Appl. Phys. A 57,521-527 (1993) Applied PhysicsA "" Surfaces

© Springer-Verlag 1993

On the Influence of Interfaces and Localised Stress Fields on Irradiation-Induced Point-Defect Distributions in Silicon

J. Vanhellemont, A. Romano-Rodriguez*

IMEC, Kapeldreef 75, B-300I Leuven, Belgium (Fax: + 32-16/281501)

Received 29 June 1993/Accepted 18 August 1993

Abstract. High-flux 1-MeV electron irradiation in a high voltage transmission electron microscope is used to study the influence of interfaces and localised stress fields on {ll3}-defect generation in silicon. A semi-quantitative model is presented to explain the observations, suggesting that the silicon oxide/silicon interface is a stronger sink for self-interstitials than for vacancies. It is shown that the position and the height of the maximum of the {ll3}- defect density strongly depends on the strength of the interface as a vacancy sink and that compressive straining of the silicon substrate slows down the diffusion of vacan- cies towards the interface.

PACS: 61.80.Fe, 61.70.Bv, 61.70.Yq

Irradiation with MeV electrons is a useful tool to generate intrinsic point defects in silicon in a controlled way. Due to the small mass of the incident electrons, no extensive collision cascades are formed and the majority of induced lattice defects are Frenkel pairs. Once individual point defects are formed, quite different concentrations of self- interstitials and vacancies can build up due to their differ- ent mobility and to the presence of sinks with different strengths. High fluxes of electrons, which can easily be obtained in a high-voltage transmission electron micro- scope (TEM), can lead to the build-up of a high super- saturation of self-interstitials and vacancies. When the supersaturation is large enough, the self-interstitials will cluster and form so called {ll3}-defects in silicon and germanium [1-6].

In the present paper results are presented of a study of { 113}-defect nucleation during in-situ irradiation of cross- section TEM specimens of a LOCal isolation Of Silicon (LOCOS) structure in order to evaluate the influence of

* Permanent address: LCMM, Departament de Fisica Aplicada i Electr6nica, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Spain

interfaces and local stress fields on { 113}-defect nucleation and thus indirectly also on the behaviour of self-intersti- tials and vacancies. A semi-quantitative model is presented allowing to estimate the density of substrate sinks for intrinsic point defects, the impact of mechanical stresses on vacancy diffusion and the relative strength of inter- face or surface sinks for vacancies and self-interstitials, respectively.

1 Experimental

A LOCOS structure is prepared by growing a 600 nm thick field oxide in wet oxygen at 950°C through a patterned oxidation mask. The oxidation mask consists of a 10 nm pad oxide grown in dry oxygen and covered with a 150 nm silicon nitride layer obtained by low-pressure chemical vapour deposition. Cross-section TEM samples are irradi- ated with 1-MeV electrons in the JEOL1250 microscope of the University of Antwerp (RUCA). The temperature of irradiation is 640K and the average electron flux J is about 2 x 1019 cm-Zs -1, determined with a Faraday cup in the electron beam. In the following it is assumed that the area which is studied and which has a diameter less than 2 gm, receives a uniform irradiation flux and has a constant specimen thickness. Care is also taken to irradiate areas with a thickness between 0.5 gm and 1 gm in order to avoid a "foil-thickness" effect. From the detailed experimental work of Aseev and Astakhov [1] it is known that for moderately doped substrates this thickness is well above the critical value for defect nucleation and that in this case a thin layer of {113}-defects is formed close to the surfaces of the specimen where interaction with the surface is im- portant. Above this critical thickness small variations of specimen thickness are not very important as they will only increase or decrease the part of the specimen where bulk recombination is dominant. The present study fo- cuses on the impact of additional sinks formed by inter- faces perpendicular to the image plane, on the distribution of { 113 }-defects in the area close to the specimen surfaces.

522

2 Observations

Figures 1 and 2 illustrate the evolution of the { 113}-defect nucleation and growth as a function of the irradiation time. In Fig. 1 an overview is given of the complete LOCOS structure and part of the silicon substrate. It is clear that during irradiation { 113}-defects nucleate prefer- entially close to the interfaces and especially near the tip of the bird's beak. In Fig. 2 a higher magnification is shown of the edge of the LOCOS structure and the interface area. The figure clearly illustrates that defects nucleate first and closest to the SiO2/Si interface, in the highly compressive strained area at the bird's beak tip (area 2). During pro- longed irradiation, it is observed that defects also nucleate preferentially close to the nitride/oxide/silicon interface (area 1) and to the field oxide/silicon interface (area 3). The defect density is higher in area 1 than in area 3 and extends closer to the pad oxide/silicon interface. Near the bird's beak tip, in the area where very high compressive strains are present, the { 113}-defects extend also much deeper into the substrate. Figure 3 summarises the observed {113}- defect distributions in the image plane. The inset shows a schematic view of the cross-section geometry. The z co- ordinate, the depth below the wafer surface, is defined as the distance from the SiO2/Si interface in the image plane.

J. Vanhellemont, A. Romano-Rodriguez

3 Discussion

In plan-view TEM specimens the {113}-defects are ob- served to nucleate dominantly near the surfaces of the

Fig. 2. Enlarged view of the area close to the bird's beak tip of the LOCOS structure of Fig. 1 illustrating the { 113}-defect nu- cleation and growth near the interfaces and the isolation struc- ture edge

Fig. 1. Time sequence illustrating {113}-defect nucleation and growth in a LOCOS structure irradiated at 640K with 2 × 1019 cm-2s -1 1-MeV electrons. {ll3}-defects nucleate first near the tip of the bird's beak (area 2) where the compressive stresses are highest

300 | - i i

s i l i c o n oxide ~-,\\\\\\\\\\\\\\\\\\\\\\\\\\'% __

. , I z l ~ - i - ~ - - . - 7 - ~ - ~ - - ¢ ' - ' - - - I z 2 /

200 -~%'- . . . . . . . _.-z _ _ _~

IOO

0 i I n I

-200 0 200 400 600 f (N/m)

Fig. 3. Dependence of z 1 and z2, defined in the inset, on the interface force f exerted on the silicon substrate. The inset shows a schematic view of the {ll3}-defect distribution in a cross- section specimen, after irradiation with 1-MeV electrons

Irradiation-Induced Point-Defect Distributions in Silicon 523

specimen [-1, 2]. Aseev and Astakhov [1] explained this phenomenon by the different strength of the surface as sink for the self-interstitials and vacancies which are created by knock-on collisions of the incident electrons with the sili- con lattice atoms.

Aseev and co-workers [1, 3, 4] have modelled the dis- tribution of { 113}-defects assuming quasi-chemical reac- tions between point defects and sinks and assuming quasi- steady state. In their approach, which was also used by the present authors in a previous paper [6], the presence of sinks at the surface is taken into account by adding a depth dependent sink term in the rate equations. One of their conclusions is that the observations can be explained by assuming that the silicon oxide/silicon interface is a stronger sink for vacancies than for self-interstitials.

In cross-section TEM samples additional interfaces are introduced perpendicular to the image plane and thus parallel to the incident electron beam. The influence of this additional sink for intrinsic point defects will superimpose to that of the two surfaces of the thinned specimen. In the present paper an new first order model is presented to explain the influence of such surfaces and interfaces, and of strain fields on the intrinsic point defect distributions which are observed in conventional plan view specimens. The developed theoretical framework allows to under- stand both the preferential nucleation of {ll3}-defects near the surfaces of plan view (and cross-section) speci- mens and the impact of additional interfaces in cross- section specimens. Further more some important material parameters can be estimated from the {ll3}-defect distri- bution in irradiated cross-section specimens.

3.I Rate Equations

Neglecting the equilibrium concentrations of intrinsic point defects, which indeed are orders of magnitude smaller than the concentrations which are generated by the high-flux electron irradiation, the well-known rate equations for bulk material, as described e.g. in [7], can be extended to include also a "depth" ( = z) dependent concen- tration of self-interstitial C~ and of vacancies Cv, giving

~Cl;v/Ot = G + Di;vO2Ci;v/t~z 2 - kl;vx;yCx;yCl; v

- klvC, C v , (1)

with z _> 0. G is the generation rate of intrinsic point defects which

can contribute to the formation of {ll3}-defects./91 and D v are the diffusion constants of self-interstitials and va- cancies, respectively, k~x , k v v and k~v are the reaction constants for the quasi-chemical reaction between a self- interstitial and a sink X (concentration Cx), a vacancy and a sink Y (concentration Cv) and between a self-interstitial and a vacancy, respectively. The presence of TEM speci- men-surface sinks (both at the upper and lower surface of the cross-section TEM specimen) is implicitly taken into account in the constants klx and kvv.

The boundary conditions are given by

D1;vt3Cl;v/t~2 -- kl;vsCl;vsCi; v = 0 for z = 0, (2)

dCl;v/dZ = 0 for z = oo . (3)

Cls and Cvs are the densities of interface sinks for self- interstitials and vacancies, respectively. The first boundary condition expresses that intrinsic point defects are lost at the surface/interface with surface recombination velocity k~.vs C~.vs, while the second one expresses that far from the stlrfacd/interface the intrinsic point defect concentration is constant. The rate equations (1) can be used to describe the influence of:

(i) specimen surfaces in a conventional (plan-view) speci- men without a distribution of additional sinks in the specimen plane and possibly covered with an inten- tionally grown silicon-oxide layer as in the experi- ments of Aseev et al. [1, 3, 4];

(ii) or, as in the present paper, of additional sinks distrib- uted in a plane perpendicular to the electron beam as is the case for cross-section specimens. In that case (1) describes the local concentration variation of intrinsic point defects (and thus also { 113}-defects) with respect to the background concentration expected for a plan- view specimen and also observed in the cross-section specimen in areas far away from the additional inter- faces.

Hereby it is assumed that the interaction between two defects X and Y can be described as a quasi-chemical reaction, i.e.

X + Y kxy , X Y , (4)

with the reaction coefficient kxv given by

kxv = 4n(Dx + D v ) r ~ v e x p ( - E b v / k T ) = Kxv(D x + Dy). (5)

/'~(y is the capture radius for the defect reaction. D x and D v are the diffusivities of defects X and Y and Exbv is the energy barrier for the reaction.

3.2 Steady-State Rate Equations

Assuming quasi steady state, one can write

Df2G/Oz 2 - klxCxC 1 - klvCiC v + G = 0,

Dvt32Cv/OZ 2 - kvyCyC v - klvC1C v + G = 0. (6)

These equations can still not be solved analytically but by making further simplifications, one can obtain analytical solutions which give some insight in the dominant param- eters determining the intrinsic point-defect distribution.

3.2.1 Steady State Without Bulk Sinks. Considering only recombination of self-interstitials with vacancies in the bulk and annihilation at the surface, one can write (6) as [8]

DIO2G/Oz 2 - k l v G C v + G = O,

Ov~2Cv/~Z 2 -- k~vqCv + G = 0 . (7)

In that case one must have

DlO2Ci/Oz 2 -- Dv~2Cv/OZ 2 = O, (8)

or with the present boundary conditions (2) and (3)

CV = Ol /OvECl + (oi/O'v - - 1)C°], (9)

524

with C °, the self-interstitial concentration for z = 0 and al = tqsC~s and av = ~cvsCvs, the reaction constants for the annihilation of intrinsic point defects at the surface sinks.

If, e.g. D~ > Dr, (9) shows that an excess of self-intersti- tials can coexist with an even larger concentration of va- cancies. Following a reasoning similar to the one of Hu [8], (7) can be solved using the elliptic functions of Jacobi. This exact solution, of which a discussion falls outside the scope of the present paper, is, however, not transparent and does not give a better insight in the dominant parame- ters influencing the intrinsic point-defect distribution. As discussed by Lain et al. [9], however, the solution for a semi-infinite substrate differs little from an exponential outdiffusion profile. It is clear, however, from (9), that considering only recombination and interaction with sur- face sinks cannot explain the build-up of a self-interstitial supersaturation close to the surface. The main reason is that in the bulk the sink for self-interstitials and for vacan- cies is identical. In the next paragraph recombination is neglected and different "bulk" sinks are assumed for both types of intrinsic point defects.

3.2.2 Steady State Neglecting Recombination. Neglecting the recombination of vacancies and self-interstitials and assuming an independent bulk sink for vacancies and for self-interstitials, the populations of self-interstitials and vacancies can be treated independently and

DIc~zc I /Oz 2 - k l x C x C 1 + G = 0,

D v ~ Z C v / ~ Z 2 - - k v y C y C v -k- G = 0 . (10)

Applying boundary conditions (2) and (3), one can calcu- late in a straightforward way

C1 = G/~fiDx[1 -- ar/(al + tq°'5)exp(--tq°'Sz)],

Cv = G/~cvDv[1 - av/(av + Xv°5)exp(-Xv°Sz)] , (11)

with

~, = ~ , x C x , ~v = K v ~ C ~ .

Considering A C = CI - Cv will tell us something about the depth dependence of the relative concentration of self- interstitials compared to the one of vacancies.

The extremum of AC is obtained at a depth Zm, deter- mined by

[d(C| -- Cv)/Mz'] . . . . ~ - 0, (12)

leading to

Z m = ( K i 0 ' 5 - - / ~ v O ' 5 ) - 1

× ln{0Cv °.5 + Wv/av)Dv/[(Ki °'s + ~q/a0Dl-]}. (13)

If tc I > •v and also Deq °'5 > DvKv °'s, the extremum is a maximum and in order to have a positive z m value, one must have a~ > av or in other words, the surface/interface must be a stronger sink for self-interstitials than for vacancies.

Equation (13) suggests that the z-position of the {113}- defect-rich layer in a cross-section specimen and thus also the distance from the specimen surface in the case of a plan-view specimen, depends strongly on the density of bulk sinks. The latter case was studied in detail by Aseev

J. Vanhellemont, A. Romano-Rodriguez

et al., [1, 4] who irradiated specimens with different dopant concentrations revealing a strong variation of the critical thickness of the specimen and of the distance of the defect- rich layer from the specimen surface, on the dopant con- centration and type (= the bulk sink density). Experimen- tal results of irradiation of cross-section specimens with different dopant concentrations were published elsewhere by the authors [5, 6J and a detailed interpretation of the results within the frame of the present theoretical model will be presented in a subsequent paper [10].

3.3 lnfluence o f Strain and lmage Forces on Intrinsic Point-Defect Diffusion

In the next paragraphs attention is given to the driving force for diffusion of intrinsic point defects to stressed and unstressed surfaces and to the influence of mechanical stress on their diffusion coefficients.

3.3.1 Chemical Potential: Driving Force for Diffusion. The chemical potential Pl.V of an intrinsic point defect close to a stressed surface carl be written as

/h,v = Gf + k T l n C~; v + p b ~ v , (14)

with Gf the Gibbs energy far from the surface, p the hydro- static pressure and 6V~. v the volume change taking into account relaxation around the point defect and image forces due to the close presence of an interface. When the local concentration of intrinsic point defects C°v is in equilibrium with the strained surface, the chemical poten- tial is zero and one has

C~°v = exp[(--Gf + pfVl ;v ) /kT] . (15)

The surface will generate or annihilate vacancies and/or self-interstitials in an attempt to maintain its chemical potential at the equilibrium value. This difference in chem- ical potential is the driving force for the vacancy and self-interstitial movement towards the free surface or the interface.

3.3.2 Activation Volume for Self-Diffusion. The observed influence of the type of layer covering the silicon surface on the {113}-defect density and depth profile, can be ex- plained by two mechanisms. Firstly the so-called surface sink for intrinsic point defects is changed by changing the covering film structure. It is, e.g. well-known that a silicon oxide layer is a sink for self-interstitials which are con- sumed for the reaction SiO2 + Si ~ 2SiO [11]. The second mechanism is the influence of mechanical stress on the diffusion coefficients D~.v of the intrinsic point defects and can be estimated fronl the so called activation volume A V1;v for self-diffusion [12-]

A Vll;v = -- k T [3 (In DI;V)/3p-]T. (16)

The hydrostatic pressure p is given by

p = -- 1/3 tr(X), (17)

with tr(Z) the trace of the stress tensor Z. The activation volume consists of a formation and a

migration component [12]

Irradiation-Induced Point-Defect Distributions in Silicon 525

AV~;v = 3Vjfv, + AV~.% , , with

" f A I / te l and A vi.fv = - , -t- ~¢~ -t- JEsh r l . V ,

fEsh = 3(1 -- V)/(1 + V). (18)

(2 is the atomic volume and r¢~ A V~.v the volume change due to the lattice relaxation around 'the point defect.f~h is the Eshelby term which corrects for the image forces which are due to the close presence of an interface or surface. Taking for silicon the Poisson ratio v = 0.262, one obtains fEsh 1.75.

In face centred cubic (fcc) materials A Vi!v is about 0.7 (2 for vacancies and very small (~ 0) for self-interstitials [12]. The migration component A V~.% is much less well-defined and is estimated to be positive and smaller than 0.2 f2. This suggests that in silicon, stress and image force fields will mainly influence the diffusion of vacancies and less that of self-interstitials. The influence of stress on the diffusion constant of vacancies and self-interstitials can thus be expressed in the first-order approximation as

Dv; ~ = D°;, exp [ - pA Vv; , / kT] , (19)

with D°a the diffusion coefficient in unstressed silicon and far aw@ from surfaces and interfaces.

3.4 Stresses and Hydrostat ic Pressure at Thin-Film Edges

The interface stress and thus also p are proportional to the deposited film thickness h and the film stress zf, which can be taken into account by considering the force f per unit length of the film edge, with f = zf h. For the nitride/pad oxide mask and the field oxide, f can be estimated as follows.

For the field oxide: Zsio2 '~ - 0 . 2 GPa [13] and f = "~Sio2hfield ~, - - 1 0 0 Nm -1.

For the nitride/pad oxide mask: ZSi3N 4 ~ 0.8 GPa [13],

f = Z'Si3NahSi3N4 + ~7SiO2 hpa d ,~ 1 0 0 Nm -1. Close to the bird's beak tip the silicon is highly stressed.

Assuming planar stress, which for a cross-section TEM sample is a good approximation as both surfaces are al- lowed to relax, one can write in a first-order approxima- tion [13-15]

"r: x = Tx 2 , "c z = Tz 2 , "Cz~ = Tzx with

T = - 2 f x / [ n ( x 2 + z2)2] . (20)

The elastic interaction energy Ein t of a point defect with a strain field is given by

Ei, , = A Vp = - A V1/3 t r (~ ) . (21)

From the elastic interaction energy one can calculate the force F exerted by the strain field on the point defect

F = OEint/C3x % + c3Eint/Oz ez . (22)

Taking into account (20), the hydrostatic pressure for the LOCOS structure is given by

p = - 1/3 T(x 2 + z 2) --- 2 fx / [3g(x 2 + z2)]. (23)

In Fig. 4, superimposed on the TEM image, a simulation is shown of three normalised hydrostatic pressure con- tours (p / f = 0.1, 0.4 and 0.7 x 10 6 m -1, respectively) near the tip of the bird's beak. The observed perimeter of the

Fig. 4. Enlarged view of the tip of the bird's beak after 5 min irradiation illustrating the impact of the film-edge stress field on the {113}-defect distribution. Superimposed is a simulation of three contours of constant normalised hydrostatic pressure with p/f = 0.1, 0.4 and 0.7 x 106m -t, from bottom to top

{ll3}-defect distribution lies close to the p/f = 0.4 x l06 m -1 contour.

A combination of TEM and micro-Raman spectros- copy analyses, showed that f is of the order of 500 N/m at the edge of the bird's beak [14, 16].

3.5 Impact o f Stresses and Surface Sinks on the {113}-Defect Distribution

In the presence of mechanical stress and taking into ac- count (19) and (23), (13) can be rewritten as

Zmg (~qO.5 __ XvO.5)-I [ln{(KvO.S + ~Cv/av)DO/

x [(~qo.5 + lq/6ODi] } _ pA Vv / ( kT ) ] . (24)

For the planar stress field of (20) one can thus write

z m = A + B f , (25)

with

B ~ - 2 f x A Vv / [3kTn(x 2 + z2)(•l °s - Xv°'5)] .

3.6 Some Quantitative Estimations

In the following paragraphs some of the important mate- rial parameters are estimated from the experimental obser- vation. First it is shown that from the position of the { 113}-defect-rich layer one can estimate the order of mag- nitude of x I and ~:v, and that the dependence on stress, as predicted by (25), is in good agreement with the observa- tion. Next the problem of the estimation of the generation rate G of intrinsic point defects is addressed. Finally some simulations are performed of the expected AC/G distri- bution by varying some of the most important model parameters.

3.6.1 Concentration o f Bulk Sinks and Impact o f Stress. As illustrated in Fig.3, z 1 and z2 as defined in the inset, are linearly dependent on f , which supports the validity of (25). From Zm ( f = 0) ~ 70 rim, one can estimate xr (and Xv) to be of the order of magnitude of 10 t° c m -2. Assuming

526

r, ~ 0.1 nm one can calculate a density of substrate sinks Cx (and Cv) of the order of magnitude of 1017 cm -3, which corresponds well with the typical interstitial oxygen con- centration in Czochralski-grown (CZ) silicon. Assuming 3 V v ~ 0.812si, an effective p/f..~ 0.4 x 106 m -1 (Fig. 4) and, e.g. Xv = 1.3 × 101° cm -2, x I = 4 × 101° cm -2, (24) and (25) predict a slope B ~ - 1 0 - 1 ° N - l m 2, in good agree- ment with the slope of -0 .82 × 10-1°N-1m2 obtained from a linear regression through the experimental Zl data points in Fig. 3.

3.6.2 Generation Rate o f Intrinsic Point Defects. It is not straightforward to estimate the generation rate G of intrin- sic point defects during high-flux irradiation in a HVEM. In general one writes

G = z a J . (26)

z (~1) is the number of Frenkel pairs created by one incident electron, a is the cross-section for the displace- ment of an atom by an elastic collision with an electron. For silicon, a = 67 barn for 1-MeV electrons and assum- ing a displacement threshold energy of 15 eV [4].

Substitution of these values in (26) leads to a generation rate G of the order of 1019 cm-3s -1. This value is orders of magnitude higher than what can be deduced from the lattice-defect densities and sizes observed during irradia- tion experiments [4, 17]. This led to the assumption that for silicon and germanium one has to define a generation rate which is corrected for the so called genetic recombina- tion. Detailed calculations show indeed that the large ma- jority of Frenkel pairs which are generated by the incident electrons recombines immediately and that only a very small fraction in which both point defects are separated far enough from each other, survives the mutual elastic and electrostatic attraction [17]. The dominant intrinsic point- defect reaction during electron irradiation is thus immedi- ate annihilation. It is assumed that only the very small minority of isolated vacancies and self-interstitials which survive will behave according to the rate equations de- scribed in (24). Under this assumption (26) becomes

G ~ K a z a J . (27)

K a is the probability that a Frenkel pair is separated far enough. According to [4], Ka ~ 10-3-10 -4, leading to a G value of the order of 1015 cm-3s-< G does not occur in (24) and will thus have no influence on the position of the { 113 }-defect-rich layer. It will, however, play an important role together with the diffusion constants in the value of 3 C obtained from (10) and (11). More detailed experimen- tal studies of {113}-defect nucleation and growth at differ- ent temperatures and for substrates with different sink densities might allow to estimate more accurately the athermal diffusion constants of intrinsic point defects and G although one can wonder if the present theoretical framework is detailed enough to extract reliable quantita- tive data.

e q

i

J. Vanhellemont, A. Romano-Rodriguez

a

-5.0

-5.5

-6.0

i] /

0 1 2 3 4

z (xlO 2 nm)

- - 2 . 0 E 4

- - - - 2 . 5 E 4

. . . . 3 . 0 F A

- - - - - 3 . 5 E 4

- - - 4 . 0 E 4

- - 4 . 5 E 4

r ~ .=

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rS

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-0 .8

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- - - - 9 1 ~ - 1 4

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- - 5 E - 1 4

i . . . . i . . . . I . , , • I . . . . I . . . . I

0 1 2 3 4

z (xlO2nm)

Fig. 5. a Simulation of (C, - Cv)/G as a function of z with a v as variable parameter, b Simulation of(Ci - Cv)/G as a function of z with D v as variable parameter and av = 3.2 × 104 cm -t. In both cases an increase of the self-interstitial concentration with respect to the vacancy concentration is observed close to the interface at z = 0

3.6.3 Simulation o f the AC/G Distribution. In Fig. 5 some simulations are shown of AC/G = (C, -- Cv)/G, as a func- tion of z for different values of D v and ~r v. One of the main problems to derive quantitative data from the application of (24) on experimental observations is that both D, and

Dv are not well known and values in literature differ by many orders of magnitude. Further more under irradia- tion conditions diffusion occurs through an athermal pro- cess leading to much larger diffusion constants especially

Irradiation-Induced Point-Defect Distributions in Silicon

at low temperatures. Fortunately, due to the assumption of steady state, for the application of (24) only the ratio of diffusion constants is important.

The fixed parameters used for the calculations are: D~ = 10 -13 cm2s -1, K v = 1.3 x 1010 cm -2, K l = 4 x 101° cm -2 and cr I = 8 x 105 cm -1. The value for the diffusion con- stant is a shot in the dark and is many orders of magnitude larger than the value obtained by extrapolating the "nor- mal" thermally activated diffusion coefficient, e.g. reported in [ 18], to the temperatures used in the present experiment. The value is however orders of magnitude smaller than the one which was used by other authors to model irradiation experiments at room temperature, e.g. in [191. Neverthe- less, as explained before, for the position of the {113}- defect concentration maximum only the ratio of the two diffusion coefficients is important. Figure 5a shows the result for D l = Dv and varying av. The figure suggests that the {113}-defect-rich layer becomes broader and shifts towards the interface and that the density of {113}-defects increases with increasing crv. In Fig. 5b a simulation is shown for different Dv values, with av = 3.2 x 104 cm -1. The simulations shows that the peak concentration of self- interstitials with respect to vacancies, or in other words, the {ll3}-defect-rich layer, shifts towards the interface with decreasing D v, while the defect density increases, cr v is not expected to vary with the strain in the same straight- forward way as described by (15) for D v but to depend rather on the composition and thickness of the covering layer. The present experimental observations can thus be understood both by a difference in behaviour as sink for intrinsic point defects for oxide and nitride layers and by the influence of strain on Dv which is certainly the domi- nant mechanism near the bird's beak tip.

4 Conclusions

It was demonstrated that assuming steady state and neglecting bulk recombination of vacancies with self- interstitials, the solution of the rate equations allows to understand the build-up of a local supersaturation of self- interstitials close to surfaces or interfaces. Due to a dif- ferent density of sinks in the bulk of the wafer for self- interstitials and vacancies, respectively, and due to the presence of strong surface and/or interface sinks, which also have different strengths for both types of intrinsic point defects, a local maximum of self-interstitial concen- tration can build up in the near-surface and/or interface region.

Contrary to a previous model to describe in-situ { 113}- defect generation during high-flux electron irradiation in a high-voltage TEM, the conclusion of the present analysis is that the observations can only be understood if the strength of the SiO 2/Si interface as sink for self-interstitials is larger than for vacancies. After prolonged irradiation, this leads to a build-up of a self-interstitial concentration maximum and thus to a preferential nucleation of { 113}- defects, near the surface or interface.

The position and the extent of the {ll3}-defect-rich layer is determined mainly by the concentration of sinks in

527

the bulk, by the ratio of the diffusion constants of self- interstitials and vacancies and by the relative strength of the surface and/or interface sinks. From the extrapolated position of the { 113}-defect band in stress-free silicon, one can estimate a bulk sink density for self-interstitials and vacancies of the order of 1017 cm -3 in moderately doped (< 1017 cm-3) CZ silicon. Further more, the experimental observations can only be explained in the frame of the presented theory if one assumes that under high flux elec- tron irradiation, the diffusion constants of self-interstitials and vacancies and the strength of the sinks for both point defects are not too different and within the same order of magnitude. Hereby it is the diffusion coefficient of vacan- cies which is mainly influenced by variation of mechanical stress and decreases with increasing compressive stress. The observations are in good agreement with an activation volume for vacancy diffusion of about 0.8 f2si as predicted for fcc materials.

The results show that using {113}-defects as a probe, in-situ irradiation of plan-view and cross-section speci- mens of integrated circuits with high fluxes of MeV elec- trons at different temperatures, is a useful tool to study the presence of localised sinks for intrinsic point defects such as interfaces and stressed or highly doped areas.

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