# Contact a very small area (impedance matched)

In my current project, I want to apply a voltage to a capacitor (top electrode on a thin film heterostructure) very rapidly. Since capacitors have their own charging rate $$\(\tau = R \cdot t = R \cdot \epsilon_r \cdot \epsilon_0 \cdot\frac{A}{d} )\$$ and the only variable I can access is $$\A\$$, I need to keep the area as small as possible. In my case, I have 50 ohm impedance, $$\ \epsilon_r \approx 200 \$$ and the distance $$\ d \$$ between the electrodes is 100 nm. To achieve a reasonable time constant $$\ \tau \$$, the area of my nearly circularly shaped electrode should be less than $$\30 \mu m^2\$$.

In my special case, I want to probe the area of the electrode with a laser shortly after the application of the voltage pulse. Thus, I cannot contact the electrode in the middle or with a bigger wire. In my current plan, I design the shape of the electrode such that it is circular with a tail of 2x2 $$\ \mu m \$$ and I contact only the tail with a SPM tip as sketched in the picture. However, this is very demanding and I cannot think of an alternative way to contact this small area without violating the impedance match or increasing the total area of the electrode.

Is there anybody with experience in this who can help me? Since I am not an electrical engineer, I would be very grateful, if the answers are as detailed as possible.

• I gather you are talking about a sphere with $r\approx 8\:\mu\text{m}$ and $\tau\approx 4\:\text{ps}$. Besides a point that this seems a question for people with experience in experimental design for physics, I think you need to provide a clear diagram. There are a number of questions I don't have any answer for, reading over your description several times already. A picture would help, I think. Along with what's under more precise control and what is not well controlled. – jonk Oct 16 '18 at 7:09
• With areas in that range, bonding a gold contact comes to mind, but I don't really have experience in this. – Arsenal Oct 16 '18 at 7:44
• Jonk: I am talking about circularly shaped electrodes. No spheres. And with the dimensions mentioned in the sketch I get $\tau ≈ 30$ ps. I hope that the sketch made it a bit clearer. If not, please tell me which parts I should explain in more detail. Arsenal: Thanks for the idea, but bonding usually increases the size of my capacitor (the bottom electrode is a full conductive layer). Do you know if there are bonding techniques creating only a very small contact area? – Marv_92 Oct 16 '18 at 9:31
• I`m sorry, very stupid mistake :/ – Marv_92 Oct 16 '18 at 9:57
• What is the gap between the electrodes filled with and how is the current structure made? Lithography? Could you add more layers on top and etch them away again? – Jack B Oct 16 '18 at 10:15