QUANTITATIVE EVALUATION OF THE EBIC CONTRAST OF DlSLOCATIONS

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QUANTITATIVE EVALUATION OF THE EBIC CONTRAST OF DlSLOCATIONS

C. Donolato

To cite this version:

C. Donolato. QUANTITATIVE EVALUATION OF THE EBIC CONTRAST OF DlSLOCATIONS.

Journal de Physique Colloques, 1983, 44 (C4), pp.C4-269-C4-275. �10.1051/jphyscol:1983432�. �jpa-

00223051�

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QUANTITATIVE EVALUATION OF THE EBIC CONTRAST OF DISLOCATIONS

C. Donolato

C.N.R. - Istituto LAMEL, V. Castagnoli 1, 40126 Bologna, Italy

Résumé. - Cette communication examine l'évaluation quantitative des images des dislocations dans les semiconducteurs, qui sont obtenues par la micro- scopie électronique à balayage en mode induit (ou EBIC) et les modèles analytiques associés. On montre qu' une théorie du premier ordre décrit d'une manière adéquate les propriétés géométriques des images EBIC, tandis que les corrections d'ordre plus élevé peuvent améliorer l'évaluation quantitative du contraste. Des résultats récents de la littérature illustrent que les données de contraste peuvent être employées pour déterminer la vitesse de recombinaison linéaire d'une dislocation et, avec quelques hypothèses supplémentaires, la densité linéaire des centres de recombinaison.

Abstract. - This paper discusses the quantitative evaluation of the images of dislocations in semiconductors, as obtained by charge collection (or EBIC) scanning electron microscopy, and the related analytical models. It is shown that a first-order theory describes adequately the geometrical properties of EBIC images, while higher order corrections may improve the quantitative evaluation of the contrast. Recent literature results illustrate that contrast data can be used to determine the line recombination velocity of a dislocation and, with some additional assumptions, the line density of recombination centers as well.

INTRODUCTION

The electrical activity of individual crystal defects like dislocations has been extensively investigated by the electron beam induced current (EBIC) mode of the scanning electron microscope. EBIC micrographs allow rapid qualitative assess- ments of the electrical influence of the defects; however, further information can be obtained by evaluating quantitatively the image contrast on the basis of a model for the carrier-defect interaction. Some reviews of charge collection microscopy have appeared in the literature /1-3/. This paper gives an account of the available contrast models and their consequences, and focusses on their use for the assign- ment of a value to the recombination activity of dislocations.

1. THEORY OF THE EBIC CONTRAST

The configurations used more frequently in EBIC studies of dislocations are shown in Fig.l. In (A) charge collection occurs through a Schottky barrier or a shallow p-n junction, in (B) a fairly deep p-n junction is employed.

The structure (A) can be represented schematically by a semi-infinite semiconductor, where the surface acts as a perfect collector of minority carriers (surface recombination velocity v = « ) . In the structure (B) the defect to be imaged usually lies in the n layer; hence the active region in this case is delimited by two planes: the surface, with a finite v , and the junction plane (v = « ) . These schemes give the advantage of leading to a pure diffusion problem for the minority carriers (e.g.

holes) injected by the electron beam. Thus the hole density P aM obeys the equation

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983432

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Fig.1 - Schematic illustration of configurations used in E B I C observations of dis-

-

locations. (A): Schottky barrier and (B): p-n junction charge collection.

where D and T are the hole diffusion coefficient and lifetime, respectively, and g(r) is the generation rate per unit volume due to the electron beam. E q . (1) holds in the defect-free semiconductor and is to be solved under the proper boundary conditions for each structure. Analytical solutions for different generation func- tions are known /4-5/. The collected current I, can be expressed by introducing the carrier collection probability cp of the structure. Since both (A) and ( B ) have translational invariance along x and y, cp will be in both cases a function of z only. For the structure (A)

,

for instance, cp (z)=exp(-Z/L)

,

^{L=(D T)}

'

being the minority carrier diffusion length; for the structure ( B ) the expression is somewhat more complicated / 5 / . Thus we have:

v

where V is the half space z >O for (A) or the layer O<z< h for (B).

Let us now introduce a dislocation in one of the structures of Fig.1. We may de- scribe the enhanced recombination of carriers at the dislocation by representing this defect as a cylindrical region C of radius E where the minority carrier lifetime is TI<< T / 4 / . Thus the hole recombination rate per unit volume inside C will be

where p(g) is the hole distribution in the structure with the dislocation. Since p(r) cannot be calculated easily, we take as a first approximation p(r) 2 p,(~).

Equation ( 2 ) shows that because of the recombinaton R =-(l/~')p~ over C , the current now is

Fig.2

-

Representation of a dislocation as a

-

cylindrical region of reduced minority carrier lifetime.

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=If$/I,

iJ' = 1

Y

[

^jpo^(LE)^(P^(zE)^dl

]

r

where

Eq. (51 shows that the contrast increases with the degree of superposition between the minority carrier cloud p,(r) and the dislocation line T . The factor cp(z )

reflects the stronger effect on the collected current of those part of

r

that lie %n regions where the charge collection probability is large, i.e. near the junction plane. The parameters e and T ' in Eq. (61 are in general poorly known, so it is probably better to consider Y as a phenomenological parameter describing the line recombination velocity of the dislocations. In this respect, y is similar t

9 :ye

recombination velocity of a surface; the different physical dimensions of Y (cm s ;

y/D is dimensionless) are due to the different spatial extension of a line in com- parison to a surface.

2. HIGHER ORDER APPROXIMATIONS

Eq.(5) gives the first order contrast function of the dislocation, since the actual value of p has been replaced by its first order approximation p, ; i.e. the changes introduced in the original hole distribution p, by the presence of the defect have been neglected in the calculation of the recombination rate of Eq. (3).

Higher order approximations have been introduced by Pasemann /6/ and essentially take into account that the defect actually reduces p, in its surroundings. We may still write Eq. (5) with p,

,

but must reduce y to a value Yeff accordingly.

This reduction is larger for larger values of y , since in this case the defect has larger influence upon p, ; for smaller values of y

,

^{we have}YzYefF. However, the defect is less effective in reducing p, when it is close to a boundary with high recombination velocity. This is a consequence of the virtual image of the defect, which must be introduced in order to satisfy the boundary conditions. The image acts as a source which weakens the sink action of the dislocation (Fig.3). The result is an increase of Yeff when the defect approaches an absorbing boundary (v = - ) , the converse being true for a reflecting boundary (v = O ) .

Pasemann /6/ succeeded in treating quantitagively higher order corrections to y for a straight dislocation parallel to the surface. His analytical expression for yeff will be discussed in Sect.5 in connection with some experimental results.

images

1

defect position

Fig.3

-

Influence of a boundary at z=0 with v = m on the minority carrier distribu-

=near a dislocation. The one-dimensionalsdistribution p(z) in this figure has only illustration purposes.

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3. RESOLUTION

Eq. (5) fully describes the EBIC image of a dislocation, so it can be used for estimating the resolution that can be achieved in a given experimental configuration. This is conveniently done by assuming a simple dislocation geometry so that the image can be described by a single line scan and the resolution by the associ- ated width at half maximum w.

Fig.4, for instance, shows the results for a dislocation perpendicular to the surface in the structure ( A ) /7/. The image width of the defect is of the order of the electron range R

,

even for very large values of L, in agreement with experimental findings / 2 / .

his

is a consequence of the three-dimensional nature of the diffusion process: the spatial extension of p,(r) and hence the resolution are of the order of R quite independently of the value of L.

P

Fig.4

-

Calculated half-width w of the

-

EBIC image of a dislocation versus the electron range R in Si for different diffusion lengths

%

/7/. The diagram holds for a dislocation perpendicular to the surface of the structure (A) of Fig.1.

Fig.5 is a scheme of STEM observations of dislocations in a thinned (B) structure.

The very small beam cross section of the STEM does not benefit very much the resolution of the EBIC images obtained by this technique / a / . The reason for this is that now the lateral extension of p, (5) is of the order of the thickness h of the n layer, even for zero beam diameter. The calculation of the image half-width yields

/ 9 /

Pennycook /lo/ has evaluated w for STEM cathodoluminescence (CL) images of dislocations in diamond samples of different thickness t, obtaining a linear relationship wz0.45 t. Similar resolution properties of CL and EBIC images are expected and have been observed in the SEM /ll/. Therefore Eq. (7) should give an estimate of the resolution of STEM-CL images as well, if h is interpreted as the sample thickness.

It is apparent that the value of w of Eq. (7) for v = m is very close to the experimental result.

electron

11

^beam

Fiq.5 - Schematic of STEM-EBIC observa-

-

tions of dislocations.

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When the dislocation configuration does not have high symetry, the corresponding EBIC image cannot be described by a single line scan and the distribution of the contrast over the whole image must be calculated. An effective way of presenting the results in this case is to produce computer simulated images of the defect.

Fig.6a shows a computer simulated EBIC image of an oxidation induced stacking fault in (100) Si /12/; since experiments indicate that the electrical activity is chiefly dqe to the fault boundary, the line defect scheme of Eq. ( 5 ) applies and

r

is given by the nearly semicircular bounding partial dislocation in the (111) plane.

The corresponding experimental image of Fig.6b shows that the model of Sect.1 gives an adequate description of the basic features of the observed contrast distribution.

This result suggests the possibility of using the model for solving the inverse problem, i.e. the specification of the defect activity from its EBIC contrast. For dislocations of known geometry this has been actually done; the related method and some results are discussed in the next section.

Fig.6

-

Computer simulated (a) and experimental (b) EBIC image of an oxidation in-

-

duced stacking fault in (100) Si /12/. The contrast arises from the bounding partial dislocation only. Beam energy E=40 keV.

5. EVALUATION OF THE LINE F33COMBINATION VELOCITY OF A DISLOCATION

The discussion about the geometrical properties of the EBIC image of a dislocation of Sect.3 and 4 was based essentially on the evaluation of the relative values of the function i* of Eq. (5) at different points of the image. However, the absolute values of i* are proportional to Y and can therefore be used to deduce the value of Y from the experimental contrast. The simplest method to do this, as suggested by Kittler and Seifert /13/, is to evaluate the maximum value of the term in square brackets in Eq. (5): this evaluation requires that excitation conditions, material parameters and dislocation geometry should be known. By dividing the maximum observed contrast by that value we obtain the first order estimate of Y

.

Let us consider in greater detail the case of a straight dislocation parallel to the surface, at a depth z,, a frequently investigated configuration. Equation (5) shows that the maximum contrast in this case is

assuming that the dislocation is parallel to the y axis. The term in square brackets in Eq. ( 8 ) , in a given experiment, is a function of z , only. As a consequence, the contrast of different dislocation at the same depth in the structure (A) or (B) is proportional to their recombination efficiency. This property was used by Ourmazd

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and Booker /14/ to relate the relative values of the recombination efficiency of a/2

<loo> edge dislocations in Si to the dissociation degree employing the configuration (B). The same argument was applied to the configuration (A) by Ourmazd et al. /15/, who compared the activity of screw and 60' members of hexagonal dislocation loops in Si, which lay on (111) planes parallel to the surface. In these studies, however, the determination of the absolute value of Y was not pursued.

Such a determination was performed by Pasemann et al. /16/ in Si, using a (B) structure. The values of the depth z, were obtained by high,voltage TEM stereosco- pic observations and used to evaluate the term in square brackets of Eq. (8). Their results are shown in Fig.7 for two sets of 60° dislocations. It is apparent that the two sets can be characterized by two distinct values of Y ; the higher degree of activity, in agreement with previous observations /14/, was attributed to the state of dissociatio/n of the dislocations.

Fig.7

-

Dependence of the line recombina-

-

tion velocity of a dislocation in the structure (B) of Fig.1 on the depth position. The full symbols represent the first order evaluations of Y/D. The open symbols give the values of Y/D after application of the depth correction (after Pasemann et al. /16/).

Fig. 7 also shows that for the high activity set the value of Y indreases as the dislocation approaches the junction plane. This behaviour, as discussed in Sect.2, can be explaned by taking into account the non-linear contribution to the contrast.

In fact, according to Pasemann /6/, the values of Y obtained by evaluating contrast data using Eq.(8) only represent effective recombination strenghts Yeff. The true value of Y is obtained by applying the correction formula

where K O is a modified aessel function and tF(z,) is the depth correction term given by Eq.(7) of Ref.16 (in Ref.16, however, z, denotes the dislocation-junction dis- tance). Figure 7 shows that the values of Y/D after the application of the depth correction are fairly constant and approximately equal to 0.7 and 0.3 for the two sets, respectively.

The full correction (91, however, was not applied by Pasemann et al. /16/, probably because of the difficulty of assigning a value to the radius E of the dislocation. For E / L = 0.1, for instance, Eq. (9) gives Y/D = 1.0 and 0.34, and for

E / L = 0.02 Y/D = 1.33 and 0.37, for each group respectively. Therefore, for large Y

the full correction becomes substantial but appears to be rather uncertain.

6. ESTIMATE OF THE LINE DENSITY OF RECOMBINATION CENTERS.

The line recombination velocity of a dislocation Y = Te2/r' (Eq.6) can be related to the line density of recombination centers using a simple argument

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volume density N and capture cross-section o

,

we have

T I = 1/ ( ~ o v ~ ~ ) (10)

where v is the carrier thermal velocity. By combining E-..- (6) and (lo), and intro-

T -

ducing Eke line density of recombination centers N' = N m we get

y = N'ov (11)

th

Since v is known, the experimental value of Y yields the value of the product N'o.

In addi%on, if some information about the nature of the recombination centers is available and a value to U can thus be assigned, we may estimate N' as well.

Eq.(11) has actually been used by Kittler and Seifert to estimate the sensivity of the EBIC technique. They calculated that the minimum EBIC contrast usually observable ( = 0.5%) corresponds- 2Y/D=0.03. Assuming that rec mbination is due to impurity states with oi= 10 "Ocm they obtained N '

-

^{200 u}^rⁿ^-^'^; i.e. a dislocation must have at least one impurity recombination centmenevery 50 A to be observable by EBIC

.

If the recomb-jyticy is only due to recombination centers at a c l e y d_il;lo- catiq with oc=10 cm

,

the minimum line density becomes N

'

. = 2 10 um =

=2 A

.

Since this value appeared to be too high, they concludegl?hat really clean dislocation are hardly detected in the usual EBIC practice. Experimental observations of a given region containing dislocations before and after a thermal treatment support this conclusion /13,17/.

7. CONCLUSIONS

The EBIC contrast of dislocations can be analyzed quantitatively on the basis of a phenomenological model of contrast formation, which describes the electrical activity of a dislocation by a line recombination velocity y

.

This parameter, unlike the contrast, is independent of the sample structure and the operating conditions employed; therefore results obtained in different experiments can be compared more easily. In addition, the determination of Y should allow more de- tailed correlations between recombination efficiency and crystallographic structure of dislocations.

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