You said perimeter capacitance?

The concept of fringe capacitance often leads to defining area capacitance and perimeter capacitance.

Fringe effect just says that part of a capacitance extends outside the space between the two electrodes. At first sight, capacitance outside the space between electrodes is proportional to perimeter.

For this reason, it is often stated that total capacitance is the sum of area capacitance and perimeter capacitance.

Is it so simple? No, it is not.

In fact, perimeter capacitance value depends on ability of electric field to extend around edges, and even, more accurately, perpendicularly to the edges.

We can use a Field Solver, such as EZMod3D to show that. We will use an integrated capacitor built from a ground plane and a metal electrode all included in an oxide layer. First, we'll consider only the volume between electrodes to find out area capacitance:

Extracted capacitance value is 2.265552E-13 F.

How does that compare to theoretical value? Area is 6561E-12 m2 and dielectric thickness is 1E-6 m. Dielectric permittivity is 3.45306e-011 F/m. So, theoretical value is:

C = 3.45306e-011 * 6561E-12 / 1E-6 = 2.2655526660000E-13. No so bad an agreement!

Now, what is we add some space around? Let's extend the ground plane and the oxide while keeping the metal electrode:

Extracted capacitance is now  2.4668919E-13 F. It is slightly increased, but there is no theoretical value to compare it to. EZMod3D has proved to be accurate and reliable over the years, it can be trusted.

We can bet that capacitance increase comes from perimeter capacitance.

Perimeter is 324 um.

Capacitance is increased by 2.0134E-14 F.

So, perimeter capacitance is 2.0134E-17 / 324 = 6.2142E-17 F/um

Now, what if we increase perimeter while keeping area constant by creating slots? Let's start with large slots:

Area is still 6561E-12 m2, but perimeter is now 540 um.

Extracted capacitance is 2.57401487E-13 F. This value is slightly larger than previously. Is that caused by perimeter capacitance?

Capacitance calculated from area and perimeter should be 2.601118E-13 F

Alternately, with the extracted capacitance and perimeter values, we can extract a new value for perimeter capacitance: 5.71226E-17 F/um. This value is smaller than extracted from the square electrode (6.2142E-17 F/um). What's the matter?

What if we go further, using smaller slots while keeping area constant?

Now, area is still 6561E-12 m2, but perimeter is now 636 um. Extracted capacitance is 2.53128E-13 F. This value is slightly smaller than with large slots... Perimeter capacitance is 4.17809E-17, even smaller than with large slots.

The point is that slots are smaller than dielectric thickness. There is no room for the electric field to extend between the slots. This phenomenon appears in the headline picture showing electric field for the large slots configuration. The field does get inside the slots but moderately. With the small slots, the field does not get in significantly. That's it!

Perimeter capacitance is a tricky concept. The value applies only for straight edges or at least for smooth edges. When edges are more "fractal", perimeter capacitance is lower. The minimum size for edges segments is 3 to 5 times dielectric thickness. Below that, perimeter capacitance decreases. The only way to get accurate values is using a Field Solver such as EZMod3D.