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Stress-driven surface evolution in heteroepitaxial thin films: Anisotropy of the two-dimensional roughening mode Cengiz S. Ozkan Process Development Group, Applied Micro Circuits Corporation, San Diego, California 92121

William D. Nix Materials Science and Engineering Department, Stanford University, Stanford, California 94305

Huajian Gao Mechanical Engineering Department, Stanford University, Stanford, California 94305 (Received 12 November 1998; accepted 17 May 1999)

We have analyzed the anisotropic behavior of surface roughening in Si1−xGex /Si(001) heterostructures by use of methods of elastic analysis of undulated surfaces and perturbation analysis on the basis of global energy variations associated with surface evolution. Both methods have shown that the two-dimensional stage of surface roughening preferentially takes place in the form of ridges aligned along the two orthogonal 〈100〉 type directions. This prediction has been confirmed by ex situ experimental observations of surface evolution by use of atomic force microscopy and transmission electron microscopy in both subcritically and supercritically thick Si1−xGex films grown on Si(001) substrates. Further experiments in supercritically thick films have revealed a remarkable interplay between defect formation and surface evolution: the formation of a network of 〈110〉 misfit dislocations in the latter stages alters the evolution process by rotating the ridge formations toward the 〈110〉 type directions.

I. INTRODUCTION

In the last two decades, much attention has been devoted to the development of novel semiconductor devices based on lattice mismatched heteroepitaxial thin films. The lattice mismatch typically results in a few percent elastic strain within the film, which can be used to tailor the electrical properties of semiconductor devices.1–4 For example, the electronic band gap of the devices can be tailored to have a specific value as a function of the elastic strain in the film, which is a function of the film composition. Applications of strained heteroepitaxial thin film structures (or heterostructures) include the fabrication of various electronic and optoelectronic devices, such as heterojunction bipolar transistors (HBTs),5,6 resonant tunneling diodes (RTDs),7 and vertical cavity surface-emitting lasers (VCSELs).8 The structural stability of heteroepitaxial films is influenced by the elastic mismatch strain in the film, which is the main driving force for the formation of defects, such as dislocations.9–14 Device fabrication requires that the density of the defects be kept to a minimum because otherwise the electrical properties and the performance of the devices will be adversely affected. Extensive efforts have been made to understand the mechanisms of defect formation and propagation in various heteroepitaxial thin film systems such as Si1−xGex/Si,15–18 J. Mater. Res., Vol. 14, No. 8, Aug 1999

In1−x−yGaxAsy/GaAs,19–21 and CdTe/GaAs.22–24 In most cases the heterostructure is capped with a final barrier layer that serves to seal or protect the underlying heterostructure from any defects that may be generated at the surface during subsequent processing steps or from surface roughening during film growth.15 Current advances are driving devices to much smaller dimensions; future devices will be fabricated by use of very thin heterostructures with either very thin or no capping layers. Ozkan et al.25 have investigated the effect of capping layer thickness on the surface roughening behavior of Si1−xGex /Si heterostructures during controlled annealing experiments. Their results indicated that as the thickness of the capping layer decreases, the surface features or islands become progressively larger. This behavior was attributed to nanometer-scale diffusion effects, which cause large stresses to develop in the initially stress-free capping layer. Further issues are related to design considerations that may require the fabrication of heterostructures with higher mismatch strain (larger composition difference). This, in turn, will influence the film deposition process such that the surface of the heteroepitaxial film may exhibit roughening caused by the large lattice mismatch during film deposition. Further efforts are necessary to understand the various processes involved in the nucleation and growth of defects related to surface evo© 1999 Materials Research Society

3247

C.S. Ozkan et al.: Stress-driven surface evolution in heteroepitaxial thin films

lution. The aim of this article is to describe the formation of a network of two-dimensional (2D) islands at the thin film surface and to relate this roughened surface to defect formation within the heteroepitaxial thin film. The stresses in heteroepitaxial films caused by lattice mismatch are very large (in the GPa range) compared with bulk material. The following example can be cited in the case of Si1−xGex heteroepitaxial thin films15: the room temperature lattice constants for Si and Ge are aSi ⳱ 5.431 Å and aGe ⳱ 5.673 Å, and using a simple rule of mixtures, the lattice parameter for a Si1−xGex alloy layer is given by aSi−Ge ⳱ xaGe + (1 − x)aSi, where x is the atomic fraction of Ge in the film. For a 20% Ge film, the lattice mismatch strain is given by ␧0 ⳱ 0.042x ⳱ 0.84%. The biaxial elastic modulus for Si and Ge are MSi ⳱ 180 GPa and MGe ⳱ 140 GPa, and MSi−Ge ⳱ 172 GPa for a 20% Ge film. Hence, the biaxial film stress in this case is equal to 1.44 GPa. This large mismatch stress provides a driving force for the movement of threading dislocations in the case of supercritically thick films and results in the formation of a square array of misfit dislocations at the film/substrate interface, resulting in strain relaxation of the heteroepitaxial thin film. Extensive research has been done on the velocity of threading dislocations and the resulting kinetics of strain relaxation. Despite all of this work, very little is known about how threading dislocations nucleate and how dislocations multiply within the thin film structure. For a flat film structure, the calculated activation energy for the nucleation of a critical-sized dislocation nucleus15 is much too large to permit dislocation nucleation at any realistic temperature. However, dislocations are observed to form in initially defect-free flat layers, possibly at imperfections within the film left from the deposition process. Strain relaxation in heteroepitaxial thin film structures can also take place by way of surface roughening. It has been shown theoretically26–34 and by experimental observations35–47 that the surface of a stressed solid is unstable with respect to variations in surface shape from a nominally flat surface. As a result of this morphologic instability, the surface is driven toward a 2D cycloid shape with cusplike features or 3D islands.15,43 Morphologic evolution takes place by mass transport by means of surface diffusion under the effect of the stress. During this stress-controlled surface diffusion process, atoms move away from surface valleys toward surface peaks. During the course of surface evolution, the magnitude of the local stress in the vicinity of the valley continues to increase as the local curvature in the valley increases. For a cycloidlike surface, the magnitude of stress concentration s is given by s ⳱ (1 + Ak)/(1 − Ak) in the vicinity of a valley region, where A is the amplitude of surface undulation and k ⳱ 2␲␭, where ␭ is the wavelength of the undulation.15 For a cycloid surface where Ak ⳱ 0.5, 3248

the biaxial film stress in the valley region is amplified by three times; for Ak ⳱ 0.75; it is amplified by seven times (Note: Ak ⳱ 1 corresponds to a singularity in the value of stress and represents a fully cycloid surface.33 Recent studies by Ozkan et al.,48 Muellner et al.,49 and Gao et al.50 have shown that such large stresses (approximately 10 GPa for a 20% Ge alloy at Ak ⳱ 0.75) can result in the nucleation of dislocations and stacking faults through the collapse of single or double ledge atomic steps at the surface of a thin film. Experimental observations by Ozkan et al.43 using x-ray rocking curve measurements and transmission electron microscopy have shown that for subcritically thick films the overall strain relaxation takes place in the heteroepitaxial film as a result of surface roughening, in the absence of any dislocation formation. Observations in the early stages of surface evolution for supercritical films15,30 have revealed two very important features: first, surface ridges or 2D islands are formed along 〈100〉 type crystal directions and they precede the formation of dislocations or any other defects in the heteroepitaxial film. Second, on the formation of misfit dislocations, the ridge structures rotate toward 〈110〉 type directions. Hence, an anisotropic character of the surface-roughening process was detected, which depends on the formation of an orthogonal network of misfit dislocations at the film/substrate interface. This is in contrast to the case of subcritical films, where the 2D ridges were observed to grow along 〈100〉 type directions only, and this was followed by a transition from 2D to 3D evolution and eventually an array of isolated islands. In the following, we will first present an analysis of the anisotropic behavior of 2D surface evolution in supercritically thick films using methods of effective elasticity and linear perturbation. Next, we will present experimental observations of this anisotropic behavior by means of controlled annealing experiments in supercritically thick heteroepitaxial Si1−xGex thin films.

II. ELASTIC ANALYSIS OF UNDULATING SURFACES

We first present an elastic analysis of the anisotropic behavior of surface roughening. A Si1−xGex film deposited on a silicon substrate is under a compressive biaxial stress as a result of the lattice mismatch, which is a function of the germanium content in the film. We assume that x1 and x2 are the in-plane directions and x3 is the out-of-plane direction. Referring to Hooke’s law: ␴i ⳱ Cij␧j,

(1)

where ␴i and ␧j are stress and strain, respectively, in the cube coordinate system and Cij is the stiffness matrix.

J. Mater. Res., Vol. 14, No. 8, Aug 1999


Using this relation, the biaxial stress state in a (001) film can be expressed as: ␴1 = ␴2 = ␴0 = C11␧0 + C12␧0 + C12␧*,

(2)

␴3 = 2C12␧0 + C11␧* = 0,

(3)

where ␧0 and ␧* are the in-plane strain and the out-ofplane strain, respectively, and ␴0 is the initial biaxial stress in the film. Rearranging Eq. (3), one can obtain, ␧* = −

2C12 ␧. C11 0

Substituting into Eq. (2), we have

冉

␴0 = C11 + C12

(4)

冊

2C212 − ␧, C11 0

(5)

(6)

We assume that the film undergoes strain relaxation because of roughening along 〈100〉 type directions at the film surface [Fig. 1(a)]. Furthermore, we will assume that strain relaxation occurs only along x2 by an amount ⌬␧, ⌬␧2 = ⌬␧,

(7)

⌬␧1 = 0.

(8)

⌬␴1 = C11⌬␧1 + C12⌬␧2 + C12⌬␧3 = C12共⌬␧2 + ⌬␧3兲, (9) ⌬␴2 = C12⌬␧1 + C11⌬␧2 + C12⌬␧3 = C11⌬␧2 + C12⌬␧3,

(10)

⌬␴3 = C12⌬␧1 + C12⌬␧2 + C11⌬␧3 = C12⌬␧2 + C11⌬␧3 = 0.

(11)

Rearranging Eq. (11), we have C12 ⌬␧ . C11 2

(12)

Substituting this into Eqs. (9) and (10), we find the corresponding changes in stress associated with strain relaxation:

冉

冊

C12 C ⌬␧ , ⌬␴1 = 1 − C11 12 2

冉

⌬␴2 = C11

冊

C212 − ⌬␧2. C11

(15)

where W is the strain energy density after relaxation, which can be expressed as; W = 1⁄2 共␴1␧1 + ␴2␧2兲 = 1⁄2 兵共␴0 + ⌬␴1兲␧0 + 共␴0 + ⌬␴2兲共␧0 + ⌬␧2兲其. (16) Substituting Eqs. (13), (14), and (16) into Eq. (15), one can obtain:

再

⌬W具100典 = ␧0⌬␧2 C11 + C12

冎

2C212 − + 1⁄2 ⌬␴2⌬␧2. C11 (17)

Using Eqs. (5) and (6) this may be expressed as:

The corresponding changes in stress are given by,

⌬␧3 = −

The change in the strain energy density on relaxation is given by the expression; ⌬W具100典 = W − W0,

where the term in brackets is the biaxial modulus of the film in the (001) plane. The strain energy density W0 at any point in the film can be expressed as, W0 = 1⁄2 ␴i␧i.

FIG. 1. Surface roughening is depicted to occur along (a) 〈100〉 type and (b) 〈110〉 type directions, respectively.

(13)

(14)

冉

⌬W具100典 = ␴0⌬␧ + C11 −

冊

C212 共⌬␧兲2 . C11 2

(18)

Now, we need to investigate strain relaxation caused by 〈110〉 roughening. Referring to Fig. 1(b), we define a new coordinate system (␣, ␤, ␥), which is oriented at 45° to the original coordinate system in the (001) plane. Furthermore, we assume that ⌬␧␣␣ ⳱ ⌬␧, ⌬␧␤␤ ⳱ 0, and ⌬␧␥␥ ⳱ ⌬␧3 ⫽ 0, which means that we impose a compressive strain along the ␣ axis. Next, we define strain transformations from this new coordinate system relative to the original coordinate system: ⌬␧1 = ⌬␧2 = ⌬␧␣␣ cos ⌬␧3 =

C12 ⌬␧, C11

冉冊冉冊

␲ ␲ ⌬␧ cos = , 4 4 2

(19)

(20)

⌬␧4 = ⌬␧5 = 0,

(21)

⌬␧6 = ⌬␧.

(22)


3249


Following the derivations given previously, it can be shown that:

冉

冊

␦⌬W = ⌬W具110典 − ⌬W具100典.

⌬␧ 2C212 C11 + C12 − , ⌬␴1 = ⌬␴2 = 2 C11

(23)

⌬␴6 = C44⌬␧,

(24)

⌬␴3 = ⌬␴4 = ⌬␴5 = 0.

(25)

We can now calculate the change in strain energy density for 〈110〉 roughening as: ⌬W具110典 = W − W0,

(26)

W = 1⁄2 兵共␴0 + ⌬␴1兲共␧0 + ⌬␧1兲 + 共␴0 + ⌬␴2兲共␧0 + ⌬␧2兲 + ⌬␴6⌬␧6其, (27) W0 = 1⁄2 ␴0␧0.

(28)

Substituting Eqs. (19)–(22) and (23)–(25) into Eqs. (27) and (28), Eq. (26) can be rewritten as:

冉

C11

(30)

With strain relaxation, ⌬W〈110〉 or ⌬W〈100〉 are negative values. Substituting equations (18) and (29) into Eq. (30), we have ␦⌬W =

再冉

C11 − C12 共⌬␧兲2 C44 − 2 2

冊冎

.

C44 共⌬␧兲2 + 2 2C212 ⌬␧ 2 + C12 − . C11 2

冊冉冊

(29)

(31)

Using Eq. (31), we can conclude the following: ␦⌬W = =0, ⌬W具110典 = ⌬W具100典: Material is isotropic

冦

⬎0, ⌬W具110典 ⬎ ⌬W具100典: 具100典 roughening

where W and W0 are given by:

⌬W具110典 = −␴0⌬␧ +

Finally, we consider the difference between the two modes of roughening, given by

is favored ⬍0, ⌬W具110典 ⬍ ⌬W具100典: 具110典 roughening is favored

冧

.

(32)

In the case of heteroepitaxial Si1-xGex films deposited on Si substrates, C44 > (C11 − C22/2) so that ␦⌬W is always greater than zero. Hence, this simple analysis has shown the remarkable result that surface roughening along 〈100〉 type directions is always energetically favored. In the next section, we will present a more advanced analysis on the basis of perturbation solutions of the surfaceroughening process that will show that strain energy is always reduced by surface roughening. III. PERTURBATION ANALYSIS OF UNDULATING SURFACES

FIG. 2. Schematic representation of morphologic evolution at a crystal surface under uniform stress. Evolution is driven by mass transfer by way of surface diffusion from regions of high chemical potential (cycloidlike valleys) toward regions of low chemical potential (peaks). 3250

In this section, we present a study of global variations associated with evolution of thin film surfaces. The pioneering research in this field was conducted by Rice and Drucker51 who studied the strain energy variation for a shape change of an elastic body subjected to an arbitrary stress field. Eshelby52 studied the energy change associated with a moving interface of arbitrary shape between dissimilar materials. More recently, several authors have studied the thermodynamic driving force and energy variations for the development of surface roughness by means of diffusional mass transport at thin film surfaces.27,53–56 Essentially, one may consider a slightly undulating surface of a thin film subjected to biaxial stresses as shown in Fig. 2. From a perturbation point of view, the slightly undulating surface may be treated as being perturbed from a reference flat surface along x2 ⳱ 0. the total strain energy change ␦U associated with forming undulations in one period 0 < x1 < ␭ of a crystal surface may be expressed as:


␦U =

兰 W共x 兲␦A共x 兲dx , ␭

0

1

1

1

(33)


where ␦A(x1) is an infinitesimal surface perturbation and W(x1) is the strain energy density function along the surface. We may assume that the thin film has a cosine wavy surface described by: n=⬁

, 冱 A cos ␲nx ␭

y共x兲 = a0 +

(34)

n

n=1

where the summation is over many frequency components over the surface. The tangential stress component ␴t at a point x over the thin film surface can be computed using the following identity26: ␴t − ␴0 2 = ␴0 ␲

兰

⬁

共dy Ⲑ dx⬘兲 dx⬘, 共x⬘ − x兲

Equation (40) suggests that strain energy is actually lowered by enlarging the surface undulation. This result is in agreement with the experimental observations of strain relaxation in subcritically thick Si1−xGex films conducted with x-ray rocking curve measurements.43 Note that Eq. (38) is based on forming undulations on the surface of an isotropic film structure. To investigate the anisotropic behavior of surface roughening, the expression for W(x) has to be modified. One such modification can be introduced through the use of the surface admittance tensor27,57: W共x兲 = 1⁄2 ␴ijuj,i = W0 − Ak␴20Re关Ye−2␲x Ⲑ ␭兴,

(35)

(41)

where (dy/dx⬘) is the slope of the undulated surface at point x⬘. Recasting the equation and substituting for (dy/dx⬘),

where W0 is the strain energy density for the reference flat surface, Y is the component of the surface admittance tensor in the direction of the undulation, and the comma indicates a differentiation. The surface admittance tensor is defined by:

冋

−⬁

n=⬁

␴t = ␴0 1 −

冱 4A␭ n 兰 n

⬁

−⬁

n=1

册

sin共2␲ Ⲑ ␭兲 dx⬘ , 共x⬘ − x兲

which can be integrated to obtain:

冋冋

␴ t = ␴0 1 − ≈ ␴0 1 −

n=⬁

冱 4␲A␭ n cos 2␲nx ␭ n

册

n=1

Y = Z−1 = iHL−1, (36)

册 (37)

where an approximation is obtained by assuming a single-frequency component for the cosine surface. Using the definition of the strain energy density function56 for a plane stress situation of the thin film surface,

冋

册

8␲A 2␲x 共1 + ␬兲 2 , ␴ t = W0 1 − cos W共x兲 = 16␮ ␭ ␭

兰 W 冋1 − ␭

0

0

册

2␲x 8␲A 2␲x cos dx. ␦Acos ␭ ␭ ␭

(38)

(39)

Dividing both sides by ␦A, then letting ␦A approach zero, one finds the rate of change of strain energy in one period as: ␦U = W0 ␦A

兰冉 ␭

0

冊

冋

−p1共C12 + C44兲

−p2共C12 + C44兲

C11 +

C11 + C44p22

冋

L = C44

C44p21

C11 − C12p21 C12p1 − C11 Ⲑ p1

2 2␲x 2␲x 8␲A − cos cos dx = −4W0␲A. ␭ ␭ ␭ (40)

册

,

(43)

册

C11 − C12p22 , C12p2 − C11 Ⲑ p2

(44)

where the functions p1 and p2 may be written in the following forms, p1 =

公共C11 Ⲑ C22兲ei␾,

p2 = −

where ␬ ⳱ 3 − 4v and W0 ⳱ (1 + ␬)/16␮)␴20. We now let the wavy surface with current amplitude A be subjected to an additional perturbation ␦Acos(2␲x/␭). This is equivalent to enlarging the wave amplitude from A to A + ␦A. Replacing ␦A(x) by ␦Acos(2␲x/␭) and substituting Eq. (38) in Eq. (33): ␦U =

where Z is called the surface impedance tensor. The matrices H and L are given by: H=

2␲nx 4␲Ann cos , ␭ ␭

(42)

公共C11 Ⲑ C22兲e−i⌽.

(45) (46)

The term ⌽ is a vector complex auxiliary function58 used in representing the displacement and the stress fields as: ui = Im关Yij⌽j兴, ␴1j = − Re关⌽j,2兴,

␴2j = Re关⌽j,1兴.

(47) (48)

The concept of the surface impedance tensor was first introduced by Ingebristen and Tonning.59 Hirth and Lothe57 investigated the properties of Z to facilitate the analysis of surface and interfacial wave problems. Barnett and Lothe60 further showed that the surface impedance tensor can be used in analyzing fracture and dislocation problems. Following the same method as in the case of Eqs. (33)–(36), we again let the wavy thin film surface be subjected to an additional infinitesimal perturbation ␦Acoskx1, which is equivalent to enlarging the wave amplitude from A to A + ␦A. Replacing ␦A in Eq. (32) by ␦Acoskx1, then dividing both sides by ␦A and


3251


letting ␦A approach zero, we find the rate of change of strain energy for one wavelength period as shown by: ␦U = ␦A

兰

␭

0

W共x1兲coskx1dx1 = −␲A␴2bRe关Y兴.

(49)

The matrix Re[Y] is always positive definite, hence the first-order term on the right is always negative regardless of material anisotropy. Therefore similar to the result of Eq. (40), the strain energy will always be lowered by enlarging the wave amplitude A, which corresponds to enlarging the perturbation. Using Eq. (49), we can calculate the energy change per unit wavelength associated with surface roughening, related to ridge formation along a set of specific crystallographic directions. For this purpose, we need to use the component of the surface admittance tensor Y in the direction of the undulation under consideration. One may rewrite Eq. (49) in the following form: ⭸U = −␲AY␴20 = −␲AYM2␧20 = −2␲YMW0 A, ⭸A

Y具110典 =

共C11

冋

C11共C11 + C12 + 2C44兲 1 + C12兲 C44共C11 − C12兲

册

(50)

1Ⲑ2

, (51)

1 共公C11共C11 + H兲 + C12兲

冋

C11共公C11共C11 + H兲 + C12 + 2C44兲 C44共公C11共C11 + H兲 − C12兲

册

Y具100典 = 0.01324 GPa−1,

(53)

Y具110典 = 0.01188 GPa−1.

(54)

Substituting these values into Eq. (50), we finally obtain:

再

冏冏

冎

1 ⭸U 800 J m−2, 具100典 roughening mode = . A ⭸A 700 °C 620 J m−2, 具110典 roughening mode (55)

where M and ␧0 are the biaxial modulus and the strain in the film, respectively. Hirth and Lothe57 derived explicit expressions for Y in the case of a cubic crystal with 2-fold symmetry, which are given by: Y具100典 =

where H ⳱ C44 − [(C11 − C12)/C44], and C11, C22, and C44 are the stiffness terms. Note that for H ⳱ 0, Eq. (52) becomes identical to Eq. (51). In the case of a Si0.8Ge0.2 alloy, C11 ⳱ C22 ⳱ 152 GPa, C12 ⳱ 57 GPa, and C66 ⳱ 75 GPa.15 Substituting these values to compute Y for surface roughening along 〈100〉 and 〈110〉 type crystallographic directions, we have

1Ⲑ2

, (52)

It is clear that the 〈100〉 roughening mode results in a larger reduction in strain energy density and it is always favored. This analysis is in agreement with the first analysis on the basis of elastic anisotropy. Figure 3 is a plot of (1/A)|⭸U/⭸A| versus the Germanium fraction in the film for the 〈100〉, 〈110〉, and isotropic modes of roughening. Note that

冏冏典冏冏 ⭸U ⭸A 具100典

冏冏

⭸U ⭸U 典 ⭸A Isotropic ⭸A 具110典

(56)

is always true regardless of the Germanium fraction in the film. These results suggest that surface roughening along 〈100〉 type directions in heteroepitaxial Si1−xGex films should always dominate for any film thickness and composition. Previous experimental research in this field had shown that 〈100〉 type roughening occurs in the case of subcritical films and 〈110〉 type roughening occurs in the case of supercritical films.34 On the basis of the discussion presented previously, it is expected that the 〈100〉 mode of roughening would be observed in supercritical films if in early stages of the roughening process. As will be shown in the next section, the 2D mode of surface roughening starts in the form of 〈100〉 ridges.

IV. FILM GROWTH AND ANNEALING

FIG. 3. Plot of (1/A)|⭸U/⭸A| versus the Germanium fraction in the film for the 〈100〉, 〈110〉, and isotropic modes of roughening. 3252

For the experimental part of this study, heteroepitaxial films 500 Å thick and containing 22% Ge were deposited on 100-mm (100) type bare silicon substrates by use of low-pressure single wafer chamber chemical vapor deposition system.15 A standard diffusion clean was done on the substrates, which consisted of 20:80 H2SO4/H2O2, 50:1 HF/H2O, and 20:80 HCl/H2O baths. This was fol-



lowed by a high-temperature H2 bake in the reactor for thermal desorption of the passivating oxide and a surface etch back using HCl at 1185°C. A 500-nm thick Si buffer layer was deposited at 800 °C before Si1−xGex deposition to ensure a high-quality nucleation layer. Si1−xGex deposition was carried out at 550–600 °C by thermal decomposition of silane and germane at 15 torr total pressure, using hydrogen as a carrier gas. Our previous studies have shown that supercritically thick films with 18–25% Ge can be grown very flat and do not contain any misfit dislocations. Film deposition was followed by annealing at temperatures between 700–800 °C in the reactor under conditions of continuous hydrogen flow over the film surface. Atomic force microscopy was used to study the surface structure of the films by use of a Park Scientific CP system. Plan view transmission electron microscopy (TEM) was done with a Philips EM 430 TEM operating at 300 KeV. V. HYDROGEN PASSIVATION OF THE THIN FILM SURFACE

Hydrogen passivation was a very crucial factor in our annealing experiments. We have discovered that surface diffusion and the resulting roughening process most readily takes place on hydrogen-terminated or hydrogenpassivated surfaces.15,34 Hydrogen passivation means that the dangling bonds at a substrate surface are flooded with hydrogen atoms; in other words, quasistable Si–H bonds form at the film surface.61,62 In the presence of hydrogen, the surface of a (001) oriented Si1−xGex film or a Si wafer exhibits 1 × 1 type reconstruction as observed by low-energy electron diffraction (LEED) studies,63 which corresponds to a minimum surface energy configuration. Further studies using thermal desorption spectroscopy63 have shown that a hydrogen-passivated Si surface can be stable in an ultra high vacuum (UHV) environment for days (and up to about 500 °K) and for up to several hours in the open air. After a prolonged duration in a UHV environment, the initially hydrogenpassivated surface transforms from a 1 × 1 reconstructed arrangement into a 2 × 1 arrangement. On the other hand, in the presence of oxygen at low or moderate temperatures, the surface energy is minimized by oxidation, which creates an impenetrable native oxide barrier, about 25–30 Å in thickness. One can also envision the process of forming an oxide layer at the surface where the atoms are locked in place in contrast to having dangling bonds. Therefore a native oxide layer on the surface of a Si1−xGex film will inhibit surface diffusion and hence the roughening process. Recent work by Ozkan et al.64 using in situ TEM annealing experiments revealed that the kinetics of surface roughening are diminished in the case of 2 × 1 reconstructed surfaces. In their experiments, they used a high-voltage TEM to be able to use thicker

samples for the purpose of maintaining the stress in the film. They dipped the TEM samples into an HF solution to etch off the native oxide and passivate the film surface with Si–H bonds before insertion into the TEM. Hydrogen atoms attached on the film surface were evaporated quickly during ramping up the temperature to 850 °C, and the surface immediately transformed into a 2 × 1 reconstructed configuration. They observed that the kinetics of surface roughening was much slower compared with the case where the film is annealed in the chemical vapor deposition (CVD) reactor under hydrogen flow right after film deposition. In the following, we will present ex situ TEM and atomic force microscopy (AFM) observations of surface roughening in supercritically thick Si1−xGex films conducted by controlled annealing experiments under hydrogen flow in the CVD reactor.30

VI. EXPERIMENTAL OBSERVATIONS OF SURFACE ROUGHENING IN SUPERCRITICALLY THICK SI1−XGEX FILMS

Figure 4 shows a bright field cross section TEM image of an as-grown heteroepitaxial Si1−xGex film, which reveals that the surface of the heteroepitaxial film is virtually flat and no dislocations are formed in the film. Note that the thickness of the film is about five times larger than the corresponding critical thickness for dislocation formation. As we have shown previously,5 kinetic limitations of dislocation nucleation and propagation can result in dislocation-free as-grown films with thicknesses much larger than the critical thickness for that particular germanium composition. Figures 5(a)–5(d) show a sequence of AFM images for a series of heteroepitaxial Si1−xGex films annealed in the reactor. For the surface of the sample shown in Fig. 5(a), the annealing experiment was carried out at 750 °C for 10 seconds after the growth process in the reactor. This image indeed reveals surface ridge formation along 〈100〉 type crystallographic direc-

FIG. 4. Cross-sectional TEM image of an as-grown 500-Å thick film containing 22% Ge.


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FIG. 5. AFM images of a 500-Å thick Si1−xGex film containing 22% Ge, which was annealed at (a) 750 °C for 10 s (A ⳱ 120 Å, ␭ ⳱ 2200 Å), (b) 800 °C for 10 s (A ⳱ 250 Å, ␭ ⳱ 3500 Å), (c) 800 °C for 1 min. (A ⳱ 510 Å, ␭ ⳱ 4700 Å), and (d) 800 °C for 5 min. (A ⳱ 950 Å, ␭ ⳱ 6200 Å). These anneal series reveal the rotation of ridges from 〈100〉 to 〈110〉 type directions.

tions, which confirms our theory of anisotropic surface evolution shown in the previous section. The corresponding plan view TEM image for this sample is shown in Fig. 6(a), which is obtained at a two-beam condition very close to the (001) zone axis. Note that the contrast distribution was convoluted by the strain distribution in the film, the changing film thickness, and the bending of the sample. This figure shows that no dislocations were formed in the film yet, which implies that the process of surface roughening precedes any dislocation formation within the heteroepitaxial film. The next image in Fig. 5(b) was obtained after annealing at 800 °C for 10 seconds, and it reveals the very first signs of ridge rotation as shown by the vertical arrows: they point to a group of islands aligned along 〈110〉 directions. The horizontal arrows point to a very interesting feature on the film surface, where we think that threading dislocations are shearing through the 〈100〉 ridges and causing them to rotate toward 〈110〉 type directions. The corresponding plan view TEM image is shown in Fig. 6(b), which reveals that a cross grid of misfit dislocations aligned along 〈110〉 directions, and most of the ridges are 3254

aligned along 〈100〉 directions. Previous research by Freund et al.65 has shown that misfit dislocations formed at the film/substrate interface act to perturb surface ridges toward 〈110〉 type directions. After the formation of misfit dislocations, the strain distribution along the surface becomes highly nonuniform, and consequently, the chemical potential develops a gradient along the surface of the film. In response to this gradient, mass rearrangement occurs over the surface to re-establish a shape with a uniform chemical potential. In this way, the ridges become aligned with the misfit dislocation network. Further ridge rotation takes place after annealing at 800 °C for 1 minute as shown in Figs. 5(c) and 6(c), with an increasing density of misfit dislocations. We observed that surface ridges were aligning themselves with the network of misfit dislocations. The last sample in these series was annealed at 800 °C for 5 minutes, and its surface structure and microstructure are shown in Figs. 5(d) and 6(d), respectively. Both of these figures reveal that the ridge rotation process is complete, and further roughening in the 2D stage continues primarily along the 〈110〉 type directions.



FIG. 6. Plan-view TEM images of a 500-Å thick Si1−xGex film containing 22% Ge, which was annealed at (a) 750 °C for 10 s, (b) 800 °C for 10 s, (c) 800 °C for 1 min., and (d) 800 °C for 5 min.

VII. CONCLUSIONS

In this article, we have investigated the anisotropic character of the surface roughening process in supercritically thick heteroepitaxial Si1−xGex films. In general, elastic strains tend to destabilize an initially flat thin film surface because the strain energy is always reduced by surface roughening. Supercritical films exhibit a more complicated picture of surface evolution compared with subcritical films because dislocations also form. We have shown that the 2D mode of roughening was actually composed of two distinct substages. In the first substage, ridge formations were observed to form along 〈100〉 directions. In the second substage, ridge formations were observed to form along 〈110〉 type directions, which were coaligned with an orthogonal network of misfit dislocations at the film/substrate interface. We have shown by two separate analyses that during the early stages of the roughening process, the formation of 〈100〉 type ridges is favored as a result of anisotropy of the roughening proc-

ess. Note that both methods of analysis presented here are generally applicable to investigate the anisotropic properties of surface evolution processes in any heteroepitaxial thin film system. Experimental observations revealed that the formation of a 〈110〉 misfit dislocation network in the latter stages of the 2D roughening mode alters the evolution pattern by rotating the ridge formations toward the 〈110〉 type directions. ACKNOWLEDGMENTS

Financial support from the United States Office of Naval Research under Grant No. ONR-N00014-92-J4094 and from the United States Department of Energy under Grant No. DE-FG03-91ER14196 are most gratefully acknowledged. We are also grateful to Professor D. Barnett of Stanford University and Professor L.B. Freund of Brown University for helpful discussions and comments.


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