a model for the formation of subboundaries in recrystallized si on sio2

Volume 7, number 1.2 MATERlALS LETTERS August 1988

A MODEL FOR THE FORMATION OF SUBBOUNDARIES IN RECRYSTALLIZED Si ON SiOl

Avid KAMGAR AT&T Bell Laboratories, Murray Hill, NJ 07974, USA

Received 15 June 1988

A new model for the formation of subboundaries is developed based on two fundamental physical properties of a thin Si film solidifying between two fairly rigid layers of SiOz. These are ( 1) the large difference between thermal conductivities of Si and SiOz, and (2) the expansion of Si upon solidification. The temperature calculations suggest that the solidification proceeds in the middle of the Si film in flap shaped structures: “flappers”, and the volume expansion accompanying freezing is accomm~ated by local twisting of the flappers. In addition to offering a mechanism for the nucleation of subbounda~es, this model provides qualitative explanations for the many essential and diverse characteristics of the recrystallized Si films.

Thin single crystal silicon layers on silicon dioxide (SOI), due to their potential advantages for inte- grated circuit technology, have become the subject of numerous studies. These films are typically 0.5 pm thick, and are deposited on l-2 pm of thermally grown oxide. A variety of techniques utilizing different heat sources have been used to melt and re- grow these films. The crucial factor in preventing agglomeration of the thin Si film during melting is the use of a SiOZ capping layer which is typically 2 pm thick. Under suitable growth conditions large area single crystal Si films are readily obtained, however, the thin recrystallized films invariably contain ex- tended networks of subboundaries.

In the past few years a remarkable wealth of experimental data and defect analysis, along with the models proposed to explain the results, have led to considerable progress in understanding the many factors involved in the fo~ation of subbounda~ patterns. Among the more widely publicized models are the “faceted” growth at the solid/liquid interface due to a preferred growth in the [ 1111 direction proposed by Geis et al. [ 11. This model was further ex- amined by Pfeiffer et al. [ 21 who simulated the flow pattern of the subbounda~es by computer modeling the motion of the faceted growth front, and more recently by Landman et al. [ 3 ] who made molecular- dynamics simulations of the equilibrium structure of

the solid/liquid interface. Another model is the “cellular” growth due to rejection of impu~ties by the solidifying film proposed by Leamy et al. [4]. This model was expanded upon by Haond et al. [ 5 ] who performed extensive transmission electron micros- copy (TEM) of the subboundaries, also by Lemons et al. [ 61, who videotaped the growth front, and by Lee [7] who took into account constitutional and pure supercooling to explain the morphological vari- ations in the subboundary pattern,

On the other hand, based on TEM studies of dislocations at the subboundaries, several groups suggested that stress was the cause for subbounda~ formation. Pinizzotto [ 8 ] proposed that droplets of Si when trapped in the solid generate dislocations upon solidification and expansion. Komem and Weinberg [ 9 ] suggested that compressive stress accompanying the growth of encapsulated Si films leads to plastic deformation which is accommodated by dislocation glide, resulting in the formation of subboundaries. Similarly, Baumgart and Phillipp [ lo] suggested that periodic internal stress in the Si film is responsible for the subboundary formation by causing plastic deformation and subsequent poly- gonization. Recently, Gibson et al. [ 111 proposed that thermal stress associated with the temperature gradient in the plane of the Si film causes buckling of the film, hence forms subboundaries. These and

0167-577x/88/$ 03.50 0 Elsevier Science Publishers B.V. ( gosh-Holland Physics Publishing Division )

35

Volume 7, number I ,2 MATERIALS LETTERS August 1988

numerous other studies have helped to understand many characteristics of these defects, However, the question of the nucleation of the snbbounda~es has not yet satisfactorily been answered.

In this Letter we propose a new model which not only deals with this question, but accounts for many basic and diverse features of the recrystallized Si film in a unified manner. We have calculated the temperature profile of the encapsulated Si layer in the direction pe~endicular to the interface during the cool-down cycle. The differential cooling of Si and SD:! gives rise to a minimum in temperature in the middle (thickness) of the Si layer, suggesting that the solidilication of the Si film proceeds in the middle of the layer, and regions near the SiOZ boundaries freeze last. Based on this result, and the fact that Si expands beyond its molten volume by 7 to 10% upon solidification, we have developed a model for the formation of subboundaries

In any zone-melt crystallization the temperature gradient in the scan direction plays a crucial role in the regrowth process. In an encapsulated thin Si film the temperature profile in the vertical direction, as we will show here, plays an equally important role in determining the growth dynamics. The thermal conductivity of SiOZ is about 0.02 W/cm K while that of liquid and solid Si is 0.67 and 0.23 W/cm K, re- spectively, hence the cooling experienced along the Si film is much more rapid than through SiOZ. As a consequence, as the heat source scans past a given zone, a temperature gradient is established in the Si layer, leaving the area near the SiOZ boundaries at a higher temperature. We have obtained the temperature profile of the three-layer structure, sketched in fig. la, during the cool-down cycle, by assuming that the heat source has been turned off, and the system dispenses of its heat via two fairly independent mechanisms, ( 1) irradiating energy from the SiO* surface, and (2) conductive cooling through contact with the colder, already solidified sections of the Si layer.

We have assumed that the Si film is uniform in the plane and calculate the heat equation in two dimensions. To simplify the problem we have further assumed a symmetrical system, as shown in fig. la, In reality the bottom layer cools down by heat conduo tion through the Si wafer, also the two ends need not be at the same temperature.

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(a) ;:

(b)

I 0

x0 x

lc00pm

iO_JZ

MSTANCE ipf

Fig. 1. (a f The three-layer structure for which the temperature profile was calculated. The temperature profile (b) perpendicular to the interface, obtained at the center of the structure, and (c) within the Si film, shown for four different ti’tm thicknesses.

We have used a powerful and elegant computer program developed by Kaufman and Schryer [ 121 for solving partial differential equations for two space variables, i.e.

aT/&=V*(tc*VT),

where IC is the thermal conductivity which is piece- wise constant (Ksi in the Si film and ~~~~~ in the Si02 layers).

This program utilizes the Galerkin method of cubic splines. The advantage of this method is that it automatically forces the normal component of ~cVT to be continuous at the interfaces, while other schemes such as finite differences, least squares, col- location, etc., make T smooth across interlace which can result in wrong answers. In addition, cubic or higher-order splines are more efficient than lower- order schemes.

Volume 7, number 1,2 MATERIALS LETTERS August 1988

The initial condition is that the system is at a uniform temperature Ti> T,,,,. The boundary conditions are: at z=O and z=z, the normal derivative dT/dn=aeT4, and at x=0 and x=x0 the temperature is brought to a constant value T, -e T,,,,,, in a time short compared with thermal relaxation of the system. This is to simulate an actual system in which the molten zone is in contact with colder, already solidified epi. The reason that the temperature is not

assumed to be T, as an initial condition is to avoid singularities in the computation.

An example of the calculated temperature profile is shown in fig. lb. Due to the two competing cooling mechanisms a maximum in temperature is reached

within the SiO, layer. The temperature in the Si layer seems fairly constant in fig. lb, however plotted on a finer scale in fig. 1 c we observe a minimum in temperature at the center of the layer.

The calculations were repeated for a more realistic system, shown in fig. 2a, by taking into account the heat conduction through the Si wafer on one side

[ 13 1. Due to this cooling the isolation oxide is in

general at a lower temperature than the capping oxide. However, similar to the symmetric case of fig. 1, there are two temperature maxima in the two SiOZ layers as demonstrated in fig. 2b, and the minimum in the temperature in the Si film is somewhat skewed towards the isolation oxide.

This minimum in temperature, however small, in-

dicates that the heat removal necessary for the solidification process takes place more efficiently in the center of the Si film as compared with its boundaries

with the capping and the buried SiO, layers. We,

therefore, propose that the solidification front resembles the sketch of fig. 3a rather than the current assumption of a nearly vertical front shown in fig. 3b.

It has been demonstrated experimentally by a number of groups [ 1,3,4,6] that the top view of the solid/liquid front has a faceted or cellular structure. In our model the uneven growth front proceeds in the form of flap-like structures rather than rigid fac-

ets or streamers. These structures are wide and thin,

Si WAFER (a)

(b)

- 5 DISTANCE (pm)

Fig. 2. (a) The four-layer structure including the Si substrate,

and (b) the temperature profile in the top three layers.

(4 (W

4 / s!- SOLIDIFIED SEGMENTS

TRANSITION “FLAPPERS”

REGION

(cl

Fig. 3. Solidification front within the thickness of the Si film in

the flapper model (a) and the current assumption (b). A sketch

of the growth front in three dimensions illustrating the “flap-

pers” (c). The arrows indicate the direction of tilt.

31


.i; I

’ 021,

Fig. 4. Evolution of recrystallized film structure normal to the growth front. (a) Cross-sectional view of the flappers in early recrystallized phase, (b) twisting of the solidified segments to accommodate the volume expansion, as regrowth progresses, (c) finally, solidified film demonstrating the tilt in the planes of subgrains, and the resulting subboundaries.

and are attached at one end to the already solidified region, while at the other end they hang fairly loosely in the molten Si medium. We have sketched these structures, referred to as “flappers” hereafter, in their idealized form in fig. 3c.

Viewing the solid/liquid front in a cross section perpendicular to the growth front we observe elongated solid segments in molten Si medium as shown in fig. 4a. Each of the elongated segments expands while freezing beyond their molten dimensions. Upon encountering adjacent solidified regions, they accommodate the volume increase by tilting in alter- nate fashion in the molten Si medium (fig. 4b). While the various segments continue to grow in their original plane towards the Si02 boundaries, the mismatch between the crystallographic planes of the neighboring segments gives rise to the subboundary formation (fig. 4~).

This model for subboundary formation can qual- itatively explain many, if not all of the experimentally observed characteristics of the recrystallized films. Here we will limit ourselves to discussing three prominent features.

(1) Particles near the SO, boundaries. Cross-sectional TEM studies of the recrystallized Si films have revealed the existence of small particles in the Si film near the Si02 boundaries. The observation of these

particles in Si films, recrystallized by using inco- herent radiation, was reported by Kamgar et al. [ 14 1. Later, Pfeiffer et al. [ 15 ] reported similar observation in their films which were regrown using a graph- ite strip-heater, and referred to them as KRK defects. Both studies showed that these particles were single crystals 50-200 A in diameter, and were likely to be SiOZ or Sic particles dissolved in Si. These partic- ulates, which were found in abundance, were ini- tially suspected to be responsible for the nucleation of the subboundaries, however, no spatial correla- tion was found between them. We now believe that the existence of these particles near the SiOZ boundaries serves as convincing evidence for the fact that the regions near these boundaries are regions which freeze last, and the particles rejected by the solidifying film are simply deposited there.

(2) Dislocation formation. The flapper model pre- sented above predicts that the subboundaries are formed between the subgrains due to the mismatch between the crystallographic orientation of their planes. This is in agreement with the experimental analysis of the subboundaries which demonstrates that they are indeed low-angle grain boundaries. The main observation is that these dislocations do not follow any particular crystallographic orientation. Their general direction is along the scan direction, indicating that they are not generated in a solid.

Our model also predicts that the strong bending force at the initiation site which is due to the local twisting of the flappers, introduces dislocations in the already solidified Si film. Defects at the initiation sites are seen in TEM micrographs obtained by Pinizzotto [ 8 1, and Komem and Weinberg [ 9 1. We have done a detailed analysis of these dislocations [ 16 1, and have demonstrated that they emanate from the initiation site toward the direction opposite to the scan. We have also shown that they are directed along ( 110) crystallographic direction, and that they are induced by slip in the ( 111) planes. These ob- servations clearly demonstrate that, unlike the subboundaries, such dislocations are generated in the already solidified Si film, and that they are caused by the strain in the solid due to the bending force at the initiation sites as indicated by arrows in fig. 3c.

In addition, our model correctly predicts that regions between the subboundaries are defect free,

38


while models based on stress such as plastic deformation or film buckling are bound to leave isolated defects in subgrain regions.

(3) Angular misorientation of the subgrain regions. The tilt angle between the adjacent subgrains is a natural consequence of the folding behavior de- scribed by our model, as fig. 3b demonstrates. This folding pattern has been observed by several groups [ 11,16,17]. In our study [ 161 we used microdif- fraction technique to determine the crystallographic orientation of the small (down to 10 nm in diameter) regions between subboundaries. We found that the tilt angle of the neighboring subgrains in the direction perpendicular to growth varied in alternating fashion, indicating a folding pattern between them, similar to the pattern shown in fig. 4b. The mis- alignment parallel to the direction of growth, on the other hand, was very small, but mixing was observed near the apex of the wish-bone structures where two subboundaries came together.

It also naturally follows that when the flappers are narrower, geometrically they have the freedom to tilt by larger angles compared with wider flappers as demonstrated in fig. 4c. This is in agreement with the observation reported by Gibson et al. [ 1 I].

Another experimental fact to recall is that the surface of the recrystallized films is perfectly smooth. Our model, which predicts that the crystallization begins in the middle of the Si layer, proceeds in mis- oriented planes towards SiOZ boundaries and ter- minates at the Si surface, leads to a smooth surface. In contrast, models based on plastic deformation [9,10], or film buckling [ 111 would predict the surface of the Si layer to have the imprint of the angular misorientation.

The principal conclusion drawn from our model for the subboundary formation is that the temperature profile perpendicular to the plane of Si layer plays a crucial role in determining the growth dynamics of the Si film. The particular temperature profile calculated here indicates that the solidifica-

tion front, rather than being a vertical wall within the thickness of the Si film, resembles thin and wide flappers. The shape and the rigidity of these flappers depend strongly on the melt-regrowth conditions, as well as the structure of the encapsulated films. Hence, suggesting that optimizing either of these two param- eters would help reduce or eliminate the subboundaries.

It is my pleasure to thank J.G. Ruth and S. Nakahara for many challenging discussions. I am in- debted to N.L. Schryer for his enthusiastic help with the temperature profile calculations.

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a model for the formation of subboundaries in recrystallized si on sio2

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