El m´etodo APW

The shape of the initial mesa, or pattern of vias, significantly impacts the resulting aperture shape. An open mesa shape is useful for making electrical contacts separate from the cavity. Alternatives are contacting the top of the device [117], or performing extra fabrication steps to route wires from the contact regions. Two primary ways of

forming oxide apertures have been studied in the work presented in this thesis. An understanding of the diffusion process led to the development of the octagon pattern of vias. The octagon pattern produces the most circularly symmetric apertures. It was revealed, however, that the shape is susceptible to polarization mode coupling from fabrication imperfections. It is therefore advantageous to sacrifice symmetry, likely at the expense of increased absorption at the aperture, in order to define the form birefringence more precisely. A number of options are available, as it is generally easy to purposefully break symmetry. A three fold pattern of arms in a radiation sign shape is discussed. The resulting apertures are triangles.

Testing of a number of mesa shapes resulted in the implementation of the radiation sign that has been used in the group for single photon sources [27]. The pattern has three arms allowing electrical access to the cavity area, without tedious fabrication steps required to contact the buried layers directly on the cavity. It has further allowed for a single contact pad to control an entire array of cavities [98]. It is conventionally expected that away from the arms, the oxide should penetrate closer to the center of the mesa. Oxidation could then ”average out” the shape with increasing oxidation length.

It is first determined that the variations do not average out far into the mesa, and an extremely non-circular aperture results. The radiation pattern produces a triangular aperture after the oxidation step, which can be expected from the three fold mesa. The second observation is the orientation of the triangle is rotated from the expected orienta- tion. The oxidation rate is enhanced along the directions of the arms, where it initially impeded because there is not a direct surface normal to this direction. To explain the en- hancement, oxidation of the arms themselves must be considered. A model is proposed, which suggests that diffusion is enhanced through the arms.

Consider the initial condition of the oxidation, as steam is initially introduced. Diffu- sion of oxidation elements proceeds directly normal to each surface, and the initial shape

Figure 5.1: Oxide diffusion through the radiation sign. The areas in red are the etched trenches, which expose the oxide layer. The oxidation is shown from left to right, with increasing time, by the blue regions. Black arrows indicate the diffusion direction from the arms.

of the oxide should resemble the initial mesa pattern. The situation is depicted in Figure 5.1. It is apparent that the arms of the pattern become oxidized completely before the mesa. As the channel of each arm is oxidized through, the diffusion elements change direction. Considering a simple diffusion process, the high concentration at the surfaces should proceed to the area of low concentration. Initially, the direction is normal to the surface. In a planar structure, such as a ridge, this remains true. However, here, as the arms become oxidized, the direction of high concentration to low concentration is pointing towards the aperture. The arms, at this point, behave as a funnel, increasing the oxidation rate in the direction of the arms.

Experimental apertures are shown in Figure 5.2. The mesa diameters are varied from top left to bottom right. The largest mesas produce a more circular aperture, and the smallest mesas produce triangles. In the last figure, the bottom sides of the triangle are significantly oxidized more than the other directions. Variations of this kind are present often, as the epitaxy is not perfect. The particular pattern could also be the result of the onset of crystallographic dependency on the oxidation rate.

The oxidation of AlGaAs is expected to be a diffusion limited process [103]. It is further not expected to be a steady state process. It is suggested that the funneling

effect may be reduced by slowing the oxidation down, possibly by introducing less steam to decrease the diffusion rate through the device. The fast and slow directions, then, may be able to be averaged out, producing a more symmetric aperture. The implementation of smaller vias, instead of arms has proven to be a method of limiting the diffusion funnel. Future design implementations should implement a two dimensional diffusion model in order to better predict the aperture shape. A circular aperture is most desirable from a loss standpoint, as the Gaussian field pattern of the fundamental mode overlaps more with non-circular apertures at high field regions. The absorption losses are therefore expected to increase.

Improvements in geometry of the aperture, to produce more circular apertures, could be obtained by increasing the number of holes, or adding multiple layers of holes, placed further from the aperture. The diffusion funnel has been introduced so far as a detriment, however, the octagon pattern is extra susceptible to imperfections, leading to polarization mode coupling. The triangle pattern defines precisely an asymmetric axis, which are made to align with the crystal major and minor axes. Therefore, the polarization mode coupling is eliminated, and the horizontal and vertical modes can be made to cross.