Method to improve the linearity of the silicon Mach-Zehnder optical modulator by doping control

Jianfeng Ding; Sizhu Shao; Lei Zhang; Xin Fu; Lin Yang

doi:10.1364/OE.24.024641

1. Introduction

Silicon photonics has developed rapidly for recent decades and shows a great potential of revolutionizing the current communication systems [1–16]. As a key component to connect the electrical signal to the silicon optical link, silicon optical modulator plays a very important role in silicon photonics. Silicon optical modulators for the digital optical communication system have been extensively and intensively explored [17–27]. Actually, it can also be employed for analog optical communication, which has been only investigated by several groups around the world [28–32]. As the fifth-generation wireless communication and other advanced communication systems are on the horizon, the applications such as radio-over-fiber, antenna remoting, and phase array control are becoming hotspots in these fields. In such analog communication systems, broad bandwidth and high linearity are two basic requirements for the constituent devices. With respect to bandwidth and linearity, silicon carrier-depletion Mach-Zehnder (M-Z) optical modulator has the better performance combination than those based on the carrier injection effect, carrier accumulation effect and the ring structure. In this paper, we analyze the linearity of silicon carrier-depletion M-Z optical modulators and find that the doping concentration plays an important role in the linearity performance. As the doping concentration gets higher, the depletion width of the PN junction will become smaller under the same driving voltage. Because the optical field distribution in the depletion region is not uniform, a shorter depletion region will weaken the distortion caused by the nonuniformity of the optical field overlapping with the depletion region. This leads to a higher linearity of the modulator. Our experimental results indicate that spurious free dynamic range (SFDR) for third-order intermodulation distortion (TID) increases from 109.2 dB.Hz^2/3 to 113.7 dB.Hz^2/3 and the SFDR for second harmonic distortion (SHD) increases from 87.6 dB.Hz^1/2 to 97.5 dB.Hz^1/2 at a driving frequency of 2 GHz by adopting a ten times doping concentration.

2. Device design

The refractive index change $Δ n_{e f f}$ of the phase shifter in a silicon M-Z optical modulator based on the carrier depletion effect is determined by the overlap integration of the carrier concentration distribution change and the optical field distribution. Figure 1(a) illustrates the optical field distribution of a silicon ridge waveguide. Figures 1(b) and 1(c) are the carrier concentration distributions of a PN junction without and with a depletion region respectively. Normally the depletion region and the optical field distribution should overlap in the middle of the optical field as the optical field is strongest in this region. This design can offer maximum modulation efficiency. $Δ n_{e f f}$ is expressed by

Δ n_{e f f} = \frac{1}{n_{e f f}^{(0)}} \frac{∯ n (x, y) \cdot n^{(0)} (x, y) \cdot {| E^{(0)} (x, y) |}^{2} d x d y}{{∯ | E^{(0)} (x, y) |}^{2} d x d y}

In Eq. (1),

Δ n (x, y)

is the material refractive index change of silicon caused by the plasma dispersion effect. And

n_{e f f}^{(0)}

is the original effective refractive index of the doped silicon waveguide without any carrier distribution change.

E^{(0)} (x, y)

is the distribution of electric-field component of the optical mode in the waveguide. The integration area

d x d y

is the optical field distribution region. For an abrupt PN junction, the depletion region is considered to have a rectangular distribution and

Δ n (x, y)

can be assumed to be constant in this area.

Fig. 1 Illustration of (a) the optical field distribution in a silicon ridge waveguide. (b) the carrier concentration distribution of a PN junction without any depletion region. (c) the carrier concentration distribution of a PN junction with a depletion region.

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Figure 2(a) shows the optical power distribution of a silicon ridge waveguide, which is 400 nm in width, 220 nm in height and 70 nm in slab thickness. When the driving voltage is applied on the PN junction, the depletion region will stretch or shrink along the x axis and remain unchanged along the y axis. Therefore we can do the integration along the y axis first to simplify the calculation and for better visualization. Figure 2(b) shows the normalized one-dimensional optical power distribution after the integration along the y axis. The depletion region usually locates in the core region of the silicon waveguide as indicated by the red lines in Fig. 2(b). In this area, the one-dimensional optical power has a Gaussian-like distribution. Figure 3 shows that the fitted Gaussian curve matches the calculated line quite well. Then we can use a Gaussian function to analyze the linearity of the devices with different doping concentrations. The fitted optical power distribution can be expressed as

{| E^{(0)} (x) |}^{2} = A e^{- {(\frac{\sqrt{2} x}{231})}^{2}} .

where A is a normalized coefficient. If the MZI modulator is optically biased at the quadrature point, the output signal will be proportional to the phase change. So the final output signal

O_{s}

can be expressed as Eq. (3). In Eq. (3),

e r f

means the error function, and

x_{L}

,

C_{d}

,

V_{b i a s}

,

V_{s}

,

f_{1}

and

f_{2}

represent the location of the PN junction, a coefficient related to the doping concentrations, the revers bias voltage, the amplitude of the signal, the frequency of one signal and the frequency of the other signal, respectively.

B

is a normalized coefficient including the photoelectric conversion.

Fig. 2 (a) Normalized power of the two-dimensional optical field distribution in an x range of 1.2 μm and a y range of 1 μm. (b) Normalized power of the one-dimensional optical field distribution in an x range of 1.2 μm after the integration along y axis.

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Fig. 3 The fitted Gaussian curve and the calculated curve of the optical field distribution in the core of the silicon ridge waveguide.

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O_{s} = B {e r f (\frac{\sqrt{2}}{231} \cdot (x_{L} - \sqrt{C_{d} \cdot V_{b i a s}})) - e r f (\frac{\sqrt{2}}{231} \cdot (x_{L} - \sqrt{C_{d} \cdot (V_{b i a s} + V_{s} \cdot (\sin (2 π f_{1} t) + \sin (2 π f_{2} t)))}))} .

$O_{s}$ contains the distortion component. By the overlap integration with the fundamental signals $\sin (2 π f_{1} t)$ and $\sin (2 π f_{2} t)$ , we can get the fundamental signals. Therefore, after the overlap integration with the distortion signals, we can get the distortion components such as $\sin (2 π \cdot 2 f_{1} \cdot t)$ and $\sin (2 π \cdot (2 f_{1} - f_{2}) \cdot t)$ . Finally, we can calculate the SFDRs and show the result in Fig. 4. The noise floor is chosen as −165 dBm/Hz, which is consistent with that in the following experiment.

Fig. 4 The simulated SFDRs for SHD and TID when the doping concentration increases from 2 × 10¹⁷cm⁻³ to 2 × 10¹⁸cm⁻³.

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When the doping concentration is higher, the depletion region will be smaller. As illustrated in Fig. 3, the width of depletion region in a high-doped PN junction varies smaller than that of a low-doped PN junction under the same driving voltage. Therefore, the high-doped PN junction experiences less nonlinear region of the Gaussian curve of the optical field distribution than the low-doped PN junction. In other words, the depletion region of high-doped PN junction sees a more uniform optical field distribution. Thus the modulated signal, as a result of the overlap of the depletion region and the optical field distribution, can have a higher linearity for the device with a high-doped PN junction. Figure 4 shows the simulated SFDR results of a 2-mm-long device for SHD and TID when the doping concentration increases from 2 × 10¹⁷ cm⁻³ to 2 × 10¹⁸ cm⁻³. The simulation only calculates the SFDR at a low speed and does not considered the EO bandwidth limitation. This result indicates that the SFDR increases as the doping concentration increases. When the doping concentration increases on and on, the depletion region will become narrower and narrower. Then the linearity enhancement caused by reducing the depletion width will become saturated. This is the reason why the slopes of the curves in Fig. 4 decrease as the doping concentration increases.

3. Experimental result and discussion

We fabricated three devices with different doping concentrations. The details on the fabrication process can be found in [22]. The low doping concentrations are 2 × 10¹⁷cm⁻³ for the p-type doping region and 1.6 × 10¹⁷cm⁻³ for the n-type doping region. The medium doping concentrations are 1 × 10¹⁸cm⁻³ for the p-type doping region and 8 × 10¹⁷cm⁻³ for the n-type doping region. The high doping concentrations are 2 × 10¹⁸cm⁻³ for the p-type doping region and 1.6 × 10¹⁸ cm⁻³ for the n-type doping region. The other design parameters such as the length, the electrode and the doping location are identical. Figure 5 is the experimental setup for the SFDR test. The light beam from a tunable laser source is coupled into and out of the fabricated device with two lensed fibers. The output optical power of the tunable laser source is 14 dBm. The polarization of the light is transformed to be parallel to the x direction by a polarization controller. Two microwave signals at two near frequencies f₁ and f₂ are combined firstly by an electrical combiner and then used to drive the device. The silicon optical modulator is optically biased at the quadrature point to have a best linearity performance. The average optical power in the output lensed fiber is around −2.2 dBm. An erbium-doped fiber amplifier (EDFA) is used to amplify the optical signal to meet the power requirement of the photodiode with an opto-electrical bandwidth of 40 GHz. Normally a higher received optical power will give a higher SFDR. When the doping concentration increases, the insertion loss will increase at the same time. The insertion loss is 2.2 dB/mm for the high-doped device while it is only 1.2 dB/mm for the medium-doped device. In order to eliminate the disturbance from the optical loss variation, the optical power fed into the photodiode is around 11 dBm, which is kept constant for different devices. An electrical spectral analyzer is used to measure the distortion components.

Fig. 5 Experimental setup of the SFDR test (LD: laser diode; PC: polarization controller; DUT: device under test; PD: photodiode; ESA: electrical spectral analyzer; E.Combiner: electrical combiner; MS: microwave source.)

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We do the measurements at frequencies of 2 GHz, 5 GHz, 10 GHz, 15 GHz and 20 GHz. The interval between f₁ and f₂ is kept to be 0.2 GHz in all cases. Figure 6 shows the results at the frequency of 2 GHz for the high-doped, medium-doped and low-doped devices. As the input power varies, the fundamental signal of 2 GHz, TID of 1.8 GHz and SHD of 4 GHz are recorded respectively. Then the dots of TID and SHD are fitted to calculate the SFDRs according to a system noise floor of −165 dBm/Hz. The electrical signal loss of the fundamental component is 22 dB. For the high-doped device, the SFDRs for TID and SHD are 113.7 dB.Hz^2/3 and 97.5 dB.Hz^1/2, respectively. These results are very close to those of the commercial lithium niobate optical modulator. Figure 7 shows the SFDR results for TID and SHD in a frequency range from 2 GHz to 20 GHz when the devices are doped by different doping concentrations. At the frequency of 2 GHz, the SFDRs for TID and SHD increase from 109.2 dB.Hz^2/3 to 113.7 dB.Hz^2/3 and from 87.6 dB.Hz^1/2 to 97.5 dB.Hz^1/2, when the doping concentration increases by ten times. At any frequency, the SFDR enhancement induced by heavy doping can be clearly observed. This is consistent with the above analysis. The SFDR for TID decreases monotonously as the frequency increases. However, the SFDR for SHD increases when the frequency is larger than 15 GHz. This result is caused by the bandwidth limitation of the testing system. The frequency of the SHD component is larger than 30 GHz as the fundamental frequency is larger than 15 GHz. This distortion component exceeds the bandwidth of the testing system. Then the distortion component is suppressed by the testing system and measured to be smaller than that generated by the device. For TID measurements, the frequency of the TID component is very close to that of the fundamental signal. Therefore the bandwidth limitation of the testing system can be neglected. This is the reason why the tendencies of the TID and SHD SFDRs seem to be different in Fig. 7. Actually we think the tendency of the SFDR for SHD will be the same with that of the SFDR for TID if the bandwidth of the testing system is larger than 40 GHz.

Fig. 6 Experimental SFDR results of (a) the high-doped device, (b) the medium-doped device and (c) the low-doped device at a frequency of 2 GHz. The SFDRs for TID are 113.7 dB.Hz^2/3, 111.3 dB.Hz^2/3 and 109.2 dB.Hz^2/3, respectively. The SFDRs for SHD are 97.5 dB.Hz^1/2, 94.8 dB.Hz^1/2 and 87.6 dB.Hz^1/2, respectively.

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Fig. 7 (a) Experimental SFDRs for TID of the devces with different doping concentrations in a frequency range from 2 GHz to 20GHz. (b) Experimental SFDRs for SHD of the devces with different doping concentrations in a frequency range from 2 GHz to 20GHz.

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4. Conclusion

We have optimized the linearity of the silicon optical modulator based on the depletion of a PN junction. As the doping concentration of the PN junction increases, the linearity of the modulated optical signal will increase. When a p-type concentration of 2 × 10¹⁸cm⁻³ and a n-type concentration of 1.6 × 10¹⁸cm⁻³ are adopted, the SFDRs for TID and SHD are 113.7 dB.Hz^2/3 and 97.5 dB.Hz^1/2 at a frequency of 2 GHz. These results indicate that silicon optical modulators are competitive with the commercial lithium niobate modulators for analog optical communication.

Funding

This work has been supported by the National High Technology Research and Development Program of China (2015AA015503, 2015AA017001), and the National Natural Science Foundation of China (NSFC) (61505198, 61535002).

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Method to improve the linearity of the silicon Mach-Zehnder optical modulator by doping control

Abstract

1. Introduction

2. Device design

3. Experimental result and discussion

4. Conclusion

Funding

References and links

Cited By

Figures (7)

Equations (3)

Optics Express