Chapter 11 Oxygen Effect on Mechanical Properties

CHAPTER I 1

Oxygen Effect on Mechanical Properties K . Surnino anti I . Y o n t ~ n a g t r INSlITLITE FOR MATFRIAL9 R I \ E ARC t i TOHOKU CINIVFRSITY SLNDAI. JAPAN

INTRODUCTION . . . . . . . . . . . . . . . . . . PLASTIC DEFORMATION , \ N I ) I ~ X X A T I O NI SN SILICON CRYSTAI s . . . . . . . . . . . . . . . . . . . . 111. INFLUENCE OF DISP~RCI U O X Y G E N A r o M s ON THE MOBII.ITY OF DISLOCATIONS I N SII ICON . . . . . . . . . . . . . . I . Methodologic trl f'roblettr,s 111 t h e Mecrsuremeiit o f 1. 11.

DiJloc,ution Veloc.itic,.\

2. V r l o c ~ i t yo f Disloc t i t r o n c 3. Velocity qf Disloc crtion 5

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in High-Purify Silicoir

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rrr Silic.on Containing O.rvgen Itnpirriries . . . . . . . . . . . . . . . . . 4. Morphology c ~ f ' I ) r . s l o c . t r r i ~ ~ irn c r Motion . . . . . . . 5 . Interpretution the, O.r?gen k y ( f k / o n D i s l ~ c ~ t i ~ n Velocity . . . . . . . . . . . . . . . . . . . IMMOBIl.IZATION O F 1 ) 1 \ 1 ( H ATIONS B Y O X Y G E N . . . . . . I . Releuse Stre.\.s of I)r.cloc.trrion.\ fininobilized by Oxygen Imprrritirs . . . . . . . . . . . . . . . . . 2 . Sture of 0.rygen S ~ g r e g ~ oir t ~ Di.7loc.ation.s d . . . . EFFECT OF OXYGEN O N I)ISIOCATIONGENERATION . . . , I . Generation i f L ) ~ . ~ l o c ~ t r r r o n .s . . . . . . . . . . ?- 0.rvgen Efect oir l h s / o ( ~ u t i o n(ienerurion . . . . .

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MI:.CHANICAL PROPERTII s cw SILI(.ON AS INFLUENCED B Y O X ~ G EIMPURITIES N . . . . . . . . . . . . . . . I . Mec,hunical Propertic\ ( J fHi,yh-Purity Silicon Crv,sttil.r 2 . O.rygeii Effie I O I I M(~c.lrutiic.ulProperties uf'

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449 Copyright cj I994 by Academi' Prer5. Inc All nghtr uf reproduction in any form re\erved ISHN 0 - 1 2 752142-Y

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VIII. EFFECTS OF NITROGEN A N D CARBON IMPURITIESON MECHANICAL PROPERTIES OF SILICON . . . . . . . . . . 1 . Nitrogen Effect . . . . . . . . . . . . . . . . . 2 . Carbon Effect . . . . . . . . . . . . . . . . . . IX. SUMMARY . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . .

499 499 504 507 5 10

I. Introduction

It is well known that wafers of Czochralski-grown silicon (CZ-Sij are much more resistive against the generation of dislocations or the occurrence of warpage than wafers of floating-zone-grown silicon (FZ-Sij during thermal cycling in device production processing. This is one of the main reasons why CZ-Si is used almost exclusively as the materials for VLSl or ULSI despite its lower purity compared with FZ-Si. It is natural to attribute such difference between CZ-Si and FZ-Si in the mechanical stability to the effect of oxygen impurities in CZ-Si on the dislocation processes occurring under stress at high temperatures. Oxygen impurities in CZ-Si are supersaturated in the temperature range below about 1250°C. Oxygen atoms in such a state effectively inhibit the dynamic activity of dislocations under stress. Supersaturated impurities naturally precipitate within a crystal when the crystal is held at temperatures at which the impurities move by diffusion at appreciable rates. Precipitation of oxygen in CZ-Si generally accompanies generation of various kinds of defects. Such defects are often reported to degrade the device function when they thread through device-active regions. They can also be utilized positively as effective gettering sites for harmful impurities incorporated by contamination. As to the effect on mechanical property precipitation of oxygen in CZ-Si leads to the softening of wafers. Understanding the effects of oxygen on mechanical properties of Si is, thus, very important in developing the production technology of Si devices. On the one hand, the mechanical properties of Si bear an important meaning also in basic study of crystal plasticity. The development of crystal growth technology in the last few decades has made it possible to grow Si crystals of high quality that are substantially free from dislocations. Dynamic properties of dislocations in Si have been studied experimentally in detail by observing the behavior of individual dislocations under stress, which were introduced intentionally into such high-quality crystals. Mechanical properties of Si measured by macroscopic mechanical tests can be analyzed on the basis of a microscopic model using the

1 1 . O Y Y - G I lu I I

I I ( 1 O N M E C H A N I C A L PKOPFRTIFS

45 1

dynamic properties of individual dislocations clarified in such a way. As it consequence, understanding the niacroscopically observed mechanical behavior of crystals in term5 of dislocation dynamics on a microscopic s a l e has now advanced the furthest in Si of all materials including impurity effects. This chapter reviews both the macroscopic and microscopic aspects of oxygen effects o n the mechanical behavior of Si. Effects of other light element impurities, such a 4 nitrogen and carbon, are also mentioned. Section 11 gives some basic aspect of plastic deformation of a crystal and also a brief description on the nature of dislocations in Si. Section I11 \bows the influence of oxygen atoms that dispersed within a Si crystal o n the dislocation motion. Section IV shows segregation of oxygen on dislocations and the resulting effect o n the dynamic activity of dislocations. Section V illustrates dislocation generation in Si as affected by oxygen. The experimental ol-wrvation is interpreted with the effect claritied in the preceding section. The effect of oxygen on macroscopic mechanical properties of Si I S described in Section V1. A description of the macroscopically observed mechanical behavior of Si crystals in terms of dislocation processes is also given there. Softening of Si caused by oxygen precipitation is described in Section VI1. Section VlIl gives the effects of nitrogen and carbon o n the mechanical strength of Si. 11. Plastic Deformation and Dislocations in Silicon Crystals

Si is completely brittle at low temperatures and becomes ductile gradually as the temperature is r a i d . This is common for all kinds of semiconductors. The temperature of the hrittlc to ductile transition can never be defined exactly. I t shifts to a high temperature when the crystal is stressed at it slow rate and shifts to ;I low temperature when stressed at a high rate. A rough measure for the tranbition temperature in Si may be taken to be about 500°C. All of w c h features reflect the dynamic property of dislocations in Si, which will be mentioned in later sections of this chapter. As in other kinds of diamond-type crystals, plastic deformation o f Si at high temperatures takes place hy means of a slip along the { 1 I I } planes in the ( I i0) directions. Such plastic deformation of Si by a slip is brought about by the glide motion of di\locations having t h e Burgers vectors of I!? ( I ( I i0) type, where (1 is the lattice parameter. along the { I 1 I } planes. During the plastic deformation of a crystal on a macroscopic scale, a high density of dislocations undergo glide motion at some appreciable velocity .

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K . SUMINO AND I . YONENAGA

To characterize the mechanical property, a crystal is usually subjected to a mechanical test by tensile or compressive deformation under a constant strain rate, and the so-called stress-strain curve is measured. In the case of a single crystal, the stress is referred to the shear stress component of applied stress, while the strain to the shear strain with respect to the slip system operating in deformation. The strain of a crystal consists of both elastic strain and plastic strain. The main part of the strain is elastic in the beginning of deformation of a crystal, namely, when the strain is small. Stress increases rapidly with increasing strain in such a deformation stage. After some amount of strain, plastic strain suddenly becomes predominant, and the stressstrain curve shows a break. This point is called the yield point. The stress at the yield point, called yield stress, is often taken as a quantity characterizing the mechanical strength of the crystal. The characteristics of the stress-strain curve of any crystal observed macroscopically are determined by a number of microscopic processes related to dislocations, such as generation, multiplication, motion, interaction with each other and with impurities. The basic equation which relates macroscopic deformation of a crystal with the dynamic state of dislocations inside it is given by ipl = NCb,

where 8,, is the plastic strain rate of the crystal, N is the density, V is the mean velocity, and b is the magnitude of the Burgers vector of dislocations in motion. The dislocation density is defined to be the length of dislocations contained in a unit volume of the crystal and has the dimension of c m - 2 . A dislocation in a Si crystal is energetically favorable when it lies along the most closely packed direction, which is one of the (1iO) directions. Thus, a stable dislocation in Si on the (1 11) plane is either a 60" dislocation o r a screw dislocation, which are the dislocation lines making the angles 60" and o", respectively, with the Burgers vector. Observations of dislocations by transmission electron microscopy have revealed that glide dislocations in Si are extended (Ray and Cockayne, 1971; Gomez, Cockayne, Hirsch and Vitek, 1975; Wessel and Alexander, 1977; Gomez and Hirsch, 1978; Foll and Carter, 1979; Sato and Sumino, 1979; Sato, Hiraga and Sumino, 1980). Namely, any such dislocations dissociate into two Shockley partial dislocations with the Burgers vectors of the (1 16) a ( 1 12) type, which bound a strip of stacking fault of the intrinsic type. The widths of the strip of stacking fault are 5.8 nm and 3.6 nm for a 60" dislocation and a screw dislocation, respectively, in Si (Gottschalk, 1979) under no stress. This means that such dislocations are

453

t I ( , . I . End-on high-resolution iniiigr\ of ( a ) ii in SI

cib\t,il

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h0' dislocation and ( b ) il screw dislocation

1980).

of a glide set. in the terminology o f Hirth and Lothe (1982). End-on high-resolution images of a 60" and a screw dislocation in Si are shown in Fig. 1 (Sato et a].. 1980). A dislocation loop generated f r o m ii source inside a crystal or a surface wurce assumes a shape of hexagon or half-hexagon, as shown schematically in Fig. 2 , when the di\lociition is isolated from other dislocations and the crystal does not contain a high concentration of impurities. 'The loop consist5 of segments of 60" dislocation and screw dislocation. The hO" segment consists of a 90' Shockley partial and a 30" Shockley partial hounding a strip of stacking fault. while the screw segment consists of two 30" Shockley partials. Atomic configurations at { h e core\ of a 30" Shockley partial and a 90" Shockley partial are shown in Fig. 3 . Geometrically, dangling bonds may

454

K. SUMlNO AND 1. YONENAGA

60° FIG.2. Schematic picture of a hexagonal-shaped dislocation loop on the ( I 11) slip plane in Si crystal. The hatched region shows stacking fault of intrinsic type.

be aligned along the dislocation core. However, such geometrical dangling bonds are now believed to be reconstructed to form bonds between two neighboring atoms along the dislocation line on the bases of electronic state of dislocations and theoretical calculations. A review on the dynamic behavior of dislocations and the characteristics of plastic deformation in various kinds of semiconductors is given by Sumino in a forthcoming issue of the Handbook on Semicouductors (North-Holland). 111. Influence of Dispersed Oxygen Atoms on the Mobility of

Dislocations in Silicon 1 . METHODOLOGICAL PROBLEMS I N THE MEASUREMENT OF

DISLOCATION VELOCITIES

Many papers have so far reported experimental results on dislocation velocities in Si as functions of stress and temperature. In most works dislocation velocities have been measured by means of intermittent technique; namely, the positions of dislocations are determined at room temperature by the etch pit technique or X-ray topography, while they are displaced by stress at elevated temperature. The intermittent technique has several origins for error in determining the accurate velocity of dislocations as pointed out by Sumino (1987). The most important and unavoidable origin of the error is the immobilization of dislocations by impurities. As demonstrated later, dislocations in a crystal act as very effective

1 1.

O X Y G E N F I t F( 1 ON ME C HANIC A 1 PKOPERTIES

455

(b)

(a)

F I G .3. Atomic configuration\ a l Ihe coi-es of (a1 a 30" Shockley partial dislocation and Ib1 >I 9 0 Shockley partial dislocation in 51crystid.

gettering sites for impuritie\ at elevated temperatures. Dislocations are locked when they getter impurities. In some cases t h e effect brings about ;L critical stress to start dislocations moving. In other cases a locked dislocation spcnds some incubation period before starting after application of stress. In the latter c a w the stress dependence of t h e dislocation velocity is measured to be htronger than the real one. Impurities are incorporated into the crystal with various origins, as residual impurities or by contamination. Dislocation\ are unavoidably held at rest at elevated temperatures in the intermittent technique. which leads to gettering of impurities by the dislocations. Thus. it is difficult to obtain the velocity of dislocation in motion avoiding the locking effects by impurities in the intermittent method. 'The most reliable experimental technique for measurements of dislocation velocity is thought to be that by means of in situ X-ray topography developed by the Sumino group (Sumino and Harada. 1981; lmai and Sumino, 1983) utiliLing a high-power X-ray source. a high-temperature tensile stage. and a highly sensitive T V system. Motion of isolated dislocations in a crystal introduced from some sources can be followed by real time observation as functions of the temperature and the applied stress with this technique. 'The technique is free from the ambiguity related to the locking effect o f irnpurities in determining the dislocation velocity.

2 Vtmcirv

OF

DISLOCATION\ I N HILH-PURITY SILICON

F i i \ t . experimental datd o n velocitie4 of di\locatlon\ i n a high-purity FZ-Si cry\tal are \hewn. The velocitie\ of i\olated 60"and \crew di\loca-

456

K . SUMINO AND 1. YONENAGA

tions at various temperatures measured by means of the in situ X-ray topographic technique are plotted against the shear stress in Fig. 4(a) (Imai and Sumino, 1983). Figure 4(b) shows the dislocation velocities under various stresses plotted against inverse temperature. It is seen that the velocities of the both types of dislocations in high-purity FZ-Si are linear with respect to the shear stress in the stress range 1-40 MPa and that the activation energies are independent of the shear stress in the temperature range 600-800°C. The dislocation velocity v is expressed well with the following equation: u =

v,,(7/To)exp(- Q / k , T ) .

(2)

The magnitudes of u,, are 1.0 x lo4 and 3.5 x lo4 m/s and those of Q are 2.20 and 2.35 eV for 60" and screw dislocations, respectively (Imai and Sumino, 1983). The shape of moving dislocations is observed to be a regular hexagon or a half-hexagon. The stress exponent of u has been determined to be higher than unity by various groups with the intermittent technique, ranging from 1.2 to 1.4, or not to be constant but to depend on the stress range where the measurements were conducted (Suzuki and Kojima, 1966; Patel and Freeland, 1967; Erofeev, Nikitenko and

3

FIG.4a. Dislocation velocity in high-purity FZ-Si crystal plotted against shear stress for various temperatures (Imai and Sumino, 1983).

1 1.

OXYGEN t t FFC T ON MECHANICAL PROPERTIES

457

2 1 0 ~ ,1 ~K"

t-'icl. 4b. Di\localion velocity in high-puritv FZ-Si crystal plotted against i n v e n e temperashear \tre\,s (Irnai ,ind Surnino. 1983).

tui-t' t'm barious

Osvenskii. 1969; George, Fscavarage. Champier and SchrBter. 1972: Fisher, 1975, 1978). The resulls obtained with the intermittent technique are not in quantitative agreement among different groups. Such disagreement may be attributed to the drawback involved in the intermittent technique.

3.

VEL.OC17 Y 01'DISLOCATIONS I N sII.ICON

CONTAINING OXYGEN

I M P U K I l IES

Figure 5 shows the relations between the velocity of a 60" dislocation and the shear stress at various temperatures in a Si crystal containing oxygen impurities at a concentration o f 7 . 4 x lo" atomsicm' obtained by means of the in situ X-ray topographic technique (Imai and Suniino, 1983). Data for high-purity FZ-Si are also shown in the figure. Dislocations in the crystal containing oxygen impurities move at velocities that are equal to those in the high-purity FZ-Si crystals in a high-stress range. However, dislocations originally in motion under high stress cease to move when the stress is reduced t o lower than about 3 MPa in the Si crvstal containing oxygen impurities. 'The velocity of dislocations in the crystal containing oxygen decreases more rapidly t h a n in the high-purity

458

K . SUMINO AND I . YONENAGA

0

0

High purity FZ 101 Z4x10'5m-3

I I

1

/

732°C

'

I 10

Shear stress,

I

1c MPa

FIG.5 . Velocity versus shear stress relations at various temperatures of 60" dislocations in a Si crystal containing oxygen impurities at a concentration of 7.4 x 1017 atomsicm'. Open circles indicate the data for high-purity FZ-Si (lmai and Sumino, 1983).

FZ-Si as the stress is decreased toward such a critical stress for the cessation of dislocation motion, shown by vertical broken lines in the figure. The stress exponent of the dislocation velocity is determined to be apparently larger than unity in the low-stress range in such a Si crystal. Figure 6 shows the velocity versus stress relations for 60" dislocations at 647°C in Si with dissolved oxygen impurities at various concentrations (Imai and Sumino, 1983). Broken lines drawn vertically bear the same meaning as those in Fig. 5, namely, the critical stresses below which dislocations originally moving under a high stress become immobile. Again, the dislocation velocities in the crystals containing oxygen impurities at a n y concentration are almost the same as those in high-purity FZ-Si under high stress. Both the deviation of the velocity from that in the high-purity FZ-Si with decreasing stress in the low-stress range and the critical stress for the cessation of dislocation motion increase with an increase in the concentration of dissolved oxygen impurhes. The magnitudes of the critical stress for the cease of dislocation motion are shown in Table I for Si crystals containing the various types of impurities.

OXYGLN F l l € ( I ON M L C H A N I C A L

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K . SUMINO AND I . YONENAGA

Essentially, the same effect of dissolved oxygen impurities on the dislocation velocity is observed also for screw dislocations. 4. MORPHOLOGY OF DISLOCATIONS IN MOTION

The shape of moving dislocations in high-purity FZ-Si crystals is observed always to be a regular hexagon or half-hexagon of which segments are straight along ( 1 10) directions over the wide stress range investigated. This is true also in Si crystals containing oxygen impurities when dislocations are moving at the velocities equal to those in the high-purity FZ-Si in the high-stress range. However, whenever the velocities of dislocations deviate from those in the high-purity FZ-Si under relatively low stresses, the shape of the moving dislocations is observed to be perturbed from the ( I 10) straight lines and to become irregular. Figure 7 shows the X-ray topographs of dislocations moving in the low-stress range in Si crystals containing oxygen impurities at various concentrations (Imai and Sumino, 1983). The impurity-related perturbation in the shape of moving dislocations is found to be reversible. When the crystal in which moving segments are perturbed from (1 10) straight lines under low stress is subjected to high stress. the segments restore the straightness along ( 1 10) directions. Upon reducing the stress, the shape is perturbed again. Further reduction of the applied stress leads to the halting of dislocation motion. Extra stress is needed to restart such an immobilized dislocation. It increases with increases in the duration and temperature where the dislocations have been kept at rest, depending on the concentration of the dissolved oxygen atoms. This phenomenon is treated in the next section. In situ observations of dislocations in motion with a high-voltage transmission electron microscope equipped with a high-temperature tensile stage have also revealed interesting features in the dislocation motion in silicon crystals on a microscopic scale (Sato and Sumino, 1977, 1979: Louchet, 1981). Dislocations in silicon crystals were observed to move in a viscous manner at elevated temperatures on the microscopic scale. In accordance with the results of in situ X-ray topography, fast-moving dislocations are observed to consist of straight segments parallel to ( 110) directions when they are isolated. In CZ-Si crystals the shape of dislocations becomes irregular when they move at low velocities. They seem to be retarded locally by impurity-related obstacles. Once the retarded portion of dislocation overcomes the obstacle, the whole dislocation has a strong tendency to become straight along ( 1 10). As a result, segments of the dislocation are observed to move by repeating the local depression and quick recovery of it.

11.

O k Y G L N L l I I ( I ON M t ( H4NIC A 1 PROPFRTlt5

46 1

FIG.7. In \itu X-ray topographs 01 dislocation half-loops in motion at h47”C in Si crystals containing oxygen impurities at conLentr;ilion\ of la) 1.5 x (hl 2.5 x IO”’, ( c ) 7.5 x 101’. and (d) 9 x l o i 7 atomsicm’. Except for ( a ) . the topographs were taken under l o w stress. where deviations of the velocit) from that in high-purity FZ-Si were rernarkahle (Imai and Suniino. 1983).

5.

~ N T E R P R E T A T I O OF N THE

O Y \ C , FENF F ~ COTN DISLOCATION VELOCITY

A dislocation interacts with impurities through the overlap of their strain fields or electrostatic fields. Theoretically, such kinds of interaction:, result in the reduction of the dislocation velocity since extra energy is spent when the dislocation overconies the potential barrier related to the interaction. We have seen in Section 11.3 that oxygen atoms dispersed in a Si crystal

462

K. SUMINO A N D I . YONENAGA

retard the motion of a dislocation only when the dislocation moves at low velocity under low stress but not when the dislocation moves at relatively high velocity. The retardation of dislocation motion is accompanied by the perturbation in shape of the dislocation in motion. The perturbation in the shape of the dislocation means per se that the obstacles against dislocation motion did not develop uniformly along the dislocation line on a macroscopic scale. Overcoming such an obstacle of dislocation is achieved by bowing out of dislocation segments around the obstacle under stress. Under such circumstance the whole dislocation keeps moving at a constant velocity, which is lower than that of an unperturbed dislocation. On a further reduction of stress the dislocation ceases to move. Immobilization of the dislocation is thought to be caused when the obstacles develop closely along the dislocation line. When a dislocation is highly mobile in the matrix region of the crystal, the theory of thermally activated motion of a dislocation overcoming pointlike obstacles leads to the stress T / , needed to keep a constant velocity v given below in its simplest formulation (Seeger, 1958): T,, =

[ E - kgTIn(Lu/u)]/b2L,

(3)

where E is the energy of interaction between the dislocation and the obstacle, L is the mean separation of the obstacles, and v is the frequency of dislocation vibration. The important interaction between a dislocation and an obstacle at high temperatures is through their strain fields. The magnitude of E for such interaction is inversely proportional to the separation between the dislocation and the obstacle. The interaction energy between a dislocation and an impurity atom is calculated to be less than 0.5 eV, even when the impurity atom with a large misfit is located at the closest position to the dislocation. For such a magnitude of interaction energy and for impurity concentrations typical in semiconductors the magnitude of T,, becomes zero at a temperature well below room temperature. This gives the theoretical reason for why oxygen atoms dissolved in the matrix crystal of CZ-Si have no appreciable effect on the dislocation velocity under high stress. Dispersed obstacles can give rise to an appreciable effect on the dislocation velocity in the temperature range where Si is ductile if the interaction energy is higher than 3-4 eV. Such obstacles are thought to be clusters or complexes of oxygen atoms in Si crystals containing oxygen impurities. We reach the following picture. In Si crystals containing oxygen impurities oxygen atoms catch up to a slowly moving dislocation and develop clusters on the dislocation line that have a high interaction energy with

I I.

OXYGEN F I I I C I ON M E C H A N I C A L PROPERTIFS

463

the dislocation. This results in both the perturbation of the line shape and retardation of the dislocation. A dislocation ceases to move when such clusters or complexes of impurities are developed closely along the dislocation line. IV. Immobilization of Dislocations by Oxygen 1.

R E L E A S E S T R E S S OF

Dlsr.oc',AI I O Y S

l M M O B I L l Z E D BY O X Y G E N IMPURITIES

When a dislocation originally moving under high stress is halted under no applied stress in a Si cryctal containing oxygen impurities at a high temperature, where the diffusion of impurities is appreciable, it is immobilized due to the development of oxygen clusters on it. Extra stress i s necessary to start such a dislocation moving. It increases with an increase in halting duration. Such stress is termed the release ,stress or uniockirig strrss of the dislocation and i s interpreted to be the stress to release the dislocation from impurity iitoms segregated on the former. Dislocations free from segregation of impurity atoms are called .fresh disloccrrions while those immobilized by impurity segregation are called riged dislocu tion s . Figure 8 shows the variation of the release stress for originally fresh 60' dislocations at 647°C in Si containing oxygen impurities at various concentrations against the duration of halting at the same temperature (Sumino and Imai, 1983). N o appreciable release stress is detected for

Fic,. 8 . Variation of the relea\e stre\\ a( h j 7 Y for initially fresh 60"dislocations against the duration of aging at M7"C in Si ci-v\t;ils containing oxygen impurities at concentrations 5hown in the figure (Sumino and 1rn;ti. 1981).

464

K . SUMINO A N D I . YONENAGA

40 -

*

30-

v)

2

;20-

c

v)

2

c

!2

100

*\

I

I

fa 5 min I

\10 I

FIG.9. Temperature dependence of the release stress for 60" dislocations in Si crystals atoms/cm3that were annealed containing oxygen impurities at a concentration of 1 .O x at 730°C for various durations between 5 and 20 min (Sato and Sumino, 1985).

dislocations in a high-purity FZ-Si crystal even after a prolonged halting at high temperatures. The increasing rate of the release stress increases with an increase in the concentration of oxygen impurities. The release stress of a dislocation that is immobilized by any given heat treatment decreases as the stressing temperature is raised. Figure 9 shows the temperature dependence of the release stress for originally fresh dislocations in Si crystals containing oxygen impurities at a concentration of 1.O x lo'* atoms/cm3after annealing at 730°C for various durations between S and 30 min (Sato and Sumino, 1985). The release stress and temperature is in a linear relationship with the same slope for all the crystals in the temperature range higher than lOS0 K while another linear relationship seems to hold in the low-temperature range. 2. STATE OF OXYGEN SEGREGATED ON DISLOCATIONS Immobilization of a dislocation in an impure crystal is often related to the development of the Cottrell atmosphere around the dislocation. We first discuss the Cottrell atmosphere in a Si crystal containing oxygen impurities. Any given impurity atom occupies some definite site in the crystal, and each site is occupied by only one impurity atom. The distribution of impurity atoms within the crystal in thermal equilibrium, then, obeys the Fermi-Dirac statistics. The probability p with which an impurity occupies the site where the energy of interaction between the impurity atom and a dislocation is E ,

11.

OXYbEW Ft t F ( I ON MFC HANICAL PROPERTIES

465

T , 'C

Fit,. 1 0 . Occupation probability p i n thermal equilibrium of an impurity atom at the site having the interaction energy E , plotted against temperature T f o r an impurity concentration of 1 ppm. E , being taken a\ a parameter (Sumino. 198%).

is given approximately by the following equation as a function of ternperature 7 (Sumino, 198%): p = 1 / 1 1 t- ( l i ( : , ) e ~ p ( - E , i k , T ) ] .

(4)

where ('(, is the mean concentration o f the impurity in the crystal. The impurity distribution around a dislocation related to the Cottrell atmosphere is governed by Eq. ( 4 ) . Figure 10 shows p calculated a s a function of T (in "C) for a mean concentration of C,, = l o - " ( = I pprn) for various values of E,. The occupation probability p changeb from unity to C,, within a rather narrow temperature range as the temperature increases, depending on the magnitude of E , . At temperatures where diffusion of most impurity atoms takes place at appreciable rates, impurities of a concentration of I pprn are known to be effectively trapped by the sites where the magnitude of the interaction energy is higher than about I .5 eV. The dependence of p on 7 is influenced also by the magnitude of C ( , .The temperature range in which impurities are trapped effectively by the sites of any given value of E , is shown to become wider ;IS the impurity concentration increases. The interaction of a dislocation with an impurity atom that plays an important role at high temperatures is that through their elastic strain fields. As has already been mentioned. the magnitude of the maximum interaction energy at the smallest separation hardly exceeds 0.5 eV even for a typical impurity atom accompanying a large misfit strain. The interaction energy decreases rapidly a s the impurity atom is separated from thc dislocation. 'Thus. an oxygen-rich or -lean region (the Cottrell atmo-

466

K . SUMINO A N D I . YONENAGA

sphere) never develops around a dislocation at the typical oxygen concentration in CZ-Si. We are led to the conclusion that the immobilization of dislocations due to oxygen segregation in Si is not related to the development of the Cottrell atmosphere around dislocations. Oxygen atoms or, more generally, impurity atoms are thought to be gettered by dislocations at high temperatures by the following two mechanisms (Sumino, 1989b): ( 1 ) impurity is supersaturated and dislocations act as preferential nucleation sites of precipitates of the impurity; ( 2 ) some special reaction that incorporates impurity atoms from the matrix region takes place at the dislocation core. Special reactions that never take place in the matrix region may occur at the dislocation core because of the peculiarity of atomic arrangement there. The reaction product may have a high interaction energy with the dislocation. Occurrence of such special reactions incorporating oxygen impurities at the dislocation core has indeed been observed in CZ-Si (Koguchi, Yonenaga and Sumino, 1982; Yonenaga and Sumino, 1985). On the basis of the conclusion that impurity gettering by a dislocation proceeds by means of preferential precipitation or development of special reaction products at the dislocation core, we can treat the kinetics of the gettering by a dislocation with a simple assumption that the dislocation core is a perfect sink for impurity atoms that arrive there. The change rate of the impurity concentration C at any place in the stress field of a dislocation is given by dCldt

=

DV[VC

+ (C/ksT)VE,],

where t is the time, D is the diffusion constant of impurities, and E , is the energy of interaction of an impurity atom with the dislocation. The first term on the righthand side of Eq. (5) is related to the diffusion flow of impurities that originates from the inhomogeneity in the impurity concentration while the second term is the drift flow due to the interaction force between the impurity atom and the dislocation. Taking the dislocation line to be straight, we have the problem in the two-dimensional space. Again considering the elastic interaction through strain fields, the problem is solved numerically with the initial condition that the impurity distribution is uniform at t = 0. The time variation of C at any position in the crystal together with the number of impurity atoms absorbed at the dislocation core can be traced numerically as a function of the aging duration at any temperature (Sumino and Imai, 1983; Yonenaga and Sumino, 1985). The results of the simulation done for the gettering of oxygen impurities by dislocations in silicon are shown in Fig. 11 together with experimental results (Yonenaga and Sumino, 1985). They are in good

11.

O X Y G E N kFI I

<

I ON M t ( H A N I C A L PROPERTIEF

467

I

t ,

5

I I . Variation of the fraction / o f oxygen atoms segregated o n dislocations in C'Z-Si containing oxygen impurities at a concentration of' 6 x 1 0 ~ ' atomsicnil and involving dislocation.; at den\itie\ shown in the figure ( i n c m ') against the duration I of aging at 900°C. Murk\ and solid line\ show expenrnent;il data and broken lines results of calculation ( Y o nenaga and Surnino, 1985). Fit,.

Fii,. 12. T E M micrograph? \bowing the debelopment of oxygen precipitate5 along a di\location in CZ-Si due to aging at 9OtY'(' l o r v t i r i o i i \ durations shown in the figure.

agreement with respect to the time law and the dependence on the dislocation density. Oxygen atoms that are gettered by a dislocation are usually not distributed uniformly but discretely along the dislocation line as clusters or particles, as shown in the T E M micrograph of Fig. 12. This observation agrees with the picture we have already obtained with respect to the locking of a dislocation in a Si crystal containing oxygen impurities.

468

K. SUMINO A N D I . YONENAGA

3

L

“ 2

*Lu’

1

0

0

I

I

10 20 Aging duration, min

I

3(

FIG.13. Variations of the interaction energy E* and the line density N * of locking particles along dislocations in CZ-Si containing oxygen at a concentration of 1 .O x lo’* atoms/ an’ against the duration of annealing at 730°C (Sato and Sumino, 1985).

Suppose that locking particles are arranged discretely along the line of an immobilized dislocation with a line density N* and each particle has the interaction energy E* with a dislocation. On the assumptions that the interaction is of a short-range nature and that free portions of the dislocation are highly mobile, the theory of thermal activation leads to the following expression for the release stress T R : TR

=

N*[E* - kgTIn(LN*~*/T)]/b2,

(6)

where L and u* are the length and vibration frequency of the dislocation, and r is the releasing rate of the dislocation from the locking particles. The theory predicts the linear relationship between the release stress and the temperature when the locking particles are of only one kind, the slope being determined by N* and the magnitude of T R extrapolated to the absolute zero temperature by N * * E ” . Such a linear relationship is seen in Fig. 9 for dislocations immobilized by gettering of oxygen impurities in all the crystals in the temperature range higher than about 1050 K. Figure 13 shows the magnitudes of E* and N * of the locking particles deduced from the results in Fig. 9 using Eq. (6) against the duration of aging at 730°C. The density of the locking particles along the dislocation line is determined to be about 0.8 x lo6 cm-’ and is almost constant

I 1.

O X Y G E N E k k t C 1 O N M E C H A N I C A L PROPERTIES

469

against the duration of aging at 730°C. The magnitude of the interaction energy increases from 2.9 to 3 . 3 eV as the aging duration increases from 5 to 30 min. This seems to reflect the fact that the locking particles grow with aging. Figure 9 shows that another linear relation holds in the lowtemperature range in crystals aged for short durations. This may be interpreted as that some other kind of locking particles also develop along the dislocation line in addition to those mentioned previously. The interaction energies determined for the both kinds of particles are much higher than the interaction energy for a single oxygen atom in silicon. The separations of locking particles are determined lo be larger than the mean separation of individual oxygen atoms in the matrix crystal. These results accord well with the picture that oxygen atoms gettered on the dislocation line are in the state of clusters or complexes. V. Effect of Oxygen on Dislocation Generation I. G E Y € , . K I I O N

OF

DISL.OC.ATIONS

When a Si crystal initially free from dislocation is stressed at a high temperature, dislocations are generated heterogeneously under stress lower than the ideal strength for dislocation nucleation by orders of magnitude (Sumino and Harada. 19x1 ). Then, macroscopic deformation of the crystal takes place by means of the propagation of Luders bands from the place where dislocations itre generated. The ideal strength is the stress necessary to cause slip in a perfect crystal and has theoretically been evaluated to be about 0.24 G tor ;I diamond-type crystal, where G is the shear modulus of the crystal. Cisually, dislocations are observed to be preferentially generated at the surface region of the crystal and to penetrate into the bulk if the crystal contains no structural irregularities inside which facilitate dislocation generation. Such an observation naturally leads to the idea that any real crystal has some irregularities on the surface that act as the preferential generation centers of dislocations under stress at an elevated temperature. The irregularities are thought to be microscopic regions with a strongly disturbed atomic structure that mity be formed by some energetical stimulation such as mechanical shock or chemical reaction at the surface. which i 4 inevitably or accidentally involved during the surface preparation. I t has been reported that several kinds of damaged structure on a microscopic scale are introduced by abrasion or indentation of Si surfaces (Stickler and Booker. 1963; Gridneva. Milman and Trefilov, 1972: Erernenko and Nikitenko, 1972). Recently an extremely tiny region of amorphous silicon surrounded by a dislocated crystalline region has been

470

K . SUMINO AND I . YONENAGA

FIG. 14. (a) Cross-sectional TEM micrograph of a scratch made on Si surface at room temperature together with the diffraction pattern, and (b) that after annealing at 600°C for I hr. Dark lines are images of dislocations (Minowa and Sumino, 1992).

found around a scratch or an indentation made on a silicon surface at room temperature by TEM observations (Clarke, Kroll, Kirchner, Cook and Hockey, 1988; Minowa and Sumino, 1992). Figure 14(a) shows a cross-sectional TEM micrograph of a scratch made with a 2 gram load on the surface of a Si crystal at room temperature. A region with a round periphery having uniform and dark contrast is the amorphized region produced by scratching. The crystalline silicon changes to amorphous silicon abruptly across the interface of the two regions. This suggests that the amorphous region was formed not as a result of heavy plastic deformation of the Si crystal but by means of phase transformation of crystalline Si under a highly localized stress. Dislocations developed around the amorphous region are on the (1 1 l} planes and have Burgers vectors parallel to the ( 1 10) directions. The magnitude of the shear stress realized in the region beneath the scratch is estimated to be close to the ideal strength of the crystal. Thus, these dislocations are thought to be generated by spontaneous nucleation under such high stress. The amorphous region is observed to transform to a heavily dislocated crystalline Si when the crystal is brought to a tempera-

47 1

FIG. I S , Changes in the imagc c o n t i i i \ t \ o f X-ray toPograph\ of indented region\ made on k%-Si \uil'ace w i t h the increase iii leniper;tlure under stresb (Sumino and Harada. I Y X I ) .

ture higher than about S0O"C a s 4hown in Fig. 14(b) (Minowa and Sumino, 1992). A scratch or an indentation on the surface of a Si crystal accompanies a strained region around it that is extended over a macroscopic scale observable with X-ray topography. Such a strained region shrinks in size when the amorphous micro-region transforms to the dislocated microregion due to annealing. When the crystal is under stress, some of the dislocations that have the maximum Schmid factor come out ot'the microregion and penetrate into the matrix and expand on a macroscopic scale (Sumino and Harada. 19x1). At this stage dislocations are usually recognized to be generated. This p r o w s is demonstrated in Fig. 15, in which X-ray topographs showing the change in the contrast around indentations on the surface of a FZ-Si crystal under stress with an increase of the temperature are shown (Sumino and Harada, 19811. The contrast at room temperature under no applied stress i s shown in Fig. 15(a). White dots show distorted regions around the indentations. The contrast under a shear stress of 10 MPa at room temperature is shown in Fig. 15(b). It is recognized that indentations have no significant stress concentration effect. In Fig. IS(c) the contrast of the indentations when the crystal is heated to 600°C under a stre44 of 10 MPa is shown. The contrast of the image5 of the distorted region4 i s seen to diminish strikingly. Figure IS(d)

472

K . SUMINO A N D 1. YONENAGA

--_---____---

_____ _-_____ 0.__----. -._._ 0-_.-------__ I I 600 650 700 Temperature, "C

''

~

FIG. 16. Critical stress for dislocation generation from a Knoop indentation plotted against temperature in FZ-Si and CZ-Si (Sumino and Harada, 1981).

is the topograph when the crystal is further heated up to 650" under the same stress. Now, the size of the white dots is seen to recover. Figure 15(e) is the topograph of the crystal that is subsequently heated to 690°C. The image size is further enlarged and dislocations in such regions are seen. The diminishing of the size of the white dots seen in Fig. 15(c) may be attributed to the release of the strain around the indentations related to the recrystallization of amorphous Si and the recovery in the size from Figs. 15(c) to 15(e) to the generation of dislocations from the indented area. 2. OXYGEN EFFECT ON DISLOCATION GENERATION Dislocations are easily generated from a flaw, such as an indentation or a scratch, in high-purity silicon crystals even under extremely low stresses at high temperature. However, in a crystal doped with a certain kind of impurities no dislocations come out of the flaw until the applied stress exceeds a critical stress even though the flaw accompanies a dislocated micro-region. The effect of oxygen impurities on the generation of dislocations on a macroscopic scale in CZ-Si has been investigated, making use of intentionally introduced surface flaws such as indentations. Figure 16 shows the critical stress for dislocation generation from a Knoop indentation made at room temperature in a FZ-Si crystal and a CZ-Si crystal as a function of the temperature (Sumino and Harada, 1981). The CZ-Si crystal contains oxygen impurities at a concentration of an order of 1OI8 ~ m - The ~ . crystals were heated quickly to test temperatures in the abscissa under stress. In high-purity FZ-Si dislocations are generated under a stress lower than 1 MPa over the whole temperature

1I.

OXYGEN EFFt ( I O N MECHANICAL PROPERTIES

473

range tested. On the other hand, in CZ-Si fairly high magnitudes of the critical stress are measured. The critical stress increases with an increase in the temperature. It has been shown in the preceding section that oxygen atoms dissolved in a Si crystal do not affect the velocity of a dislocation moving under a high stress. The velocity of a dislocation increases with an increase in the temperature. From these facts it is concluded that the critical stress for dislocation generation is not related to the resistance against the dislocation motion due to oxygen atoms dissolved in the crystal. Thus, the critical stress for dislocation generation is related to the release stress of dislocations in the flaw region that are immobilized during heating of the crystal due to the gettering of oxygen atoms. When stress is low enough to allow the development of clusters or complexes of oxygen atoms along dislocations in the recrystallized dislocated region at a flaw. the dislocations ar-e immobilized and do not come out of the flaw region until the applied stress exceeds the release stress. This is

FIG. 17. X-ray topographs showing the generation of dislocations from scratcheh and peripheries of wafers due 10 thermal cycling in C‘Z-Si containing oxygen impuritieh at a c o n c e n t i d o n of 1.7 x 10’x.a high-purity FZ-SI and FZ-Si containing nitrogen impurities at a concentration of 1.5 x I O ” a t o m ~ / c n i (Ahe ‘ et al.. 1981).

474

K. SUMINO AND I . YONENAGA

thought to be the mechanism of suppression of dislocation generation in the CZ-Si crystal. Figure 17 shows dislocation generation due to thermal cycling at a scratch and the periphery of wafers of CZ-Si, high-purity FZ-Si and FZ-Si doped with nitrogen impurities (Abe, Kikuchi, Shirai and Muraoka, 1981). Dislocations are abundantly generated in high-purity FZ-Si while generated less in CZ-Si and nitrogen-doped FZ-Si. This observation demonstrates oxygen and nitrogen impurities are effective in suppressing dislocation generation in device production processing of wafers. The effect of nitrogen impurities on the dynamic activity of dislocations is given in a later section. VI. Mechanical Properties of Silicon as Influenced by Oxygen Impurities 1. MECHANICAL PROPERTIES OF HIGH-PURITY SILICON CRYSTALS

First in this section, we show the characteristics in mechanical behavior of high-purity FZ-Si crystals that are free from the effect of oxygen impurities. They are the mechanical properties inherent to Si. Oxygen effects are then described in following sections. Figure 18(a) shows the stress-strain curves of high-purity FZ-Si crystals subjected to tensile deformation along the [123] direction at various temperatures under a shear strain rate of 1.1 x s - ' . The crystals initially contain dislocations at a density of 2 x lo4 cm-2 (Yonenaga and Sumino, 1978). Figure 18(b) shows stress-strain curves of the same FZ-Si crystals at 900°C under various shear strain rates. The stress-strain curve of FZ-Si is characterized by a noticeable drop in stress from the upper to the lower yield points. The magnitudes of the upper and lower yield stresses and the amount of the stress drop after the upper yield point depend sensitively on the temperature and strain rate. They all decrease rapidly with an increase in the temperature and increase markedly with an increase in the strain rate. There is another important parameter that affects the characteristics of stress-strain curve in the yield region; namely, the density of generation centers or multiplication centers for dislocations initially contained in the crystal. Figure 18(c) shows how the upper and lower yield stresses and the stress drop diminish with an increase in the density of dislocations initially contained in FZ-Si crystals in the deformation at 800°C under a shear strain rate of 1.1 x s-' (Yonenaga and Sumino, 1978). Specimens with initial dislocation densities higher than 2 x lo6 cm-* show no stress drop in yield deformation. Most dislocations originally contained in high-purity FZ-Si crystals are observed to be mobile even under an extremely low stress and to undergo self-multiplication during their motion along the slip planes.

I I.

475

OXYGEN F f F F ( 1 O N M F C H A N I C A L PROPFRTIES

0

lo

20

30

1

Shear strain, Yo

(h)

Shear strain, "/. (CI }I(,. I X Stre\s-\lrain curves of high-puritv FL-SI crystals in tensile deformation along the 11231 direction as dependent on ( a ) temperature. ( h ) shear strain rate and ( c ) inilial dcn\ity of dislocations (Yonenaga and Sunllno. 1978).

476

K. SUMINO AND I. YONENAGA

The upper yield stress T , , ~and the lower yield stress T~~ depend on the temperature T and the strain rate i: in such a way as described with the following relation: T,,~

or

(7)

T , CK~ ~ ‘ “ e x p ( U l k , T ) ,

where the magnitudes of n and U for T , are ~ reported to be 2.1-2.5 and 0.94-1.25 eV, respectively, and those for T~~ to be 2.9-3.3 and 0.80-0.92 e V , respectively (Patel and Chaudhuri, 1963; Siethoff and Haasen, 1968; Yonenaga and Sumino, 1978; Schroter, Brion and Siethoff, 1983). 2. OXYGEN EFFECTON MECHANICAL PROPERTIES OF DISLOCATION-FREE CRYSTALS

Figure 19 compares stress-strain curves of dislocation-free Si crystals with various concentrations of interstitially dissolved oxygen atoms together with that of high-purity FZ-Si deformed at 900°C under a shear s - ’ (Yonenaga, Sumino and Hoshi, 1984). All strain rate of 1 . 1 x specimens have been subjected to annealing at 1300°C followed by rapid cooling to homogenize them before deformation tests. The stress-strain curve of the crystal with any oxygen concentration is characterized by an extremely high upper yield stress and a sharp stress drop after the upper yield point. The shape of all the curves from the upper yield point to the lower yield point is rather irregular. This reflects the fact that

N

OL

I

10

I

20 Shear

1

30

I

40

strain , %

FIG. 19. Stress-strain curves of dislocation-free crystals of Si containing oxygen irnpurities at various concentrations shown in the figure and high-purity FZ-Si deformed in tension along the [I231 direction at 900°C under a shear strain rate of 1 . 1 x s - ’ (Yonenaga et al.. 1984).

11.

O X k C L Y I=f 1.1

(

I O N MI C H A N I C A I PROPFRlIES

477

deformation proceeds by nucleation and propagation of Luders bands. It may be said from the figure that both the upper and lower yield stresses and the amount of yield drop a s well as overall stress-strain characteristics show no systematic dependencies on the oxygen concentration: namely, they are almost independent of the oxygen concentration. Several groups reported that the yield stress of dislocation-free crystals of usual CZ-Si was almost the same a s that of usual FZ-Si (Mahajan. Brasen and Hassen, 1079; Sumino, Hiiracla and Yonenaga. 1980; Doerschel and Kirscht. 1981). It is concluded that individually dispersed oxygen atoms have little influence on dislocation processes occurring in the deformation of a Si crystal. This agrees with the ohservation that oxygen impurities at any concentration do not affect the velocities of dislocations in motion as seen in Figs. 5 and 6.

3 . OXYGEN EFFLCTON

ME(.HANI(’AI.

PROPERTIES OF DISLOCATED CRYS.TA1.S

Figure 20(a) shows stress-strain curves of dislocated CZ-Si crystals in deformation at various tempct-atures under a shear strain rate of 1 . 1 x 10 5 I , while Fig. 20(b) those under various strain rates at 900°C. The crystals are originally dislocated at a density of 2 x lohcm-’ and contain oxygen impurities at a concentration of 7 x to” atoms/cm3. I t is seen that the dislocated CZ-Si crystals show the same type of dependencies of the yielding behavior on both the temperature and the strain rate as those in dislocated high-purity FZ-Si crystals seen in Fig. 18. Essential difference between C Z S i and FZ-Si is in the dependence of the yield behavior on the dcnsity of dislocations initially contained in the crystals. Figure 21 show\ the stress-strain curves of CZ-Si crystals dislocated at two different densities deformed at 800°C under a shear strain rate of I . I x 10 s - I together with those of FZ-Si crystals dislocated also at two different densities. A CZ-Si crystal with a dislocation density of 5 x 10‘ c m - ’ shows the yield behavior similar to that of a dislocation-free crystal in Fig. 19. A FZ-Si crystal dislocated at a density of 1.7 x 10‘ c m - shows no stress drop in yielding, while a CZ-Si crystal dislocated at 9 x 10‘ c m - ? shows a more remarkable stress drop than that of a FZ-Si crystal dislocated at 2 x lo4 cm-’. Thus, dislocated CZ-Si crystals show yield behavior that corresponds to that of a FZ-Si crystal with tin initial dislocation density more than two orders of magnitude lower. The effect becomes increasingly remarkable as the concentration of oxygen impurities increases. Figure 22 shows stress-strain curves in the yield region of Si crystals dislocated at densities of approximately 1 x 10‘ c m - ’ , containing at a variety of concentrations of oxygen impurities. deformed at 800°C under a shear strain rate of 1 . 1 x s - ’ (Yonenaga

’

478

K. SUMINO A N D I . YONENAGA

N

E

2

r-

1

0 3ln

?

+ m

Shear

10

20

strain

.

1

30

Shear strain , %

40

50

FIG.20. Stress-strain curves of CZ-Si crystals dislocated at a density of 2 x lo6 cm-? and containing oxygen impurities at a concentration of 7 x 10” atoms/cm3 as dependent on (a) temperature and (b) shear strain rate.

J

N

E

cz 5x10'crn\

m

_. oL-L-..L

0

10

20

LO

30 Shear

50

60

70

strain , Yo

Fic,. 2 I . Stress-\train curves of dislocated c q s t a l s of CZ-Si and FZ-Si i n tensile deiorinaInitial lion along the 117-31 direction at 800Y' undei- a 5hear strain rate of 1 . 1 x l o - ' di5location densitie\ of the cry\tal\ are \hewn in the figure (Surnino et al.. 1980).

0

5

lo

Shear strain, '10

Fic;. 22. Stres\-strain curves of S I crystals dislocated at densities of about I x I O h c m - ' and containing oxygen at various concentration\ shown in the figure deformed at 800°C under a shear strain rate of 1 . 1 x I0 ' \ (Yonenaga et al.. IY84).

'

480

K . SUMINO AND I . YONENAGA

60 -

$

50-

$ 40-

k v)

P .g 30\

B

3

2010 -

01

'

1 o4

I

!

I I 106 Dislocation density, cm-2 /

lo5

I

I

I

lo7

FIG.23. Upper yield stresses of Si crystals containing various concentrations of oxygen SC' shown in the figure in the deformation at 800°C under a shear strain rate of 1 . 1 x plotted against the density of dislocations contained in the crystals prior to deformation (Yonenaga et al., 1984).

et al., 1984). All the specimens were annealed at 1300°C and cooled rapidly to avoid the precipitation of oxygen. The upper yield stress is seen to increase with an increase in oxygen concentration. Figure 23 shows the upper yield stress in the deformation at 800°C under a shear strain rate of 1.1 x s - ' for crystals with various concentrations of oxygen impurities plotted against the density of dislocations initially contained in the crystals (Yonenaga et al., 1984). For any values of the oxygen concentration, the upper yield stress is affected noticeably by the initial density of dislocations. It is seen that the upper yield stress of crystals with an oxygen concentration of 1.5 x 10'' atoms/ cm3 is approximately equal to that of a high-purity FZ-Si crystal of which dislocation density is lower than that in the former by about one order of magnitude, and that in the crystals with an oxygen concentration of 9 X lOI7 atoms/cm3 is equal to that of the high-purity FZ-Si crystal of which dislocation density is more than two orders of magnitude lower. Figure 24 shows the dependence of the upper yield stress in the deformation of 800 and 900°C on the oxygen concentration for crystals with dislocation densities of 2 x lo5 cm112and 1 x lo6 cm-2 (Yonenaga et al., 1984). For both dislocation densities, the upper yield stress is seen to increase with the oxygen concentration, the increasing rate being enhanced at high oxygen concentrations.

11.

OXYGEN F1FI-C 1 O N MECHANICAL PROPERTIES

48 1

G 5
k

Z

4-

t-

o ,-

.3-

x 1

IJ

21 -

t IC 24 Dependence of the uppei vield \tres\ T", at 800°C and 900°C o n the concentrdtion C of oxygen a t o m i n cry\talc with initirll di\location densitie5 of 2 x 10' and I x 106 cni ' (Yonenagd ct dl , 1984)

,4s has been demonstrated in preceeding sections, in situ X-ray topographic observations have verified that the mobility of dislocations in a Si crystal is little influenced by dispersed oxygen atoms but that the locking of individual dislocations takes place pronouncedly in the crystals with high concentrations ot' dissolved oxygen (Imai and Sumino. 1983: Sumino and Imai. 1983). Thus. it i s natural to think that high upper yield stresses of crystals with high oxygen concentrations are closely related to the immobilization of d i h c a t i o n s initially contained in the crystals due to the development of oxygen clusters or complexes along them. Dislocations initially contained in oxygen-doped Si crystals are locked firmly by oxygen impurities and t h e locking strength increases with an increase in the concentration of oxygen. In the next section it is shown how such dislocation immobilization gives rise to the effect that corresponds to an apparent decrease in the initial density of dislocations. 4.

T H t O R E T I C A L D E R I V A T I O N OF Y I L l I) C H A R A C T E R I S T I C S

u . Si Crystctls in the Ahsrnc.r,

I)i.vlocutioti Locking by I m p u r i t i t ~ s

Plastic deformation of' a crystal proceeds by means of the motion of a high density of dislocations in the crystal. Yielding of a crystal may be regarded as the transient \t:ige during which the internal state of the crystal changes from the static one t o the dynamic one when the crystal

482

K. SUMINO AND I . YONENAGA

is subjected to deformation of a constant rate. Both the upper and lower yield points as well as the stress-strain curve of the crystal in yield deformation are determined by various dislocation processes that take place during such transience. The basic equation that relates the dynamic state of dislocations in a crystal to macroscopic deformation of the crystal is kp, = NGb,

(8)

which is identical to Eq. (I). In Eq. (8), it is assumed that deformation of the crystal takes place by means of a single slip along the primary slip plane and, as a consequence, dislocations of only the primary slip system contribute to deformation. The total shear strain rate i: is the sum of the plastic shear strain rate given by Eq. (8) and the elastic shear strain rate iel. Thus,

.

&

=

.

+ kel.

(9)

The flow stress T , of a crystal is equal to the stress needed to move dislocations within the crystal at a certain velocity, which is determined by the strain rate and the density of dislocations in motion. It is proportional to the elastic strain. Thus, the time derivative of the flow stress is given by where 5 is the elastic constant of the system consisting of the specimen and deformation apparatus. In deformation under a constant strain rate, Eq. (10) turns to be dT,/d&

=

.$(&- N G b ) / i .

(11)

The flow stress consists of two components: One is the effective stress which is necessary to make a dislocation overcome the intrinsic resistance of the crystal lattice at some given rate, and the other is the , is necessary to overcome the interaction beathermal stress T ~ which tween dislocations. Namely,

Teff,

The mean velocity of dislocations moving in the crystal during defor~ ~ Eq. (2): mation is obtained by substituting T , into According to the dislocation theory, T~ =

T~

is given by

GbN;"/P,

II

O Y Y b F N t F I kC 1 O N h l l ( HANIC A 1 PROPERTIES

483

where G is the shear modulus, h is the magnitude of the Burgers vector, N , is the density of all dislocations in the crystal and p is a constant of about 3-4. Dislocations multiply thenisclves during motion and a simple model of self-multiplication leads to the following multiplication rate of dislocations (Peissker. Haasen and Alexander. 1961): clNldl = Kr,,NV, (15) where K is a constant. Equation (IS)is valid when the dislocation multiplication process is controlled by dislocations of only the primary slip \ystem and is deduced on the physical model that the multiplication takes place by means of a double cross glide of screw dislocations or a local pinning of dislocations by a fixed number of obstacles. We assume N = N , in the following; namely, that all dislocations in the crystal are in motion. This assumption may he valid in the beginning stage of deformation such as yield deformation. The stress-strain curves of a Si crystal are calculated by solving simultaneous differential equations ( 1 1 ) and (15) with Eqs. (13) and (14) in a numerical way. The initial condition is taken to be T ~ = , GbNA”/p for F = 0. where N,, is the density of dislocations initially contained in the crystal. Derivation of the stress-\train curves on the preceding model have been performed by Suezawa, Sumino and Yonenaga (1979). Only K is the fitting parameter of the model, the value of which has been determined from the magnitude of the upper yield stress of a specimen with a certain value of N,) in the deformation at some fixed temperature and strain rate. The stress-strain curves of a Si crystal calculated for various deformation conditions are in good agreement with the experimental ones with respect to the dependencies of the both upper and lower yield stresses on the temperature and the strain rate. However, the calculated magnitudes of the lower yield \tress are systematically lower than the experimental ones. Further. t tic calculated upper and lower yield stresses both show weaker dependencies on N,, than experimental ones. This ahove discrepancy between calculation and experimental is removed by taking into account of activity of dislocations of the secondary slip system (Sumino and Yonenaga, 1991, 1993). It is commonly observed that dislocations of slip systems other than the primary slip system are i i l s o active in yield deformation of a Si crystal. When two slip systems are active in deformation of a crystal, the total plastic shear strain rate is given by the following equation instead of Eq. (8):

t,,, = N , i ) , b t yN,C,b,

(16)

484

K. SUMINO AND 1. YONENAGA

where N , and N 2 are the densities of dislocations of the primary and secondary slip systems, respectively, V , and V 2 are the mean velocities of dislocations on the primary and secondary slip systems, respectively, and y is a geometrical factor that is smaller than unity. The velocities V , and V , are obtained by substituting the following effective stresses on the primary and secondary slip systems into Eq. (13): T , ~ I~ ,= T ~I ,

GbN!‘2/f!- GbN:I2/P*,

(17a)

~ = T~, , ~ ~

GbN;”/P* , ~ - GbNii2/P,

(1%)

T

where T , , , ~and T , , ~ are the resolved shear stresses of the applied stress with respect to the primary and secondary slip systems, respectively, and P and p* are constants characterizing the interaction between dislocations of the same slip system and that between dislocations belonging to different slip systems, respectively (p > p*). In situ observations of dislocation multiplication processes by means of X-ray topography (Sumino and Harada, 1981) and transmission electron microscopy (Sato and Sumino, 1977; Sumino and Sato, 1979) have revealed that dislocation multiplication takes place by two basically different mechanisms in Si crystals: one is spontaneous multiplication of gliding dislocations, for example, by means of double cross slip and the other multiplication through interaction of dislocations belonging to different slip systems. The multiplication rates of dislocations of the primary and secondary slip systems are then given by dN,ldt

=

dN,ldt

=

K N l ~ l ~ e f+f ,K, * N I N : ! v I T ~ ~ ~ , I ,

K N 2 v 2 ~ e K+, 2K * N 2 N I v 2 ~ e f f , 2 ,

( 18a)

(18b)

respectively, where K and K* are constants that characterize the two multiplication processes. Stress-strain curves calculated with Eqs. (16) through (18) are shown in Fig. 25, which is in good agreement with experimental observations shown in Fig. 18. Figure 26 shows the calculated upper and lower yield stresses with solid lines as functions of various parameters. Experimental data are shown by open and filled circles. The agreement between calculation and experiment is excellent. b. Effect of Dislocation Locking by Oxygen Impurities

We have seen in Sections VI.2 and 3 that an increase in the oxygen concentration in Si results in a significant increase of the strength of the

11

OX’rCrFlu t l I t ( I O N MF( H A N I C A L PROPtRTIF\

900°C I .L I 5 10 IS Shear strain

30

r--

o/o

-

485

L

I I 10 15 Shear strain , ‘lo

5

~

T- 600°C

Shear strain, Yo (C)

Fiti. 7 5 . Calculated \li-e\\-\trdin ctine\ o f high-purity si crystals a\ dependent o n ( a ) temperature. (h) sheai- strain rate ,ind I C ) initial density of dislocations. which corre\pond t o experimental strea\-strain curve\ in Fig. I X ( a ) . ( b ) . and ( c ) . respectively (Sumino and Yonenaga. 1993).

486

K . SUMINO AND 1. YONENAGA

T , 'C 850

800

L 0.85 0.9 0.95 1 0 3 / ~ K-' ,

1 10-5

10-4 € , s-'

Ir 3

(b)

E

-

0

lo4

105 lo6 N o , cm-2

107

(C)

FIG.26. Upper yield stress T , and ~ lower yield stress T , of ~ high-purity Si crystals as dependent on (a) temperature, (b) shear strain rate and ( c ) initial density of dislocations. Solid lines show the results of calculation while open and filled circles show experimental points for T~~ and T , ~ ,respectively (Sumino and Yonenaga, 1993).

crystal only when the crystal is initially dislocated. We have concluded that the strengthening of Si crystals due to oxygen impurities is not related to the resistance of oxygen atoms dispersed within the crystal against the dislocation motion but to the locking of dislocations due to the segregation of oxygen atoms on the dislocation core. Here, we discuss how such locking of dislocations affects the yield behavior of the crystal. Let us consider a simplified case in which dislocations of only the

II

O X Y G E N Et I-f

(

I O N M F C H A N I C A L PROPFRTltS

487

primary slip system are activated in deformation and they multiply themselves, being controlled by Eq. ( 1 5 ) . Suppose that the applied stress T , , increases at a constant rate q ; namely. T , = q t . When the dislocation density N is low enough that T , in Eq. ( 14) is much lower than T,,.~. T , , is approximately equal to T,,,. Assuming that all dislocations in the crystal are in motion. Eqs. (13) and ( 15) lead to N as a function of^,, to be given as follows (Sumino. I989a): N

=

N,,exp(
(19)

with

<=

(

vi, K/3qTo)exp(- Q / k , T ) .

where N,, is the density of mobile dislocations initially contained in the cry st al. When dislocations are locked by impurities, a stress T , . is needed to release the dislocations from the impurities and to start them moving. In such a case N turns o u t t o be its follows:

It is known that once applied stress exceeds the release stress the density of dislocations increases with stress in such a way as if the initial density of mobile dislocations were reduced by locking by a factor of ~ X P ( < T < ' ) This . is just the explanation for our observation in Section V1.3. The magnitude of T , increases with the oxygen concentration and also depends on the period and temperature where the dislocations are kept under no stress. We can estimate the magnitude of release stress of dislocations from the magnitude of the upper yield stress if the deformation condition and the initial density of dislocations are known. Figure 27 shows the release stress as a function of the oxygen concentration, which is obtained from the analysis of data in Fig. 14 with the model that dislocations of the primary and secondary slip systems are activated. It is seen that the release stress increases with the concentration of oxygen impurities and that the magnitude of the release stress at 900°C is lower than that at 800°C:. The latter reflects the fact that the release process of dislocations from impurities is thermally activated. Oxygen segregation along dislocations in the specimens of Fig. 14 IS thought to have taken place while the specimens are heated to deformation temperature o r they were kept at that temperature before the deformation test.

488

K. SUMINO A N D I. YONENAGA

I I

B

5ot

= 40ffl-

ffl

gul al ffl

-3 2

302010-

5 10 Oxygen concentration, 10’ 'ern-3 FIG.27. Release stress of dislocations in CZ-Si crystals estimated from the upper yield stress in Fig. 24 shown as a function of the oxygen concentration.

5 . WAFERSTRENGTHENING BY OXYGEN IMPURITIES In the following, an explanation is given of why CZ-Si wafers are more resistive than FZ-Si wafers to warpage caused by thermal-stress-related thermal cycling even if they are free from dislocations (Sumino, 1986). Any real wafer used in device fabrication processing is never free from some structural irregularities, especially at the edge of the wafer, which are effective generation centers for dislocations. In fact, dislocations are observed to be generated from such surface irregularities during device production processing. Once generated, dislocations multiply during motion and, as a result, increase their density as described by Eq. (15) or (18).

We consider the simplified case of a wafer that is subjected to stress cycling with the amplitude T~ at a constant temperature T , as shown in Fig. 28 and dislocation multiplication controlled by Eq. (15). The density of dislocations increases with stress in each cycle in such a way as described by Eq. (19) where No in the first stress cycle is taken to be proportional to the density of generation centers for dislocations in the crystal. After the first stress cycle the density of dislocations attains a certain magnitude determined by T and T ~ In . the absence of locking by oxygen impurities, as in FZ-Si, dislocations of such a density all act as dislocation sources. Thus, the density of dislocations starts increasing from such a value in the second cycle and attains an increased magnitude after the second cycle. After repetition of some number of cycling, the density of dislocations increases up to a magnitude that is high enough to cause appreciable warpage of the wafer. In Fig. 29 curves marked

11.

OXYGEN EFFkC'l ON MECHANICAL PROPERTIES

489

Time

FIG.28. Stress verws lime relation in stress cycling.

I

Nc

-

Cycling number

FIG. 29. Variation in the dislocation density aga~nstthe number of stress cycles calculated for F-Z-Si and CZ-Si wafers. Calculafion wah done for stress cycling at 900°C with a stressing rate of 5 x l o - ? MPaIs and stress :implitude\ of 7.5 and 10 MPa (Sumino. 1992).

490

K . SUMINO AND 1. YONENAGA

FZ-Si show how the density of dislocations increases with the number of cycling at 900°C for stress amplitudes T~ = 7.5 and 10 MPa and a stressing rate of -q = 5 x lo-* MPa/s. The case of thermal cycling is more complicated. Thermal stress is induced by inhomogeneous distribution of temperature during the heating and cooling course of the cycling. Thus, the temperature as well as the stress varies with time. In the case of a Si wafer containing impurities, such as oxygen, which immobilize dislocations effectively, there are two effects that prevent dislocations from increasing their density. First, dislocations are not generated from the dislocation sources if the amplitude of stress cycle does not exceed the critical stress for generation of dislocations seen in Section V.2. In such a case the wafer is kept practically free from dislocations, even after a number of stress cycling. Second, in actual device production processing a wafer is kept under no stress at high temperatures for a certain duration, since the temperature is uniform throughout the wafer. Even if dislocations are generated from the dislocation sources and move into the wafer during the preceding heating or cooling course of the cycling, they are immobilized due to gettering by oxygen atoms when the wafer is kept at the high temperature. Thus, the density of dislocation sources after each cycle returns to the initial value before the cycling is started. As a consequence, the density of dislocations keeps a low value even after a number of cycles. Curves marked CZ-Si in Fig. 29 show the variation of the dislocation density against the number of cycles on the simplified assumption that the temperature is a constant 900°C (Sumino, 1992). This is the reason why wafers of CZ-Si are more resistive to warpage due to thermal cycling than wafers of FZ-Si. VII. Influence of Oxygen Precipitation on Mechanical Strength

1. GENERAL FEATURES IN THE SOFTENING OF SILICON RELATED TO PRECIPITATION OF OXYGEN

It is known that the high resistance against wafer warpage in CZ-Si is lost when the wafers are kept at temperatures around 1000°C for a rather long period. This phenomenon is related to the precipitation of supersaturated oxygen in CZ-Si. Interstitially dissolved oxygen atoms in CZ-Si crystals become supersaturated in the temperature range below about 1200°C. Figure 30 shows the effect of annealing at 1050"C, 1175°C and 1320"C, each for 24 hr on the stress-strain curves of originally dislocation-free CZ-Si crystals with an oxygen concentration of 9 x lo" atoms/cm3 in tensile deformation at s - ' (Yonenaga and Sumino, 1982). 900°C under a strain rate of 1 x

1I

49 1

O X Y G E N F F b F C IO N M l ( H A N l C A l PROPERTIES

~~

q-

I

0

10

30

20 Shear strain

,

40

I

50

'1.

FIG. 30. Stress-strain curves of originally dislocation-free CZ-SI crystals annealed at varioub temperatures shown in the figure measured each for 24 hr deformation at 900°C under a shear Strain rate of 1 x 10 s (Yonenaga and Surnino, 1982).

'

Annealing at 1175°C or 1320°C does not affect the magnitude of the upper yield stress significantly. Deformation of crystals that are subjected to such heat treatment and that are in the as-grown state all proceed by means of the propagation of 1,iiders hands in the yield stage. Annealing at I0So"C drastically reduces the magnitude of the upper yield stress and t h e flow stress throughout all deformation stages. as has been first demonstrated by Patel (1964). The deformation of a crystal annealed at 1050°C proceeds homogeneously like a FZ-Si crystal containing dislocations at a density higher than lo4 cmVarious types of defects as well as SiOz precipitates are developed in the crystals due to annealing at 1050°C. Figure 31 shows an extrinsic stacking fault and punched-out dislocation loops developed around precipitate particles in such crystals (Yonenaga and Sumino. 1982).The details of the generation of defects induced by oxygen precipitation are given in another chapter. Annealing of precipitation-softened crystals at temperatures higher than 1200°C leads to the restoration of the high upper yield stress and large stress drop in the yield defcmnation, as shown in Fig. 32 (Yonenaga and Sumino. 1982). SiO, precipitates its well as various kinds of defects around them are observed to be diminished by such dissolution treat-

'.

492

K . SUMINO A N D I . YONENAGA

ment. The change in the stress-strain curve is similar to that caused by the decrease in the density of the dislocation sources. The stress-strain curve of the crystal subjected to dissolution treatment at 1320°C for 1 hr is almost the same as that of the crystal subjected to no precipitation treatment. It may, thus, be concluded that the precipitation softening in CZ-Si crystals is caused by the generation of defects that can act as effective dislocation sources under stress. A CZ-Si crystal that is annealed at 1320°Cfor 24 hr and cooled directly to 1050°C and held there for 24 hr shows upper and lower yield stresses higher than those of a crystal in the as-grown state. N o defect related to precipitation of oxygen is observed to be developed. Contrarily, in crystals that are annealed at 1320°C and cooled to room temperature, drastic reductions in both the upper and lower yield stresses take place on subse-

FIG. 31. TEM micrographs of (a) an extrinsic-type stacking fault and (b) punched-out dislocations developed around oxygen precipitates in CZ-Si annealed at 1050°C for 24 hr (Yonenaga and Sumino, 1982).

1I

0'

493

OXYGEN € I f k < 1 O N M F C H A N I C A L PROPFRTIES

10

I

20 30 Shear strain

.

40

50

"/.

FIG.3 2 . Stress-strain curves of CZ-SI crystals precipitation-treated at 1050°C f o r 24 hr a s influenced by dissolution treatments at 1240. 1280 and 1320°C each for 5 min. and also by that at 1320°C for 60 min, meawred in deformation at 900°C under a shear strain rate of 1 x S C ' (Yonenaga and Sumino. 1982).

quent annealing at 1050"C, and at the same time, numerous defects were observed to be developed. This observation implies that the nuclei of precipitates o r defects causing the softening of CZ-Si crystals are formed during the cooling to room temperature from 1320°C or during the heating from room temperature to 1050°C. Thus, we know that the development of precipitates and associated defects is strongly influenced by the thermal history of the crystal. Usually, different ingots of CZ-Si follow different precipitation processes and, as a consequence. show different softening kinetics. Thus, in order to study the process of precipitation softening in detail, we must choose the crystals that have identical thermal hi stories.

2.

YIELD

STRENGTH OF CZ-SI

Wl' lH

OXYGEN

PRECIPITATION

In this section we show the characteristics in precipitation softening that proceeds at 1050°C in dislocation-free CZ-Si crystals all homogenized initially by annealing at 1300°C followed by rapid cooling. Figure 33 shows the stress-strain curves of crystals containing oxygen at various concentrations after annealing at 1050°C for 24 hr (Yonenaga et al.. 1984). It is seen that the magnitude of the upper yield stress and

494

K. SUMINO AND I. YONENAGA N

0’

1

1

I

I

10

20

30

40

Shear strain

,

%

FIG.3 3 . Stress-strain curves of originally dislocation-free CZ-Si crystals containing oxygen impurities at various concentrations shown in the figure after annealing at 1050°C for 24 hr measured in deformation at 900°C under a shear strain rate of 1 x s - ’ (Yonenaga et al.. 1984).

the amount of the stress drop from the upper yield point to the lower yield point are reduced drastically upon such heat treatment in crystals with high concentrations of oxygen atoms. The reduction becomes increasingly significant as the concentration of dissolved oxygen atoms increases. The upper yield stress and the general characteristics of the stress-strain curve of a FZ-Si crystal with an oxygen concentration lower than 10l6atoms/cm3and those of a CZ-Si crystal of which oxygen concentration is as low as 2.5 x lo’’ atoms/cm3 are not influenced by annealing at 1050°C. Figure 34 shows how the stress-strain behavior of CZ-Si with an oxygen concentration of 9 x 10” atoms/cm3 changes with the duration of annealing at 1050°C (Yonenaga and Sumino, 1982). The crystals are softened rather rapidly with an increase in the duration of annealing in agreement with the work by Pate1 (1964). The softening is seen most drastically in the magnitude of the upper yield stress. The yield deformation proceeds by means of the propagation of Luders bands in the crystals subjected to annealing shorter than 3 hr. Figure 35 shows how the upper yield stress changes with the duration of annealing at 1050°C for the crystals with various oxygen concentrations (Yonenaga et al., 1984). Variation in the concentration of interstitially dissolved oxygen atoms due to the annealing is also shown in the bottom of the figure. It is confirmed that the softening of the crystals is related closely to the increase in the density of SiO, precipitates with direct

I 1.

O X Y b C N F I I 1 C I O N MFCHANICAL PROPERTIFS

495

observation of precipitates. I t is also related to the decrease in the concentration of interstitially dissolved oxygen atoms as seen in the figure. It is interesting to note that the concentration of interstitially dissolved oxygen atoms in the crystal with an original oxygen concentration of 9 x lo’’ atomsicm7 decreases rapidly in the early stage of annealing and becomes lower than those in the crystals with lower concentrations of oxygen for annealing durations longer than about 5 hr. This suggests that the density of nuclei of precipitate\ depends strongly on the concentration of oxygen atoms even in crystals having been subjected to the homogenization treatment. Figure 36 shows the relation hetween the upper yield stress and the amount of precipitated oxygen atoms for crystals with different concentrations of oxygen atoms (Yonenuga et al.. 1984). For a given amount of precipitated oxygen atoms, t h e upper yield stress is measured to be higher for the crystal of a higher oxygen concentration than for the crystal of a lower oxygen concentration. I t is also to be noted that the magnitude of upper yield stress decreases very rapidly against the amount of precipitated oxygen atoms. These ohw-vations give clues to clarify the mechanism of precipitation softening of CZ-Si as described in the next section.

SHEAR STRAIN ( % )

FIG. 34. Stress-strain curves of (11-iginally dislocation-free CZ-Si crystals annealed at 105O’C for various durations shown in the figure. measured in deformation at 900°C under a shes \train rate of I x I W 4s - ’ IYonenaga and Sumino, 1982).

496

K . SUMINO AND I . YONENAGA

-

*b-.

10 3

E

kU

5

P 6

0

10 20 Annealing duration, h

0

FIG. 35. Variations of upper yield stress T , ~and the concentration 0,of interstitially dissolved oxygen atoms against the duration of annealing at 1050°C in Si containing oxygen atoms at various concentrations shown in the figure. Here T , was ~ measured in deformation at 900°C under a shear strain rate of 1 x s - ' (Yonenaga et al., 1984).

3. MECHANISM OF PRECIPITATION SOFTENING

The stress-strain curve of a CZ-Si crystal softened due to oxygen precipitation is characterized by a low magnitude of the upper yield stress and a small stress drop in yield deformation, which is characteristic of that in a FZ-Si crystal with a rather high density of dislocations. Thus, we may suppose that some defects are induced in CZ-Si in connection with oxygen precipitation that can act as effective dislocation sources under stress. Figure 37 shows a row of etch pits of dislocations around a SiOz precipitate observed after slight deformation of a crystal subjected to precipitation treatment (Yonenaga and Sumino, 1982). At first sight, this micrograph seems to suggest that precipitates act as dislocation sources by themselves, which leads to the precipitation softening.

I 1.

O X Y G E N EFf I-( 1 O N ME( HANlCAL PROPERTltS

497

FIG. 36. Variation of the upper vield s ~ i e \ \T , , ~against the amount of precipitated oxygen atom\ O,, in Si crystals with differznt concentrations C,, of oxygen atoms. measured in deformation at 000°C under a shear strain irate of I x I O - ' s - ' iYonenaga et al.. 19x4).

Fit,. 37. Rows of dislocation etch pit\ around a SiO: precipitate observed after slight deformation of a crystal rubjected t o precipilalion treatment (Yonenaga and Sumino, 1982).

498

K . SUMINO AND 1. YONENAGA

On the assumption that SiO, precipitates act as dislocation sources, an analysis in terms of dislocation dynamics has been done to describe quantitatively the experimental relation in Fig. 36. With the model that the decrease in the upper yield stress is related to the increase in the density of precipitates, it turns out that the density of precipitates has to increase more than six orders of magnitude against the change in the amount of precipitated oxygen atoms of a factor 2-2.5 to account for the experimental results. This result is unreasonable, and thus, the model is concluded to be inadequate. With the alternative assumption that the density of precipitates is constant in the intermediate stage of precipitation and also during the dissolution of the precipitates, the nucleation rate of dislocations at a precipitate under a given applied stress has to increase by more than 10 orders of magnitude against the change in the size of the precipitate of a factor 2 to account for the experimental result. This result is again unreasonable. From elasticity calculations, Kayano (1968) reported that the magnitude of the stress concentration coefficient at a rigid inclusion in a crystal was 2 at maximum. Similarly, Yasutake, Umeno and Kawabe (1982) reported that the stress concentration coefficients at a sphere-shaped particle of amorphous SiO, and a platelet of cristobalite SiO, in silicon were 1.25 and 2, respectively. Such low magnitudes of the stress concentration coefficient are insufficient to nucleate dislocations under ordinary applied stresses. In any event, it is concluded that SiO, precipitates themselves are not dislocation sources that bring about precipitation softening in CZ-Si. Now, we discuss the possibility that prismatic loops of dislocations developed around precipitates owing to large misfit strain are dislocation sources responsible for the precipitation softening. As seen in Fig. 38, the prismatic loops of punched-out dislocations are elongated around a SiO, precipitate after slight deformation (Yasutake et al., 1982). This TEM micrograph corresponds to the observation in Fig. 37. In an early stage of precipitation each precipitate is small in size and a low density of dislocations are punched out from it owing to a small misfit strain. The punched-out dislocations are quickly locked by oxygen and immobilized, since a rather high concentration of dissolved oxygen atoms remain in the matrix at this stage. As the precipitation process proceeds, precipitates grow and the number of punched-out dislocations increases as the misfit strain increases. Locking for such dislocations is less effective because rather low concentrations of oxygen atoms remain in the matrix now. At the same time, the oxygen atoms segregated along dislocations that have been punched out in the earlier stage change to precipitate particles. Oxygen atoms, originally distributed uniformly along the dislocations, are now concentrated at discrete positions, as

1 1 OXYGtN

EFFI

(

I O N M t C H A N I C A L PROPFRTIES

499

FIG.38. TEM micrograph of punt hed-oul dislocations elongated by slight deformation (Yawtahe et

21..

1982).

shown in Fig. 12. leaving oxygen-free portions on the dislocations. Such portions are free from locking and are able to act as dislocation sources under applied stress. The occurrence of these phenomena has indeed been observed by TEM. With this picture, the relations in Fig. 36 are reasonably understood. The concentration of oxygen atoms remaining dissolved in the matrix crystal is higher in the crystal with a higher oxygen concentration than in that with a lower oxygen concentration for a given amount of precipitated oxygen atoms. Such oxygen atoms remaining at a high concentration are thought to lock dislocations punched out from precipitate particles and the locked dislocations cease the function as dislocation sources. Thus, a higher upper yield stress may be attained in the crystal with a higher oxygen concentration than in the crystal with a lower oxygen concentration for a given amount of precipitation. VIII. Effects of Nitrogen and Carbon Impurities on Mechanical Properties of Silicon 1 . NITROGEN EFFECI (I.

Effc3ct.v on the

Dynumic BcJliuisior of' Individuul Dislocutions

Nitrogen atoms are reported to be electrically inactive and thought to be located on the interstitial sites in Si lattice (Tokumaru, Okushi, Masui

500

K . SUMINO AND 1. YONENAGA

and Abe, 1982). The effect of nitrogen on the dynamic behavior of individual dislocations in Si crystals has been investigated by the Sumino group with nitrogen-doped FZ-Si by means of in situ X-ray topography (Sumino, Yonenaga, Imai and Abe, 1983; Imai and Sumino, 1983; Sumino and Imai, 1983). Dislocations originally in motion at elevated temperatures under rather high stress in nitrogen-doped FZ-Si cease to move when the applied stress is lowered beyond some critical stress as have been observed in the case of Si containing oxygen impurities in Section 111.3. Such cessation of dislocation motion is never observed in usual FZ-Si of high purity. The critical stress for cessation in a crystal with a nitrogen concentration of 5.4 X lo'-' atoms/cm3 has been measured to be 3.0 MPa at 600°C and 5.5 MPa at 800"C, increasing monotonically with the temperature. The velocities of dislocations in crystals of this nitrogen concentration are measured to be the same as those in high-purity FZ-Si under stresses higher than the critical stress for the cessation of motion. When a dislocation ceases the motion in the nitrogen-doped crystal, the stress necessary to start the dislocation increases with the period during which the dislocation is kept at rest, as we have seen with crystals containing oxygen impurities. Figure 39 shows the release stress of 60" dislocations at 647°C in Si doped with nitrogen at the preceding concentration plotted against the duration of aging of dislocations at the same temperature. Data for Si

0

I

10

I

20

I

30

Aging duration,

1

40

I

50

min

FIG.39. Variation of the release stress at 647°C for initially fresh 60" dislocations against the duration of aging at 647°C in FZ-Si doped with nitrogen at a concentration of 5.4 x 10" atorns/cm3. Data for CZ-Si with two different oxygen concentrations of 1.5 x and 7.5 x IOl7 atorns/crn' and FZ-Si doped with phosphorus at a concentration of 1.2 x IOl9 atomsicm' are also shown (Surnino and Irnai, 1983).

II.

LO

. = I

h

OXYGEN EFI r

cr

50 1

O N MFCH A N I C A L PROPFRTIES

.~

/ .'

N

"CZ

€

1

I1

5: W

a:

I

0

10

I

I

I

20 30 LO SHEAR STRAIN ( 7 0 )

0

FIG.40. Stresh-atrain curves of initially dislocation-free crystals of nitrogen-doped FZ-SL (.YF%)b i t h a nitrogen concentration of 5.4 x 10'' atomsicm'. high-purity FZ-Si and CZ.-Si uith an oxygen concentration o f 9 10'' a t o m s / c r n ' in deformation at 900°C under a shear \train rate of 1 x 1 0 j - 't s u m i n o et d.. 19x3).

'

doped with two different concentrations of oxygen at I.S x 10'' and 7.5 x 10" atoms/cm3and that doped with phosphorus at a concentration of 1.2 x 10" atomsicm? are also shown in the figure for comparison. Nitrogen impurities at a concentration as low as 5.4 x 10" atomsicm' has a locking effect on dislocations approximately equal to that of oxygen impurities at a concentration higher by a factor of about 30. The locking strength of individual impurity atoms has been compared for different kinds of impurities from the number of the impurity atoms accumulated on a unit length of a dislocation during aging. It has been shown that an individual nitrogen atom has ii much stronger locking effect than an individual oxygen atom. b. Ejfcct on M r c h a n i c d Str.c*rrgtli

Abe et al. (1981) reported that wafers of a FZ-Si crystal doped with nitrogen at a concentration as low as 1.5 x atoms/cm3 were less susceptible to thermal slip than those of normal FZ-Si or CZ-Si crystals. This seems to reflect a strong locking effect o n dislocations due to nitrogen in Si. The stress-strain characteristics of a nitrogen-doped FZ-Si crystal in the as-grown state at elevated temperatures are similar to those of a usual FZ-Si crystal and a CZ-Si crystal when they are all free from dislocations

502

K. SUMINO AND 1. YONENAGA

I

SHEAR STRAIN ('1.1

FIG.41. Stress-strain curves of FZ-Si crystals doped with nitrogen at a concentration of 5.4 x 10'' atoms/crn3 containing dislocations at various densities prior to deformation in deformation at 800°C under a shear strain rate of I X s - ' . Numerals attached to the curves show initial densities of dislocations in unit of cm-' (Sumino et al., 1983).

prior to deformation. Figure 40 shows the stress-strain curve of a nitrogen-doped FZ-Si crystal (denoted NFZ in the figure) with a nitrogen concentration of 5.4 x lo" atoms/cm3deformed at 900°C under a strain rate s-l together with those of a high-purity FZ-Si crystal and a of 1 x CZ-Si crystal with an oxygen concentration of 9 x lo" atoms/cm3 (Sumino et al., 1983). They are all characterized by a marked stress drop and the deformation by means of propagation of Luders bands during yielding. Though the upper yield stress and the flow stress over a whole strain range are somewhat higher in the CZ-Si crystal than in the others, the difference among the three kinds of crystals is not significant, being much smaller than that found in dislocated crystals, which will be described next. Figure 41 shows stress-strain curves of the nitrogen-doped FZ-Si crystals with various densities of dislocations between 4 x lo4 and I .O x lo6 cm in deformation at 800°C under a strain rate of I x s - I (Sumino et al., 1983). The specimens in the figure all deform homogeneously during yielding. In comparison with the stress-strain curves of high-purity FZ-Si crystals in Fig. 18(c), we see that the stress-strain curves of the nitrogen-doped FZ-Si crystals show high magnitudes of the upper yield

-'

1I.

OXYGEN EFFb( 1 ON MFC HANICAL PROPERTIES

LO

503

L ,

0

I

in

FZ

\

2 20wt

0,

',

'0.

LI W

g 103

- 0

0

10 20 AGING DURATION ( h )

FIG.42. Variations of the upper yield $tress against the duration of annealing at IOSOT in initially dislocation-free crystals of nitrogen-doped FZ-Si ( N F Z ), high-purity FZ-Si and CZ-Si measured in deformation at YO0"C under a shear strain rate of I x S C ' . The crystals are the same as those in Fig. 40 (Sumino el al.. 1983).

stress and large stress drops from the upper yield point to the lower yield point. which are the characteristics of silicon crystals with low initial densities of dislocations. This suggests that a considerable part of dislocations initially existing in the nitrogen-doped FZ-Si crystals are locked effectively by nitrogen impurities and are inactive during deformation. We have already seen in the preceding section a quite similar phenomenon in CZ-Si crystals. We show the thermal stability of mechanical strength of nitrogen-doped FZ-Si crystals in the following. The variation of the upper yield stress of the nitrogen-doped FZ-Si crvstal against the duration of annealing at 1050°C is shown in Fig. 42 together with those of a high-purity FZ-Si crystal and a CZ-Si crystal. Tensile tests were conducted at 900°C under a strain rate of I x 10 ~ ' I .s The ~ upper yield stress of the nitrogen-doped FZ-Si crystal exhibits a peculiar behavior against the annealing duration; namely. a maximum is attained after about 6 hr of annealing. The origin of such increase in the yield stress has not yet been clarified. The strength of the crystal after annealing at I0SO"C for 24 hr is no lower than that before the annealing. No development of defects due to annealing at 1050°C was detected by etch pit observations.

504

K . SUMINO A N D 1. YONENAGA

It is concluded that nitrogen atoms in silicon crystals immobilize dislocations effectively on segregating along them and do not bring about the softening related to precipitation. 2. CARBON EFFECT Carbon impurities in FZ-Si at concentrations up to I x 10” atoms/ cm3 reveal neither a locking effect on dislocations nor an enhancementretardation effect on the dislocation velocity (Imai and Sumino, 1983). It is natural to suppose that the interaction between carbon atoms and a dislocation in a silicon crystal is so weak that no appreciable effect appears on dynamic behavior of dislocations since a substitutional carbon atom accompanies a rather small misfit strain and is electrically neutral in Si lattice. On the other hand, carbon atoms dissolved in CZ-Si are known to facilitate the precipitation of oxygen impurities in the temperature range between 600 and 1000°C. In comparison with carbon-lean CZ-Si, precipitate particles developed in carbon-rich CZ-Si are characterized by their small size and abundant density (Leroueille, 1981; Kishino, Matsushita, Kanamori and Iizuka, 1982). These observations lead to the supposition that carbon atoms or their clusters play the role of nucleation centers for oxygen precipitates in CZ-Si (Kishino et al., 1982). Since the strengthening of CZ-Si is achieved by the segregation of oxygen impurities on dislocations, it is interesting to know how carbon impurities affect such a process and, consequently, the mechanical strength of CZ-Si. Figure 43 shows the stress-strain curves in the yield stage of FZ-Si crystals containing carbon impurities at a concentration of 1.7 x l o i 7 atomsicmi with various dislocation densities in deformation at 800°C under a strain rate of 1 x s - ’ (Yonenaga and Sumino, 1984). The yield behavior, the magnitude of the upper yield stress and their dependencies on the dislocation density in the carbon-doped FZ-Si are almost identical to those in high-purity FZ-Si seen in Fig. 18(c). Thus, it is confirmed that carbon atoms dissolved in a silicon crystal play little role in locking dislocations by themselves alone, in accordance with the result of direct observation (Sumino and Imai, 1983). Next, we compare the mechanical strength of carbon-doped CZ-Si with that of carbon-lean CZ-Si. It has been reported that the upper yield stress of carbon-rich CZ-Si crystals is almost the same as that of carbon-lean CZ-Si crystals when the crystals are free from dislocations (Yasutake, Umeno and Kawabe, 1980). Figure 44 shows the upper yield stresses of dislocated crystals of CZ-Si doped with carbon at various concentrations together with those of car-

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OXYGEN E F F t ( 1 O N MECHANICAL PROPERTIFS

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r

Y

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In

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I-

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FIG.43. Stress-strain curves of F%-Sicrystals doped with carbon at a concentration of I.7 x I O " atom>/cm' that contain didocations at various densities shown in the figure ( i n cm :) in deformation at 800°C under a shear \train rate of I x IW4 5 - ' .

FK,.44. Upper yield stress T " , of carbon-doped FZ-Si and CZ-Si crystals with dislocation densitieb of about I x loh c m - ' plotted against the concentration 0 , of dissolved oxygen atoms. Open circles are the dala for carbon-lean Si. Filled marks are for carbon-doped Si at the carbon concentrations shown in thc figure. The upper yield stresses are for defcormation at X(WC and 900°C under a shear strain rate of I x s (Yonenaga and Sumino. 1984).

'

506

K . SUMINO A N D I . YONENAGA

-

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FIG.45. Upper yield stress T , and ~ lower yield stress T , of ~ CZ-Si crystals with dislocation densities of about 1 x lo6 cm-? and dissolved oxygen concentrations of about 6 x lo” cm-’ plotted against the concentration C , of dissolved carbon atoms. The yield stresses are for deformation at 800°C and 900°C under a shear strain rate of 1 x s - ’ (Yonenaga and Sumino. 1984).

bon-lean CZ-Si plotted against the oxygen concentration for deformation at 800°C and 900°C (Yonenaga and Sumino, 1984). Data for usual FZ-Si and carbon-doped FZ-Si crystals are also shown. The initial densities of dislocations in all the crystals are about 1 x lo6 ern-'. Open circles and solid lines are the data for carbon-lean FZ-Si and CZ-Si (Yonenaga et al., 1984). Filled triangles, circles and squares are for CZ-Si doped with carbon at concentrations of 0.9 x lOI7, 1.7 x loi7and 2.5 x lOI7atoms/ cm’, respectively. It is seen in the figure that carbon impurities at concentrations of the order of lOI7 atoms/cm3 have almost no influence on the magnitude of upper yield stress of Si crystal when the concentration of oxygen is lower than about 4 x 1017 atoms/cm3. However, the upper yield stress is enhanced distinctly by the presence of carbon impurities if the crystals contain oxygen at concentrations higher than about 5 x loi7atoms/cm3. Figure 45 shows the upper and lower yield stresses of CZ-Si crystals at 800 and 900°C plotted against the concentration of carbon atoms (Yonenaga and Sumino, 1984). All the crystals are dislocated at densities of about 1 x lo6 cm-* and contain oxygen at concentrations of about 6

I 1.

OXYGEN E l I F C 1 ON M F C H A N I C A L PROPERTIE5

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x lo” atoms/cm3. The upper yield stress increases monotonically with increase in the carbon concentration. Carbon atoms dissolved at a concentration of 2.5 x IO” atomsicrnj enhance the upper yield stress of the crystal by a factor of 1.4. From these results, it is concluded that carbon impurities bring about the increase in mechanical strength of silicon crystals if they coexist with oxygen impurities the concentration of which is higher than about 5 x l o ” atoms/cm’. Since it has been clarified from direct measurements (Sumino and Lmai. 1983) that carbon impurities by themselves have no appreciable effect on the dynamic property of dislocations. carbon atoms in CZ-Si are thought to promote the dislocation locking due to oxygen atoms. It is conceivable that such promotion of dislocation locking is caused by carbon atoms that are incorporated in the core region of a dislocation and act as the preferential nucleation sites of oxygen clusters. IX. Summary

The characteristics in mechanical behavior of a Si crystal on a macroscopic scale are determined by dynamic processes of dislocations in the crystal that take place on a microscopic scale under stress. Important among such processes are the generation, multiplication and motion of dislocations as well as interaction of dislocations with each other. The effect of oxygen on mechanical properties of Si is interpreted in terms of knowledge on how oxygen impurities affect such dislocation processes. Difficulty appears in measuring the dislocation velocity when oxygen impurities are dissolved in Si. ‘This is related to immobilization of dislocations caused by segregation of oxygen atoms on the latter. The difficulty has been overcome by adopting the technique of in situ X-ray topographic observation . Dislocation mobility in Si increases very rapidly as temperature increases. The dislocation velocity in high-purity FZ-Si depends on the stress linearly down to a very low stress. The linear dependence of the dislocation velocity on the stress holds also in Si containing oxygen impurities at a concentration of the level in CZ-Si when a dislocation moves at a rather high velocity under a high stress. The dislocation velocity in CZ-Si under such a high stress is the same as that in high-purity FZ-Si. On the other hand, the dislocation velocity in Si containing oxygen impurities is lower than that in high-purity Si when the dislocation moves at a low velocity under a low stress. The retardation of dislocation motion caused by oxygen impuritie\ is accompanied by the disturbance in the shape of moving dislocations. Under a stress lower than some critical

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stress, a dislocation ceases to move in Si containing oxygen impurities. The magnitude of the critical stress for cessation of dislocation motion increases with an increase in the oxygen concentration. Such observations together with theoretical analysis lead to the conclusion that oxygen atoms individually dispersed in a Si crystal do not affect the dislocation velocity in the concerned temperature range. However, they catch up to slowly moving dislocations and develop clusters on the dislocation line. The development of oxygen clusters results in the perturbation in the line shape and retardation of the dislocation in motion. An originally fresh dislocation is immobilized in Si containing oxygen impurities when it is halted at high temperatures under no applied stress. A theoretical treatment shows that the immobilization of dislocation is caused not by the development of the Cottrell atmosphere of oxygen atoms around the dislocation but by the development of clusters of oxygen atoms on the dislocation line. Oxygen atoms or, more generally, impurity atoms are gettered by dislocations by means of (1) preferential nucleation of precipitates of supersaturated impurities on the dislocation line or (2) some special reaction that takes place at the dislocation core to incorporate impurity atoms from the matrix region. Oxygen impurities effectively suppress the dislocation generation in Si under stress. The mechanism of suppression is closely related to the generation process of dislocations in a Si crystal. Dislocations are generated heterogeneously from some structural irregularities in the crystal under stress. Surface damage in a Si crystal such as scratches and indentations acts as effective generation centers for dislocations. Small amorphous Si regions are developed around such damages made at room ternperature. Such an amorphized region recrystallizes into a dislocated region when the crystal is brought to high temperatures. Dislocations come out of such a region and penetrate into the matrix if the crystal is under stress, leading to the dislocation generation. Dislocation generation from the damaged region takes place even under a very small stress in high-purity FZ-Si. However, dislocations are not generated under stresses lower than a certain critical stress in CZ-Si. This is caused by the locking of dislocations in the recrystallized regions due to gettering of oxygen atoms while the crystal is heated up. The yield strength and stress-strain characteristics of Si are well understood on the basis of a theoretical model using various dislocation processes observed in experiments. Oxygen impurities give no appreciable influence on the mechanical strength of Si if the crystal is initially free from dislocations. The oxygen effect appears in initially dislocated Si crystals. Oxygen impurities in Si give rise to the same effect on mechani-

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OXYGEN E r t t ( I

o~

ME( H A N I C A L PROPERTIFS

509

cal behavior a s the decrease in the density of dislocations initially contained in the crystal does. These are successfully described with the theory by taking account of the locking of dislocations by oxygen impurities. The high resistance of CZ-Si wafers in comparison with FZ-Si wafers to warpage due to thermal cycling is well interpreted with the idea of dislocation locking by oxygen impurities. Precipitation of supersaturated oxygen in Si results i n a decrease in the mechanical strength. The mechanical behavior of a precipitation-softened Si crystal is very similar to that of a Si crystal with a high density of dislocations initially contained in the crystal. Dislocations punched out from precipitate particles act a s dislocation sources and bring about the reduction in the yield strength of the crystal. Dissolution of precipitates in precipitation-softened Si at high temperatures results in restoration of the high yield strength. Nitrogen impurities in Si effectively immobilize dislocations even though nitrogen atoms dispersed within the crystal have no appreciable effect o n the velocity of dislocations in motion. The immobilization of dislocations is related to gettering of nitrogen by the dislocation core. The strength of locking per one nitrogen atom is about 30 times higher than that of an oxygen atom. Nitrogen impurities enhance the yield Ytrength of a Si crystal when the crystal is initially dislocated. It does not give rise t o precipitation softening due to annealing at temperature around 1 ooooc.

Carbon impurities in Si at concentrations up to I x 10’’ atomsicm’ do not give rise to any appreciable effects on both dislocation mobility and yield strength. However, they enhance the mechanical strength of Si when they coexist with oxygen impurities. Oxygen impurities in Si are amphoteric in nature from the view of its effect on the mechanical strength. Oxygen atoms individually dissolved in Si enhance the mechanical stability of Si at elevated temperatures. This effect originates from gettering of oxygen atoms by dislocations. which leads to immobilization of the dislocations. The effect becomes increasingly remarkable as the oxygen concentration in Si increases. On the other hand, precipitation of supersaturated oxygen impurities accompanies the generation of defects that act as dislocation sources and leads to the softening of Si. However. such precipitation-related defects can be effectively utilized as gettering sinks for heavy metallic impurities in device production technology. In conclusion. i t is empha\ired that defect control in Si technology is most effectively accomplished on the basis of correct understanding of oxygen effects on various dislocation processes in Si.

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Surnino, K . (198%). M u t e r . Sci. E n g . 84. 3 3 5 . Surnino. K. (1989b). I n Point und b,’.rrc,nclcd Dc;fi.cts in Semic~o,7duc./or.s.G . Benedek. A . Cavallini and W. Schroter ( e d \ . ) .p. 77. Plenum Press, New York and London. Surnino. K. ( 1992). In P r o ( . . lsr Puc.ific RIM Internail. Conf. oti Advunc.ed Muteriuls und Proc,e.s~ting,C. Shi. H. Li and A . Scott (eds.). p. 49. The Minerals. Metals & Material.; Soc.. Warrendale. P.A. Sumino. K., Harada, H..and Yonenaga. I . ( I Y X O ) . J p n . J . Appl. Phy.~.19, L49. Sun~ino.K., and Harada. H. (1981). phi lo^. Mtrg. A44, 1319. Suniino. K . . and Irnai. M . (1983). P / i i l ( ~ aMtrg. . A47, 753. Surnino. K.. and Sato. M . (1979). Krr.sttr// r r ! 7 d Icclrnik 14, 1343. Sumino. K . . and Yonenaga. I . ( 1991 .Yo/rd Stcrtc’ Phenotnenu lYi20. Gettering trnd l)efr,c/ Etigineering in .Semiccindrrc./or I , c . h t i ( ~ l ~Y gl . ~M. Kittler and H.Richter (eds.). p. 295. Sci-Tech Publication. Liechten\tein Sumino. K . . and Yonenagn. 1. (1997). fJ/iv.s. S t u t . Sol. f u ) . 138, 573. Sumino. K . . Yonenaga. 1.. Irnai. M . arid Abe. T. (1983). J . Appl. Pl7vs. 54, 5016 SuLuki. T.. and Kojinia. H.(1966) 4 c . t ~Mutull. 14, 913. Tokurnaru. Y., Okushi. H..Masui. T . . and Abe. T (19x2). J p n . 1.A p p i . P k v s . 21, L443. We