Differential optical absorption spectroscopy and X-ray characterization of symmetrically strained GeSi superlattices

Thin Solid Fihns, 222 (1992) 254 258

254

Differential optical absorption spectroscopy and X-ray characterization of symmetrically strained Ge-Si superlattices T. P. Pearsall, C. C. M. Bitz and L. B. Sorensen University of Washington, Seattle, WA 98195 (USA)

H. Presting and E. Kasper Daimler Benz Forschung und Technik, Wilhelm-Runge-Strasse

11, W-7900 Ulm (Germany)

Abstract We have used a differential spectroscopy technique to measure and characterize the optical absorbance spectrum of a 2500 A symmetrically strained Ge Si superlattice. Using X-ray diffraction we found that the average periodicity of the superlattice in the growth direction is 11 atomic layers, to measure the strain and disorder of the superlattice, and to show that the superlattice is pseudomorphic with its Geo.75Sio.25 buffer substrate with a precision of 2 x 10 3. At room temperature, the absorption coefficient increases linearly with photon energy above the band edge, exceeding 104 cm ~ at 1.55 lam. Because the band-edge electronic structure is fundamentally different in nature from either that of Si or Ge, we argue that conventional models for absorption v e r s u s photon energy in bulk semiconductors may not apply to this kind of Ge-Si superlattice.

1. Introduction The absorption spectrum is a fundamental property of semiconductors because it contains information about the magnitude and nature of the bandgap. In particular this measurement can be used to determine the rate of band-to-band recombination, the strength of which may give some indication of direct bandgap behavior. There is both theoretical and experimental evidence to support the possibility that G e - S i superlattices can show direct bandgap behavior. While there seems to be a consensus among theorists that some superlattices with a 10 atomic monolayer periodicity show a global minimum in the conduction band energy at F, the zone center [1-6], experiments are more ambiguous with the result that the measurement proving the existence of direct bandgap material has yet to be made [7-10]. In this paper we examine differential absorption spectroscopy as a means of determining the bandgap and the strength of absorption in G e - S i superlattices.

2. Sample preparation In this paper we have approached the problem of measuring the absorption coefficient in thin superlattice films by optimizing the measurement and the sample structure. When Ge Si superlattices are grown commensurately on Si or Ge substrates, the superlattice

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thickness is limited to about 50/~ in order to avoid the nucleation of a substantial concentration of threading misfit dislocations [11]. Before additional superlattice material can be grown, it is necessary to grow a thicker buffer layer (typically 200 A) of material with the same lattice parameter as the substrate. The final sample may contain many layers of superlattice structure separated by buffer layers of substrate material. The structure acts as a dielectric multilayer stack, and this composite material may contribute regions of enhanced optical transmission and reflection that make interpretation of an absorption measurement difficult. An alternative to this structure is the symmetrically strained superlattice [12] developed by first growing a buffer of composition such that the in-plane lattice parameter of the buffer lies between that of the two components of the superlattice. Once this buffer is grown, alternating growth of superlattice layers with lattice parameters symmetrically larger than and smaller than that of the buffer layer will tend to produce a structure with little net average strain, while maintaining the same large level of microscopic strain in the individual layers. The sample used in this study was a symmetrically strained superlattice. Conventional cleaning techniques were used to prepare the sample for deposition [ 13]. At 450 °C a buffer layer of Ge0.758i0.25 alloy 200 ~ thick was first grown, followed by 2500 A of a structure grown at 320 °C consisting of an alternation of ns~ atomic monolayers of Si and nee atomic monolayers of

1992

Elsevier Sequoia. All rights reserved

255

T. P. Pearsall et al. / Symmetrically strained Ge Si superlattices

Ge. A major improvement in sample quality is obtained because the volume of superlattice material can be increased without limit, the density of superlattice material is increased by a factor of about 5, and the material no longer has a dielectric stack of differing composition in the growth direction.

3. X-ray measurements The strain, composition, epitaxy and disorder of the superlattice and of the Geo.75Sio.25 buffer layer were determined using specular and nonspecular X-ray diffraction [14]. Measurements were made using the double crystal geometry with the sample mounted in a four-circle spectrometer. An Si(111) monochromator was used to select Cu Kal radiation (2 = 1.54056 A) from a rotating anode generator operated at 4.2 kW. Figure 1 shows the measured specular reflectivity in the growth direction along the (00L) axis; seven Bragg peaks were observed: the (001), (002), (009), (00 10), and (00 11) superlattice peaks; the (004) Geo.758io.25 buffer layer peak; and the (004) Si substrate peak. The missing (003) to (008) superlattice peaks are predicted to be weak owing to destructive interference between the Si and Ge diffraction away from the allowed Si and Ge (000) and (004) Bragg peaks [15, 16]; in addition, disorder of the superlattice has been shown to reduce these reflections [ 17]. The measured positions of the observed specular superlattice peaks are shown in Table 1, together with lO000t

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. . . .

m . . . .

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u . . . .

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1000 100, a

¢:

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.1

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20

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30

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40

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50

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Two Theta (degrees) Fig. 1. Measured specular X-ray diffraction intensity for the Ge-Si superlanice sample. Seven Bragg peaks were observed: ( a ) - ( d ) are the (001), (002), (009), and (00 10) superlattice peaks respectively; (e) is the (004) Geo.75Si025 buffer layer peak; (f) is the (00 11) superlattice peak; and (g) is the (004) Si substrate peak. The very sharp unlabeled peaks are from the Si substrate. The measured superlattice perpendicular lattice constant is d± = 15.195 + 0.005 A. These measurements show that the superlattice unit cell has a nominal periodicity of I1 atomic monolayers in the growth direction.

TABLE 1. Measured positions of observed specular superlattice peaks and corresponding superlattice perpendicular lattice constant d I Peak

20 (°)

d I (A)

(001) (002) (009) (00 10) (00 I 1)

5.84_+0.04 11.66 + 0.04 540.25 _+0.04 60.95 _+0.04 67.80 _+0.04

15.12 _+0.10 15.166 + 0.052 15.205 ± 0.010 15.188 + 0.009 15.192 _+0.008

the corresponding superlattice perpendicular lattice constant, d3, calculated from Bragg's Law. The average d± = 15.195 _+0.005 A is determined quite precisely by the (009), (00 10), and (00 11) reflections. To accurately relate d± to the average structure of the superlattice unit cell, the strain in the superlattice should be included (see below). However, a rough estimate of the average unitcell structure can be made by comparing di with the sum of the unstrained monolayer spacings of Si (1.3566 A) and Ge (1.4144/~); 15.195/~/2.7721 A -~ 5.5 unstrained Si and Ge monolayer spacings per superlattice unit cell. Consequently, the nominal periodicity of the superlattice in the growth direction is 11 atomic layers. The parallel momentum transfer components of the nonspecular superlattice peaks and of the Geo.75Sio.25 buffer layer peaks were measured to determine the strain and epitaxy. The superlattice parallel lattice constant, dl, = 5.547 _+0.009/k, was determined from the measured parallel momentum transfer for nonspecular superlattice peaks along the ( l l L ) and (04L) rods [15]. The measured value agrees very well with the measured Geo75Sio.25 buffer layer parallel lattice constant, all = 5.548 +_0.012A,, determined from the Geo.75Sio.25(113) reflections. This demonstrates that the superlattice is pseudomorphic with the Geo.75Sio.z5 layer within the precision of the measurements, about 2 × 10 -3. Surprisingly, the Geo.vsSio.z5 buffer layer is pseudomorphic with the superlattice and is incommensurate with the Si substrate. The perpendicular lattice constant, ai = 5.624 _+0.006/~, of the Geo.75Sio.25buffer layer was determined using its (004) reflection. The measured parallel and perpendicular values show that the Geo.75Sio.25layer is tetragonally distorted. Assuming the composition of the buffer layer is Geo.75Sio.25, the strains in the buffer layer are ell = (Aahl/a) = 0.4% and ~1 = ( A a ± / a ) = -0.9%, since Vegard's Law predicts an unstrained lattice constant a = 5.601 A. Using the measured parallel and perpendicular lattice constant and the estimated macroscopic elasticity to calculate the composition via the X-ray measurements [14, 15] yields GexSil_x with x = 0.71 + 0.02. Although X-ray composition measurements have been shown to be as precise as Rutherford backscattering measurements for GeSi pseudomorphic layers, the buffer layer is labeled

256

T. P. Pearsall et al. / Symmetrically strained Ge -Si superlattices

throughout this paper by its nominal growth composition, Ge0.75Sio.25, instead of its X-ray composition, Ge0.71Sio.29, for simplicity, The measured superlattice parallel lattice constant, dll =5.547 0 . 0 0 9 ~ , can be combined with the unstrained lattice constants of Ge (5.6577/~,) and Si (5.4307 A) to calculate the parallel strains of the Ge and of the Si in the superlattice, ell(Ge) = - 2 . 0 % and Epi(Si) = 2.1%. The corresponding perpendicular strains, el = -2(C~2/CIj)~II, can be calculated from the macroscopic elasticity [18] and are e , ± ( G e ) = l . 5 % and el(Si) = - 1 . 7 % . The X-ray results demonstrate that both the parallel and the perpendicular superlattice strains are large and very symmetrically distributed between the Ge and the Si in the superlattice. Considerable information about the structure of the average superlattice unit cell can be determined from the measured superlattice perpendicular lattice constant, d~, and from the calculated perpendicular strains, ~ ( G e ) and e~(Si). Because of the strain, the tetragonally distorted Ge and Si monolayer spacings (a/4) in the superlattice are 1.435 ~ and 1.335 A, respectively. For an ideal superlattice unit cell, d~ should correspond to an integer number of strained Si monolayers plus an integer number of strained Ge monolayers. The calculated values of di and A(A = d±(calculated) - dj (measured)) for the 5Si × 5Ge to 6Si × 6Ge structures are shown in Table 2. The calculations show that for integer numbers of monolayers, only 5Si × 6Ge monolayers or 6Si x 5Ge monolayers produce unit-cell sizes close to the measured value, d l = 15.195 + 0.005 A. The 5Si x 5Ge and 6Si x 6Ge structures are not consistent with the X-ray data; the A for these two structures show the calculated 5Si × 5Ge lattice constant is about one monolayer too small and the 6Si × 6Ge lattice constant is about one monolayer too large. Thus the nominal periodicity of the superlattice in the growth direction is still 11 atomic layers when the strains in the Ge and Si monolayers are included because the net strain is small. Raman measurements on this sample, performed independently of our work, concluded that the structure consists of 5Si x 6Ge monolayers [19]. This agrees qualitatively with our X-ray measurements, but disagrees quantitatively since A :# 0. Although the calculated lattice constant for the perfect 6Si x 5Ge monolayer structure is extremely close to the measured d±, the actual TABLE 2. Calculated values of d ± a n d A Nc~

Nsi

d I (calc.)(A)

A (A)

5 5 6 6

5 6 5 6

13.850 15.185 15.285 16.620

-1.341 0.010 0.090 1.425

superlattice structure is quite disordered (see below). Without a specific model for the disorder, the present X-ray measurements show that the nominal periodicity is close to 11 atomic monolayers, but cannot distinguish between the disordered 5Si x 6Ge and 6Si x 5Ge structures. More complete X-ray diffraction measurements may be used to distinguish between the 5Si x 6Ge and 6Si x 5Ge structures, and are planned for this sample. The disorder in the superlattice has been determined from the measured width of the superlattice specular Bragg peaks. For a disordered system, the correlation length, ~, is related to the linewidth, AQ, by ~ ~ Qo/ AQ. The measured linewidth, AQ = 0.028 A ~, and periodicity, Q,, = 0.4135 A-~, show that the superlattice is actually quite disordered since ~ is only 14.8 superlattice unit cells, or 225 A. A perfect superlattice would have peak widths determined by the finite number of superlattice unit cells, N, in the structure. For this sample N = 145, and consequently if there were no mistakes in the growth process Q o / A Q would be 145 instead of 14.8. Simple random growth errors which produce the correct average perpendicular lattice constant, d± = 15.195 +0.005 A, do not produce the observed linewidths and peak positions [15].

4. Absorption measurements The procedure used to measure the differential transmission spectrum for G e - S i superlattices has been described in an earlier publication [20]. In these measurements the transmission of the G e - S i superlattice was compared with the transmission through the same substrate with no superlattice grown on it. By comparing these two spectra digitally we can extract the absorbance due to the film alone. The sensitivity of the technique is about three orders of magnitude larger than that of a conventional absorption experiment, and permits the probing of absorption by the film over a larger wavelength range than would be otherwise possible. The absolute value of the absorption coefficient is determined by measuring in addition the absorbance in the substrate alone. The measurements are interpreted subject to the assumption that differences in transmission are directly related to absorption in the superlattice. These transmission measurements are made in the absence of an electric field, and thus we have avoided introducing the quantum-confined Stark effect (QCSE) shift of the absorption edge toward longer wavelengths that may occur in G e - S i quantum well structures. Park et al. first showed [211 that this effect can be significant in G e - S i with shifts of up to 70 meV in the absorption edge. The presence of a large QCSE shift could mean that

T. P. Pearsall et al. / Symmetrically strained G e - S i superlattices ~o~, Photon energy (eV) 0.701 0.71 0.8

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1~¢o- Eg, Photon energy above band gap (eV) Fig. 2. Measured optical absorption coefficient for the superlattice. The superlattice bandgap measured at 295 K is 0.70 + 0.01 eV. The absorption coefficient varies linearly with photon energy and reaches 1.2 × 104cm -1 at 2 = 1.41.tm. Open and filled circles distinguish separate measurements on the same sample.

photocurrent measurements of absorption, which require an electric field similar to those tested by Park et al., may lead to erroneous results [22, 23]. In Fig. 2 we show the results of the absorption measurement on the symmetrically strained Ge-Si structure. The Si substrate has an absorption edge near 1.1 lam, and the unstrained Ge-Si buffer has an absorption edge at 1.35 lam [24]. Therefore the absorption of the superlattice in the region of 1.4 p.m to 1.6 lam is easily resolved and substantial, contributing to about 20% of the total absorption. The symmetrically strained growth technique is directly responsible for the extended wavelength "window" through which the superlattice optical properties can be probed. In earlier work, the absorption of similar superlattice structures, grown commensurately strained on Ge, could be measured only between 2.0 ~tm and 1.55 lam [20]. The optical wavelength of the band edge was determined to be 1.77 Ixm, corresponding to a room temperature bandgap energy of 0.70 + 0.01 eV. This appears to be in reasonable agreement with the low temperature bandgap energy of 0.75 eV for similar superlattice structures calculated using the envelope function method [25]. Because of the type II nature of the Ge-Si superlattice band-edge alignment, the bandgap does not change very much with the relative number of superlattice monolayers, provided the overall period is kept the same. Essentially making the conduction band "well" more narrow also makes the valence band "well" wider, with the result that the bandgap, which is the difference between the conduction-band and valence-band energy levels, stays about the same. Thus, 10-monolayer superlattices such as Ge6Si4, GesSis, and Ge6Si4 may be expected to have about the same bandgap energy, while Olajos has shown that there is a

257

systematic downward shift in the bandgap as the total period becomes longer [26]. The absorption coefficient is determined by measuring the absorption of the Si substrate and the differential absorption of the substrate-superlattice combination. In Fig. 2 our results show a near-linear dependence of the absorption coefficient on photon energy above the bandgap for most of the measurement range. At 1.4 ~tm, the absorption coefficient is 1.2 x 104cm -1, which is substantial. If the absorption were due entirely to superlattice transitions, this result would provide support for the presence of an energy gap at 0.70 eV with a substantial interband matrix element. This caveat is important because the experimental result may be affected by the bulk Ge Si states at the edge of the superlattice region. However, in the symmetrically strained structure, there is only one such interface. It appears unlikely that it alone would dominate the absorption spectrum, so we believe that this kind of absorption appears not to be important.

5. Discussion

The absorption coefficient plays a role of fundamental importance in determining the radiative recombination rate of semiconductors. The van RoosbroeckSchockley relation states R(v) dv = P(v)p(v) dv

(1)

That is, the radiative recombination rate is equal to the probability per unit time of absorbing a photon of energy hv, and p(v) is the density of photons of frequency v in an interval dv [27]. The photon density is given by the Planck radiation law. Therefore: ~(v) 8~v2n 2 R(v) dv - c 2 [ e x p ( h v / k T ) _ 1] dv

(2)

where e(v) is the absorption coefficient and n is the index of refraction [28]. The energy dependence of absorption coefficient on photon energy has been given by Johnson, in an elegant presentation based on a derivation from first principles [29]. One particular issue in these experiments is the behavior of absorption for allowed transitions occurring at an indirect absorption edge. For 3-dimensional materials, this has the familiar form: indirect and allowed: e(hv) = Ct (hv - eg)2

(3)

For 2-dimensional systems, this transforms to: indirect and allowed: ct(hv) = Cl(hv - % )

(4)

The basic assumptions leading to this functional form are: one simple parabolic band edge and no competing absorption from other closely spaced ( < 10kT) energy-

258

T. P. Pearsall et al. / Symmetrically strained Ge- Si superlattiees

band minima. These assumptions are well obeyed by Si, Ge, and most common direct band-gap materials. The situation for short-period (2 < 20/k) Ge Si superlattices is different. Because the band edge indirect gap states and the zone-folded F-states are fundamentally related, such superlattices formed from indirect gap materials always have a zone center minimum only a few meV ( < 10kT) different in energy from the zone edge minima [1-6]. Since the basic assumptions no longer hold, the conventional analysis for c4hv) summarized in eqns. ( 3 ) - ( 4 ) requires revision for these new structures.

6. Conclusion Using differential transmission spectroscopy, we have characterized absorption in a G e - S i superlattice symmetrically strained on a Ge0.vsSi0.25 buffer layer. Based on these measurements, the value of the bandgap at 295 K is 0.70 _+ 0.01 eV. The difference in transmission between the superlattice and the substrate results in a measured absorption coefficient greater than 104 c m i. The relatively large value for the absorption coefficient, and the apparent band-like nature of the spectrum provide some supporting evidence for the notion that this material may have a substantial rate of optical recombination. We used X-ray diffraction to determine the average perpendicular superlattice unit cell and the strain in the superlattice. We found di = 15.195 _+ 0.005/~, corresponding to a nominal periodicity in the growth direction of 11 atomic monolayers and symmetrically distributed macroscopic strains in the superlattice: eil(Ge) = - 2 . 0 % vs. ~ll(Si)= + 2 . 1 % and e l ( G e ) = + 1.5% v s . e±(Si) = - 1.7'7o. The X-ray measurements

also show that, within the precision of the measurement (about 0.2%), the superlattice is pseudomorphic with the Geo75Sio.25 buffer layer and that the superlattice is quite disordered: the correlation length is only = 14.8 superlattice unit cells or 225/k.

Acknowledgments The authors wish to thank Dr. Eli Yablanovitch for helpful discussions regarding optical recombination, particularly for pointing out the importance of eqns. (1) and (2). This work was made possible through the support of the Washington Technology Center, Seattle, Washington, 98195, USA.

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