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Design of a 1550nm SiGe/Si quantum-well optical modulator Xia, Guangrui; Rouger, Nicolas; Tasmin, Tania; Jaeger, Nicolas A. F.; Chrostowski, Lukas 2010

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Design of a 1550 nm SiGe/Si Quantum-Well Optical Modulator Tania Tasmina , Nicolas Rougerc , Guangrui Xiab , Lukas Chrostowskia , and Nicolas A. F. Jaegera a Department  of Electrical and Computer Engineering, University of British Columbia, Vancouver, British Columbia, Canada; b Department of Materials Engineering, University of British Columbia, Vancouver, British Columbia, Canada; c Grenoble Electrical Engineering Lab, National Center for Scientific Research/ Grenoble University, France ABSTRACT An electrooptic modulator containing a single SiGe/Si quantum-well has been designed for operation at λ 0 = 1.55 μm. This single quantum-well modulator has a lower V π Lπ than the 3 quantum-well modulator recently designed and optimized by Maine et al. for operation at λ 0 = 1.31 μm, for which the V π Lπ product was 1.8 V · cm. This single quantum-well modulator contains a Si 0.8 Ge0.2 quantum-well with Non-Intentionally Doped (NID) and P + highly doped layers on either side. With no field applied, holes from the P + layers are captured by and confined in the quantum-well and when a reverse bias is applied holes are released from the quantum well and drift to the P + contact layer. Variations of the hole distribution lead to changes in the free-carrier absorption and the refractive index of each layer and subsequently to phase modulation of guided TE modes. The V π Lπ product of the single quantum-well modulator is estimated 1.09 V · cm for low voltage linear modulation and 1.208 V · cm for 0 to 1.6 V digital modulation, whereas the 3 quantum-well modulator gives a Vπ Lπ of 2.039 V · cm for 0 to 6 V digital modulation for operation at λ 0 = 1.55 μm. Also, the optical loss in the single quantum-well (5.36 dB/cm at V = 0 V ) is lower than that of the 3 quantum-well structure (5.75 dB/cm at V = 0 V ). This single quantum-well modulator should also offer higher frequency operation than the 3 quantum-well modulator.  1. INTRODUCTION Metal interconnects have become the primary bottleneck for the improvement of microprocessor performance due to their RC delay and high power consumption. 1 Optical interconnects offer a promising way to alleviate this bottleneck. 1 Siliconbased materials are the best platform for the various components of on-chip optical interconnects. Due to their Complementary Metal-Oxide-Semiconductor (CMOS) compatibility, both the electronic circuit and photonic circuit can be grown monolithically on the same substrate, reducing the cost. 2 Moreover, stronger optical confinement can be obtained with Silicon On Insulator (SOI) waveguides due to the higher refractive index contrast between Si and SiO 2 as compared to those obtained with III-V based optical interconnects grown on Si substrates. 3 One of the pivotal components of future optical interconnects are optical modulators. Various techniques have been developed to obtain optical modulation from Si and Si-based materials. Recently electroabsorption modulators were reported that used the quantum confined stark effect 4 or used the Franz Keldysh effect. 5 Typically electroabsorption modulators suffer from chirp which can be reduced by using electrorefraction modulators as these modulators can be implemented in a Mach-Zehnder push-pull configuration. To date, the free-carrier depletion effect 6 has become the most commonly used approach to obtain the electrorefraction effect in Sibased materials. Multiple configurations have been developed by various groups using this free-carrier depletion effect. 7–10 However, the Vπ Lπ product, which is commonly used as the figure of merit, is quite high in these devices. Recently SiGe/Si modulation-doped 11 quantum-well optical modulators based on the free-carrier depletion effect were studied for operation at λ0 = 1.31 μm12–15 by Marris et al. which are very promising due to their low drive voltage, small length and low free-carrier absorption loss. They also designed these quantum-well modulators for operation at λ 0 = 1.55 μm16 but the design was not optimized. They have also fabricated this structure and have conducted some experiments on it 16 which shows that the effective index variation depends on both the refractive index change of the layers and the thermal heating of the device. In this paper, we designed a single quantum-well modulator giving a V π Lπ of 1.09 V · cm for operation at λ 0 = 1.55 μm. This structure has a much lower V π Lπ than the most recent published structure designed and optimized by Maine et al. for operation at λ 0 = 1.31 μm.17 We have based our single quantum-well structure design on their 3 quantum-well structure.18 Photonics North 2010, edited by Henry P. Schriemer, Rafael N. Kleiman, Proc. of SPIE Vol. 7750, 77501N · © 2010 SPIE · CCC code: 0277-786X/10/$18 · doi: 10.1117/12.870014  Proc. of SPIE Vol. 7750 77501N-1 Downloaded from SPIE Digital Library on 30 May 2011 to 137.82.117.28. Terms of Use: http://spiedl.org/terms  2. DESIGN OF THE SiGe/Si OPTICAL MODULATOR Marris et al. designed a 3 quantum-well modulator for operation at λ 0 = 1.31 μm using coupled electrical-optical simulations in Ref. [18] (in which they provided all of the physical parameters of their design as well as key operating values, which we will use for comparison). We re-analyzed the same structure for operation at λ 0 = 1.31 μm. Our result (effective index variation at V = 6 V ) was consistent with their result. We then repeated the analysis of this structure for operation at λ0 = 1.55 μm, which gives a much lower V π Lπ . For this structure we found that the quantum-wells are being depleted sequentially, and one at a time, with the application of voltage which is also noted in Ref. [18]. Therefore, we designed a single quantum-well structure keeping the thickness and doping level constant for every layer. This structure leads us to a much lower Vπ Lπ and higher frequency operation as compared to those obtained for the 3 quantum-well structure for operation at λ0 = 1.55 μm. In this section, we will describe the general structure of these modulators followed by the coupled electrical-optical analysis used to design these modulators. We performed the electrical analysis in two different modes: DC analysis and transient analysis. We performed the DC analysis in order to investigate the electrical and optical behaviors of the device with the application of various reverse bias voltages. For this analysis we varied the applied reverse voltage from 0 V to 10 V (10 V is smaller than the simulated voltage breakdown). Then we performed the transient analysis in order to investigate the frequency response of the device. For this analysis, at first a reverse bias voltage step from 0 to x V (where x = 6 for the 3 quantum-well modulator and 1.6 for the single quantum-well modulator) with a rise time of 1 f s is applied to the device and the electrical and optical behaviors of the device are observed at several times ranging from 0 to 100 ps. Then, a reverse bias voltage step from x to 0 V with a fall time of 1 f s is applied to the device and the electrical and optical behaviors of the device are observed at several times for the next 100 ps. The results obtained using the DC analysis for the 3 quantum-well modulator and the single quantum-well modulator are described in section 3. The transient response for the 3 quantum-well modulator and the single quantum-well modulator are described in section 4.  2.1 Device Structure The modulator consists of a P-Intrinsic-N (PIN) diode; the active region consists of ’k’ periodic stacks of layers (where k = 3 for the 3 quantum-well modulator and 1 for the single quantum-well modulator). Each period consists of a 10 nm Si0.8 Ge0.2 quantum-well surrounded by 10 nm Si-NID (Non-Intentionally Doped-10 16 cm−3 ) layers and 5 nm P+ highly doped (2 × 10 18 cm−3 ) layers (P+ -δ-doped layers). The PIN diode (thickness t) is grown on a 30 nm Si-NID layer at the bottom of the PIN diode. 14 This structure is simulated using a 700 nm SiO 2 layer, which is thick enough to prevent the light leaking towards the Si substrate. 19 For the lateral confinement of light, a rib structure is defined using the partial etching of the upper layers. The dimensions of the rib structure are defined such that this modulator can be integrated with a single mode SOI rib waveguide. 19 The mole fraction of Ge is chosen to be 0.2 to keep the bandgap of SiGe higher than the energy of the incident light to avoid band-to-band absorption and to maintain the total thickness below the critical thickness.14  2.2 Electrical and Optical Analysis With no field applied, holes from the P + layers are captured by and confined in the quantum-wells and when a reverse bias is applied holes are released from the quantum wells and drift to the 30 nm P + contact layer. Variation of the hole distribution leads to a free-carrier absorption change and a refractive index change in each layer and, subsequently, the phase modulation of the guided optical wave. We calculated the hole distribution in the various layers of the structure using Silvaco ATLAS T M .20 The solution of Poisson-Fermi-Schroedinger equations is needed for the calculation of the hole density in the quantum-wells of the SiGe/Si modulator. 21 However, it was shown by Marris et al. (in Ref. [18]) that, if the quantum-well is equal to or thicker than 10 nm, the hole density profile in the structure at V = 0 V obtained by solving the Poisson-Fermi-Schroedinger equations is similar to that obtained by solving the Poisson-Fermi equations. That is why we used the Poisson-Fermi solver in Silvaco ATLAS T M for the calculation of the hole density distribution at various applied voltages. The carrier transport in bulk material and at heterojunctions is calculated, respectively, using the drift-diffusion expressions and thermionic emission expressions. 22, 23 The models used by Marris et al. are the concentration dependent SRH (Shockley-Read-Hall) recombination model, the concentration dependent mobility model, the Auger model, and the Fermi-Dirac statistics model.18 We used these models as well as two additional models: the field dependent mobility model and the band gap narrowing model. These additional models do not affect the DC analysis, but the field dependent mobility model affects the transient analysis as described in section 4. Experimental results show that higher reverse bias voltages  Proc. of SPIE Vol. 7750 77501N-2 Downloaded from SPIE Digital Library on 30 May 2011 to 137.82.117.28. Terms of Use: http://spiedl.org/terms  lead to higher reverse leakage currents, and, therefore, higher leakage power that might create a self heating of the device which, in turn, affects the effective index variation. 16 This thermo-optical index variation becomes more significant at higher reverse bias voltages. However, as well as Marris et al., we ignored these effects in our calculations. The material parameters used for this simulation are the default parameters for Si and Si 0.8 Ge0.2 used in Silvaco ATLAS T M . We have tuned the bandgaps of these materials to be E G−Si = 1.12 eV and EG−Si0.8 Ge0.2 = 0.972 eV as defined in Ref. [14] and also the electron affinities to be χ Si = 4.05 eV and χSi0.8 Ge0.2 = 4.04 eV .24 The hole concentration obtained using the electrical simulation in Silvaco ATLAS T M is averaged in each layer at each applied voltage. 12 As the layers are very thin, this approximation gives a refractive index profile similar to the refractive index profile obtained using the actual hole concentration profile. The absorption coefficient variation and refractive index variation in the doped Si layers with respect to undoped Si at λ 0 = 1.55 μm, is calculated from the hole distribution using the following formulae 10 Δα = 8.5 × 10−18 ΔN + 6.0 × 10−18 ΔP  (1)  Δn = −8.8 × 10−22 ΔN − 8.5 × 10−18 ΔP 0.8 where ΔN and ΔP are, respectively, the electron and the hole concentration variations (cm carrier concentration of every layer.  (2) −3  ) with respect to the intrinsic  To calculate the absorption coefficient change and the refractive index change in Si 0.8 Ge0.2 we used equation 1 and 2 due to the unavailability of separate equations for free carrier absorption for Si 0.8 Ge0.2 .25 The intrinsic hole concentration of Si and Si0.8 Ge0.2 are, respectively, taken as 0.668 × 10 10 cm−3 and 10 × 1010 cm−3 , as defined in Silvaco ATLAS T M at T = 300oK. The refractive index of undoped Si and Si 0.8 Ge0.2 are taken as 3.475 and 3.505, respectively, for λ 0 = 1.55 μm. The absorption coefficient for undoped Si and Si 0.8 Ge0.2 is considered to be negligible at λ 0 = 1.55 μm. In our calculations, we considered only the hole concentration change in the various layers, as the electron concentration is negligible with respect to the hole concentration except in the N + layer, where the electron concentration is relatively high. For this N+ layer, the refractive index and the absorption coefficient at V = 0 V is calculated from both ΔN and ΔP (ΔN is taken to be the doping density of this layer). The free carrier absorption and the refractive index of each layer are used as the input to a mode solver, 26 which provides the effective index as well as the optical loss for TE polarized light at various voltages using the 2D semi-vectorial finite-difference approach.  3. DC ANALYSIS IN SiGe/Si MODULATORS 3.1 3 Quantum-Well SiGe/Si Modulator A schematic diagram of the 3 quantum-well SiGe/Si modulator is shown in Fig. 1. For the DC analysis, we applied reverse bias voltages ranging from 0 V to 10 V to this modulator. The hole distribution in the structure was calculated using Silvaco ATLAS T M at each applied reverse bias voltage. The hole concentrations for the 3 quantum-well structure at several specific voltages are shown in Fig. 2. The absorption coefficient variation and refractive index variation in every layer is calculated from the hole distribution using equations 1 and 2, respectively. Fig. 3(a) shows that the refractive index changes in the quantum-wells are much higher at λ 0 = 1.55 μm than at λ0 = 1.31 μm, which implies a higher effective index variation at λ 0 = 1.55 μm. Fig. 3(a) shows that the refractive index change saturates with a saturation value of 1.6 × 10 −3 , 1.95 × 10−3 , and 2.1 × 10−3 at 2.1 V , 4.3 V , and 7.5 V , respectively, in quantum-wells 1, 2, and 3 which indicates the depletion of the quantum wells. Also, Fig. 3(a) shows that the onset of the change in refractive index in each of the quantum-wells occurs near the saturation value of the preceding quantum-well. After the depletion of all 3 quantum-wells, the NID layer on the P + side starts depleting as well. The refractive index change in the NID layer is shown in Fig. 3(b). The effective index variation curve for the 3 quantum-well structure is shown in Fig. 4(a). When the bias is lower than 7.5 V the effective index variation in the modulator is mainly caused by the refractive index change in the quantum-wells. Above 7.5 V , the refractive index changes in all of the quantum-wells become constant but the contribution from the NID  Proc. of SPIE Vol. 7750 77501N-3 Downloaded from SPIE Digital Library on 30 May 2011 to 137.82.117.28. Terms of Use: http://spiedl.org/terms  Figure 1. Schematic view of the 3 quantum-well SiGe/Si optical modulator.  Figure 2. Hole distributions in various layers at various reverse bias voltages. With the increase in the reverse bias, holes deplete from the quantum-wells. Holes start to deplete from the NID layer on the P+ side after all the quantum-wells are fully depleted i.e., above 7.5 V the NID layer starts to deplete.  layer on the P+ side to the effective index variation becomes significant. In other words, after the depletion of all of the quantum-wells, the quantum-well modulator turns into a NID-layer modulator. The two most important performance parameters obtained for this modulator are the effective index variation and optical loss which are found to be around 2.28 × 10 −4 and 3.13 dB/cm at V = 6 V for the wavelength of λ 0 = 1.55 μm, as shown in Fig. 4(a) and Fig. 4(b), respectively. To evaluate the modulation efficiency of the phase modulator, a figure of merit is the Vπ Lπ product, where V π and Lπ are, respectively, the applied voltage and the length required to obtain a π phase shift of the guided wave. An efficient modulator should posses a low V π Lπ (for low drive voltage and/or small size) with low absorption losses. L π can be calculated from the formula L π = λ0 /2Δneff .10 The effective index variation of 2.28 × 10−4 at V = 6 V leads to a Vπ Lπ of 2.039 V · cm for the 3 quantum-well structure for λ 0 = 1.55 μm, which is much lower than the V π Lπ of 2.37 V · cm obtained for λ 0 = 1.31 μm, predicted by our analysis, at V = 6 V . The optical loss is slightly higher at λ0 = 1.55 μm, as compared to that at λ 0 = 1.31 μm, which is consistent with the experimental results.6  Proc. of SPIE Vol. 7750 77501N-4 Downloaded from SPIE Digital Library on 30 May 2011 to 137.82.117.28. Terms of Use: http://spiedl.org/terms  (a)  (b)  Figure 3. Refractive index changes (Δnv = nv − n0 ) at λ0 = 1.55 μm and λ0 = 1.31 μm (a) in the quantum-wells, with a dash-dot line, a dotted line, and a solid line for quantum- well 1, 2, and 3, respectively (b) in the NID layer on the P+ side.  (a)  (b)  Figure 4. (a) Effective index variation (Δneff-v = neff-v − neff-0 ) of the 3 quantum-well modulator; the blue point shows the effective index variation at 6 V obtained by Marris et al. in Ref.18 (b) optical loss at various voltages.  3.2 Single Quantum-Well SiGe/Si Modulator A schematic diagram of the single quantum-well SiGe/Si modulator is shown in Fig. 5. In the 3 quantum-well structure, when the voltage is lower than V = 1.5 V , the effective index variation Δn eff is mainly caused by the refractive index change in the first quantum-well. The onset of the change in the refractive index in the second quantum-well occurs after the refractive index change in the first quantum-well approaches its saturation value. This implies that only one quantum-well is needed to obtain the same effective index variation as that obtained in the 3 quantum-well structure for voltages below about V = 1.5 V . Therefore, we designed a single quantum-well modulator keeping the thicknesses and doping levels constant for all of the layers (i.e., 2 QW layer stacks were removed). The refractive index change in the single quantum-well saturates at about 2 V as shown in Fig. 6. The single quantumwell structure changes from a quantum-well modulator into a NID-layer modulator at this voltage. The effective index variation curves and their slopes are shown in Fig. 7. Fig. 7(a) shows that below 2 V the effective index variation in the single quantum-well structure is slightly higher than that in the 3 quantum-well structure. Above 2 V ,  Proc. of SPIE Vol. 7750 77501N-5 Downloaded from SPIE Digital Library on 30 May 2011 to 137.82.117.28. Terms of Use: http://spiedl.org/terms  Figure 5. Schematic view of the SiGe/Si optical modulator.  Figure 6. Comparison of the refractive index change in the single quantum-well structure and in the first quantum-well of the 3 quantumwell structure at λ0 = 1.55 μm. The refractive index change in the NID layers on the P+ side are shown for both the single quantum-well and the 3 quantum-well modulator.  and considering only the refractive index changes in the quantum-wells, the effective index variation in the single quantumwell structure becomes smaller than that in the 3 quantum-well structure as shown by the dotted line in Fig. 7(a). However, due to the onset of the refractive index change in the NID layer on the P + side, the single quantum-well structure shows significantly higher effective index variation than the 3 quantum-well structure does until the cross-over point at about 6.5 V . Above 6.5 V , the 3 quantum-well modulator turns into a NID-layer modulator and the effective index variation in the 3 quantum-well structure becomes greater than that in the single quantum-well structure due to the combined effects of the refractive index changes in the quantum-wells and the NID layer. The optical loss in the single quantum-well structure is lower than that of the 3 quantum-well structure due to the removal of the two quantum-wells and the other doped layers. The optical losses for both of the structures are shown in Fig. 8. The highest slope of the effective index variation (0.71 × 10 −4 V −1 ) for the single quantum-well modulator occurs at about 1.6 V as shown in Fig. 7(b). At this voltage the effective index variation is 1.02 × 10 −4 with respect to 0 V . If we desire a Vπ of 1.6 V for digital signal modulation, the V π Lπ of this modulator will be 1.208 V · cm which is much lower as compared to the V π Lπ of the 3 quantum-well structure previously defined. For low voltage modulation, we can apply a voltage between 1.4 V and 1.8 V (i.e., ±0.2 V from 1.6 V ). Hence, if we desire such a V π of 0.4 V for low voltage modulation, the V π Lπ of this modulator will be 1.09 V · cm, which is also lower than the V π Lπ of the 3 quantum-well modulator. This device can be further improved. Specifically, the location of the mode profile and the quantum-wells have  Proc. of SPIE Vol. 7750 77501N-6 Downloaded from SPIE Digital Library on 30 May 2011 to 137.82.117.28. Terms of Use: http://spiedl.org/terms  (a)  (b)  Figure 7. Comparison of the (a) Effective index variation (b) Slope of the effective index variation for single quantum-well and 3 quantum-well structure.  Figure 8. Comparison of the optical loss in the single quantum-well modulator and the 3 quantum-well modulator.  not been optimized. If we can improve the confinement factor, it can provide further improvement.  4. TRANSIENT ANALYSIS Transient analysis is performed to evaluate the response time of the 3 quantum-well modulator and the single quantum-well modulator using thermionic emission, tunneling, and field dependent mobility model. Marris et al. did not use the field dependent mobility model while doing the transient simulations. 18 But we found that, in case of transient analysis, the field dependent mobility significantly affects the transient response. The drift velocity of the carriers is the product of the mobility and the electric field in the direction of the current flow. The carrier velocity will increase with the increase of the electric field but at high electric fields, it will begin to saturate due to the reduction of the effective mobility. Hence, without using the field dependent mobility model, the response will be much faster than when using this model and the modulation speed will be overestimated. For the 3 quantum-well modulator, at first, a reverse bias voltage step from 0 to 6 V , with a rise time of 1 f s, is applied to the device. The hole density distributions in the case of 3 quantum-well modulator obtained at several specific times, are plotted in Fig. 9(a). The holes are initially confined in the three quantum-wells at t = 0. As time increases, initially the  Proc. of SPIE Vol. 7750 77501N-7 Downloaded from SPIE Digital Library on 30 May 2011 to 137.82.117.28. Terms of Use: http://spiedl.org/terms  (a)  (b)  Figure 9. Hole density distribution with time in the (a) 3 quantum-well modulator (b) single quantum-well modulator.  (a)  (b)  Figure 10. Hole density distribution with time (a) in the 3 quantum-well modulator for (b) in the single quantum-well modulator.  holes do not escape from the quantum-wells, they simply distribute themselves along the left side of each quantum-well. By t = 36 ps and t = 80 ps the 1st and the 2nd quantum-wells are depleted, respectively. By t = 100 ps, only a few holes are left in the 3rd quantum-well. Fig. 10(a) shows that the quantum-wells are depleting sequentially in time as described in Ref. [18]. After 100 ps, the applied voltage returns to zero with a fall time 1 f s. The hole density distributions obtained at several specific times, during which the holes are returning to the quantum-wells, are plotted in Fig. 9(a). Fig. 10(a) shows that at t = 150 ps, the average hole distribution becomes constant in the 2nd quantum-well and at t = 180 ps, the hole density distribution in the 1st and in the 3rd quantum-well are approaching the constant value. In the case of the single quantum-well modulator, at first, a reverse bias voltage step from 0 to 1.6 V , with a rise time of 1 f s, is applied to the device. The hole density distributions obtained at several specific times, are plotted in Fig. 9(b). The holes are initially confined in the quantum-well at t = 0. Most of the holes have been removed from the quantum-well by t = 36 ps. By t = 100 ps, only a few holes are left in the quantum-well as shown in Fig. 10(b). Hence, we can say that the hole depletion process is much faster in the case of the single quantum-well modulator than in the case of the 3 quantum-well modulator. After 100 ps, the applied voltage returns to zero with a fall time 1 f s. Fig. 10(b) shows that at t = 140 ps, the average hole distribution becomes constant in the quantum-well. The effective index variation curves for the 3 quantum-well modulator and the single quantum-well modulator are  Proc. of SPIE Vol. 7750 77501N-8 Downloaded from SPIE Digital Library on 30 May 2011 to 137.82.117.28. Terms of Use: http://spiedl.org/terms  (a)  (b)  Figure 11. Effective index variation with time in (a) the 3 quantum-well modulator for 0 to 6 V variation and (b) in the single quantumwell modulator for 0 to 1.6 V variation.  shown in Fig. 11(a) and Fig. 11(b), respectively. From these figures we can conclude that transient response of the electrorefractive effect in the single quantum-well modulator will be faster than that in the 3 quantum-well modulator.  5. CONCLUSION Using our DC analysis, we showed that the 3 quantum-well modulator gives a lower V π Lπ for the wavelength of λ 0 = 1.55 μm as compared to the V π Lπ obtained for λ 0 = 1.31 μm. We also verified that the quantum-wells in the 3 quantum-well structure deplete sequentially and one at a time with the application of voltage and, also, after the depletion of all of the quantum-wells, the quantum-well modulator turns into a NID-layer modulator. Then, we designed a single quantumwell modulator which gives a lower V π Lπ as compared to the V π Lπ of the 3 quantum-well modulator. Also, this single quantum-well modulator gives very high slope of the effective index variation before it turns into a NID-layer modulator. 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