystal, the vacancy is a stable p o i n t defect. T h e f o l l o w i n g facts about vacancies have b e e n o b t a i n e d e x p e r i m e n t a l l y : (12).

1. E l e c t r o n paramagnetic resonance measurements o n l y identify vacancies or vacancy complexes i n S i i r r a d i a t e d b y electrons. T h e absence of S i self-interstitials has b e e n ascribed to r a p i d a t h e r m a l m i g r a t i o n e v e n at 2 Κ (13). In Microelectronics Processing; Hess, D., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1989.

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279


Foreign interstitial atoms Ca, Ni, Fe, Li, H


Self-interstitial I

ρ type: B, Al» Ga η type: P, As, Sb Figure 9. Examples of point defects in the silicon lattice. {Reproduced with permission from reference 118. Copyright 1988 Noyes Publications.) 2. Diffusion p h e n o m e n a , as w e l l as calculations of diffusion e n tropy a n d e n t h a l p y , have b e e n successfully e x p l a i n e d b y as c r i b i n g m u l t i p l e i o n i z a t i o n levels to vacancies that are the same as those o b s e r v e d for the vacancy i n l o w - t e m p e r a t u r e irradiation e x p e r i m e n t s (14-16). Vacancies a n d s e l f - i n t e r s t i tials are interchangeable as far as diffusion is c o n c e r n e d , p r o v i d e d that b o t h have charge states. 3. T h e o r e t i c a l estimates of the heats a n d entropies of formation of vacancies c o r r e s p o n d w e l l w i t h those of the native defects o b s e r v e d i n diffusion a n d q u e n c h i n g experiments (25,17-19).


280


4. C h a n n e l i n g studies of i m p u r i t y - d e f e c t interactions i n S i show that u n d e r h e l i u m i o n b o m b a r d m e n t the t r a p p i n g efficiency of i m p u r i t i e s for r a d i a t i o n - p r o d u c e d defects is v e r y l o w , near 30 Κ (19). Vacancies are not m o b i l e i n S i b e l o w this t e m p e r ature, whereas interstitials still are. T h i s observation i m p l i e s that the i m p u r i t y - d e f e c t interactions i n v o l v e vacancies. 5. P o s i t r o n a n n i h i l a t i o n l i f e t i m e measurements have b e e n p e r formed on

float-zone

S i at h i g h temperatures a n d show that


vacancy-like defects are f o r m e d (20). The Silicon Self-Interstitial Atom. A s i m i l a r consistent statistical t h e r m o d y n a m i c analysis of the existence of self-interstitials shows that s i l i c o n self-interstitials are stable p o i n t defects. T h e f o l l o w i n g arguments f u r t h e r support the s i l i c o n self-interstitial. 1. T h e majority of dislocation loops a n d stacking faults o b s e r v e d b y transmission e l e c t r o n microscopy of S i are j u d g e d to b e o f extrinsic o r interstitial character. A l t h o u g h there are four p r o posed m e c h a n i s m s b y w h i c h extrinsic-type dislocations m a y be f o r m e d w i t h o u t any self-interstitials b e i n g present (12), most w o r k e r s b e l i e v e that self-interstitial p r e c i p i t a t i o n is the d o m i n a n t m e c h a n i s m i n extrinsic-type dislocations. 2. T h e p i c t u r e of self-interstitials i n S i d e v e l o p e d b y Seeger a n d F r a n k (21) is consistent w i t h observations i n d i c a t i n g s e l f - i n terstitial m i g r a t i o n at l o w a n d h i g h temperatures. 3. E v i d e n c e for the l i q u i d - d r o p character of B - s w i r l defects i n S i comes from the observation that u p o n m e l t i n g , droplets of l i q u i d S i are f o r m e d i n the i n t e r i o r of the solid phase (22). 4. I n n - p structures f o r m e d b y sequential diffusions of Β a n d P, dislocation c l i m b o c c u r r e d at the same t i m e that the e m i t t e r p u s h effect was seen i n the Β layer (23). T h i s result i m p l i e s that the same p o i n t defect is responsible for b o t h p h e n o m e n a . 5. Stacking-fault g r o w t h b e l o w Ρ diffusion a n d the e n h a n c e d dif fusion of the b u r i e d layer occur simultaneously (24). 6. C a l c u l a t i o n s o f total e n e r g y show that self-interstitials f o r m a n d migrate i n S i w i t h a total activation energy r o u g h l y the same as that of self-diffusion (25). A f t e r the balance sheet of pros a n d cons s u r r o u n d i n g the q u e s t i o n of the native defect i n S i is r e v i e w e d , the q u e s t i o n remains. W h a t is the native defect responsible for the diffusion of i m p u r i t y a n d g r o w t h of defects i n Si? So far w e o n l y have clues.


6.

281


FAIR

T h e c u r r e n t majority o p i n i o n is that b o t h types of p o i n t defects are i m p o r t a n t . T h e r m a l e q u i l i b r i u m concentrations of p o i n t defects at the m e l t i n g p o i n t are orders of m a g n i t u d e l o w e r i n S i t h a n i n metals. T h e r e f o r e , a direct d e t e r m i n a t i o n of t h e i r nature b y S i m m o n s - B a l l u f f l - t y p e experiments (26) has not b e e n possible. T h e accuracy of calculated enthalpies of formation a n d m i g r a t i o n is w i t h i n ± 1 eV, a n d the calculations do not h e l p i n d i s t i n g u i s h i n g b e t w e e n the d o m i n a n c e of vacancies or interstitials i n diffusion. T h e i n t e r p r e t a t i o n of l o w - t e m p e r a t u r e experiments o n the m i g r a t i o n o f i r r a d i a t i o n - i n d u c e d p o i n t defects is c o m p l i c a t e d b y the occurrence of r a d i a t i o n i n d u c e d m i g r a t i o n of self-interstitials (27, 28).


I n a d d i t i o n , the structure a n d properties o f p o i n t defects at l o w t e m peratures a n d at h i g h temperatures may b e different (29). T h e observation of extrinsic-type dislocation loops i n dislocation-free,

float-zone

S i indicate

that self-interstitials m u s t have b e e n present i n appreciable concentrations at h i g h t e m p e r a t u r e d u r i n g or after crystal g r o w t h (30, 32). H o w e v e r , it is unclear w h e t h e r these self-interstitials w e r e present at t h e r m a l e q u i l i b r i u m or w e r e i n t r o d u c e d d u r i n g crystal g r o w t h b y n o n e q u i l i b r i u m processes. I n v i e w of the uncertainties r e g a r d i n g the native p o i n t defect i n S i , it is necessary i n discussions of self-diffusion a n d dopant diffusion to take account o f b o t h types o f defects. Point Defect Models of Diffusion in Silicon.

U n d e r conditions of t h e r -

m a l e q u i l i b r i u m , a S i crystal contains a c e r t a i n e q u i l i b r i u m concentration of vacancies, C ° , a n d a certain e q u i l i b r i u m concentration o f S i self-interstitials, v

C°.

F o r diffusion models based o n the vacancy, C °

ficients

v

»

C°

a n d the coef-

o f dopant diffusion a n d self-diffusion can be d e s c r i b e d b y e q u a t i o n

27 (25) Di = D , + Dr 1

+ Dr

+ 2V

(27)

w h e r e D is the m e a s u r e d diffusivity a n d D * , Dr, Dr, a n d D+ are the i n t r i n s i c diffusivities o f the species t h r o u g h interactions w i t h vacancies i n the n e u t r a l , single-acceptor, double-acceptor, a n d d o n o r charge states, r e spectively. T h e s e i n d i v i d u a l c o n t r i b u t i o n s to the total m e a s u r e d diffusivity w e r e d e s c r i b e d i n a p r e v i o u s section. F o r diffusion models based o n self-interstitials, C° » C °. D o p a n t x

v

diffusion a n d self-diffusion are assumed to occur v i a an interstitialcy m e c h anism (32). M o b i l e complexes consisting of self-interstitials i n various charge states a n d i m p u r i t i e s are assumed to exist. I n p r i n c i p l e , b o t h vacancies a n d self-interstitials may occur s i m u l t a n e ously a n d somewhat i n d e p e n d e n t l y . I n d e e d , any relationship b e t w e e n C ° a n d Cj° may b e d o m i n a t e d b y the S i surface, w h i c h can act as a source or sink for e i t h e r species. I f a local d y n a m i c a l e q u i l i b r i u m exists b e t w e e n r e v


282


c o m b i n a t i o n a n d spontaneous b u l k generation, vacancies (V) a n d self-inter stitials (I) w o u l d react as follows V + I ±5 Ο

(28)

w h e r e Ο denotes the u n d i s t u r b e d lattice. T h e l a w of mass action at e q u i l i b r i u m for this reaction is g i v e n b y


CjCy

=

Ci°Cy°

(^^)

A t sufficiently l o n g times a n d h i g h temperatures, equation 29 is fulfilled (33, 34). H o w e v e r , a substantial a m o u n t of t i m e m a y be r e q u i r e d to reach d y n a m i c a l e q u i l i b r i u m (34, 35). T h i s observation suggests that v a c a n c y - s e l f interstitial r e c o m b i n a t i o n is an activated process. I n a d d i t i o n , u n d e r c o n ditions i n w h i c h p o i n t defects are i n j e c t e d , equation 29 m a y not b e v a l i d . I f b o t h types o f point defects are i m p o r t a n t , t h e n diffusion processes may i n v o l v e b o t h types, a n d the f o l l o w i n g relation applies D , = Of + D

t

(30)

v

w h e r e D} is the interstitialcy c o n t r i b u t i o n a n d D , is the vacancy c o n t r i b u t i o n to the total m e a s u r e d diffusivity, D , . Vacancies a n d self-interstitials can cooperate i n effecting the diffusion of i m p u r i t y b y the W a t k i n s r e p l a c e m e n t m e c h a n i s m (36) s h o w n i n F i g u r e 10. Interstitial dopant i m p u r i t i e s can be created b y the exchange b e t w e e n a self-interstitial a n d a substitutional dopant atom. T h e n e w l y created interstitial i m p u r i t y w i l l migrate u n t i l it finds a vacancy, a n d t h e n it is free to diffuse again as a substitutional i m p u r i t y . v

Ο Ο oo ο ο ο ο ο ο ο ο Figure 10. A schematic diagram of the Watkins replacement mechanism. (Reproduced with permission from reference 118. Copyright 1988 Noyes Publications.)


6.

FAIR


283

Vacancies a n d self-interstitials can exist i n e q u i l i b r i u m w i t h each other i n the silicon lattice. T h e concentration of each species can b e d e s c r i b e d b y e q u i l i b r i u m equations of the f o l l o w i n g type. C°

= exp (S /k) exp (-àHf/kT)

(31a)

Cf

= exp (S//k) exp ( - Δ Η / / & Γ )

(31b)

v

v

f

F o r s i l i c o n self-diffusion, the total diffusion coefficient c o u l d be expressed as


D

S i

= fyDyCyO

+ ffoCf

(32)

w h e r e f a n d f are the fractional contributions of vacancies a n d self-inter stitials, respectively, to self-diffusion. A substantial debate exists as to the values of these fractional coefficients ( F i g u r e 11). T h e concept that i m p u r i t y diffusion is d o m i n a t e d b y vacancies o n l y was h e l d u n t i l 1968, w h e n Seeger a n d C h i c k (37) p r o p o s e d that b o t h self-interstitials a n d vacancies can c o n t r i b u t e to difiusion i n s i l i c o n . H o w e v e r , the concept of vacancies a n d i n t e r stitials coexisting i n silicon leads to several u n r e s o l v e d questions. Is there v

l

Figure 11. A diagram of the spectrum of the debate on the dominance vacancies vs. self-interstitials.


of

284


d y n a m i c e q u i l i b r i u m b e t w e e n self-interstitials a n d vacancies? W h a t is the t i m e to establish this d y n a m i c e q u i l i b r i u m ? Experimental Observations. Various experiments y i e l d n u m e r o u s i n d i r e c t results that can h e l p d e t e r m i n e w h e t h e r vacancies or self-interstitials are i n v o l v e d i n diffusion. T h e f o l l o w i n g is a partial list of such experiments. • O x i d a t i o n studies — e n h a n c e d a n d r e t a r d e d difiusion


— b a c k s i d e oxidation — r o l e of S i N 3

4

surface films a n d n i t r i d a t i o n

— d e p e n d e n c e of oxidation-enhanced

a n d oxidation-retarded

difiusion o n d o p i n g —effect o f c h l o r i n e i n the o x i d i z i n g a m b i e n t —effects of d o p i n g o n oxidation • D e t e r m i n a t i o n of the effect of d o p i n g o n oxidation stacking fault shrinkage or g r o w t h • D e t e r m i n a t i o n of the effect of difiusion o n Ο p r e c i p i t a t i o n • C o d i f l u s i o n studies • T r a n s m i s s i o n electron microscopic studies of precipitates a n d defects • D e t e r m i n a t i o n of the relation b e t w e e n total d o p i n g a n d e l e c trically active d o p i n g • D o p a n t profile

measurements

• D e t e r m i n a t i o n of the role of stress o n difiusion F o r e x a m p l e , d u r i n g oxidation, e n h a n c e d difiusion of phosphorus, b o r o n , a n d arsenic are o b s e r v e d , as w e l l as r e t a r d e d difiusion of a n t i m o n y . H o w e v e r , i f d i r e c t n i t r i d i z a t i o n of the silicon surface occurs, t h e n the inverse effects are o b s e r v e d , that is, e n h a n c e d a n t i m o n y difiusion a n d r e t a r d e d phosphorus diffusion. A l s o , oxidation-enhanced difiusion is significantly affected b y d o p i n g . A s e i t h e r p - or η-type d o p i n g concentration increases above n , o x i d a t i o n - e n h a n c e d difiusion d i m i n i s h e s . I f c h l o r i n e is i n t r o d u c e d into the o x i d i z i n g a m b i e n t , oxidation-enhanced difiusion is l i k e w i s e d i m i n i s h e d . f

N o t o n l y is e n h a n c e d difiusion of i m p u r i t i e s o b s e r v e d d u r i n g oxidation, b u t i n a d d i t i o n , stacking faults can grow. A stacking fault is a plane of dislocated m a t e r i a l that m a y intersect the silicon surface b u t that also has a b o u n d i n g partial dislocation. T h e s e faults g r o w w h e n sufficient n u m b e r s of self-interstitials are generated such that the concentration of self-interstitials i n the lattice is h i g h e r than that i n the b o u n d i n g partial-dislocation core


6.

FAIR

285


( F i g u r e 12). Because oxidation is a process that generates excess s e l f - i n t e r stitials, stacking faults w i l l g r o w d u r i n g oxidation. O t h e r e x p e r i m e n t s that have b e e n p e r f o r m e d i n c l u d e i r r a d i a t i n g u n i f o r m l y d o p e d silicon wafers w i t h protons a n d o b s e r v i n g the diffusion o f the dopant after irradiation. A d d i t i o n a l discussion o f these effects w i l l follow.

Diffusion in the Presence of Excess Point Defects. Enhanced Diffusion.

Oxidation-

O x i d a t i o n generally enhances the diffusion o f g r o u p

III a n d g r o u p V elements except for a n t i m o n y ( F i g u r e 13). O x i d a t i o n - e n Downloaded by CORNELL UNIV on May 10, 2012 | http://pubs.acs.org Publication Date: May 5, 1989 | doi: 10.1021/ba-1989-0221.ch006

h a n c e d diffusion is generally o b s e r v e d b y d e p o s i t i n g a silicon n i t r i d e mask on the silicon surface that w i l l p r o h i b i t oxidation i n the regions that i t covers.

CONCENTRATION

Figure 12. A model of self-interstitial diffusion from the bulk to the partial dislocation bounding a stacking fault. Under nonoxidizing conditions, the concentration of self-interstitiah at the fault line, C i , is greater than the equilibrium bulk interstitial concentration, C\. Under oxidizing conditions, C i is greater than C i until the retrogrowth temperature is reached. (Reproduced with permission from reference 45. Copyright 1981 The Electrochemical Society, Inc.) L

L



286


Figure 13. Experiments that illustrate oxidation-enhanced or oxidation-retarded diffusion of dopants in silicon. The supersaturation of self-interstitials associated with the oxidation process drives both effects. (Reproduced with permission from reference 118. Copyright 1984 Noyes Publications.)

O x i d a t i o n is p e r f o r m e d i n a w i n d o w o p e n e d to the silicon surface, a n d the differential changes i n j u n c t i o n d e p t h can be observed. T o e x p l a i n these results, H u (38) p r o p o s e d a m o d e l w i t h the f o l l o w i n g essential points:

1. O x i d a t i o n of S i at the S i - S i 0 interface is usually i n c o m p l e t e to the extent that a p p r o x i m a t e l y 1 S i atom i n 1000 is u n r e a c t e d . 2

2. T h e u n r e a c t e d S i , severed from the lattice b y the a d v a n c i n g S i - S i 0 interface, becomes m o b i l e . T h e s e atoms can e n t e r 2


6.

287


FAIR

the S i lattice interstices a n d cause a flux of self-interstitials away from t h e interface. 3. G r o w t h o f o x i d a t i o n - i n d u c e d stacking faults proceeds b y t h e absorption o f t h e generated self-interstitials. O x i d a t i o n - e n h a n c e d diffusion c a n o c c u r as a result o f the presence o f the excess interstitials v i a t h e W a t k i n s (36) r e p l a c e m e n t m e c h a n i s m o r b y a n interstitialcy process. If the W a t k i n s r e p l a c e m e n t m e c h a n i s m is i g n o r e d , t h e diffusivity (D) o f an i m p u r i t y atom u n d e r conditions of n o n e q u i l i b r i u m p o i n t defect c o n c e n Downloaded by CORNELL UNIV on May 10, 2012 | http://pubs.acs.org Publication Date: May 5, 1989 | doi: 10.1021/ba-1989-0221.ch006

trations is g i v e n b y D = D/iQ/C, ) 0

where C and C l

v

+ O?(C IC °) V

(33)

V

are t h e excess self-interstitial a n d vacancy concentrations,

respectively. T h e fractional interstitialcy factor is defined as (34) (34)

fi = D}ID? and w e can write D

t

+ (1 - MC /C °)

= m/Cf)

V

(35)

V

Calculations o f the fractional interstitialcy components for Β, P, A s , a n d S b are s h o w n i n T a b l e I (33, 39-42). A significant spread i n t h e values o{f is o b t a i n e d . T h e value o f f has b e e n correlated w i t h t h e a m o u n t of energy r e q u i r e d to make a substitutional dopant atom b e c o m e interstitial. E n e r g i e s of interstitial formation i n S i are s h o w n i n Table I I . T h e larger the energy t

{

Table I. Fractional Interstitialcy Components of Diffusion via Self-Interstitials in Silicon at 1000-1100^C Element

Fair (39)

Antoniadis (34) 0.32

Matsumoto (41)

Gosele (40)

Mathiot (42)

0.41

0.8-1.0

0.18

Β

0.17

Al

0.2

Ρ

0.12

0.40

0.35-0.5

0.5-1.0

0.19

As Sb

0.09

0.43

0.45-0.75

0.2-0.5

0.16

0.13

0.015

0.6-0.7

0.02

Table II. Estimated Interstitial Formation Energies in Silicon Element Si Al

Interstitial Formation Energy (eV) 2.2

2 +

2.21

Β

2.26

Ρ

2.4

As

2.5


288


of interstitial formation, the smaller is the fractional interstitialcy c o m p o n e n t of diffusion.


T h e diffusion of Sb is r e t a r d e d d u r i n g oxidation of the S i surface (33). T h i s retardation can be e x p l a i n e d b y assuming that Sb diffuses p r e d o m i n a n t l y b y a vacancy m e c h a n i s m a n d that the self-interstitials generated at the ox i d i z i n g surface c o m b i n e w i t h vacancies to r e d u c e t h e i r concentration. T w o recent experiments have y i e l d e d considerable support for an i n terstitialcy m e c h a n i s m for Ρ diffusion. F a h e y et a l . (43) o b s e r v e d that d i r e c t n i t r i d a t i o n o f S i p r o d u c e s a supersaturation of vacancies s u c h that Ρ diffusion is substantially r e d u c e d i n the u n d e r l y i n g S i . O n the other h a n d , w h e n an oxide is g r o w n o v e r the d o p e d S i a n d t h e n o x y n i t r i d a t i o n is p e r f o r m e d at the S i O surface, excess self-interstitials are generated a n d Ρ diffusion is greatly e n h a n c e d . T h e s e results are shown i n F i g u r e 14 a n d are c o m p a r e d w i t h those for Ρ diffusion i n a n e u t r a l a m b i e n t . S i m i l a r results w e r e o b t a i n e d w i t h B. T h e average e n h a n c e d o r r e t a r d e d diffusivities of P, A s , a n d S b after d i r e c t n i t r i d a t i o n are s h o w n i n F i g u r e 15. F r o m these data the authors c o n c l u d e d that the fractional interstitialcy c o m p o n e n t of Ρ diffusion is 70-100%. £

Dependence of Oxidation-Enhanced Diffusion on Doping. Taniguchi (44) f o u n d that oxidation-enhanced diffusion decreases as the concentration

η

1 1 1 Ρ diffusion N H 1100 °C 2 h 3

10

20

%.

\

\

* * \

^-oxynitr.

\ \

direct_ nitr.

\ 10 16

U

" \

-inert

\ initial^ \ 3.0

1.5 Depth 0*m) Figure 14. Phosphorus profiles after direct nitridation, oxynitride and inert ambient diffusion at 1100 °C.

formation,


6.

10

-

•

-

Δ

τ

Λ O

Ρ

As Sb χ

-

6

289


FAIR

4

V

-

Î

—

τ

—

Λ < Ο V

1

û

10

"Τ"ΓΊΠ ι


—

_J

!

I I I II 1

1

f

ι

t « t ι il

1

ι

1

ι ι ι ι ι 10

10*

10

Time (min) Figure 15. Average enhanced- and retarded-diffusion coefficients ofP A s , and Sb following direct nitndation experiments. Data are from Fahey (43). Ab breviations: < D > , time-averaged diffusion coefficient; D * , intrinsic diffusion coefficient. (Reproduced with permission from reference 118. Copyright 1984 Noyes Publications.) 9

A

A

o f the diffusing i m p u r i t y increases b e y o n d the p o i n t w h e r e c o n c e n t r a t i o n d e p e n d e n t diffusion occurs. T h i s effect was e x p l a i n e d i n terms of the r e d u c t i o n of o x i d a t i o n - p r o d u c e d self-interstitials b y r e c o m b i n a t i o n w i t h the i n c r e a s i n g s u p p l y of vacancies. F a i r (45) assumed that the e q u i l i b r i u m v a cancy c o n c e n t r a t i o n is unaffected i n i t i a l l y b y the self-interstitials generated at the o x i d i z i n g surface. H o w e v e r , the quasi steady-state value of interstitial supersaturation is i n v e r s e l y p r o p o r t i o n a l to the vacancy c o n c e n t r a t i o n , w h i c h increases w i t h d o p i n g above n,. T h e o x i d a t i o n - e n h a n c e d dopant diffusivity, D, e

is t h e n D

e

=

D

S I

+

A D

= D^Cy/Cy ) 0

0

+ DjiCjCfitCy'lCy)

(36)

w h e r e ( C J / C J ) , - is the self-interstitial supersaturation u n d e r i n t r i n s i c d o p 0

i n g conditions a n d C /C ° v

v

is the vacancy e n h a n c e m e n t w h e n d o p i n g ex

ceeds η j.


J


290

E q u a t i o n 36 is d i v i d e d i n t o the contributions to the diffusion o f s u b s t i tutional i m p u r i t y u n d e r n o n o x i d i z i n g conditions, D , a n d the e n h a n c e d c o n t r i b u t i o n d u e to o x i d a t i o n , ΔΌ . F i g u r e 16 shows the data o f T a n i g u c h i et al. (44) for o x i d a t i o n - e n h a n c e d diffusion o f Ρ a n d Β versus the total n u m b e r of dopant i m p u r i t i e s p e r square c e n t i m e t e r , Q . T h e calculated values of D a n d àD are s h o w n i n c o m p a r i s o n w i t h the e x p e r i m e n t a l data. R e a s o n able agreement is o b t a i n e d . T h u s , Taniguchi's m o d e l of self-interstitial r e c o m b i n a t i o n w i t h vacancies is consistent w i t h the models of h i g h - c o n centration diffusion of Β a n d Ρ used b y F a i r i n his calculations. S I

0

T

Q


S I

A d d i t i o n a l w o r k is n e e d e d to refine these models. F o r example, r a p i d vacancy generation a n d v a c a n c y - i n t e r s t i t i a l r e c o m b i n a t i o n are assumed. T h e s e effects c o m b i n e to modulate the self-interstitial supersaturation. T h u s , the s u p p l y o f self-interstitials at the o x i d i z i n g interface cannot k e e p u p w i t h r e c o m b i n a t i o n effects. R a p i d r e c o m b i n a t i o n m a y b e j u s t i f i e d at h i g h d o p i n g levels, because species s u c h as V a n d I " o r V " a n d I m a y be p l e n t i f u l . +

+

15

y 3.0χ10ρ _ - ο CO

D | CALCULATED S

Δ D CALCULATED 0

£

1.0

10"

1015

10"

10" 2

TOTAL IMPURITY DOPING, Q (em- ) T

15

3.0xl0- h D | CALCULATED S

2.0 CO D CALCULATED

1.0

0

CO

ο Figure 16. Measured and calculated values of boron and phosphorus diffusivities as a function of total impurity doping. Data are divided into contributions to substitutional impurity diffusion under nonoxidizing conditions, D / , and the enhanced contribution due to oxidation, A D . Data are from Taniguchi et al. (44). (Reproduced with permission from reference 45. Copyright 1981 The Electrochemical Society, Inc.) S

0


6.

FAIR

291


T h e cross-section for charged-defect r e c o m b i n a t i o n w i l l l i k e l y b e larger than that for neutral-defect r e c o m b i n a t i o n . I n a d d i t i o n , dopant ions w i l l l i k e l y p r o v i d e a d d i t i o n a l r e c o m b i n a t i o n sites w h e n the dopant is p a i r e d w i t h a p o i n t defect. Effect of Chlorine

on Oxidation-Enhanced

Diffusion.

I f c h l o r i n e is

a d d e d to oxygen i n the furnace i n sufficient concentrations such that stackingfault r e t r o g r o w t h occurs (46), t h e n oxidation-enhanced diffusion b e c o m e s n e g l i g i b l e (47). T h i s result is b e l i e v e d to b e d u e to the generation of vacancies at this S i - S i 0

2

interface w h e n C I reacts w i t h S i atoms o n lattice sites to


p r o d u c e S i C l b y the f o l l o w i n g reaction

Si + - C l 2

2

(37)

SiCl + V

T h e vacancy generated is t h e n available to r e c o m b i n e w i t h a S i self-interstitial p r o d u c e d b y oxidation: ί + V-^

(38)

Ο

As a result, the supersaturation of self-interstitials i n the s i l i c o n surface a n d the b u l k is r e d u c e d or e l i m i n a t e d , t h e r e b y i n h i b i t i n g stacking-fault g r o w t h and e n h a n c e d difiusion ( F i g u r e 17). Point Defect Generation During Phosphorus Diffusion. At Concen trations above the Solid Solubility Limit. T h e m e c h a n i s m for the difiusion of phosphorus i n silicon is still a subject of interest. H u et a l . (46) r e v i e w e d the models of phosphorus diffusion i n silicon and p r o p o s e d a d u a l v a c a n c y - i n t e r s t i t i a l c y m e c h a n i s m . T h i s m e c h a n i s m was p r e v i o u s l y a p p l i e d b y H u (38) to e x p l a i n oxidation-enhanced difiusion. H a r r i s a n d A n t o n i a d i s (47) s t u d i e d s i l i c o n self-interstitial supersaturation d u r i n g phosphorus diffusion and o b s e r v e d an e n h a n c e d diffusion of the arsenic b u r i e d layer u n d e r the phosphorus diffusion layer a n d a r e t a r d e d diffusion of the a n t i m o n y b u r i e d layer. F r o m these results they c o n c l u d e d that d u r i n g the diffusion of p r e deposited p h o s p h o r u s , the concentration of silicon self-interstitials was e n h a n c e d a n d the vacancy concentration was r e d u c e d . T h e y r u l e d out the possibility that the increase i n the concentration of s i l i c o n self-interstitials was d u e to the oxidation of s i l i c o n , w h i c h was c o n c u r r e n t w i t h the phosphorus p r e d e p o s i t i o n process. M o r e recently, Tsai et a l . (24) s t u d i e d the diffusion of b u r i e d A s a n d S b layers i n response to surface diffusion of P. F l o a t - z o n e S i wafers ( < 1 0 0 > orientation, p - t y p e , a n d 100 Ω-cm) w e r e u s e d i n this study. A s ions w e r e i m p l a n t e d at 100 k e V to a dose of 1 X 1 0 / c m to h a l f of the wafers, a n d S b ions w e r e i m p l a n t e d at 150 k e V to a dose of 5 X +

1 4

+


2

292


(HCI oxidation)


0

2

CI

Figure 17. Diagram of SiCl formation during oxidation with the subsequent injection of vacancies. The injection of vacancies reduces the concentration of self-interstitiab in the bulk and causes oxidation stackingfaults (OSF) to shrink. (Reproduced with permission from reference 118. Copyright 1988 Noyes Publications.) 1 0 / c m to the o t h e r h a l f o f the wafers. A f t e r b e i n g c l e a n e d , the wafers w e r e annealed at 900 °C for 30 m i n i n a n i t r o g e n a m b i e n t to activate the i m p l a n t e d ions a n d to anneal out the major i m p l a n t damage. T h i s a n n e a l i n g c o n d i t i o n was s i m i l a r to that u s e d b y H a r r i s et al. (47). P - t y p e epitaxial films (100 Ω-cm) w e r e g r o w n o n these wafers to a thickness close to 10 μιη b y u s i n g a standard a t m o s p h e r i c reactor. A b o u t 9000 to 10,000 Â of oxide was d e p o s i t e d o n most o f the wafers to f o r m the diffusion mask against p h o s p h o r u s . T h e oxide films w e r e d e p o s i t e d i n a L P C V D (low-pressure c h e m i c a l vapor deposition) system b y u s i n g S i C l H a n d oxygen at 900 °C. T h e s e wafers w e r e t h e n m a d e dense i n oxygen at 800 °C for 30 m i n . O x i d e w i n d o w s w e r e f o r m e d , a n d Ρ was diffused f r o m a P O C l source. A l l of these c h e m i c a l source diffusions w e r e p e r f o r m e d at surface concentrations above the s o l i d s o l u b i l i t y l i m i t . I o n i m p l a n t a t i o n created d o p e d layers w i t h Ρ concentrations b e l o w s o l i d s o l u b i l i t y . Samples w e r e analyzed b y u s i n g T E M ( X T E M ) m i crographs, s p r e a d i n g resistance, defect e t c h i n g , a n d S I M S . 1 3

2

2

2

3

A t y p i c a l result is shown i n F i g u r e 18, w i t h micrographs s h o w i n g v a r i ations of stacking faults i n s i d e a n a r r o w P-diflused r e g i o n a n d the e n h a n c e -



Figure 18. Micrographs showing variation of stacking faults inside a narrow phosphorus diffusion region and the slight enhancement of arsenic diffusion and retardation of antimony diffusion. Ρ diffusion was at 1150 °C for 60 min. (Reproduced with permission from reference 24. Copyright 1987 The Electrochemical Society, Inc.)


294


m e n t of A s diffusion a n d retardation of Sb difiusion. M e a s u r e m e n t s of e n h a n c e d A s diffusion a n d r e t a r d e d Sb diffusion w e r e m a d e o v e r a w i d e temperature range w i t h a fixed surface concentration of P. T h e s e diffusion coefficients are p l o t t e d i n F i g u r e 19 w h e r e D is the A s difiiisivity a n d D is the Sb diffusivity. T h e s e data are c o m p a r e d w i t h i n t r i n s i c diffusion coeffi cients.


e

r

T h e data i n F i g u r e 19 suggest that high-concentration Ρ difiusion w i t h surface d o p i n g i n excess of s o l i d s o l u b i l i t y produces silicon self-interstitials that difiuse to the silicon surface a n d into the b u l k crystal. T h i s c o n c l u s i o n is based on the f o l l o w i n g observations: (1) Stacking-fault g r o w t h w e r e f o u n d i n the regions u n d e r the w i n d o w i n w h i c h Ρ diffuses. (Stacking faults g r o w b y absorbing self-interstitials). (2) T h e difiusion of A s was e n h a n c e d , whereas the diffusion of the Sb b u r i e d layers was r e t a r d e d , results w h i c h are consistent w i t h observations of oxidation-enhanced difiusion i n w h i c h self-interstitials are p r o d u c e d . T h e activation e n e r g y for e n h a n c e d difiusion d u e to an interstitialcy m e c h a n i s m is d e t e r m i n e d from equation 39 D (I) e

(39)

= DiflGi

w h e r e G , is a self-interstitial supersaturation factor. G is b e l i e v e d to be related to self-interstitial formation due to Ρ p r e c i p i t a t i o n a n d difiusion. T h u s from F i g u r e 19, Gj has an activation energy of - 2 . 5 9 eV. T h i s result i m p l i e s that self-interstitial generation decreases w i t h increasing t e m p e r a t u r e , w h i c h is w h y no e n h a n c e d diffusion was o b s e r v e d i n this study at 1200 °C. T h e activation energy for vacancy-dominated diffusion is g i v e n b y e q u a tion 40 l

D ( V ) = DIV)G

V

(40)

= C /Cy°

(41)

where G a n d Cy/C ° v

v

v

is the vacancy supersaturation ratio. A t t h e r m a l e q u i l i b r i u m , C,C

V

= CfCy

0

(42)

w h e r e C is the self-interstitial concentration above or b e l o w the i n t r i n s i c concentration C / . Because l

G , = CtlCf

(43)

then G

v

=

1/Gz


(44)

6.

FAIR


°C

1200 1150 1100 1070

1000


-12

6

7

8 4

ιο /τ

1

(K- )

Figure 19. Plots of intrinsic diffusion coefficients of Sb and As vs. 1/Ύ. Also shown are diffusivity data for Sb and As buried layers from Table I in the presence of a phosphorus surface diffusion. Abbreviations: D , reduced Sb diffusivity; D , enhanced As diffusivity; D . , intrinsic diffusivity. (Reproduced with permission from reference 24. Copyright 1987 The Electrochemical So ciety, Inc.) R

E


296


and equation (40) can be written as D(V) = D,{V)IG

(45)

t

Applying equation 45 to the Tsai study is risky, because externally injected self-interstitials render equation 42 invalid. However, as a general guide to understanding the origin of reduced Sb diffusion in the presence of excess self-interstitials, the activation energy of Sb difiusion from equation 45 is given by D (V)ocexp(-4.08eV/fcT)/exp(2.59eV/fcT)a Downloaded by CORNELL UNIV on May 10, 2012 | http://pubs.acs.org Publication Date: May 5, 1989 | doi: 10.1021/ba-1989-0221.ch006

r

exp (-6.67 eV/kT)

(46)

This result agrees well with the observed value of 6.62 eV and supports the notion that the reduced difiusion of Sb is a result of a reduced vacancy population caused by self-interstitial generation from the P-difiused layer. At Concentrations below the Solid Solubility Limit.

Defect generation

during phosphorus difiusion at concentration levels below solid solubility was also investigated by Tsai et al. (48). Diffusions of ion-implanted Ρ were performed in low-oxygen ambient and in nitrogen with a silicon nitride cap. Markers of buried layers of arsenic and antimony were used to study the effect of point defect generation on the diffusions. Defects were revealed by using the Schimmel etch. The following results were obtained: (1) Stacking faults were formed below the phosphorus-diffused region in a low-oxygen ambient and at 1050-1150 °C. (2) With long difiusion times, the difiusion of buried layers of As was enhanced and that of buried layers of Sb was retarded. (3) Difiusion in nitrogen with a silicon nitride cap yielded few stacking faults, reduced Ρ difiusion, and neither enhancement nor retardation of the As or Sb buried layers, respectively, for the same processing conditions that pro duced the results in (2). (4) At phosphorus concentrations above solid sol ubility, difiusion in N with a nitride film cap enhanced the difiusion of the As buried layer, and stacking faults were also observed. Thus, the intrinsic difiusion of phosphorus generates excess silicon self-interstitials. The silicon nitride cap apparently ties up the silicon surface with Si-N bonds, making it more difficult to generate the self-interstitials required for Ρ difiusion. In addition to generating excess self-interstitials, high-concentration Ρ difiusion also causes the local equilibrium vacancy concentration to increase. Nishi et al. (49) showed that significant enhancement of Sb difiusion occurs inside the highly doped Ρ profile, a result suggesting a strong enhancement of the vacancy concentration there. 2

Excess Point

Defects and Low~Thermal-Budget

Annealing.

Sub-

micrometer VLSI (very-large-scale integration) technologies require low thermal budgets (the product of dopant diffusivity and difiusion time) to limit the difiusional motion of dopants. Two options exist to reduce the thermal


6.

FAIR

297


budget: (1) r e d u c e d process temperatures w i t h e x t e n d e d furnace-annealing times or (2) h i g h process temperatures w i t h r a p i d t h e r m a l - a n n e a l i n g (RTA) times. H o w e v e r , for b o t h options, e n h a n c e d dopant difiusion is sometimes o b s e r v e d (50-54). F o r example, l o w - t e m p e r a t u r e furnace anneals of i o n i m p l a n t e d Β layers i n S i can e x h i b i t substantial difiusion d e p e n d i n g u p o n the completeness of activation of the i m p l a n t (52). M o d e l s that have b e e n


p r o p o s e d to explain these results (55, 56) lack generality a n d do not p r e d i c t the correct t i m e d e p e n d e n c e of annealing, nor do they deal w i t h electrical activation a n d damage r e m o v a l (51). R e c e n t l y , M i c h e l (51) proposed that the e n h a n c e d difiusion of Β d u r i n g l o w - t e m p e r a t u r e furnace annealing results from the presence of an active species that is m o b i l e . A s a n n e a l i n g proceeds, the inactive Β species, w h i c h may be defect clusters, converts to the active species exponentially w i t h t i m e . T h e t i m e constant has an activation energy of ~ 5 eV, as d e t e r m i n e d b y S e i d e l a n d M a c R a e (57). A s a result of the annealing of defect clusters, the e n h a n c e d diffusion of Β is assumed to occur u n i f o r m l y throughout the i m p l a n t e d region but at a l i m i t e d p e r i o d that decays exponentially. I n t e r actions that may result from damage p r o d u c e d b y high-dose i m p l a n t s as p r o p o s e d b y F a i r et a l . (53) are i g n o r e d . T h u s , M i c h e l ' s m o d e l applies p r i m a r i l y to low-dose Β i m p l a n t s w h e r e the peak concentration of Β is b e l o w the solid s o l u b i l i t y at the a n n e a l i n g t e m p e r a t u r e . T h e effects of damage b y i o n i m p l a n t a t i o n o n the l o w - t e m p e r a t u r e dif fusion of dopant can also be s t u d i e d b y i m p l a n t i n g S i or G e ions into p r e d e p o s i t e d layers i n S i . R e c e n t l y , S e r v i d o r i et al. (58) s t u d i e d the influence of lattice defects i n d u c e d b y S i i m p l a n t a t i o n . U s i n g t r i p l e crystal X - r a y diffraction a n d T E M , they c o n f i r m e d (1) that b e l o w the o r i g i n a l amorphous s u r f a c e - c r y s t a l interface, interstitial dislocation loops and interstitial clusters exist a n d (2) that epitaxial r e g r o w t h leaves a vacancy-rich r e g i o n i n the surface. +

+

+

T h e r e f o r e , dopants exhibit different amounts of e n h a n c e d or r e t a r d e d diffusion d u r i n g a n n e a l i n g a c c o r d i n g to w h i c h r e g i o n the dopant is i n a n d w h e t h e r it diffuses v i a a vacancy or self-interstitialcy m e c h a n i s m . F o r the case of Β p r e d e p o s i t e d from a B B r source to an i n i t i a l j u n c t i o n d e p t h of 1200 Â, subsequent S i i m p l a n t a t i o n a n d annealing at 7 5 0 - 9 0 0 °C caused r e t a r d e d diffusion. H o w e v e r , for d e e p predepositions (3400 A ) , this p r o c essing p r o d u c e d substantial e n h a n c e d diffusion. T h u s , any m a t h e m a t i c a l m o d e l m u s t i n c l u d e the spatial d e p e n d e n c e of i m p l a n t damage, the nature of the damage (whether the damage is r i c h i n vacancies or self-interstitials), a calculation of the damage a n n i h i l a t i o n d u r i n g annealing, a n d estimates of point defect p r o d u c t i o n d u r i n g annealing. T h e different k i n d s of defects p r o d u c e d b y b o t h l o w - a n d high-dose Β i m p l a n t s are s h o w n schematically i n F i g u r e 20. 3

+

P o i n t defect p r o d u c t i o n as a result of i m p l a n t a t i o n damage of the k i n d shown i n F i g u r e 20 gives rise to anomalous Β diffusion d u r i n g subsequent annealing. A s u m m a r y of recent models that explain these effects follows


298


11


Low-Dose Β Implants:

Depth

OVP© dislocations)

•

Depth

•

High-Dose Β Implants

Depth—• Figure 20. Ion implantation defect production models for low- and high-dose Β implants into crystalline and preamorphized Si. C i is the solid solubility ofB. so

(59). T h e s e m o d e l s have b e e n i n c o r p o r a t e d i n the P R E D I C T p r o g r a m for c o m p u t e r s i m u l a t i o n (60). • Β i m p l a n t s a n d l o w - t e m p e r a t u r e furnace a n n e a l i n g w i t h t r a n sient difiusion that is associated w i t h the activated r e m o v a l o f i m p l a n t damage i n the tail region o f the i m p l a n t . T h e m a g n i t u d e of the e n h a n c e d , transient diffusivity increases w i t h i m p l a n t dose a n d energy b u t reaches saturation at 2 Χ 1 0 " c m / s . 13

2

• P r e a m o r p h i z a t i o n a n d postamorphization w i t h S i or G e i m plants. T h e solid s o l u b i l i t y of Β w i t h i n the r e g r o w n surface +

+


6.

299


FAIR

layer a n d the diffusion of Β b e y o n d the d e p t h of the o r i g i n a l amorphous l a y e r - c r y s t a l interface are enhanced. A l s o , r e d u c e d diffusion may occur i n the vacancy-rich r e g r o w n surface layer. • H i g h - d o s e Β implants w i t h a l l - t e m p e r a t u r e furnace a n n e a l i n g a n d r a p i d t h e r m a l a n n e a l i n g (RTA). L o c a l diffusivity d e p e n d s o n e x t e n d e d defect formation a n d a n n i h i l a t i o n . A l s o , Β c l u s t e r i n g occurs above s o l i d s o l u b i l i t y . • L o w - d o s e Β a n d Ρ implants w i t h R T A . T i m e - d e p e n d e n t

dif

fusion is associated w i t h a n n e a l i n g of i m p l a n t damage.


E a c h of these effects are d e s c r i b e d i n the following sections, w i t h the discussion l i m i t e d to the case w h e r e the Β concentration does not e x c e e d solid s o l u b i l i t y at the a n n e a l i n g t e m p e r a t u r e .

Low-Temperature Furnace Annealing. T h e enhanced diffusion of l o w dose Β implants i n S i d u r i n g l o w - t e m p e r a t u r e annealing can be dramatic. E x a m p l e s are g i v e n i n F i g u r e s 2 1 - 2 3 . F o r F i g u r e 21, two c h a n n e l Β i m plants, one at 35 k e V (6.6 x 1 0 c m " ) and the other at 75 k e V (1.4 Χ 1 0 / c m ) , w e r e p e r f o r m e d t h r o u g h a p o l y / g a t e oxide structure, a n d a two-step anneal (600 °C, 30 m i n ; 700 °C, 30 min) was p e r f o r m e d (61). A f t e r the anneal, the surface concentration decreased b y a factor of 2, a n d the tail p o r t i o n of the Β profile m o v e d b y approximately 400 Â. F o r F i g u r e 22, a 2 X 1 0 / c m , 5 - k e V i m p l a n t was p e r f o r m e d t h r o u g h 100 Â of S i 0 a n d furnace a n nealed for 35 m i n . V e r y little diffusion o c c u r r e d for Β concentrations above 3 X 1 0 / c m (approximate n at 800 °C), whereas a m o v e m e n t of 1 5 0 - 2 5 0 Â o c c u r r e d i n the Β tail (A. E . M i c h e l , u n p u b l i s h e d ) . 1 2

2

1 1

2

1 4

2

2

1 8

3

{

F i g u r e 23 shows profiles of a s - i m p l a n t e d Β (1 X 1 0 / c m at 800 k e V a n d 1.2 a n d 2.0 M e V ) (62). A f t e r a two-step anneal (500 °C, 1 h ; 850 °C, 0.5 h), substantial diffusion i n the o r d e r of 9 0 0 - 1 6 0 0 Â o c c u r r e d . U n d e r n o r m a l conditions, the diffusion l e n g t h for this case s h o u l d be less t h a n 150 A . 1 4

2

T h e diffusional displacement of Β is a function of i m p l a n t dose a n d energy. T h e e n e r g y d e p e n d e n c e is i l l u s t r a t e d i n F i g u r e 24, w h i c h shows the diffusion of Β at a concentration of 1 X 10 1 c m versus fi , the p r o j e c t e d range of Β i m p l a n t a t i o n . T h e implants w e r e 1 Χ 1 0 - 2 X 1 0 Β atoms p e r c m annealed at 8 0 0 - 8 5 0 °C for approximately 0.5 h . T h e d i s p l a c e m e n t increases w i t h i m p l a n t d e p t h a n d t h e n reaches saturation. T h e calculated c u r v e i n F i g u r e 24 is based o n the concentration of excess self-interstitials i n the tail of the i m p l a n t that increases d i r e c t l y w i t h range, u p to a m a x i m u m value. 11

3

p

1 4

1 4

2

T h e l o w - t e m p e r a t u r e e n h a n c e d diffusion of Β can be m o d e l e d b y c a l c u l a t i n g an effective diffusivity that is t h e n a p p l i e d to the calculation of the Β profile b y u s i n g the P R E D I C T p r o g r a m (59). T h e d u r a t i o n of e n h a n c e d diffusion is related to the damage a n n e a l i n g t i m e . E m p i r i c a l l y , the r e m o v a l


300


Τ

18

— B

Τ

τ

SIMS — Mete et al. Predict. Cal.

Implants: 35 keV, 6.6x10 c m " 75 keV, 1.4x10 c m "

+

12


11

2

2

Annealed: 600 °C, 30 min 700 °C, 30 min.

As-lmplanted

15

0.1

0.2

0.3

xO*m) Figure 21. Example of two MOSFET channel Β implants performed through a poly gate/oxide structure and annealed at 600 °C for 30 min and at 700 °C for 30 min. The substantial enhanced diffusion is shown modeled with calcu lations from the Predict program. Data are from Mêle et al. (61). Abbreviation and symbols: SIMS, secondary ion mass spectrometry; measured after implant; A , measured after anneals. (Reproduced with permission from reference 59. Copyright 1988 Institute of Electrical and Electronics Engineers, Inc.)



10

10

18

16

17

10

-

:

-

I

500

I

I

I

\

\

ι

I

fOOO

V

I 2

2

ι

/

/

ι 'VV

X

1500

^Si?

I

I

ο ο oo

I

A. Michel Data

2000,

PREDICT

ο Furnace anneal 35 min at 800 ° C

ο No anneal

Beam Direction along

through 10 nm S i 0

Depth (Â)

_i

14

ι

Boron Implant 2 x 1 0 / c m at 5 keV

I

^feOv/ /

I

2500

-

-

-

Figure 22. Example of enhanced tail diffusion of a 5-keV-channeled Β implant annealed at 800 °C for 35 min. Data are from. Michel (unpublished results). (Reproduced with permission from reference 59. Copyright 1988 Institute of Electrical and Electronic Engineers, Inc.)

ο c ο ϋ

Έ ω

1

Ε ο, c

1019

CO J


302


1.0E+19

0.8 MeV

,—As implanted

1.2 MeV

-550 °C, 1 hr 850 °C, V2 hr

1

#r ·0Ε+18

1.0E+17 c


1 1.0E+16

1.0E+14h 1.0E+13 Depth (jim) Figure 23. Examples of measured profile broadening of high-energy Β implants at low annealing temperatures. SIMS data are from Ingram et al. (62). (Re produced with permission from reference 59. Copyright 1988 Institute of Elec trical and Electronics Engineers, Inc.)

of excess p o i n t defects occurs at t i m e t , w h i c h is defined b y equation 4 7 a

t = 4 Χ ΙΟ" a

exp (5 eV/fcr)(second)

2 2

(47)

T h e fraction o f the i m p l a n t damage that anneals, f , is assumed to d e p e n d d i r e c t l y o n t i m e at t h e annealing temperature: a

(48)

fa = J T h e annealing o f damage occurs u n t i l f is used i n a process, t h e n

a

/„ = f

+

l

f

= 1. I f m o r e than one t e m p e r a t u r e

+ . . .

T h u s , t h e annealing is c u m u l a t i v e .


(49)

6.

303


FAIR

Ε ^ 1.0 CO

Έ

DATA ο 2x10 B/cm (800 °C, 35 min)

ϋ

14

2

14

2

• 1x10 B/cm (850 °C, 30 min)

Ο Χ

CO Έ

Saturation

Φ

•

Ε Φ


8

CL (Ο Û Ίο c ο CO

-

0.1

b c ρ £0.01 0.01

y I 1.0

0.1 Rp 0*m)

Figure 24. Measured and calculated Β diffusional displacement versus proj ected ion implantation range (R ) after annealing 1 Χ 10 -2 X 10 /cm implants at 800-850 °C. (Reproduced with permission from reference 59. C opyright 1988 Institute of Electrical and Electronics Engineers, Inc.) 14

p

14

2

F o r < 1 0 0 > a n d < 1 1 1 > S i , a n additive diffusivity describes Β diffusion for i m p l a n t doses < 2 X D

1 4

2

= 9 X 10- (dose/10 ) 12

e n h

where R then

10 /cm

p

13

1/4

(R /7 X 1 0 e x p p

( - 0 . 6 eV/kT)

is i n centimeters. I f t h e Β dose is greater than 2 X

D

e n h

= 1.4 X 1 0 - ( R / 7 n

p

(50)

10 /cm , 1 4

x 10" )exp(-0.6eV/fcr)

2

(51)

6

D is expressed i n square centimeters p e r second. T h e dose d e p e n d e n c e of D has b e e n v e r i f i e d for implants i n t h e range from 5 X 1 0 to 1 X 1 0 / c m . T h e calculated profiles i n F i g u r e s 21 a n d 22 are based o n this model, with D used as a n additive t e r m to the n o r m a l t e m p e r a t u r e d e p e n d e n t diffusion. e n h

1 2

e n h

1 6

2

e n h

Reverse Time Effect of Diffusion. M i c h e l (51) observed two n e w effects associated w i t h t h e l o w - t e m p e r a t u r e annealing o f B - i m p l a n t e d layers: (1) a n


304



apparent " r e v e r s e " t i m e effect for furnace diffusion w h e n p r e c e d e d b y r a p i d t h e r m a l a n n e a l i n g a n d (2) l o w - t e m p e r a t u r e e n h a n c e d diffusion o n l y for Β at concentrations b e l o w n , ( F i g u r e 25). T h e concentration d e p e n d e n c e o f e n h a n c e d Β difiusion has b e e n o b s e r v e d p r e v i o u s l y b u t o n l y w h e n t h e peak Β concentration exceeded s o l i d s o l u b i l i t y (53, 63). T h e r e d u c e d Β diffusion i n t h e profile peak has b e e n a s c r i b e d to Β c l u s t e r i n g a n d e x t e n d e d defects i n t r o d u c e d b y high-dose i m plants. H o w e v e r , the i m p l a n t u s e d for the data i n F i g u r e 2 5 does n o t exceed solid solubility. T w o o t h e r possibilities exist: (1) t h e Β peak is i n a vacancyrich region p r o d u c e d b y i m p l a n t a t i o n a n d cannot diffuse because o f an i n sufficient s u p p l y o f self-interstitials o r (2) the generated self-interstitials d u r i n g damage a n n e a l i n g change charge state w h e n C > n „ a n d this change affects Β difiusion. N o data exist to resolve this q u e s t i o n . B

T h e reverse t i m e effect o f difiusion was m o d e l e d b y u s i n g equations 4 7 - 5 1 . T h e 900 ° C R T A step causes the damage anneal t i m e , t to decrease relative to t h e 8 0 0 °C anneal. T h u s , t h e d u r a t i o n o f transient e n h a n c e d difiusion decreases as t h e R T A anneal t i m e increases. C a l c u l a t i o n s u s i n g this m o d e l are s h o w n i n F i g u r e 2 5 . a>

—l io

1 9

1 1 Boron Implant 2x10 /cm at 60 keV

U

14

1

2

— \

DATA—A. Michel Cal—PREDICT

10

1 8

c ο φ |ιο-

ϋ

Rapid Anneal at 900 °C • Osec • 5 sec χ 15 sec • 30 sec Subsequent Furnace Anneal 30 min at 800 °C •

10

PREDICT CAL _30 sec RTA /15 sec RTA £ sec RTA 0 sec RTA

No anneal

16

2000

4000 Depth (A)

6000

Figure 25. Data and calculations showing the reverse diffusion effect from implantation damage annealing. As the RTA time increases, the amount of enhanced diffusion during the subsequent 800 °C furnace anneal decreases. Data are from Michel (51). (Reproduced with permission from reference 59. Copyright 1988 Institute of Electrical and Electronics Engineers, Inc.)


6.

305


FAIR

Pre- and Postanneal Impfantations of Si. I m p l a n t a t i o n of S i ions into p r e d e p o s i t e d Β layers i n S i p r o d u c e e i t h e r e n h a n c e d or r e t a r d e d diffusion of Β d u r i n g subsequent a n n e a l i n g (58, 63-66). S e r v i d o r i et a l . (58) s h o w e d that r e d u c e d diffusion of Β predeposits occurs at 750 a n d 900 °C i f the i n i t i a l Β j u n c t i o n d e p t h is 1200 Â, a n d that e n h a n c e d difiusion occurs i f the i n i t i a l j u n c t i o n d e p t h is 3400 Â. T h e S i i m p l a n t s p r o d u c e d amorphous layers w i t h depths of about 2000 Â. T h e s e results a n d other data indicate that e n h a n c e d Β difiusion occurs i n the end-of-range r e g i o n of the S i i m p l a n t w h e r e excess self-interstitials a n d interstitial defects exist. I f the S i dose is sufficient to create an amorphous S i layer that is shallower than the i m p l a n t d e p t h , t h e n the e n h a n c e m e n t of Β diffusion d u r i n g subsequent a n n e a l i n g is r e l a t i v e l y i n d e p e n d e n t of S i dose (A. E . M i c h e l , u n p u b l i s h e d findings). T h u s , for Β concentrations < n „ +

+

+


+

D

e n h

= 5 Χ ΙΟ"

1 3

(52)

cm /s 2

for the first 100 s of the anneal for temperatures > 7 2 5 °C. T h i s a t h e r m a l diffusivity is a d d e d to the n o r m a l t e m p e r a t u r e - d e p e n d e n t terms to get the total difiusion coefficient. A sample calculation u s i n g these conditions is s h o w n i n F i g u r e 26. B was i m p l a n t e d (1 X 1 0 / c m a n d 50 k e V ) a n d annealed b y R T A at 1150 °C for 10 s. T h e n S i was i m p l a n t e d to create an amorphous layer, a n d the R T A cycle was repeated. T h e s e data w e r e c o m p a r e d w i t h a Β profile o b t a i n e d w i t h no S i i m p l a n t b u t w i t h the same heat treatment. T h e e n h a n c e d dif fusion of Β was calculated b y u s i n g e q u a t i o n 52, a n d good agreement was a c h i e v e d . T h i s m o d e l has b e e n v e r i f i e d for R T A a n d furnace anneals at temperatures as l o w as 750 °C. +

1 5

2

+

+

W h e n the B - d o p e d layer is c o m p l e t e l y c o n t a i n e d w i t h i n the amorphous layer caused b y the S i i m p l a n t , r e t a r d e d diffusion is o b s e r v e d . G o d f r e y et al. (63) s h o w e d that at 950 °C, 1-h furnace anneals of 2 5 - k e V Β i m p l a n t s ( 1 0 - 1 0 Β atoms p e r c m ) p r o d u c e d shallower results w h e n the Β i m p l a n t s w e r e done i n p r e a m o r p h i z e d S i . T h e Β diffusion coefficient for a n n e a l i n g of p r e a m o r p h i z e d samples that are Β i m p l a n t e d is g i v e n b y +

1 2

1 6

2

D

B

(53)

= 0.56 exp ( - 3 . 4 2 eV/JfcT)

O n the other h a n d , w i t h o u t p r e a m o r p h i z a t i o n , the i n t r i n s i c diffusivity of Β implants is D

B

= 0.0019 exp ( - 2 . 7

F o r e x a m p l e , at 950 ° C , the ratio D 0.32.

B

(54)

eV/fcT)

(preamorphized)/D

B

(crystalline) is


306


15

2

IMPLANT: 50 keV, 1x10 B/cm RTA: 1150 °C/10 sec Β + RTA + RTA 11

28

15

2

2. ο ο ο B + RTA + Si (80 keV, 10 cm" ) + RTA


a

PREDICT CAL of 2.

0.2

0.3

0.4

0.5

0.6

Si Depth (μπ\) Figure 26. Example of the effect of S i ion implantation on the subsequent diffusion of RTA-annealed B. Data are from Cho et al. (65). (Reproduced with permission from reference 59. Copyright 1988 Institute of Electrical and Elec tronics Engineers, Inc.) +

E q u a t i o n 54 for D

B

applies o n l y for Β i m p l a n t doses of > 7 X 1 0 / c m , 1 3

2

< 1 0 0 > S i substrates, a n d temperatures b e t w e e n 900 a n d 1180 °C. T h e l o w e r activation energy i n equation 54 p r o b a b l y reflects the self-interstitial d o m inance of Β diffusion i n the i n t e r s t i t i a l - r i c h i m p l a n t e d r e g i o n . H o w e v e r , a high-dose S i i m p l a n t can p r o d u c e a v a c a n c y - r i c h amorphous r e g i o n that may account for the r e d u c e d Β diffusion w i t h i n the r e g r o w n r e g i o n a n d D a c c o r d i n g to e q u a t i o n 53. +

B

Transient Diffusion During Rapid Thermal Annealing. W h e n the Β i m p l a n t dose is less than 3 X 10 1 c m a n d an R T A is p e r f o r m e d , transient diffusion is o b s e r v e d (66). E x a m p l e s are shown i n F i g u r e 27 for i m p l a n t s of 1 Χ 1 0 - 2 X 1 0 Β atoms p e r c m p e r f o r m e d at energies from 1 to 60 keV. T h e p r e v i o u s l y p u b l i s h e d data of S e d g w i c k (66) are i n c l u d e d . T h i s case is m o d e l e d s i m i l a r l y as the low-dose Β i m p l a n t - f u r n a c e anneal case, except for the m a g n i t u d e of D . T h u s , i f n e u t r a l a n d d o n o r p o i n t defects c o n t r i b u t e to Β diffusivities D * a n d D , r e s p e c t i v e l y , t h e n the total Β diffusion coef ficient ( D ) is g i v e n b y (59) 2

14

1 4

1 4

2

e n h

f

+

B

D

B

= (Of

+ D

e n h

) + D +


(55)

6.

FAIR

307


where D

e n h

= 3.6 X 1 0 - ( d o s e / 1 0 ) ( R / 7 X 10-*) 13

13

1/4

(56)

p

T h e i m p l a n t range d e p e n d e n c e has b e e n v e r i f i e d for Β i m p l a n t s f r o m 1 to 60 k e V ( F i g u r e 27). E q u a t i o n 56 is a p p l i e d to the calculations u n t i l the i m p l a n t damage has b e e n a n n e a l e d , a n d t h e n D a l l o w e d value of D

e n h

is 1.5 Χ 1 0 "

12

e n h

=

0. T h e m a x i m u m

c m / s . T h e damage anneal t i m e c r i t e r i o n 2

was d e r i v e d from data that show i n i t i a l r a p i d Β diffusion d u r i n g R T A a n d t h e n a m a r k e d s l o w - d o w n (51). Downloaded by CORNELL UNIV on May 10, 2012 | http://pubs.acs.org Publication Date: May 5, 1989 | doi: 10.1021/ba-1989-0221.ch006

L o w - d o s e Ρ i m p l a n t s e x h i b i t s i m i l a r e n h a n c e d difiusion d u r i n g R T A (67) i n the 8 0 0 - 1 1 5 0 °C range. T h e m a g n i t u d e of this effect is a diffusivity of 6 X 10~ c m / s for 10 s (68). H o w e v e r , M o r e h e a d a n d H o d g s o n (56) m o d e l e d 13

2

l o w Ρ difiusion d u r i n g R T A w i t h an effective t e m p e r a t u r e - d e p e n d e n t diffu sivity g i v e n b y e q u a t i o n 57. D

1150 1100 10 c 4

e n h

= 0.007 exp ( - 2 . 2

1050 τ

(57)

eV/kT)

RTA Temperature (°C) 1000 950 900

800

850

Τ 3

τ

A

A

m

Measured Calculated

χ BECAUSE OF HIGH %\) VACANCY GENERATION DOPING LEVELS AT INTERFACE J D

0

M

I

N

A

N

T

I

N

Si

Figure 32. Role of silicon point defects in the oxidation reaction (115). rate constants as a function o f any variables. T h i s p r o b l e m results from t h e fact that n o exact d e t a i l e d m o d e l o f oxidation exists o n w h i c h to base such calculations. H o w e v e r , recent proposals seem p r o m i s i n g as a basis for such calculations.

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6.


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