Appl. Phys. A 80, 1335–1338 (2005)
Applied Physics A
DOI: 10.1007/s00339-004-3163-3
Materials Science & Processing
Diamond cubic Sn-rich nanocrystals: synthesis, microstructure and optical properties
r. raganu,∗ h.a. atwater
Thomas J. Watson Laboratory of Applied Physics, California Institute of Technology, Mail Stop 128-95, Pasadena, CA 91125, USA
Received: 15 September 2004/Accepted: 23 November 2004 Published online: 11 March 2005 • © Springer-Verlag 2005 ABSTRACT Diamond cubic Sn-rich nanocrystals were fabricated with radii less than 20 nm by post-growth annealing at T = 750 ◦ C of Snx Ge1−x alloys grown on Ge(001) by molecular beam epitaxy. The crystal phase of the Sn-rich nanocrystals was determined to be diamond cubic from Fourier transform analysis of high-resolution transmission electron microscopy images. Optical transmittance of these Snx Ge1−x /Ge (001) films demonstrated changes in optical absorption that can be attributed to absorption from the nanocrystals. The energy bandgap was measured to be 0.45 eV for nanocrystals arrays in Ge with a mean diameter of 32 nm. PACS 68.37.Lp;
1
78.67.Hc; 81.07.Ta; 81.16.Dn; 68.65.Hb
Introduction
The fabrication of nanostructured materials allows for engineering material properties with those that are quite different from their bulk counterparts. Using self-assembly to fabricate nanostructures has the advantage of small feature sizes without costly lithographic techniques. Previously we showed that phase separation during epitaxial growth of Snx Ge1−x /Ge (001) films produced ordered arrays of nanowires parallel to the substrate normal in the absence of lithography and that the Snx Ge1−x nanowire arrays embedded in Ge had different optical properties than homogeneous Snx Ge1−x alloys [1]. In this paper, we demonstrate the fabrication of diamond cubic Sn-rich nanocrystals embedded in a Ge matrix by driving the system toward thermodynamic equilibrium via a post growth anneal. Diamond cubic Sn (α-Sn) is a semi-metal with a low electron effective mass [2, 3]. Hence, excitonic confinement effects should be manifest at relatively large nanocrystal (NC) radii. A semi-empirical tight-binding bandstructure calculation predicts that the energy bandgap varies between 0 and 2.5 eV for bulk α-Sn and nanowires with 10 nm radii, [4] respectively. Similar tunability is expected for α-Sn NCs. Hence, α-Sn NCs enable the achievement of u Fax: +1-949-824-2541, E-mail:
[email protected] ∗ Present address: Department of Chemical Engineering and Material Science, University of California, Irvine, 916 Engineering Tower, Irvine, California 92697-2575, USA
a group IV direct bandgap semiconductor with a high degree of tunability of the bandgap energy for monolithic integration of optically active materials with silicon. At room temperature, the tetragonal unit cell (β-Sn) is the thermodynamically stable phase of Sn. We have stabilized the diamond cubic phase of Sn-rich NCs by using phase-separation to embed the NCs in a Ge diamond cubic matrix. The optical properties measured for α-Sn rich NCs embedded in Ge exhibit a different dependence on Sn concentration than homogeneous Snx Ge1−x alloys and Snx Ge1−x nanowire arrays with the same average Sn composition. 2
Experimental
Metastable Snx Ge1−x epitaxial films with x = 0.025 and film thickness of 1 µm were grown by molecular beam epitaxy on Ge (001) at T = 160 ◦ C [5] The thermodynamic equilibrium solid solubility of Sn in Ge and Ge in Sn is 0.005 [6, 7] The Snx Ge1−x films were annealed post-growth in ultra high vacuum, 10−8 Torr, and the microstructure was characterized by cross-section transmission electron microscopy (TEM) both before and after annealing at T = 550 ◦ C and 750 ◦ C. Fourier transform infrared spectroscopy (FT-IR) was employed to probe the changes in the optical properties due to the evolution of the microstructure associated with annealing at T = 550 ◦ C, 650 ◦ C and 750 ◦ C. Infrared absorption measurements of diamond cubic NCs at room temperature indicate that quantum size effects are observable. The estimated bandgap of NC arrays with a mean diameter of 32 nm embedded in a Ge matrix is 0.45 eV in comparison to 0 eV, the accepted value of the bandgap for bulk α-Sn. 3
Material characterization
3.1
Transmission electron microscopy analysis
Cross-sectional TEM images were obtained before and after annealing Sn0.025 Ge0.975 films at T = 550 ◦ C and 750 ◦ C for 30 minutes and are shown in Fig. 1a,b and c, respectively. The average composition of the pre-annealed film was determined to be 2.5% Sn from Rutherford backscattering spectroscopy. The TEM image of the pre-annealed Snx Ge1−x film seen in Fig. 1a consisted of Sn enriched Snx Ge1−x nanowires oriented along (001) embedded in
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Applied Physics A – Materials Science & Processing Cross-sectional TEM image of a Snx Ge1−x film with x = 0.025 grown by MBE at T = 160 ◦ C (a) prior to annealing (the inset is a schematic of the microstructure where the arrow points to Sn-rich regions in the microstructure), (b) annealed at T = 550 ◦ C and taken down the [110] zone axis, and (c) annealed at → T = 750 ◦ C and imaged under − g = [220] 2 beam conditions FIGURE 1
a Ge matrix [1]. The dark regions are the Sn-rich Snx Ge1−x nanowires and the light regions are nearly pure Ge. A schematic of the microstructure is shown in the inset of Fig. 1a in which the white regions, indicated by an arrow, represent the Sn-rich Snx Ge1−x nanowires. The characterization of the microstructure and the physical mechanism behind phase separation in the pre-annealed sample is described in detail elsewhere [1]. The TEM image of the Sn0.025 Ge0.975 film that was annealed at 550 ◦ C, shown in Fig. 1b, reveals NCs with an average measured diameter of 7 nm. Dark bands oriented along (001) are still observable indicating that some Sn remains in the Snx Ge1−x nanowires. In Fig. 1c, a dark → field TEM image taken under 2-beam conditions (− g = [220]) ¯ with the (220) diffraction planes excited is shown of the → Sn0.025 Ge0.975 film annealed at T = 750 ◦ C. Under − g = [220] 2-beam imaging conditions, strain contrast is enhanced between the Sn-rich Snx Ge1−x nanowires and the Ge matrix in the pre-annealed microstructure [1]. Snx Ge1−x nanowires are no longer observable in Fig. 1c although the diffraction conditions are highly sensitive to strain associated with nanowires. Thus, the 750 ◦ C anneal has transformed the microstructure; NCs are observed rather than nanowires. The volume density of NCs in the 100 nm TEM cross section is estimated at 2% and the average NC diameter is measured as 32 nm. 3.2
Results and discussion
Further examination of Fig. 1c shows that strain contrast is evident around a majority of the NCs in this dark field TEM image. Moir´e fringes are discernable in other NCs and are consistent with the formation of single crystalline particles. Threading dislocations are also observable in Fig. 1c and in the resulting film are confined near the epitaxial film/Ge (001) interface. High resolution TEM images of a NC with strain contrast and a NC with Moire fringes in the Sn0.025 Ge0.975 film annealed at T = 750 ◦ C are shown in Fig. 2. In Fig. 2a, a high resolution TEM image of a NC with a diameter of 26.5 nm that was surrounded by strain contrast in Fig. 1c is shown. The lattice fringes are continuous across the NC/Ge interface although local defects such as stacking faults are evident in the NC. A fast Fourier transform (FFT) was calculated for this high resolution TEM image to examine the periodicities in the NC lattice. The FFT, shown in Fig. 2b,
consists of periodicities from both the Ge matrix and the NC. The periodicities in Fig. 2b have the symmetry of a diffraction pattern taken down the (110) zone axis of a diamond cubic crystal. The reflections are indexed and the periodicities and angles between reflections are consistent with a Ge diamond cubic lattice. A diamond cubic lattice is expected for the matrix since pre-annealed epitaxial film is composed mainly of Ge. The fact that only one set of periodicities are evident in Fig. 2b indicates that the NC has the same lattice constant and crystal structure as the diamond cubic Ge matrix. Since Snx Ge1−x nanowires are not present, the solubility of Sn in Ge is negligible at the annealing temperature, and the estimated volume density of the NCs is approximately that of the average Sn composition, the NC is determined to be composed mainly of Sn after the anneal at 750 ◦ C. The NC seen in Fig. 2c has a diameter of 28.5 nm and is representative of NCs seen in Fig. 1c having Moir´e fringes. ¯ ¯ . The shape of The NC has facets along Ge 111 and 110 the NC is nearly spherical; a spherical surface minimizes surface area and therefore interfacial energy between the NC and Ge matrix. A FFT was also calculated from this TEM image to analyze the crystal structure. The Ge periodicities are circled in Fig. 2d to differentiate from the periodicities associated with the NC. The dashed lines are drawn to highlight periodicities associated with dynamical scattering of the Ge 111 diffracted beams with the NC’s lattice. The Ge periodicities are used as a calibration to calculate the interplanar spacing in the NC. The measured periodicities are 6.3 ± 0.1 Å, 4.8 ± 0.1 Å, and 10.7 ± 0.3 Å. These measured periodicities are consistent with the interplanar spacings, dhkl , of α-Sn, d100 = 6.48 Å and d110 = 4.58 Å, and incongruous with those expected for β-Sn, d100 = 5.83 Å and d110 = 4.12 Å. The measured value of the periodicity, 10.7 ± 0.3 Å, highlighted with an arrow is consistent with a Moir´e reflection, calculated as 10.9 Å, that arises due to the difference in lattice constants along [001] between Sn and Ge and a 15.5◦ tilt between the two lattices. As seen from the periodicities shown in Fig. 2d, there is a 15 degree angular separation between Ge (002) and Sn (001). Yet the measured periodicities deviate from the accepted values of α-Sn by up to 3.1%. In addition, the angle measured between the two reflections labeled 6.3 Å and 4.8 Å in Fig. 2d is 68.5◦ rather than 90◦ as expected for the diamond cubic lattice. The deviation was at-
RAGAN et al.
Diamond cubic Sn-rich nanocrystals: synthesis, microstructure and optical properties
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MBE grown Sn0.025 Ge0.975 /Ge (001) annealed at T = 750 ◦ C. (a) HR-TEM image of a coherently strained NC with a diameter of 26.5 nm, embedded in Ge and taken down the Ge [110] zone axis. (b) FT of NC and Ge matrix shown in (a). The NC and Ge matrix have the same crystal structure and lattice parameter. (c) HR-TEM image of NC with a diameter of 28.5 nm, embedded in Ge and taken down the Ge [110] zone axis. (d) FT of NC shown in (c) and Ge matrix. The periodicities associated with Ge are circled. Arrows point to Moir´e reflections. The dashed lines are drawn as a guide to the eye to highlight dynamical scattering from the Ge {111} diffracted beams FIGURE 2
tributed to elongation of reciprocal lattice points along [111] due to twinning [8]. Diffraction patterns of twinned Si NCs [8] and Si nanowires [9, 10] showed deviations from the expected values of the interplanar spacing by 20% and differences of up to 15◦ in the measured interplanar angles. Thus, the presence of twin planes may explain the deviation of the reciprocal lattice reflections with respect to the accepted values observed in Fig. 2d. Annealing Six Sn1−x films at 800 ◦ C produced Sn NCs via a void mediated growth mechanism [11]. It is possible that a similar mechanism is responsible for αSn NC formation in Ge. The melting temperature of bulk Sn is 232 ◦ C. Therefore at the annealing temperature of 750 ◦ C, Sn is molten in a Ge void. If solidification occurs at multiple fronts during cooling, the NC may form a low angle grain boundary (twin). Based on the measured values of the interplanar spacings and Moir´e reflection in the diffraction pattern and the low solid solubility of Sn in Ge, the NC shown
in Fig. 1c was determined to be in the diamond cubic phase of Sn. 4
Optical characterization
4.1
Fourier transform infrared spectroscopy
Optical transmittance measurements were performed between 1000– 8000 cm−1 at 300 K on Sn0.025 Ge0.975 samples before and after annealing at T = 550 ◦ C, 650 ◦ C and 750 ◦ C using a Nicolet Magna 760 FT-IR spectrometer. In Fig. 3a, a small decrease in transmittance is observed below 4000 cm−1 for all the annealed samples in comparison to the pre-annealed sample. This decrease that is slightly greater than the measurement error of the FT-IR signal, 1%, was attributed to free carrier absorption. A significant decrease in transmittance with respect to the pre-annealed sample was observed above 4000 cm−1 for only the sample annealed at
FIGURE 3 (a) Transmittance versus wavenumber for Sn0.025 Ge0.975 /Ge (001) preannealed (line), annealed at T = 550 ◦ C (circles), 650 ◦ C (crosses) and 750 ◦ C (triangles). (b) Absorption coefficient versus wavenumber spectra: generated from the best fit of the simulation with experimental transmittance spectrum (closed triangles) and the calculated spectrum assuming bulk like behavior (open circles) for Sn0.025 Ge0.975 /Ge (001) annealed at T = 750 ◦ C
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Applied Physics A – Materials Science & Processing
750 ◦ C. It is this sample that TEM analysis demonstrated an evolution of the microstructure from nanowires to NCs. 4.2
Results and discussion
The absorption associated with the NCs in the film annealed at 750 ◦ C did not have a narrow line shape as may be expected for quantum-confined carriers but exhibited a “bulklike” absorption edge. The density of NCs in this 1 µm thick film was estimated as 2% yielding an effective optical thickness of 30 nm that gives rise to infrared absorption below the Ge bandgap. Using a thin film approximation with multiple interfaces, the transmittance curve was simulated between 3000 and 8000 cm−1 to obtain the dielectric function. The absorption versus wavenumber spectrum generated by the best fit with the experimental transmittance curve was fit to the functional form of the absorption coefficient assuming bulklike behavior [12–14]. In Fig. 3b, the absorption coefficient generated from the simulation (closed triangles) and the functional form of the absorption coefficient (open circles) are shown. Using this method, the best fit of the absorption coefficient generated an estimate of 0.45 eV for the direct bandgap absorption energy. The absorption coefficient was estimated as 3 × 103 cm−1 near the bandgap edge. The absorption edge below the measured bandgap of 0.45 eV has an exponential dependence on energy that is characteristic of Urbach’s rule and this type of absorption is typically associated with defect states, possibly occurring in the Ge matrix [15]. In comparison, photoluminescence measurements of Ge NC [16] and Si NC [17] demonstrated emission associated with defect states in the silicon dioxide matrix. Figure 4 demonstrates how the evolution of microstructure of Snx Ge1−x alloys transforms the optical properties. The measured energy bandgap was different for homogeneous Snx Ge1−x alloys (circles) [14], Snx Ge1−x alloy nanowire arrays embedded in Ge (squares) [1] and Sn-rich NCs in a Ge matrix (triangle). As described in this paper, in the case of Sn-
Evolution of the optical properties of Snx Ge1−x alloys as the microstructure is transformed from homogeneous Snx Ge1−x alloys (circles), Snx Ge1−x nanowire arrays embedded in Ge (squares), and Sn-rich NCs (triangle) FIGURE 4
rich NCs, the observation of “bulk-like” absorption below the Ge bandgap, 0.67 eV, and above 4000 cm−1 may be attributed to absorption between a distribution of higher lying electron and lower lying hole states, where the electron (hole) states are closely-spaced in energy due to inhomogeneous broadening arising from the size and possible composition variation in the NC arrays. 5
Summary
The fabrication of NCs embedded in Ge was achieved by annealing 1 µm thick Sn0.025 Ge0.975 films. The average diameter of the NCs increased from 7 nm to 32 nm by increasing the annealing temperature from 550 ◦ C to 750 ◦ C. Annealing at T = 750 ◦ C produced α-Sn-rich NCs with a mean diameter of 32 nm and a 2% volume density. Analysis of optical transmittance measurements of the sample annealed at T = 750 ◦ C generated a value of 0.45 eV for the onset of absorption and an estimated value of 3 × 103 cm−1 for the absorption strength. Absorption above 0.45 eV and below the Ge bandgap may be attributed to exciton generation in α-Sn-rich NCs arrays with a mean NC diameter of 32 nm. It is clear that the evolution of the microstructure affects the measured optical properties; thus one could tune the optical properties via nanostructure formation as well as Sn composition in Snx Ge1−x alloys. ACKNOWLEDGEMENTS This work was supported by the National Science Foundation. One of us (RR) acknowledges support in the form of an Intel fellowship. C.C. Ahn is gratefully acknowledged for illuminating scientific discussions of electron microscopy.
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