# A spacial characterization of the TCT

We are using our Particulars scanning TCT to characterize the spacial resolution of different devices. But, what is the spacial resolution of the TCT itself? What is the size and shape of the beam spot in the surface of the silicon?

## Spacial scan with the spaghetti diode

Though there is not much documentation on the spacial characteristics of the device, fortunately it came with a “type 3 spaghetti diode” which proves to be useful for this type of characterization. There is not much information available for this spaghetti diode too, the only information I was able to find is in this slide were we can see a picture of the device and a couple of facts. From that side we know this:

So basically the spaghetti diode has a pitch of 80 µm with metal strips of 20 µm.

I placed the spaghetti diode in the TCT and performed a linear scan in the $$y$$ direction, as shown below:

### Finding the focus

The first step is to find the focus of the laser in the $$z$$ coordinate. We want the focus to be exactly in the surface of the device to have the smallest possible beam spot, thus the higher spacial resolution. There is a systematic procedure for this, it consists in moving the laser by hand until we find the edge of some metalized area as shown below:

When we have placed the beam axis as close as possible to the edge of the metal, we perform a $$z$$ scan and observe the amplitudes. The result of this scan looks like this:

As can be seen there is a minimum at $$z \approx 67.6 \text{ mm}$$, and this corresponds to $$z_\text{focus}$$. So after this we move the laser to $$z = z_\text{focus}$$ and we do not move the $$z$$ coordinate anymore.

### Data from the scan

Once the focus has been found I performed a scan in the $$y$$ direction as shown before. For this scan I:

• Moved in steps of 1 µm.
• Recorded 33 laser pulses in each position.
• I extracted the collected charge in each laser pulse.

The results for the average collected charge in each point along the scan look like this:

We can clearly see the difference in the collected charge between the areas where the silicon is exposed (high collected charge) and the areas where there are metallic strips (low collected charge). I have also plotted the “theoretical spaghetti profile” which is nothing more than a function defined as

\text{spaghetti profile}(y):=\left\{ \begin{aligned} & 1 & & \text{if }y\text{ is on silicon}\\ & 0 & & \text{if }y\text{ is on metal} \end{aligned} \right.

and for this I used the pitch of 80 µm and the width of 20 µm for the metallic strips. I also added a fit of

$\text{collected charge model}(y):=(\text{spaghetti profile}*\text{laser profile})$

where $$*$$ denotes convolution and

$\text{laser profile}(y)=\exp\left(-\frac{\left(x-\mu\right)^{2}}{2\sigma^{2}}\right)$

Some conclusions we can draw from this plot:

• There seems to be some kind of jitter in the measured charge because its minimums have a visible random component on the horizontal axis (you have to zoom in horizontally to appreciate this).
• There seems to be a small scale factor to apply in order to correct for the pitch.
• The model for the collected charge provides a first approximation but it cannot account for everything we see, because it does not fit perfectly.

If we look at these functions in the Fourier space (via an FFT transformation) we observe this:

The presence of small peaks next to each of the components of the collected charge FFT are a clear evidence of jitter. There is also a missing component in the spectrum of the spaghetti profile (my model) with respect to the actual data, specifically the 4th component for the collected charge FFT is missing in the spaghetti profile FFT. Assuming that the laser has a soft spectrum similar to that shown (Gaussian profile) then the spaghetti diode must be different.

## The spaghetti diode in the microscope

The collected charge must be the convolution of the spaghetti profile with the laser profile. However, it may happen that the simple models I am using for these profiles cannot account for everything. I decided to start studying the easiest one: the $$\text{spaghetti profile}$$. The reason for this is simply that if the metallic strips are not perfectly spaced, this can explain the spacial jitter. I have also access to a microscope to observe the spaghetti diode.

So I took the spaghetti, placed in the microscope and took these photos:

The first thing we can appreciate is a non negligible amount of garbage. This clearly introduces noise in the TCT measurements, however it is hard to quantize this noise. Another interesting thing we can see is the presence of circular structures on the metallic strips for the zoomed images. I don’t know what they are and/or how they affect the measurements in the TCT.

In order at least rule where the jitter is coming from, I took one of these pictures and extracted the intensity profile. This I did using the nice program SAOImageDS9. Below there is a screenshot I took while extracting the intensity profile:

I took this profile and plotted it against the $$\text{spaghetti profile}(y)$$ I presented before, and this is what I got:

From here I concluded that the pitch of 80 µm and the width of the metallic strips of 20 µm in the spaghetti diode can be regarded as “perfect”, in the sense that the jitter I observed before cannot be coming from an “non-perfect construction” of the spaghetties in the diode.

## Obtaining the beam shape by deconvolution

Since the $$\text{collected charge model}(y)$$ model is not fitting very good to the data, I proceeded in a different way to obtain the profile of the laser. Basically I “deconvoluted” it from the data by doing the convolution of the data with the “inverse spaghetti diode profile”. If the random jitter component were not present then we could just deconvolute the two signals “measured charge” with $$\text{collected charge model}(y)$$. Because the random jitter is there, if we do this we will get a single peak for the laser which has somehow averaged all these random contributions. To avoid this what I did is to deconvolute the measured collected charge with a single “inverse spaghetti window”, basically a non periodic square signal defined as

\text{inverse spaghetti}(y)=\left\{ \begin{aligned} & 1 & & \text{if }0<y<20\ \text{µm}\\ & 0 & & \text{else} \end{aligned} \right.

By doing the convolution between this inverse spaghetti and the collected charge, we should get an approximation of the laser profile at each fringe:

Keeping the simple model of a Gaussian function for the laser, we can fit it to each of these peaks:

We can see that the agreement is nice. From this analysis I combined the $$\sigma$$ of each fit into a single $$\sigma_\text{average}$$ and, up to now, it is my best estimation for the shape of the laser beam:

This is, a Gaussian beam with $$\sigma_\text{laser} \approx 9.1 \text{ µm}$$.

## Conclusions

• The spaghetti diode is a powerful tool to measure the spacial characteristics of the TCT.
• The origin of the spacial jitter is not yet clear, some possible origins may be:
• Errors in the positioning of the TCT stages.
• The garbage on top of the spaghetti diode that I observed with the microscope.
• Others?
• The shape of the laser is, to a first approximation, Gaussian with a standard deviation of about 9 µm.
• All this analysis was done in the $$y$$ direction, it is probably symmetric for $$x$$ but we cannot ensure this right now.