## Abstract

One-dimensional stress dependence on the fundamental absorption edge of pure germanium (Ge) waveguide has theoretically and experimentally been studied, considering built-in two-dimensional stress-tensile Ge grown on Si. Based on the results, we have designed Ge Franz-Keldysh (FK) electroabsorption (EA) modulators to work at 1550 nm. Application of one-dimensional [110] compressive stress above −350 MPa on a pure Ge [-110] waveguide should allow 1550 nm light transmission, unless otherwise a pure Ge modulator can only operate at 1600 nm or longer due to the built-in two-dimensional tensile stress in Ge. The prediction has experimentally been verified using a SiN_{x} stressor film. This concludes that the presented stress-tuning approach of the pure Ge waveguides should expand the operation wavelength of Ge FK-EA modulators to C band. Since stress tuning can be locally done in the back-end-of-line of complementary metal oxide semiconductor (CMOS) process, the presented stress-tuning method should enable “field-programable” control of the operation wavelengths of the monolithically integrated Ge modulators in Si photonics platform.

© 2015 Optical Society of America

## 1. Introduction

Germanium (Ge) on Si is the fundamental material for various active devices to ignite major technology transition from discrete components to monolithically integrated circuits in Si photonics [1]: It functions as waveguide integrated photodetectors [2,3 ], modulators [4–8 ], and light emitters [9–11 ]. It is well conceived that built-in tensile stress accumulated in Ge on Si is beneficial to redshift its detection limit of photodetectors to 1605 nm from 1550 nm [12] and to contribute this indirect bandgap semiconductor to lase [9]. However, the redshift actually squeezes the operation wavelength window of Franz-Keldysh (FK) electroabsorption (EA) Ge modulators to around 1600 nm, i.e., longer [6,7 ]. This is a severe drawback of FK-EA Ge modulator, despite of its significant advantages: small footprint and high power efficiency [5]. To restore the redshift and control the operation wavelength, GeSi FK-EA modulators have been demonstrated [5,8 ] by alloying Ge with 0.8% Si. However, this approach requires epitaxial growth at least twice for modulators and photodetectors, as most of integrated circuits in Si photonics nowadays use pure Ge as a material for photodetectors. We have proposed the new approach, based on the effect of one-dimensional stress on the fundamental absorption edge of Ge devices [13,14 ]. The present paper reports the theoretical dispersion relations under one-dimensional stress compressive and tensile Ge waveguides fabricated from built-in two-dimensional stress-tensile Ge, and experimental verification that stress-compressive pure Ge waveguides show blueshifts in transmission spectra and allow 1550 nm transmission. The stress-compressive pure Ge waveguide should enable the pure Ge FK-EA modulators working at C band. The presented approach using dielectric stressors for stress-tuning is local and done in the back-end-of-line, opening a new way of “field-programmable” approach to control operation wavelengths of Ge FK-EA modulators.

## 2. Stress tuning of the fundamental absorption edge of Ge

We have first calculated the effect of stress on the dispersion relation in the built-in two-dimensional stress-tensile Ge due to epitaxial growth on Si. Here, we used the k·p theory and deformation potentials [15,16 ]. We define the Ge waveguide structure and stress configuration as in Fig. 1 ; the Ge waveguide is along [-110] direction and stress is applied along [110] direction horizontally to the waveguide. Figure 2 shows typical results of the valence bands and clearly indicates that:

- i) The one-dimensional stress splits the light hole and heavy hole bands from the origin (E = 0, k = 0). We hereafter define LH to as the band split to a higher energy and HH as the band to a lower energy.
- ii) The stress generates perturbation in the density of states (DOS) of the LH and HH bands, leading to the higher overall DOS effective mass of LH band toward −0.5 GPa compressive stress.
- iii) Anti-crossings of LH and HH bands occur, as clearly shown in the case of −0.5 GPa compressive stress along [110] direction.

These should affect the fundamental absorption of Ge: splitting into two fundamental absorption edges, alternation of the absorption coefficients due to the DOS change, and possible generation of absorption anomalies near the anti-crossings. In the modulator application, such anomalies near the anti-crossing should be carefully avoided.

One dimensional [110] stress dependence of Γ point in energy was also calculated and found it approximated to a linear equation within a stress range from −1 to 1 GPa, as follows.

Here,*E*denotes the energy of Γ point (in eV),

_{Γ}*K*a constant,

*σ*stress in GPa and

*E*bandgap energy ( = 0.8 eV). We found that

_{G}*K*is calculated to be ~-32 meV/GPa within the stress range in the present paper. Thus, the bandgaps of LH and HH can be given by

*E*and

_{Γ}-E_{LH}*E*. The stress dependence of the fundamental absorption edges is calculated and shown in Fig. 3 . The valence band splitting at zero stress is due to the built-in two-dimensional tensile strain (0.17%) [12]. It predicts that the fundamental absorption edge due to LH to the conduction band should be around 1580 nm. It was demonstrated that the pure Ge FK-EA modulator (400 nm thick x 600 nm wide x 40 µm long) would shift to 1590 ~1600 nm [6]. Thus, the experiment data reported agree well with the case of LH in Fig. 3. This leads us to conclude that 1550 nm light should transmit through the Ge waveguide under application of one-dimensional [110] compressive stress of −350 MPa or higher. In other words, pure Ge waveguide modulators can operate at any wavelengths in C-band under application of compressive stress shown in the figure.

_{Γ}-E_{HH}## 3. Design of modulator performance of stress-tuned pure Ge

To apply the stress-tuning approach to Ge FK-EA modulators working at 1550 nm, we have optimized the amount of stress to get a higher figure of merit (FOM) as well as a larger extinction ratio (ER). Equation (2a) and (2b) express FOM and ER of Ge FK-EA modulators.

Here, α(V) and α(0) are the absorption coefficients of Ge (in cm^{−1}) with and without an external electric field and L is the length of Ge waveguide (in cm). The absorption coefficient due to the direct bandgap is estimated by the generalized Franz-Keldysh formalism. We consider the contribution by the indirect bandgap as well, using one phonon model [17].

Figure 4
shows the stress dependences of FOM and ER when stress is applied to these two directions, [110] and [100]. We assume here the waveguide is 100 µm long and a reserve bias of −3 V is applied to a 400 nm-thick Ge vertical *p-i-n* diode waveguide. It is clear that FOM is higher in the stress range −350 MPa up to −700 MPa at [110] stressing. The FOM is ~2, which is similar to GeSi alloys with the same applied reserve electric field [18]. There is no difference in ER between two stress directions in this stress range as well and at least 10 dB of ER could be obtained. This leads us to conclude the stress direction should be [110] and the strength should range from −350 MPa to −700 MPa.

## 4. Experimental procedures

We fabricated Ge waveguides monolithically integrated incoming and outgoing Si waveguides, using Si on insulator (SOI) substrates. Here, the stressor films of the Ge waveguide were silicon nitride (SiN_{x}) to apply compressive stress. 400 nm thick pure Ge (001) epilayers were selectively grown in a 100 x 100 µm area with SiO_{2} masks on SOI substrates at 600 °C using ultra-high vacuum chemical vapor deposition (UHV-CVD). There was a 100 nm thick Si cap layer on Ge. The Ge waveguides and Si waveguides were simultaneously fabricated using reactive ion etching (RIE). The Ge waveguide is 400 nm thick and 400 nm wide to assure single mode propagation. 600 nm thick SiN_{x} stressors were deposited over the Ge waveguides by electron cyclotron resonance plasma-enhanced chemical vapor deposition (ECR-PECVD) with SiH_{4} and N_{2} gases. The Ge waveguide was 70 µm long. Finally, chemical mechanical polishing (CMP) was used to remove the SiN_{x} stressors to reveal the Si cap layer or Ge surfaces. Figure 5
shows a typical cross sectional image of the Ge waveguide and the SiN_{x} stressor films by scanning electron microscopy. It is clear that the Ge waveguide on SOI is sandwiched with the SiN_{x} films side by side. The Ge waveguide is 400 nm thick and 400 nm wide as designed. The top Si layer of the SOI wafer is over-etched by ~100 nm when the Ge waveguide is fabricated by RIE. The SiN_{x} layer is 600 nm as designed.

## 5. Results and discussions

The SiN_{x} film deposited on the Ge epi on Si shows built-in two-dimensional compressive stress of −760 MPa measured from the warpage measurement of the wafer. As the compressive SiN_{x} stressors tend to pull Ge waveguide from both sides, Ge will shrink itself against that pull force, leading to the compressive stress induced inside Ge. After [-110] Ge waveguide fabrication, we have measured −500 MPa of compressive stress along [110] direction remaining in the Ge waveguides by micro Raman scattering spectroscopy. We reported that stress induced by SiN_{x} stressors is uniform in depth up to 440 nm deep region [14]. From these characterizations, it can be predicted from Fig. 3 that the Ge waveguide should blueshift the fundamental absorption edge by 35 nm or larger.

Figure 6
shows typical results under −500 MPa stress by the SiN_{x} film and with no stress. The absorption spectra show about 35 nm blueshift under the stress, which is in good agreement with Fig. 3. This work clearly demonstrates that uniaxial stress-compressive Ge waveguides blueshift the fundamental absorption edge of Ge and the SiN_{x} stressors can control the operation wavelength of pure Ge FK-EA modulators in C-band.

It should be remarked here that the presented stress-tuning of the fundamental absorption edge should be local and can be done in CMOS back-end-of-line. This would open up a new pathway for “field-programmable” working wavelength control of Ge FK-EA modulators by not only changing the stressor structures such as the width or thickness of the SiN_{x} layer statically, but also controlling the applied force dynamically using beam structures [19].

## 6. Conclusions

We have studied one-dimensional stress dependence of Ge band structures and applied the understanding to design Ge FK-EA modulators. It has been demonstrated the blueshift of the fundamental absorption edge of pure Ge waveguides by applying [110] one-dimensional compressive stress side by side. The amount of blueshift is 35 nm, which is in good agreement with the theoretical prediction. The presented stress tuning approach should be an enabler of pure Ge FK-EA modulators to work at C band with FOM of ~2 and ER of 10 dB or higher without introducing dilute GeSi alloy to alter its bandgap of each modulator [5,8
]. Based on the presented approach, the operation wavelength can be controlled by the structure of the SiN_{x} stressors in the CMOS back-end-of-line. This can be a new way for “field-programmable” operation wavelength control of strained pure Ge FK-EA modulators.

## Acknowledgments

A part of this research is granted by JSPS through FIRST Program initiated by CSTP. 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.

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