Strain engineering has proven to be vital for germanium-based photonics, in particular light emission. However, applying a large permanent biaxial tensile strain to germanium has been a challenge. We present a simple, CMOS-compatible technique to conveniently induce a large, spatially homogenous strain in circular structures patterned within germanium nanomembranes. Our technique works by concentrating and amplifying a pre-existing small strain into a circular region. Biaxial tensile strains as large as 1.11% are observed by Raman spectroscopy and are further confirmed by photoluminescence measurements, which show enhanced and redshifted light emission from the strained germanium. Our technique allows the amount of biaxial strain to be customized lithographically, allowing the bandgaps of different germanium structures to be independently customized in a single mask process.
© 2015 Optical Society of America
With electrical interconnects emerging as a severe performance bottleneck in silicon (Si) complementary metal-oxide-semiconductor (CMOS) devices, optical interconnects have become a leading contender for future CMOS technology . However, Si’s indirect bandgap limits its use in optoelectronics and there remain substantial manufacturing and cost concerns with hybrid Si/III-V approaches. It would therefore be advantageous if an optical link on Si can be realized using only group IV materials . As such, germanium (Ge) has garnered much attention [2–4] recently due to advances in Ge-on-Si heteroepitaxy  and because of Ge’s ability to perform useful optoelectronic functions . Although Ge is nominally an indirect bandgap semiconductor, it also has a direct bandgap of 0.800 eV which is only 133 meV larger than its indirect bandgap of 0.667 eV . This difference is small enough that researchers have successfully realized efficient Ge-on-Si photodetectors  and modulators . An electrically-pumped Ge-on-Si laser has also been demonstrated, but with an enormous threshold of ~300 kA/cm2 which necessitates drastic improvements . Two approaches, n-type doping and tensile strain, have been proposed to remedy the situation  and tensile strain is a particularly promising route to an efficient, low-threshold Ge-on-Si laser .
Tensile strain improves the performance of Ge lasers by narrowing the direct bandgap relative to the indirect gap, with 4.6% uniaxial strain or 1.7% biaxial strain yielding a direct bandgap . Tremendous advances have been made in realizing large uniaxial strains in Ge using nanowire and micro-bridge structures , including a maximum reported uniaxial strain of 5.7% which represents direct bandgap Ge-on-Si . Similar advances for biaxially strained Ge-on-Si, however, have been lacking even though biaxial strain is best suited to the radial symmetry of microdisk and microgear resonators which combine high Q factors and compact form factors. While biaxially strained direct bandgap Ge has been demonstrated using pseudomorphic growth on lattice-mismatched GaAs/InGaAs substrates  or by temporarily applying gas pressure to a suspended Ge nanomembrane , neither approach produces a permanently-sustained biaxial tensile strain in Ge integrated on a Si platform. A permanent biaxial tensile strain of 1.1% was achieved in a freestanding Ge membrane supported on a Si substrate with a tungsten stressor , but the tungsten metal adjacent to the Ge and the out-of-plane deflection would compromise any optical cavity design. Truly CMOS-compatible structures with up to about 1% strain have been shown by depositing a stressed silicon nitride layer on a Ge stripe  or on a pedestal-mounted Ge disk , however the strain in those structures was extremely inhomogeneous in the vertical direction. Lastly, a recent technique using an all-around stressor layer has achieved a large and spatially uniform permanent biaxial strain in germanium  and can in principal become CMOS-compatible with some future modifications, but at present that work involved growth on III-V substrates and a problematic gold layer covering the entire substrate. There is therefore a need for a CMOS-compatible structure that induces large homogeneous biaxial tensile strains in Ge-on-Si that can truly be an effective platform for Ge lasers. Here we present such a structure and report experimentally measured biaxial tensile strains up to 1.11%. This strain can be conveniently customized from one device to another by lithographically modifying the dimensions of each structure, thereby allowing multiple strains – and therefore multiple bandgaps – to be realized across a single wafer in a simple one-mask process. For lack of a better term we refer to these structures as “microdisks,” especially the highly strained central regions, though we emphasize that no optical cavity or optical modes are present. We will also compare our fabricated structure to a related structure for inducing biaxial tensile strain in germanium that was theoretically proposed by Süess  and show that our structure offers a more uniform strain distribution, better size scalability, and a more practical fabrication.
2. Theoretical investigation
In order to achieve a large Ge volume under a tensile strain that is both large in magnitude and spatially homogenous, we have created a structure which concentrates a pre-existing tensile strain biaxially using a special geometry, in analogy with previous work which used a micro-bridge geometry [13,14,22,23] to concentrate a pre-existing tensile strain uniaxially. Our structure consists of a ~500 nm thick Ge disk with several etch slits in a radially symmetric pattern as shown in a simplified schematic (Fig. 1(a) ) which helps visualize the stress concentration process intuitively. These structures are then deflected downward and brought into the contact with the substrate for improved thermal dissipation . This small (< 1 µm) deflection is not included in our modeling because it is negligible compared to the total size of the structures (>50 µm) and thus cannot meaningfully affect the strain distribution. We have then investigated the strain distribution using finite element method (FEM) COMSOL as shown in Fig. 1(c) and (d) for the case of a 5 µm inner microdisk diameter and a 50 µm outer (total) diameter, with a 20 µm wide ring between the etch slits and the fixed outer boundary. This 20 μm wide ring approximates the outward etching of the sacrificial oxide during the final fabrication step which leaves a halo of freestanding germanium near the outer boundary. Further FEM studies confirmed that the strain can indeed be made arbitrarily large by increasing the total (outer) diameter and also that this strain is exceedingly homogenous: the biaxial strain at the center of the inner microdisk (inner 5 µm diameter region) of Fig. 1(d) is 0.435%, and remains constant to the third decimal place over an area of >10 µm2.
The mechanism by which stress concentration occurs this can be understood by considering only the eight “main” etch slits which touch the central microdisk region as shown in the FEM simulation of Fig. 2(a) . These eight main slits create eight Ge “wedges” which are all pulling on the central microdisk region. Because there are Ge wedges pulling on the central regions from all directions, the resulting tensile strain is biaxial, in contrast with Ge microbridges [13,14,23] which could only produce a uniaxial strain. However, the structure of Fig. 2(a) with only the eight main etch slits is difficult to fabricate because it is difficult to properly remove the underlying oxide. This oxide is removed by an isotropic etch in hydrofluoric acid (HF) that emanates laterally outward from all of the slits. We must therefore etch enough oxide to exceed the maximum distance between any two adjacent features. Near the outer boundary of the 100 µm diameter structure of Fig. 2(a), the maximum distance between slits is about ~40 µm. Increasing the total diameter beyond 150 µm, e.g. to increase the strain or to increase the physical size of the active region, would cause the maximum distance between slits to exceed ~60 µm. This is problematic because this oxide etch is known to be highly irregular and asymmetric [21,25]. For such a lengthy oxide etch, this irregularity would affect the reproducibility of the strain result and hence limit manufacturability, meanwhile the asymmetry of the oxide removal may introduce unwanted shear components to the stress. This is of course in addition to the needlessly large footprint that accompanies such long oxide etches.
To overcome this problem we have added additional etch slits, as shown in Fig. 2(b), such that the distance between adjacent slits never exceeds 10 µm. This makes removing the oxide straightforward even for arbitrarily large dimensions: larger structures simply have more additional etch slits. Comparing the FEM simulations of Fig. 2(a) and Fig. 2(b) shows that the additional etch slits have only a slight impact on the strain distribution. Both of these FEM simulations are for a 5 μm inner microdisk diameter and a 100 μm total structure diameter, with 20 μm between the total structure dimensions and the fixed boundary; the two simulations differ only in whether or not additional etch slits are present. All etch slits were taken to be 500 nm wide with rounded tips on each end, in accordance with our experimental design parameters. Quantitatively analyzing the zoomed-in views of the microdisk region in Fig. 2, we find that the simulation without additional etch slits resulted in a 0.590% biaxial strain at the microdisk center whereas the simulation with the additional etch slits resulted in a 0.582% biaxial strain at the microdisk center. Meanwhile, the maximum biaxial strain in the corner regions, which we want to minimize, decreases from ~0.82% to ~0.77% upon adding the additional etch slits. Thus, we conclude that the only substantive effect of adding additional etch slits is to slightly reduce the strain without otherwise altering the overall strain distribution, an effect which can be compensated by simply making the total diameter very slightly larger.
To investigate how changing the number of “main” etch slits (i.e. slits which touch the inner microdisk) affects the strain distribution we have performed additional FEM simulations, shown in Fig. 3 , wherein we have fixed the inner microdisk diameter to 5 μm, the total structure diameter to 50 μm, and assumed a constant 20 μm between the total structure dimensions and the fixed boundary to approximate the outward etching of the sacrificial oxide. All etch slits were again taken to be 500 nm wide with rounded tips on each end, in accordance with our experimental design parameters. Meanwhile, the number of main etch slits was varied from 3 to 20. From Fig. 3(a) we find that increasing the number of main etch slits drastically increases the spatial homogeneity of the strain in the microdisk. The relationship between the number of main etch slits and the microdisk strain and the corner strain, shown in Fig. 3(b) is more complex. For the design parameters used in this series of FEM simulations, it would appear that somewhere between 10 and 15 main etch slits offers the optimal combination of relatively high microdisk strain and relatively low corner strain, however we expect this number to change significantly if the microdisk diameter is changed and/or the width of the etch slits is changed. In the experimental section of this work, we have limited our studies to structures with exactly eight main etch slits, but changing the number of main etch slits may be an avenue to achieve even higher biaxial tensile strain in a future work or for other researchers looking to replicate our efforts.
Independently to our research, Süess has theoretically proposed a structure that concentrates a biaxial tensile strain  by patterning a “Maltese cross” of four rounded trapezoidal etch slits. However, it was found theoretically that unwanted corner stresses can be minimized for the case of rectangular slits , which is what we already employ in our structure. A key difference of our structure is that, unlike any existing proposal , we have considered having more than four etch slits touch the central active region. Our FEM simulations in Fig. 3(a) plainly show that increasing the number of these “main” etch slits substantially improves the uniformity of the strain distribution, and our FEM simulations in Fig. 3(b) further show that changing the number of main etch slits is also a critical parameter for minimizing unwanted corner stresses. This key point for reducing the corner stress will allow us to realize large and spatially uniform biaxial tensile strain in our experimental fabrications. Also, our unique idea of having additional etch slits, illustrated in Fig. 2, is what makes experimental fabrication even feasible by minimizing problematic lateral under-etching of the sacrificial oxide. Therefore, our structure represents a substantial improvement over any existing proposal  with regard to both performance and manufacturability, and is indeed the first such structure to be manufactured.
3. Fabrication and characterization
Fabrication began with an Si/SiO2/Ge substrate. Using electron-beam lithography, the top Ge layer of this substrate is patterned and etched into a disk with many slits as shown in Fig. 1(b). During the final fabrication step, the oxide from the material stack is removed using an isotropic wet etch in hydrofluoric acid and the small pre-existing tensile stress redistributes and concentrates in the microdisk at the center of each structure. The small microdisks with diameters of 5.0-7.5 µm therefore become very highly strained, while most of the remaining Ge in the structure relaxes somewhat to compensate. Each entire structure was permanently adhered to the underlying silicon substrate due to stiction after release  as experimentally confirmed by the measured surface profile of the fabricated structure as shown in Fig. 4(c) . For simplicity, we have kept the number of etch slits constant at eight and the width of each etch slit constant at 500 nm in our fabricated structures. With those parameters held constant, the strain in the inner microdisk is purely a function of the initial stress in the Ge and the ratio of the inner microdisk diameter to the total structure diameter. The initial stress in the Ge is usually ~0.2% which arises from the mismatch in the thermal expansion coefficients between Ge and Si during the epitaxial growth of Ge on Si . By varying the ratio of the total diameter to the inner microdisk diameter, the strain in the microdisk can be varied lithographically from device to device and even be made arbitrarily large, limited only by material fracture of the Ge.
Structures were successfully fabricated with an inner microdisk diameter of 5 µm and with outer (total) diameters ranging from 30 to 130 µm along with a thickness of ~500 nm, and are shown in the optical and scanning electron micrographs in Fig. 4(a) and (b) as well as the optical surface profile of Fig. 4(c). A few devices were also successfully fabricated with 7.5 µm inner microdisk diameters for use in photoluminescence (PL) measurements. The strain in successfully fabricated structures was then measured by Raman spectroscopy using a 514 nm excitation laser operated at ~100 µW with 1 second integration time. This Raman excitation is known to be low enough that no significant heating effects occur during measurements on substrate-adhered germanium . The observed Raman shifts were then converted to biaxial strain values using a strain-shift coefficient of 390 cm−1 . According to the measured Raman spectra of Fig. 5(a) , the observed biaxial strains in the structures’ inner microdisks ranged from 0.2% to 1.11%; the lower bound of 0.2% strain represents the residual Ge strain in the absence of patterning. The relationship between the observed strain and the outer diameter is shown in the inset of Fig. 5(a) for a series of devices fabricated side-by-side in the same run. From Fig. 5(a) it is clear that the measured strain has not saturated even for our largest unbroken sample (130 µm outer diameter), and FEM simulations predict no hard limit on the achievable strain if fracturing is ignored. Thus if the material fractures can be eliminated, perhaps by reducing the initial defect density in the Ge or by alleviating the corner stresses from which the fractures originate, even larger biaxial strains may be within reach with larger dimensions. To experimentally confirm the strain uniformity, predicted by FEM modeling in Fig. 1(d), an area scan of the Raman shift was performed. As shown in Fig. 5(b), the observed Raman shift is nearly constant over a large area in the inner microdisk, indicating an excellent strain uniformity except for some sharp increases near the corner regions. This confirms that our structure achieves a uniform strain over a large area in practice as well as in theory.
Finally, the biaxially strained structures were characterized by PL measurements, as shown in Fig. 6(a) , taken at the center of the inner microdisks. The structures characterized by PL had a relatively large inner microdisk diameter of 7.5 µm to accommodate the finite spot size of the excitation laser, and the use of substrate-adhered Ge structures in this work precludes any significant heating effects from the 12 mW laser excitation . Biaxial strain is well understood to enhance Ge luminescence by increasing the fraction of electrons in the direct conduction valley [3,12,28], and we observe this phenomenon in our PL measurements. As shown explicitly in the inset of Fig. 6(b), the integrated intensity of the PL emission from our Ge structures increases by a factor of ~2.3x as the strain increases from zero to 0.98%. However, this is significantly smaller than the ~20x enhancement in Gamma valley occupancy expected from Ge’s deformation potentials . The most likely explanation for this discrepancy is that valence band splitting and polarization selection rules favor in-plane emission over out-of-plane emission as the biaxial strain increases . In a previous work , polarization dependent PL measurements on 1.6% uniaxially strained Ge showed that photon emission polarized parallel to the strain axis was suppressed by ~5x relative to the emission polarized perpendicular to the strain axis. We expect by analogy that in-plane biaxial tensile strain significantly reduces the fraction of photons that are polarized in the strain plane and propagate out of plane. Our setup cannot collect the photons propagating in plane because of the free-space PL setup configuration. Demonstrating the true emission enhancement by strain would require a burdensome workaround to collect such these in-plane emitted photons, for example fabricating an optical grating on the Ge surface . Another possibility is that pseudo-heterostructure effects  are causing carriers to drift to the highly-strained corner regions where the bandgap is smallest. Because these corners represent a surface, this might increase surface recombination and suppress the PL, though it is difficult to estimate the magnitude of this effect. It is unlikely that our unexpectedly low PL enhancement is due to dislocations arising from our strain technique: it has been previously demonstrated that uniaxial strain from stress-concentrating micro-bridges does not affect Ge’s defect-limited minority carrier lifetime  and we therefore do not expect our biaxial strain to noticeably affect Ge’s defect density either. Carrier diffusion may also help explain the PL enhancement discrepancy since biaxial tensile strain enhances carrier mobilities . This means that for our highly strained structures, carriers may diffuse away from the excitation area more quickly before radiative recombination can take place. Nevertheless, we can easily confirm the observed strain level in our Ge by verifying that the observed PL redshifts with strain follow the energy separations between the Gamma (Γ) valley and the two separate valence bands, the heavy hole (HH) and light hole (LH) bands, as has been observed in previous works [24,32]. As shown in Fig. 6(b), employing larger strains does indeed redshift the PL emission in accordance with the narrowing of the Γ–HH and Γ–LH bandgaps predicted by theory. These PL measurements therefore confirm that large strains are indeed achieved within our structures as previously shown by Raman spectroscopy.
In summary, we have experimentally achieved large biaxial strains of up to 1.11% in circular structures fabricated in Ge nanomembranes. Theoretical investigations showed that our structure can deliver better strain uniformity and is also much easier to fabricate than a previous proposal for a biaxial stress concentration  which has so far never been successfully fabricated. Unlike previous experimental works on biaxially tensile strained Ge [15–20,33], our fabricated biaxial tensile strain simultaneously satisfies all of the following conditions: the biaxial strain is permanently-sustained (unlike [16,33]), the biaxial strain is vertically and laterally homogenous over arbitrarily large volumes (unlike [16–19,33]), and the germanium is integrated directly on a Si substrate without using III-V materials so as to preserve full CMOS-compatibility (unlike [15,20,33]). Our process has the further advantage of simplicity and reduced cost since it involves only one lithography step and does not require external stressor layers (unlike [17–20]) or out-of-plane deflections (unlike [16–19]). The amount of strain in our structures and the lateral homogeneity of the strain distributions were experimentally determined using Raman spectroscopy, and found to be in good agreement with FEM simulations. Vertical homogeneity of the strain distribution was presumed since the geometry is purely in-plane with no relevant vertical features, and lateral homogeneity was experimentally confirmed by means of a Raman area scan. Red-shifted PL spectra from the strained disks offer further confirmation of the high strain levels in these Ge structures, validating the Raman spectroscopy results; although the observed PL enhancements were smaller than expected, this can be explained quantitatively by polarization selection rules which favor in-plane emission (which we cannot detect) over out-of-plane emission. Additionally, the permanent stiction between the Ge nanomembrane and the Si substrate provides excellent thermal conductivity and eliminates heating problems which have traditionally plagued other membrane approaches .
The biaxially strained Ge structures presented herein also offer an extraordinary level of design flexibility: the strained regions can be of any size; the strain level of each structure can be precisely customized at the lithography stage; and structures with difference strains, and therefore different bandgaps, can be fabricated side-by-side in a simple one-mask process. This size scalability is important for enabling versatile resonator design if the structures are further patterned into micro-disk or micro-gear resonators, a task which we leave for a future work. Meanwhile, the presence of multiple bandgaps means that a much wider range of wavelengths can be accessed for emission, modulation and detection, thus raising the possibility of employing these structures in extended wavelength-division multiplexing systems for on-chip optical interconnects, and all without the cost or complexity of additional heteroepitaxy. Such flexibility was previously only possible using uniaxial strain [13,14,22,23], but our technique extends this design flexibility to biaxial tensile strain. This functionality of precisely changing bandgaps using lithography may find applications not only using Ge but also with III-V materials, and our approach should be highly transferable to any arbitrary material system provided that the active material begins with some initial tensile stress.
This work was supported by the Office of Naval Research (grant N00421-03-9-0002) through APIC Corporation (Dr. Raj Dutt) and by a Stanford Graduate Fellowship. This work was also supported by an INHA UNIVERSITY Research Grant and by the Pioneer Research Center Program through the National Research Foundation of Korea funded by the Ministry of Science, ICT & Future Planning (2014M3C1A3052580).
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