University of Rochester, Department of Physics
Quantum computers are powerful machines that are able to do computation and simulations that would be impossible on a normal computer. A standard computer uses bits for its computational processes, but a quantum computer uses qubits. While a normal bit can only have the value of 1 or 0, a qubit can exist as a superposition of the two states. In addition, this qubit can be entangled with other qubits, so that the state of one is intrinsically dependent on the state of the other.
Spin qubits are a promising implementation of qubits, as they demonstrate long coherence times and can be manipulated with high fidelity. Designing these qubits with an overlapping gate architecture is becoming one of the most feasible design options, as this allows for gates to be closer together, which leads to tighter electron control. To fabricate such devices, nanometer level precision is required so that the layers are aligned to each other and the electrons can be spatially controlled to a very fine degree.
Previously, this alignment was done manually. By implementing auto alignment and XY focus features in the NPGS software, the robustness and quality of the alignment was improved.2. Device Fabrication
The substrate of the device is a Si/SiGe heterostructure. Three layers of aluminum gates stacked on top of each other must be well aligned in order to control the electrons. A set of three alignment marks as well as bond pads were written using photolithography, and then a CrAu layer was deposited using the PVD. The sample was then descummed, oxidized, and coated with PMMA before each layer. One of the three layers, consisting of small inner features, as well as larger features that connect to the bond pads, was then written using e-beam lithography.
For each layer, the e-beam lithography procedure involved finding burnspots, aligning the pattern to previous layers, and then writing the pattern. The pattern was then developed, and aluminum of increasing thicknesses for layers 1, 2, and 3 was deposited using an evaporator.I. Dose Testing and Proximity Effect Correction
E-beam lithography works by bombarding a very focused beam of electrons in the desired areas on a sample with a thin coat of PMMA. However, the accuracy and resolution of the features this process is able to write is limited not just by the spot size of the electron beam, but by how far electrons are forward and backward scattered in the PMMA. This scattering essentially exposes the PMMA surrounding the areas that are being written as if they too were being written, and can greatly impact the successfulness of a device.
In order to account for this proximity effect, a dosage test was done to determine the optimal doses for the different features that minimized the proximity effect as much as possible. This involved writing each of the smallest features at a series of different dosages, and imaging them to see which dosage was optimal for each pattern.
To further correct for proximity effects, the Nichol Group has developed proximity effect correction software called urpec available on GitHub.II. XY Focus Testing and Results
The XY focus feature in NPGS calculates a linear regression across the plane of the chip to find the focus at any given point on the chip after a stage movement. Each chip has a 3x3 array of bond pads written in photolithography that can house a device. Each element in this array is a square pattern of about 2mm, meaning each chip is about 6mm in x and y. Because the beam is so sensitive to slight changes, moving over even just a single pattern can significantly change the focus.
Before implementing this feature, doing multiple writes on a chip in different locations meant tuning up the beam at each pattern location where something was to be written. When writing multiple devices, this can be time consuming. When writing larger features or features spread out across the chip, finding a focus that worked for this broad range was extremely challenging. Testing and implementing XY focus allows for fast and accurate e-beam writes across the chip. This feature is particularly useful for writing the series of three alignment marks that must be present on each of the nine patterns on each chip. Coarse alignment marks are written using photolithography, but fine alignment marks can only be written using e-beam lithography. It is important for later alignment during the writing of the actual device that these marks are written in focus, but because they are spread out across the full span of the chip, this requires tuning up the beam at each location without the use of XY focus.
The burnspot boxes are some of the smallest features written, so they are most susceptible to "blurring" as a result of poor focus. The resulting images coming out as well as they did shows the robustness of using XY focus to write patterns across the chip as a whole, as well as its usefulness.III. Auto Alignment Testing and Results
Previously, when writing a pattern, the procedure was to use a manual alignment entity in NPGS before writing to ensure that the current layer was aligned to previously written layers. Although this process works, the manual alignment can vary from person to person, and introduces an element of human error into one of the most important aspects of the write, as the layer to layer alignment is a big factor in why a device might succeed or fail. In addition, manual alignment is tedious and one of the more time consuming aspects of doing an e-beam write.
This created a strong motivation for implementing auto alignment into the e-beam writing process. Although alignment accuracy is a very important aspect of the alignment, it is also important that the alignment process does not result in the alignment marks being scanned for too long, as overexposing these marks that are very close to important features on the chip can cause them to short together.
The auto alignment was first tested using the default settings, but this was found to scan the alignment marks very slowly, resulting in them getting exposed for far too long and shorting the device together.
To correct for this, several parameters in the auto alignment file, including the number of pixels it scans, the tolerance of the algorithm before it accepts something as a "good fit", and the number of times it scans each alignment mark as much as possible where changed. With these changes, the alignment runs as fast, if not faster, than manual alignment, meaning that the exposure of the alignment marks is kept to a minimum. Further directions for this project could include investigating exactly how much this could be optimized, although for the time being it is enough to see that just these alterations are more reliable than the equivalent manual alignment. The difficulty with this optimization comes from the fact that as more layers of Al are deposited, the alignment marks become harder and harder to discern.
The true test of alignment comes from how well the auto alignment feature was actually able to write the fine inner features of the device where the electrons will be confined.
The alignment between layers here is clearly very good and can be observed to be significantly better than manual alignment, in addition to the fact that it is more consistent and therefore a more robust method of alignment. A typical manually aligned device has alignment within ±10 nm. Here, the alignment along the y axis is too perfect to measure, as it can be seen that the gates that run parallel down the image are very well aligned, although this image was taken at a slight stage tilt so it is a little difficult to see. In layer 2, we can see a slight misalignment in x, as the left features have a slightly smaller overlap with the center bridge than the right features. Measuring the overlap of the left gates with the bridge and the overlap of the right gates with the bridge using the photoshop analysis tools yielded an average overlap of 32 nm on the left and 39nm on the right, making the alignment accurate to ±3.5 nm, which is well within the tolerance of the qubit design, and is significantly better than manual alignment. In addition, the fact that layer 3 had the exact same offset in x suggests, if not something systmatic about the misalignment, then a degree of consistency to it that does not make it a concern.3. Discussion
The implementation of XY focus allows for a significant increase in ease when writing on different patterns on the chip, such as in the case of writing the fine alignment marks with e-beam lithography. Implementing auto alignment, after optimizing the speed with which it scanned over the alignment marks, resulted in a qualitatively and quantitatively better aligned qubit than a manual alignment would yield. This will be useful to implement into the normal qubit fabrication process, as it removes the degree of human error, speeds up the process, and yields the most accurate results during the alignment process.
I would like to sincerely thank Brian McIntyre for all of his assistance on this project, Elliot Connors for all of his knowledge and encouragement, and John Nichol and the Nichol Group for all of the resources and assistance.
1. R.J. Needs, M.D. Towler, N.D. Drummond and P. López Ríos, J. Phys.: Condensed Matter 22, 023201 (2010)