7.3 Frequency modulation response
7.3.3 The total frequency chirp
The combined frequency chirp due to QW and silicon plasma eects can be calculated using the partial derivatives:
∆ν =−vg λ0
ΓQWdnr dne
∆ne+ ΓSidnr dnSi
∆nSi
(7.45) The exact phases of ∆nQW and ∆nSi have to be taken into account in the addition.
Figures 7.6(a)-(c) show the (total) frequency modulation response vs. the same re- sponse in the absence of nonlinear eects. TPA and free-carriers in silicon have a
(a)
(b)
(c)
Figure 7.6: Frequency modulation response for several dierent spacer thicknesses, with and without nonlinear eects for αH = 7, I = 2·Ith, QSi = 106 . (a) 30nm spacer (b) 100nm spacer (c) 150nm spacer
Figure 7.7: Frequency modulation response for several dierent spacer thicknesses for αH = 7,I = 2·Ith, QSi= 106
major impact on the frequency response in the thicker spacer designs. A very clear dip in the response curve, followed by a resonance, is a unique consequence of free- carrier-dispersion in silicon, and is very dierent from a conventional III-V, where TPA is negligible. The frequency modulation curves of the dierent spacer thick- nesses are compared in Figure 7.7 The eect of pump current on the response curve is shown in Figure 7.8(a)-(b) for thin and thick spacers. In the thin 30nm spacer, as the pump current increases, the eect of free-carriers becomes more prominent, as indicated by the appearance of the extra pole before the resonance frequency. In the thick 150nm spacer, as the pump current increases, the resonance is pushed to higher frequencies, and the frequency response curve is altered accordingly.
In this chapter, I analyzed the the laser dynamics in both the intensity and the fre- quency response. The analysis predicts much lower relaxation resonance frequencies than a conventional semiconductor laser. This is due to grossly reduced connement in the QW, which reduces the induced transition rate. This is the base of this plat- form. The eect of free-carriers in silicon was also analyzed. It was predicted that it will add a zero to the intensity modulation transfer function, and a unique dip to the frequency modulation response. In the next chapter I will present experimental
(a)
(b)
Figure 7.8: Eect of pump current on frequency modulation response for two dierent spacer thicknesses αH = 7, I = 2·Ith, QSi= 106. (a) 30nm spacer (b) 150nm spacer
results from fabricated devices and compare them to these predictions.
Chapter 8
Dynamic operation - Experimental results
In this chapter, I will discuss the modulation response experiments that were per- formed with a number of dierent spacer designs. The experimental setup and pro- cedures are described in detail in appendix B. The experimental results presented in this chapter are the rst published results for the dynamics of low active connement hybrid Si/III-V lasers. They will be used to point out some of the special character- istics of the low-noise spacer design, and to probe and quantify some of the nonlinear eects described in earlier chapters.
8.1 Intensity modulation response
Intensity modulation response experiments were conducted using the setup described in appendix B.3. The intensity modulation transfer function HIM(ν) was calculated by computing the ratio between the relative intensity modulation and the laser's input current at a given modulation frequency:
HIM(ν) = ∆Pout
∆I · 1
P0 (8.1)
The response of the driving circuitry was divided out from this calculation to isolate the response of the laser only. Details on this calibration process can be found in appendix B.3.2.
Experimental results from intensity modulation experiments of dierent spacer lasers and at dierent bias currents are shown in Figures 8.1-8.3. Each gure shows the measured magnitude and phase of the amplitude modulation (AM) transfer function.
Several interesting features are present in the AM transfer function of dierent spacer lasers:
1. Resonance frequency position vs spacer thickness - As expected from the theo- retical analysis, the resonance frequency shifts towards lower frequencies as the overlap with the QW is reduced. The 150nm spacers show relaxation frequency as low as∼100MHz. This is one to two orders of magnitude lower than conven- tional III-V lasers, and to the best of our knowledge, the lowest-ever reported for a semiconductor laser. Figure 8.4 compares the AM response of dierent spacer lasers for the same oset current from threshold. It is worth noting that though the trend is in perfect agreement with the theory, the theory predicts that the ratio between the resonance frequency at the 30nm spacer and the 150nm spacer should be:
ωn(30nm spacer) ωn(150nm spacer) =
s
ΓQW(30nm spacer)
ΓQW(150nm spacer) ≈4 (8.2) where the connement factors used are based on Comsol simulation. Based on the experimental AM curve, the ratio is ωn(30nm spacer)
ωn(150nm spacer) ≈8, . Since theory pre- dicts a square root relationship between connement and resonance frequency, it might indicate that the 150nm spacer has lower connementΓIII−V (by about a factor of 4) than estimated by the simulation. If this is the case, and the sim- ulation over-estimates the connement in the QW, it can explain the low yield of the 150nm spacer and the zero yield of the 200nm spacer (the gain is reduced and is no longer compensated by an increase of Q).
2. The presence of a zero of the transfer function for the 150nm spacer (Figure 8.3) - What might look like very broad resonance in Figure 8.3 is in fact a zero of the transfer function. This observation is consistent with both the shape of the
(a)
(b)
Figure 8.1: Intensity modulation response of 30nm spacer laser (Chip 1, bar 5, Slot 1, device 7) for dierent bias currents. 3.5mA current modulation. Measured with New-Focus 1544B photodetector and HP 8722C RF network analyzer (a) Normalized magnitude (b) Phase
(a)
(b)
Figure 8.2: Intensity modulation response of 100nm spacer laser (chip 1, bar 1, slo t2, device 19) for dierent bias currents. 6mA current modulation. Low frequency response (<50MHz) was measured using New-Focus 1544B photodetector and Agilent 4395A network analyzer. High frequency response (>50 MHz) was measured using HP 8722C RF network analyzer (a) Normalized magnitude (b) Phase
(a)
(b)
Figure 8.3: Intensity modulation response of 150nm spacer laser (chip 1, bar 1, slot 2, device 19) for dierent bias currents. 3.3mA current modulation. Measured using New-Focus 1544B photodetector and Agilent 4395A network analyzer (a) Normalized magnitude (b) Phase
Figure 8.4: Intensity modulation response (magnitude in a.u.) of dierent spacer lasers for pump current oset of 40mA.
magnitude response curve, and the phase-lead in the phase response. This is in very good agreement with the theoretical analysis (see Figure 7.2), attributing the zero to free-carrier-absorption. The very clear zero of the transfer function at ν ≈5M Hz, can be used to experimentally estimate the eective lifetime of carriers in Si, by comparing it to the theoretical transfer function of Equation 7.19. For the AM response of the 150nm spacer, the resulting experimental carrier lifetime is estimated to be:
τef f ≈30ns (8.3)
This is, to the best of our knowledge, a novel experimental technique to measure the eective lifetime of carriers in Si, and the rst time it is measured in Si/III- V lasers. As discussed in section 3.2.5, this value is comparable to previously reported values in the literature, but is at the high end of the range. It indicates that surface recombination velocity is diminished due to the high-quality of surfaces and interfaces induced by the high-temperature anneal and oxidation.
3. Resonance frequency position vs pump current - The resonance frequency is
Figure 8.5: Frequency modulation response of 30nm spacer laser (Chip 1, bar 5, Slot 1, device 7) for dierent bias currents. 0.1mA current modulation. Measured with Optilab BPR-20-M balanced photodetector and HP 8722C RF network analyzer, using MZI with FSR = 7.06GHz
pushed to higher frequencies with pump current, as expected from classic laser dynamics theory.
4. Resonance frequency damping - All spacer lasers have damped relaxation reso- nance. This is expected due to the high-Q and TPA that suppresses intensity peaks.