Metal Finger Capacitors: Layout of a Subset of Level Combinations for All Level Combinations (03-Nov-2009)

Metal Finger Capacitors: Layout of a Subset of Level Combinations for All Level Combinations

Back-End-Of-Line (BEOL) metal finger capacitors (also called vertical natural capacitors, see Fig. 1) use connected combs of inter-digitated metal fingers on multiple BEOL metal levels. The device is popular with designers because it is "free" with the standard process and has quality factor Q that can usually beat Front-End-Of-Line (FEOL) capacitors.

Fig. 1. Top view of VNCAP devices.

Since there are multiple BEOL levels are involved/allowed in a metal finger capacitor design, there are many level combinations. For example, when a Vertical Natural Capacitor (VNCAP) is allowed to use the first N = 8 metal levels (say, three 1x levels, two 1.3x levels, and three 2x levels; or five 1x levels and three 2x levels) in a semiconductor technology, there are N(N + 1)/2 = 36 possible level combinations. In an example of three 1x levels, two 1.3x levels, and three 2x levels, let's call three 1x levels as M1, M2, and M3, call two 1.3x levels as C1 and C2, and call three 2x levels as B1, B2, B3. Including substrate Sub, ..., and contact level CA below M1, via levels V1, V2, AY, A1, W0, W1, W2 connecting eight metal levels M1, ..., B3, and 4x via YY and 4X metal level E1 in the BEOL, the level sequence can be written as:

Sub, ..., CA, M1, V1, M2, V2, M3, AY, C1, A1, C2, W0, B1, W1, B2, W2, B3, YY, E1, ...

All N(N + 1)/2 = 36 level combinations in this example of N = 8 consists of N = 8 groups.

Group A. There are N (= 8 here) single-level cases:
1) (M1);
2) (M2);
3) (M3);
4) (C1);

1

5) (C2);
6) (B1);
7) (B2):
8) (B3).

For a fixed VNCAP device length L and width W, the single-level (M2) VNCAP is represented by Fig. 2.

     … M3 n V2 M2 M2

U V1 M1 CA

Sub

Fig. 2.

Group B. There are (N - 1) (= 7 in this exampel) two-level combinations (must be two neighboring metal levels):
9) (M1 + M2);
10) (M2 + M3);
11) (M3 + C1);
12) (C1 + C2);
13) (C2 + B1);
14) (B1 + B2);
15) (B2 + B3).

For the same VNCAP device length L and width W, the two-level (M1 + M2) VNCAP is represented by Fig. 3.

     … M3 n V2 M2 M2 + V1 M1 M1

U CA

Sub

Fig. 3.

For the same VNCAP device length L and width W, another two-level (M2 + M3) VNCAP is fully represented by Fig. 4.

2

  … C1 n A

Y

M3 M3 + V2 M2 M2

U V1

M1 CA

Sub

Fig. 4.

Group C. There are (N - 2) (= 6 here) three-level combinations (must be three consecutive metal levels):
16) (M1 + M2 + M3);
17) (M2 + M3 + C1);
18) (M3 + C1 + C2);
19) (C1 + C2 + B1);
20) (C2 + B1 + B2);
21) (B1 + B2 + B3).

For the same VNCAP device length L and width W, three-level (M1 + M2 + M3) VNCAP is represented by Fig. 5.

     … C1 n AY M3 M3 + V2 M2 M2 + V1 M1 M1

U CA

Sub

Fig. 5.

Group D. There are (N - 3) (= 5 in this example) four-level combinations (must be four consecutive metal levels)...