Narrow-linewidth Si/III-V lasers

Scott Steger guided me through the III-V fabrication process, and was instrumental in the fabrication of the lasers used in this thesis. The work presented in this thesis is a direct continuation of the work by Steger and Christos Santis [89].

Narrow-linewidth semiconductor lasers

They can also be easily integrated with other electronic components to allow control and manipulation of the laser field. If you e.g. wish to detect small changes in the optical delay τ, the laser noise term will eventually limit the achievable resolution.

Laser sources for coherent communication

The increase in modulation speed is mainly due to advances in the miniaturization of light modulators. In the context of light sources for future optical communication networks, this means that the rate of increase in demand for narrower linewidth lasers for telecommunications should stagnate somewhat due to these competitive trends.

Linear and non-linear performance limiting factors

If the frequency noise is white (setting ai = 0 in Equation 2.1), the mean square of the phase deviation will follow Equation 1.6. The gain, or stimulated emission rate, depends on the level of population inversion, that is, the difference between the density of excited electrons and electrons in the ground state.

Figure 1.2: Phasor diagram demonstrating the eect of a spontaneous emission event linear loss can be described through the equation:

Hybrid Si/III-V platform

The bonded Si/III-V acts as a composite material, where the Si devices are an integral part of the active device. After bonding, the III-V stack is modeled and processed to create a current injection mechanism at the specific device location.

Figure 2.1: Hybrid Si/III-V laser schematics

Noise reduction in hybrid Si/III-V

High-Q silicon resonator

The coupling coefficient κ is chirped such that the resulting photonic band gap has an infinite parabolic potential.

Modal gain and loss

General description
The spacer lasers

It is evident from Figure 2.3(a) that losses can be reduced by reducing the overlap with the lossy III-V material, a process shown schematically in 2.3(b-c). Reducing mode overlap with III-V requires a physical mechanism to push the mode lower in silicon.

Figure 2.3: (a) Quality factor of hybrid Si/III-V composite resonator (b) Mode prole of a traditional III-V laser (c) Prole of a high-Q hybrid Si/III-V laser

Schawlow-Townes linewidth

In the hybrid Si/III-V laser, the field intensity increases in the presence of gain and the high Q resonator. In the context of laser noise, TPA has been used to suppress relative intensity noise (RIN) [3] and to generate photon number squeezed light [36].

Figure 3.1: Schematic description of two-photon-absorption monochromatic light E(t) = cos( ωt) as [6]:

Free-carrier-absorption

General methodology
Bulk recombination
Surface recombination
Carrier diusion
Eective carrier lifetime

The gradient in carrier density in the longitudinal direction is much weaker than that in the transverse direction. This will motivate us to approximate the carrier density as uniform near the mode.

Figure 3.2: Model for FCA in silicon. Model #1 by [58, 101]. Model #2 by [70]

Working with densities or total numbers?

It is worth noting that in many textbooks the quantum wells are located on top of the state. In these cases, it is common to use the volume of the quantum well to calculate the strength of the interaction.

Pump

For all these reasons, it will be useless to write the rate equations in terms of total numbers. On the other hand, some features that distinguish our hybrid spacer lasers from conventional lasers will become more apparent in the density representation.

Linear loss

Gain

The quantum-well: a two or three dimensional creature?

The density of states per volume unit ρ(2D) will be inversely proportional to the WQW, but now the gain will be calculated using an overlap integral between the state and the electron wave function, and will be summed over all QWs in the volume. It is a matter of choice how to represent the gain, either by using the field at a point E2(z0), or by using the overlap integral and the coupling factorΓQW.

Active connement factor

In this case, the QW stack is no longer a well-defined two-dimensional entity, although it can still be treated as such. The fact that this approximation no longer holds in our particular case will have major consequences for small-signal dynamics and gain saturation.

Material gain

Spontaneous emission

Model for the population inversion factor

To calculate nsp precisely, we need to know the exact shape of the quasi-Fermi levels. In general, the two quasi-Fermi levels are different and not symmetrical with respect to the center of the electronic band gap.

Two-photon-absorption

To express the average equation, I specify the factor MT P A and express the integral on the RHS by:. 4.21), so that the integral in the RHS can now be expressed using the connection factor in Si ΓSi and the average photon density np:.

Spontaneous recombination in the QW

It is therefore different from the denition of the coupling factor, which is linear in the photon density. It is possible to capture the dependence of the time constant on the density of electrons to better account for radiative and Auger recombination.

Rate equation for free-carriers in silicon

Free-carrier-absorption

Total loss rate

The modied rate equations

The first step toward understanding the effect of the nonlinear terms on the laser performance is to solve the set of equations for the steady-state point. 2βThνvg2MT P AΓSin2pτef f (5.1) The average density of the Si carriers is proportional to the square of the photon density and to τef f.

Gain saturation

Threshold current

However, the modal loss is also reduced due to the increased overlap with the low-loss material and the reduced overlap with the lossy materials. This is one of the key features and strengths of this platform and design approach.

Output power

Wall-plug eciency

An example is shown in figure 5.2 for Qintsi = 106 and for several values of coupling factors. The definition of optimal coupling defined in equation 4.6 can now be better understood: at the point of optimal coupling, where the total Q is exactly half the internal Q, the efficiency is below the optimal levels, but only slightly.

L-I curve

Numerically obtained L-I curves for Qintsi = 106 for different values of connection factors are shown in Figure 5.4, with and without inclusion of nonlinear eects. As can be seen in Figure 5.4, although TPA itself affects the linearity of the L-I curve, FCA has a much greater influence.

Figure 5.2: Eciency (left axis) and total Q (right axis) vs. mirror Q. Q int si = 10 6 ; η i = 1 ; I I tr = 10 (a) 30nm spacer (b) 100nm spacer (c) 150nm spacer

Slope eciency

As a result, the cavity cannot increase photon storage at the same rate as the current pump and the L-I curve becomes nonlinear. The nonlinear loss will reduce the slope effect and the outlier effect, as shown in Figure 5.5.

Figure 5.4: L-I curves for dierent values of connement factors with and without nonlinear eects for Q int si = 10 6 (a) spacer 150nm (b) spacer 100nm (c) spacer 30nm

Schawlow-Townes linewidth

Threshold current

In the high III-V coupling regime, the loss reduction is a quasi-linear function of the coupling factor. The magnitude of the surface recombination effect will depend on the specific wave geometry.

Figure 1.1: Constellation diagrams. (a) Binary Amplitude Phase Shift Keying (b) 16 Quadrature Amplitude Modulation.

L-I curves

From Figure 6.2 it is clear that while the 30 nm and 100 nm spacers have an almost linear L-I curve, the 150 nm spacer is highly non-linear. In Figure 6.3 it is shown that even in pulsed operation the L-I curve of the thick distance laser is nonlinear, in agreement with the theoretical analysis of Chapter 5, which attributes the nonlinearity to free carrier absorption.

Schawlow-Townes noise oor

Intensity modulation response

Analytical investigation

Low nonlinear loss regime
High nonlinear loss regime

In the highly nonlinear regime, this is no longer the case and we expect to see the zero of the transfer function. For example, if the system is strongly damped, we can expect to see a transfer function pole at low frequency, then zero at intermediate frequency, and a pair of poles at high frequencies.

Numerical investigation

When FCA is on, the entire curve changes: the zero of the transfer function appears at f = 2πτ1. This is best shown in Figure 7.2, where we compare the amplitude and phase of the three dividers in the same plot with nonlinear eects.

Figure 7.1: Intensity modulation response curves with and without nonlinear eects.

Frequency modulation response

Eect of Quantum Well carriers

Gain compression
Henry's alpha parameter
Frequency modulation response curve

In addition, the derivative of the gain with respect to the photon density must be included. The resulting response due to the plasma effect in quantum wells can be seen in Figure 7.4.

Figure 7.4: Frequency modulation response due to quantum well electrons for dierent values of spacer thickness

The eects of free-carriers in silicon

Plasma eects in silicon

Changes in the refractive index of the QW have a smaller effect on the mode due to the low confinement factor. This in turn causes changes in the refractive index due to the plasma effect, which causes frequency chirping.

The total frequency chirp

Frequency modulation curves of different spacer thicknesses are compared in Figure 7.7 The effect of pump current on the response curve is shown in Figure 7.8(a)-(b) for thin and thick spacers. In the 30 nm thin spacer, as the pump current increases, the effect of free carriers becomes more prominent, as shown by the appearance of the additional pole before the resonance frequency.

Frequency modulation response

This is consistent with the nonlinear rate equation analysis that attributed the increase in response to the accumulation of free carriers in Si. This approach was later justified both in connection with classical self-sustaining oscillators [53] and for laser oscillators [51].

Source of noise - uctuations

Photon density
Carriers in the quantum wells
Free-carriers in silicon
Temperature

The expression for the PSD of the photon density in Equation 9.25 has two terms that are unique to the hybrid platform and relate uctuations of Si carrier density to uctuations of photon density. Note that in the case of Si carriers, the dominant contribution is from the intrinsic uuctuation of Si carriers ( term.

Figure 9.1: Particle reservoir picture of the system

Frequency noise

Spontaneous emission

The expression for the frequency noise that I derived in the previous section considers the contribution of carriers and temperature fluctuations. Spontaneous emission affects the frequency spectrum by injecting photons with random phase, which is uncorrelated with the mode's phase.

Henry's linewidth enhancement

Noise due to the plasma eect in silicon

High-frequency noise decays much more slowly due to diffusion than in the recombination-only model. However, in a high-Q hybrid platform, the noise due to the silicon carriers increases with power.

Figure 9.6: The eect of Si-carrier uctuation on the frequency noise spectrum:

Noise due to the thermo-optic eect in silicon

Inherent temperature fluctuations - The temperature of the laser cavity is set by coupling to the thermal bath through a stochastic process. This demonstrates that the noise at low frequencies is dominated by uctuations of Si carriers inducing temperature uctuations.

Total noise spectrum

This figure shows that due to the Si supports, the low-frequency component of the frequency noise spectrum is higher for thicker spacers. In fact, it increases the lower frequency noise level in accordance with the theory that attributed this behavior to free carrier oscillation in Si.

Figure 9.10: Frequency noise related to temperature uctuations for dierent spacer designs ( Q Si = 10 6 , I = 2 · I th )

Future directions

One can address all of these noise-limiting processes (besides the inherent temperature variations) by reducing the free carrier density in the silicon. Role of free carriers from two-photon absorption in Raman amplification in silicon-on-insulator waveguides.

Chrome deposition

A detailed description of the design of the Si resonator can be found in [89], while details of the spacer platform and the III-V treatment can be found in [106]. Detailed description of the resonator design methodology can be found in [89] and details of design and dimensions can be found in [106].

Figure A.1: Spacer laser device Schematics

Lithography

Etch

Oxidation

Wafer bonding

Surface treatment

Bonding

Substrate removal

Increase the low temperature to 150 C and hold for one High temperature increase to 285 C and hold for 5 hours. Anti-spin protective coating, PMMA A4 spin at 2000 rpm, followed by a 5-minute soft bake on the hotplate at 180C.

III-V processing

Ion implantation
P-metal deposition
Mesa formation
N-Metal deposition
Cleaving

30 seconds at 200 C (N and P metals annealed together after . N metal deposition) Table A.10: Steps and conditions used to deposit P metal stack. Pattern mask for InP mesa Same PL process as in table A.9 InP mesa etch 22 seconds in HCl(bottle . strength = 37%).

Table A.12: steps and conditions used to form the mesa

Mounting and probing the lasers

Mounting of laser bars

Thermal management

L-I curves

CW excitation

Pulsed excitation

Intensity modulation response

Setup and equipment

The output SM was connected to a photodetector (New Focus 1544B, DC-12 GHz, -600V/W maximum conversion factor). The RF output signal of PD connected to the return gate to NA.

Calibration and measurement procedures