Abstract

We have demonstrated that bandgap energy of Si can be controlled by micro-mechanically structured Si beams (250 nm thick, 3 μm wide, and 15 μm long) elastically deformed by an external force. Microscopic photoluminescence spectroscopy reveals that downward bending of the beam by 3 μm reveals a red shift in the peak from ~1100 nm up to ~1300 nm. It is found from calculations based on deformation potentials and finite element method that tensile strain as large as ~1.5% is generated in the top surface of the deformed beam and responsible for the red shift of the peak. The presented result should be a proof of concept to cancel wavelength fluctuation unavoidably occurring on uncooled LSIs in terms of stress application, and thereby an enabler of wavelength division multiplexing implementation on a chip. The applications of other beam materials such as Ge and GaAs are discussed.

©2010 Optical Society of America

1. Introduction

Electronic-photonic convergence is one of the most important approaches to enhance information capacity on a chip. Si photonics is a promising solution for it, since we can utilize built-in LSI technologies for photonic devices as well. A current challenge is to implement wavelength division multiplexing (WDM), especially dense WDM (DWDM) on a chip [1], which should substantially increase the information capacity on a chip. It has recently been reported that temperature on LSIs fluctuates from 20 to 80°C in operation [2]. Such fluctuation should incur instability of operation wavelength through bandgaps and refractive indices of the device materials and lead malfunctioning WDM devices on an uncooled chip. Light emitters (EMTs), multiplexer/demultiplexer (MUX/DEMUXs), and optical modulators (MODs) such as electro-absorptive (EA) MODs are among the devices. The present paper proposes an approach to lock the operation wavelengths in such thermal environment based on strain engineering using micro-mechanical Si beam structures. Strain engineering has originally been proposed for optoelectronic devices, successfully applied to strained InGaAsP lasers and recently to sensing devices [36]. We also reported a theoretical calculation of Ge EMTs using a crossing beam structure [7]. The present paper has reported a large red shift (~200 nm) in the PL peak of a Si single beam elastically deformed by applying mechanical stress. We have found that strain as large as 1.5% is induced and modifies the bandgap and refractive index of the beam. Therefore, strain engineering of this kind is an enabler of the operation wavelength locking even in the local temperature fluctuation. We have discussed applications of the presented approach to the other materials such as Ge and GaAs.

2. Theoretical background

To study the stress-bandgap relation, we have selected a Si single beam structure, i.e., cantilever as an example. When an external force is vertically applied at the tip of beam, the top (backside) surface is stretched (compressed) especially near the fixed edge of the beam, indicating that a tensile (compressive) strain is generated there.

A theoretical calculation is carried out on the strain-induced change in Si bandgap for the [100] uniaxial stress using the deformation potentials reported in ref [8]. Figure 1 shows the relation of the indirect bandgap energies of Si with the [100] uniaxial stress. Under the compressive (tensile) stress in the [100] direction, the conduction band minima at the Δ points in the [ ± 100] directions are higher (lower) in energy than those in the [0 ± 10] and [00 ± 1] directions, while the heavy-hole (HH) valence band maximum is higher (lower) in energy than the light-hole (LH) valence band maximum. Bandgap narrowing thus occurs for both sides of the compressive and tensile stresses.

 figure: Fig. 1

Fig. 1 Indirect bandgap energies calculated for Si under [100] uniaxial stress. HH and LH indicate heavy-hole and light-hole valence bands respectively.

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The strain distribution is simulated using a finite element analysis for a simple straight beam structure of (001) Si in the [100] direction, which is fixed to a wide Si slab. Figure 2 also shows a typical example of strain and its distribution of a beam structure 5 μm wide, 10 μm long and 1 μm thick. The force is vertically applied to bend the beam by 3 μm as in Fig. 2. It is found that a large strain is generated near the beam edge connected to the slab. The maximum tensile strain of 2.1% is accumulated at the top surface near the corners of the beam edge. A slightly smaller but still large tensile strain of 1.8% is also generated at the center of the beam edge. Simultaneously the compressive strain is generated on the backside with the same amount (not shown here). A larger strain should be generated by further bending. It is important to note that the bandgap of the bent Si beam is shrunk at both top and backside surfaces as understood from Fig. 1. Thus, when the Si beam is pre-strained to adjust its operation wavelength as an initial state, the wavelength should be locked by increasing or releasing external forces.

 figure: Fig. 2

Fig. 2 A typical strain distribution for a Si micro-beam structure. The x, y, and z axes correspond to the crystallographic axes [100], [010] and [001] respectively. Positive strain values are tensile.

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Thus, when the Si beam, equipped with a photonic device, is pre-strained as an initial state to adjust the working wavelength of device, the wavelength should be locked by increasing or releasing the external force, e.g., an electrostatic force, even under the temperature fluctuation. The theoretical fracture stress for Si is more than 20 GPa [9], although the actual fracture stress is strongly dependent on the sample size and the crystalline quality. Namazu, et al. reported that the average fracture stress for submicron Si beams (17.5 GPa) is almost 40 times larger than that for millimeter-sized samples [10], and Alan et al. [11] achieved a higher stress of 18.2 GPa for [110] Si beams with surface passivation by a methyl mono layer. These reports indicate that the micro-beam structure is promising to induce a strain as large as several %, which is enough for the wavelength locking under the temperature fluctuation on a Si chip.

3. Experimental procedure

3.1 Fabrication

Figure 3 shows a schematic illustration of the fabrication process of Si beams. As the starting substrate, a Si on insulator (SOI) wafer was used where the top Si layer was 0.25 μm thick and the buried oxide (BOX) layer 3 μm thick. The patterns were defined by electron-beam (EB) lithography with an EB resist of ZEP520A. After the formation of resist patterns using the F5112 + VD01 EB lithography system, the top Si layer was selectively etched with the resist mask using a reactive ion etching with Cl2 and O2 gases. The ion etching time was typically 220s to etch the top Si layer. In order to remove SiO2 under the Si beams, the sample was dipped in a 1 HF (50wt%): 1 H2O solution. A typical example of Si beams fabricated is shown in Fig. 4 as a scanning electron microscopic (SEM) image. The HF dipping simultaneously removed SiO2 under slab region near the pattern edge. The cross sectional SEM of the etched area revealed the undercut by ~2 μm wide, i.e., about a half of the beam width. The simulation of strain distribution in Fig. 2 has taken the undercut of the slab region into account.

 figure: Fig. 3

Fig. 3 Fabrication process of Si beams. Patterning of top Si layer through EB lithography and reactive ion etching were done. BOX layer was removed by HF wet etching.

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 figure: Fig. 4

Fig. 4 SEM image taken for a fabricated Si beam sample

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3.2 Evaluation of bandgap

Microscopic (μ)-PL spectroscopy was carried out to evaluate the bandgap energy of the fabricated Si beams. The beams were typically 3 μm wide, 15 μm long, and 0.25 μm thick. A solid state laser at 457 nm was used to excite the Si beam. The laser power and spot size were ~4 mW and ~1 μm on the beam. An objective lens was used for reducing the spot size as well as the collection of PL light. We employed a microprober to apply a mechanical force onto the beam. Figures 5(a) and 5(b) show optical microscope images for the fabricated Si beam without and with pushing by a microprober tip (appeared as a dark regions), and the points (A, B, and C shown as Fig. 5(a)) on the beam to push by the microprober. The position of A is 15 μm away from the slab region, B 10 μm, and C 5 μm, respectively. To reproduce the stress amount on the beam in each experiment, we always lower the microprober to push these points down by 3 μm. Since the BOX layer was 3 μm thick, the amount of the beam bending was precisely determined. One uncertainty to simulate the amount was actual position of the microprober to touch the beam because the position was behind the microprober. We assumed the uncertainty to be ± 2μm along the beam length, considering the radius of the microprober tip. Thereby the amount of strain and distribution by the force was simulated at each point including such uncertainty. We will come back this point later on.

 figure: Fig. 5

Fig. 5 Top optical microscopic images of fabricated Si beam and micro-probe needle (a) without and (b) with applying force. The most strained area was excited by ~4 mW 457 nm laser to get PL while external stress was applied on three points (A, B, and C) on beam by microprobe tip.

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4. Result and Discussion

We have detected significant differences in each μ−PL spectrum of the bent beam. Figure 6 shows typical μ-PL spectra obtained with and without pushing by the microprober. It is clearly demonstrated that the broader peak shifts towards a lower energy with increasing the stress from A to C. After removing the microprober from the beam, the PL spectrum as “straight” restored, indicating the deformation of the beam is elastic. The μ−PL peak after Lorenzian fitting was at 1121 nm in wavelength under no stress, at 1164 nm upon pushing A, at 1209 nm upon B, and at 1301 nm upon C. The red shift should thus be ascribed to the bandgap narrowing induced by the bending of the beam.

 figure: Fig. 6

Fig. 6 Typical PL spectra from a Si beam with and without external stresses. Straight and A~C indicate spectra of the beam with different amount of strain. Sharp peaks observed were due to the Fabry-Perot resonances occurred in the beam, and thus ignored in this context.

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Figure 7 shows strain and bandgap energy relation from the theoretical and experimental peak positions of μ-PL spectra in Fig. 6. The large error bars are due to the uncertainty of the beam positions pushed by the microprober, i.e., ± 2 μm along the beam length. It can be said that the experimental data is in broad agreement with the theoretical prediction. The amount of the maximum shift is ~0.2 eV, corresponding to the uniaxial strain of ~1.5%, according to Fig. 1.

 figure: Fig. 7

Fig. 7 Comparison between theoretical bandgap shrinkage under tensile strain and experimental results. Strain in experimental data were estimated by finite element analysis as shown above, and bandgap energies were determined from peak positions of PL spectra. The error bars show the possible error of the beam position pushed by the microprober: the positioning error was assumed ± 2 μm.

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The amount of the bandgap shrinkage due to temperature fluctuation is calculated to be ~20 meV [12] assuming that temperature change is 60°C on a chip in operation as reported [2]. The oscillation of temperature fluctuation on a chip should be slower than kHz, while the stress application can be done at speed of kHz. Therefore, wavelength shift due to temperature fluctuation should be compensated employing the presented approach. Thus, the above-mentioned results are a proof of concept to cancel the wavelength shift induced by temperature fluctuation on a chip. It should work for EMTs and MODs.

The refractive index of the Si beam should also be dependent on the stress. Biegelesen measured the photoelastic effect of Si bulk under biaxial strain and reported a photoelastic coefficient is −3.2 ± 0.2 x 10−2 [13]. On the other hand, the refractive index dependence on temperature of Si is reported to be ~2 x 10−4 K−1 [14]. Thus the refractive index of Si should shift by the amount of 1.2 x 10−3 by the temperature change of 60°C on a chip [2]. The index shift can thus be compensated by ~0.1% strain. Thus, 1.5% generated by the present approach should be able to lock the operation wavelength of MUX/DEMUXs against on-chip temperature fluctuation as well.

Finally we should like to discuss the material for EMTs using the present approach. Si may not be a good candidate to discuss active devices, particularly EMTs. Strained Ge on Si beam or strained GaAs on Ge on Si beam, for example, should be good candidates. It is well known that a large tensile strain should lead to indirect-direct transition of the Ge band structure [15]. According to the deformation potential calculations, Ge becomes a direct bandgap semiconductor under ~2% biaxial tensile strain where the bandgap is reduced to 0.5 eV (λ = 2.5 μm). Thus, tensile-strained Ge can be a mid-infrared light emitter material for the sensing application of bio-molecules. Furthermore, GaAs on Ge on Si can be a light emitter material in the optical communication band with ~5% biaxial tensile strain. Although the bandgap of unstrained GaAs is 1.42 eV, it was reduced to 0.8 eV (λ = 1.55 μm) by the strain. The wavelength locking against temperature fluctuation should be readily implemented on a chip in terms of the beam structures studied in the present paper. The results for Ge on Si and GaAs on Si will be presented in forthcoming papers.

5. Conclusion

We have proposed a strain engineering approach of wavelength locking of Si WDM devices against temperature fluctuation on uncooled LSIs. We have employed a Si single beam structure with a microprober to mechanically strain the beam. It has been shown from the μ-PL analyses of the strained Si beam that the PL peak shows a red shift as large as ~200 nm, corresponding to bandgap shrinkage by ~0.2 eV corresponding to strain induced in the beam ~1.5%. The microprober employed to bend the beam can be replaced to an electrostatic structure in future commercial products. Strain engineering using beam-shaped device materials should be promising to give immunity against temperature fluctuation on uncooled LSIs integrated with WDM to achieve extremely high information capacity.

Acknowledgements

This work was partly supported by the Grant-in-Aid for Creative Scientific Research on Si CMOS Photonics. The samples were fabricated using an EB writer F5112 + VD01 in VLSI Design and Education Center (VDEC), the University of Tokyo, donated by ADVANTEST Corporation with the collaboration with Cadence Corporation.

References and links

1. L. C. Kimerling, “Photons to the resque: microelectronics becomes microphotonics,” Electrochem. Soc. Interface 9, 28–31 (2000).

2. H. F. Hamann, A. Weger, J. A. Lacey, Z. Hu, P. Bose, E. Cohen, and J. Wakil, “Hotspot-Limited Microprocessors: Direct Temperature and Power Distribution Measurements,” IEEE J. Solid-state Circuits 42(1), 56–65 (2007). [CrossRef]  

3. G. C. Osbourn, “InGaAs-InGaAs strained-layer superlattices: A proposal for useful, new electronic materials,” Phys. Rev. B 27(8), 5126–5128 (1983). [CrossRef]  

4. H. K. Choi and C. A. Wang, “InGaAs/InGaAs strained single quantum well diode lasers with extremely low threshold current densisty and high efficiency,” Appl. Phys. Lett. 57(4), 321–323 (1990). [CrossRef]  

5. W. Xiang and C. Lee, “Nanophotonics sensor based on microcantilever for chemical analysis,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1323–1326 (2009). [CrossRef]  

6. H. Okamoto and D. Ito, “K. Onomitsu1, T. Sogawa1, and H. Yamaguchi, “Controlling quality factor in micromechanical resonators by carrier excitation,” Appl. Phys. Express 2, 035001 (2009). [CrossRef]  

7. P. H. Lim, S. Park, Y. Ishikawa, and K. Wada, “Enhanced direct bandgap emission in germanium by micromechanical strain engineering,” Opt. Express 17(18), 16358–16365 (2009). [CrossRef]   [PubMed]  

8. C. G. Van de Walle, “Band lineups and deformation potentials in the model-solid theory,” Phys. Rev. B Condens. Matter 39(3), 1871–1883 (1989). [CrossRef]  

9. A. L. Ruoff, “On the ultimate yield strength of solids,” J. Appl. Phys. 49(1), 197–200 (1978). [CrossRef]  

10. T. Namazu, Y. Isono, and T. Tanaka, “Evaluation of size effect on mechanical properties of single crystal silicon by nanoscale bending test using AFM,” J. Micromech. Syst. 9(4), 450–459 (2000). [CrossRef]  

11. T. Alan, A. T. Zehnder, D. Sengupta, and M. A. Hines, “Methyl monolayers improve the fracture strength and durability of silicon nanobeams,” Appl. Phys. Lett. 89(23), 231905 (2006). [CrossRef]  

12. O. Madelung, “Semiconductors- Basic Data” 2nd edition (Springer-Verlag Berlin Heidelberg, 1996) p.12.

13. D. K. Biegelesen, “Photoelestic tensor of silicon and the volume dependence of the avarate Gap,” Rhys. Reb. Lett. 32(21), 1196–1199 (1974). [CrossRef]  

14. G. Ghosh, “Temperature dispersion of refractive indices in semiconductors,” J. Appl. Phys. 79(12), 9388–9389 (1996). [CrossRef]  

15. K. Wada, J. F. Liu, S. Jongthammanurak, D. D. Cannon, D. T. Danielson, D. H. Ahn, S. Akiyama, M. Popovic, D. R. Lim, K. K. Lee, H.-C. Luan, Y. Ishikawa, J. Michel, H. A. Haus, and L. C. Kimerling, “Si Microphotonics for optical interconnection,” in Optical Interconnects, The Silicon Approach, eds L. Pavesi, G. Guillot (Springer Berlin Heidelberg New Yok, 2006), pp. 291–310.

References

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  1. L. C. Kimerling, “Photons to the resque: microelectronics becomes microphotonics,” Electrochem. Soc. Interface 9, 28–31 (2000).
  2. H. F. Hamann, A. Weger, J. A. Lacey, Z. Hu, P. Bose, E. Cohen, and J. Wakil, “Hotspot-Limited Microprocessors: Direct Temperature and Power Distribution Measurements,” IEEE J. Solid-state Circuits 42(1), 56–65 (2007).
    [Crossref]
  3. G. C. Osbourn, “InGaAs-InGaAs strained-layer superlattices: A proposal for useful, new electronic materials,” Phys. Rev. B 27(8), 5126–5128 (1983).
    [Crossref]
  4. H. K. Choi and C. A. Wang, “InGaAs/InGaAs strained single quantum well diode lasers with extremely low threshold current densisty and high efficiency,” Appl. Phys. Lett. 57(4), 321–323 (1990).
    [Crossref]
  5. W. Xiang and C. Lee, “Nanophotonics sensor based on microcantilever for chemical analysis,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1323–1326 (2009).
    [Crossref]
  6. H. Okamoto and D. Ito, “K. Onomitsu1, T. Sogawa1, and H. Yamaguchi, “Controlling quality factor in micromechanical resonators by carrier excitation,” Appl. Phys. Express 2, 035001 (2009).
    [Crossref]
  7. P. H. Lim, S. Park, Y. Ishikawa, and K. Wada, “Enhanced direct bandgap emission in germanium by micromechanical strain engineering,” Opt. Express 17(18), 16358–16365 (2009).
    [Crossref] [PubMed]
  8. C. G. Van de Walle, “Band lineups and deformation potentials in the model-solid theory,” Phys. Rev. B Condens. Matter 39(3), 1871–1883 (1989).
    [Crossref]
  9. A. L. Ruoff, “On the ultimate yield strength of solids,” J. Appl. Phys. 49(1), 197–200 (1978).
    [Crossref]
  10. T. Namazu, Y. Isono, and T. Tanaka, “Evaluation of size effect on mechanical properties of single crystal silicon by nanoscale bending test using AFM,” J. Micromech. Syst. 9(4), 450–459 (2000).
    [Crossref]
  11. T. Alan, A. T. Zehnder, D. Sengupta, and M. A. Hines, “Methyl monolayers improve the fracture strength and durability of silicon nanobeams,” Appl. Phys. Lett. 89(23), 231905 (2006).
    [Crossref]
  12. O. Madelung, “Semiconductors- Basic Data” 2nd edition (Springer-Verlag Berlin Heidelberg, 1996) p.12.
  13. D. K. Biegelesen, “Photoelestic tensor of silicon and the volume dependence of the avarate Gap,” Rhys. Reb. Lett. 32(21), 1196–1199 (1974).
    [Crossref]
  14. G. Ghosh, “Temperature dispersion of refractive indices in semiconductors,” J. Appl. Phys. 79(12), 9388–9389 (1996).
    [Crossref]
  15. K. Wada, J. F. Liu, S. Jongthammanurak, D. D. Cannon, D. T. Danielson, D. H. Ahn, S. Akiyama, M. Popovic, D. R. Lim, K. K. Lee, H.-C. Luan, Y. Ishikawa, J. Michel, H. A. Haus, and L. C. Kimerling, “Si Microphotonics for optical interconnection,” in Optical Interconnects, The Silicon Approach, eds L. Pavesi, G. Guillot (Springer Berlin Heidelberg New Yok, 2006), pp. 291–310.

2009 (3)

W. Xiang and C. Lee, “Nanophotonics sensor based on microcantilever for chemical analysis,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1323–1326 (2009).
[Crossref]

H. Okamoto and D. Ito, “K. Onomitsu1, T. Sogawa1, and H. Yamaguchi, “Controlling quality factor in micromechanical resonators by carrier excitation,” Appl. Phys. Express 2, 035001 (2009).
[Crossref]

P. H. Lim, S. Park, Y. Ishikawa, and K. Wada, “Enhanced direct bandgap emission in germanium by micromechanical strain engineering,” Opt. Express 17(18), 16358–16365 (2009).
[Crossref] [PubMed]

2007 (1)

H. F. Hamann, A. Weger, J. A. Lacey, Z. Hu, P. Bose, E. Cohen, and J. Wakil, “Hotspot-Limited Microprocessors: Direct Temperature and Power Distribution Measurements,” IEEE J. Solid-state Circuits 42(1), 56–65 (2007).
[Crossref]

2006 (1)

T. Alan, A. T. Zehnder, D. Sengupta, and M. A. Hines, “Methyl monolayers improve the fracture strength and durability of silicon nanobeams,” Appl. Phys. Lett. 89(23), 231905 (2006).
[Crossref]

2000 (2)

T. Namazu, Y. Isono, and T. Tanaka, “Evaluation of size effect on mechanical properties of single crystal silicon by nanoscale bending test using AFM,” J. Micromech. Syst. 9(4), 450–459 (2000).
[Crossref]

L. C. Kimerling, “Photons to the resque: microelectronics becomes microphotonics,” Electrochem. Soc. Interface 9, 28–31 (2000).

1996 (1)

G. Ghosh, “Temperature dispersion of refractive indices in semiconductors,” J. Appl. Phys. 79(12), 9388–9389 (1996).
[Crossref]

1990 (1)

H. K. Choi and C. A. Wang, “InGaAs/InGaAs strained single quantum well diode lasers with extremely low threshold current densisty and high efficiency,” Appl. Phys. Lett. 57(4), 321–323 (1990).
[Crossref]

1989 (1)

C. G. Van de Walle, “Band lineups and deformation potentials in the model-solid theory,” Phys. Rev. B Condens. Matter 39(3), 1871–1883 (1989).
[Crossref]

1983 (1)

G. C. Osbourn, “InGaAs-InGaAs strained-layer superlattices: A proposal for useful, new electronic materials,” Phys. Rev. B 27(8), 5126–5128 (1983).
[Crossref]

1978 (1)

A. L. Ruoff, “On the ultimate yield strength of solids,” J. Appl. Phys. 49(1), 197–200 (1978).
[Crossref]

1974 (1)

D. K. Biegelesen, “Photoelestic tensor of silicon and the volume dependence of the avarate Gap,” Rhys. Reb. Lett. 32(21), 1196–1199 (1974).
[Crossref]

Alan, T.

T. Alan, A. T. Zehnder, D. Sengupta, and M. A. Hines, “Methyl monolayers improve the fracture strength and durability of silicon nanobeams,” Appl. Phys. Lett. 89(23), 231905 (2006).
[Crossref]

Biegelesen, D. K.

D. K. Biegelesen, “Photoelestic tensor of silicon and the volume dependence of the avarate Gap,” Rhys. Reb. Lett. 32(21), 1196–1199 (1974).
[Crossref]

Bose, P.

H. F. Hamann, A. Weger, J. A. Lacey, Z. Hu, P. Bose, E. Cohen, and J. Wakil, “Hotspot-Limited Microprocessors: Direct Temperature and Power Distribution Measurements,” IEEE J. Solid-state Circuits 42(1), 56–65 (2007).
[Crossref]

Choi, H. K.

H. K. Choi and C. A. Wang, “InGaAs/InGaAs strained single quantum well diode lasers with extremely low threshold current densisty and high efficiency,” Appl. Phys. Lett. 57(4), 321–323 (1990).
[Crossref]

Cohen, E.

H. F. Hamann, A. Weger, J. A. Lacey, Z. Hu, P. Bose, E. Cohen, and J. Wakil, “Hotspot-Limited Microprocessors: Direct Temperature and Power Distribution Measurements,” IEEE J. Solid-state Circuits 42(1), 56–65 (2007).
[Crossref]

Ghosh, G.

G. Ghosh, “Temperature dispersion of refractive indices in semiconductors,” J. Appl. Phys. 79(12), 9388–9389 (1996).
[Crossref]

Hamann, H. F.

H. F. Hamann, A. Weger, J. A. Lacey, Z. Hu, P. Bose, E. Cohen, and J. Wakil, “Hotspot-Limited Microprocessors: Direct Temperature and Power Distribution Measurements,” IEEE J. Solid-state Circuits 42(1), 56–65 (2007).
[Crossref]

Hines, M. A.

T. Alan, A. T. Zehnder, D. Sengupta, and M. A. Hines, “Methyl monolayers improve the fracture strength and durability of silicon nanobeams,” Appl. Phys. Lett. 89(23), 231905 (2006).
[Crossref]

Hu, Z.

H. F. Hamann, A. Weger, J. A. Lacey, Z. Hu, P. Bose, E. Cohen, and J. Wakil, “Hotspot-Limited Microprocessors: Direct Temperature and Power Distribution Measurements,” IEEE J. Solid-state Circuits 42(1), 56–65 (2007).
[Crossref]

Ishikawa, Y.

Isono, Y.

T. Namazu, Y. Isono, and T. Tanaka, “Evaluation of size effect on mechanical properties of single crystal silicon by nanoscale bending test using AFM,” J. Micromech. Syst. 9(4), 450–459 (2000).
[Crossref]

Ito, D.

H. Okamoto and D. Ito, “K. Onomitsu1, T. Sogawa1, and H. Yamaguchi, “Controlling quality factor in micromechanical resonators by carrier excitation,” Appl. Phys. Express 2, 035001 (2009).
[Crossref]

Kimerling, L. C.

L. C. Kimerling, “Photons to the resque: microelectronics becomes microphotonics,” Electrochem. Soc. Interface 9, 28–31 (2000).

Lacey, J. A.

H. F. Hamann, A. Weger, J. A. Lacey, Z. Hu, P. Bose, E. Cohen, and J. Wakil, “Hotspot-Limited Microprocessors: Direct Temperature and Power Distribution Measurements,” IEEE J. Solid-state Circuits 42(1), 56–65 (2007).
[Crossref]

Lee, C.

W. Xiang and C. Lee, “Nanophotonics sensor based on microcantilever for chemical analysis,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1323–1326 (2009).
[Crossref]

Lim, P. H.

Namazu, T.

T. Namazu, Y. Isono, and T. Tanaka, “Evaluation of size effect on mechanical properties of single crystal silicon by nanoscale bending test using AFM,” J. Micromech. Syst. 9(4), 450–459 (2000).
[Crossref]

Okamoto, H.

H. Okamoto and D. Ito, “K. Onomitsu1, T. Sogawa1, and H. Yamaguchi, “Controlling quality factor in micromechanical resonators by carrier excitation,” Appl. Phys. Express 2, 035001 (2009).
[Crossref]

Osbourn, G. C.

G. C. Osbourn, “InGaAs-InGaAs strained-layer superlattices: A proposal for useful, new electronic materials,” Phys. Rev. B 27(8), 5126–5128 (1983).
[Crossref]

Park, S.

Ruoff, A. L.

A. L. Ruoff, “On the ultimate yield strength of solids,” J. Appl. Phys. 49(1), 197–200 (1978).
[Crossref]

Sengupta, D.

T. Alan, A. T. Zehnder, D. Sengupta, and M. A. Hines, “Methyl monolayers improve the fracture strength and durability of silicon nanobeams,” Appl. Phys. Lett. 89(23), 231905 (2006).
[Crossref]

Tanaka, T.

T. Namazu, Y. Isono, and T. Tanaka, “Evaluation of size effect on mechanical properties of single crystal silicon by nanoscale bending test using AFM,” J. Micromech. Syst. 9(4), 450–459 (2000).
[Crossref]

Van de Walle,, C. G.

C. G. Van de Walle, “Band lineups and deformation potentials in the model-solid theory,” Phys. Rev. B Condens. Matter 39(3), 1871–1883 (1989).
[Crossref]

Wada, K.

Wakil, J.

H. F. Hamann, A. Weger, J. A. Lacey, Z. Hu, P. Bose, E. Cohen, and J. Wakil, “Hotspot-Limited Microprocessors: Direct Temperature and Power Distribution Measurements,” IEEE J. Solid-state Circuits 42(1), 56–65 (2007).
[Crossref]

Wang, C. A.

H. K. Choi and C. A. Wang, “InGaAs/InGaAs strained single quantum well diode lasers with extremely low threshold current densisty and high efficiency,” Appl. Phys. Lett. 57(4), 321–323 (1990).
[Crossref]

Weger, A.

H. F. Hamann, A. Weger, J. A. Lacey, Z. Hu, P. Bose, E. Cohen, and J. Wakil, “Hotspot-Limited Microprocessors: Direct Temperature and Power Distribution Measurements,” IEEE J. Solid-state Circuits 42(1), 56–65 (2007).
[Crossref]

Xiang, W.

W. Xiang and C. Lee, “Nanophotonics sensor based on microcantilever for chemical analysis,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1323–1326 (2009).
[Crossref]

Zehnder, A. T.

T. Alan, A. T. Zehnder, D. Sengupta, and M. A. Hines, “Methyl monolayers improve the fracture strength and durability of silicon nanobeams,” Appl. Phys. Lett. 89(23), 231905 (2006).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 Indirect bandgap energies calculated for Si under [100] uniaxial stress. HH and LH indicate heavy-hole and light-hole valence bands respectively.
Fig. 2
Fig. 2 A typical strain distribution for a Si micro-beam structure. The x, y, and z axes correspond to the crystallographic axes [100], [010] and [001] respectively. Positive strain values are tensile.
Fig. 3
Fig. 3 Fabrication process of Si beams. Patterning of top Si layer through EB lithography and reactive ion etching were done. BOX layer was removed by HF wet etching.
Fig. 4
Fig. 4 SEM image taken for a fabricated Si beam sample
Fig. 5
Fig. 5 Top optical microscopic images of fabricated Si beam and micro-probe needle (a) without and (b) with applying force. The most strained area was excited by ~4 mW 457 nm laser to get PL while external stress was applied on three points (A, B, and C) on beam by microprobe tip.
Fig. 6
Fig. 6 Typical PL spectra from a Si beam with and without external stresses. Straight and A~C indicate spectra of the beam with different amount of strain. Sharp peaks observed were due to the Fabry-Perot resonances occurred in the beam, and thus ignored in this context.
Fig. 7
Fig. 7 Comparison between theoretical bandgap shrinkage under tensile strain and experimental results. Strain in experimental data were estimated by finite element analysis as shown above, and bandgap energies were determined from peak positions of PL spectra. The error bars show the possible error of the beam position pushed by the microprober: the positioning error was assumed ± 2 μm.

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