Method of Modeling Metal Finger Capacitors (03-Nov-2009)

Method of Modeling Metal Finger Capacitors

Background. Stacked metal finger capacitors -- also called Vertical Natural Capacitors (VNCAP) -- are a "cost-free" or "mask free" design of capacitors. Vertically stacked BEOL metal fingers are used to form capacitors (see Fig. 1).

Fig. 1. Two cross-section (side) views of NVCAPs.

Circuit designers use VNCAP models in SPICE simulation to aid their design and to obtain electric performance of VNCAP devices. A good VNCAP needs to be correct for capacitance values among various metal level combinations, needs to have correct statistical behavior, which must come from a reasonably good extraction model of capacitance as a function of metal finger widths, metal finger thicknesses, metal finger sidewall angles, and via heights of those involved

1

BEOL metal and via levels. Various capacitance components must be included in VNCAP models.

Problem solved. This disclosure is about a method of accurately modeling BEOL metal finger capacitors, including its statistical behavior.

Prior art.

There are some patents on the structures of metal finger capacitors, such as
[1] A. C. C.

Ng and M. Saran, "Capacitor structure for an integrated circuit", US Patent

5,583,359, Date of Patent -- Dec. 10, 1996, Assignee --

Northern Telecom Limite

d.

[2] T.-L. Tsai, Y.-T. Chia, and J. Guo, "Interdigited capacitor structure for an integrated circuit", US Patent 6,819,542, Date of Patent - Nov. 16, 2004, Assignee- TSMC.

But there are few publications or patents on the modeling of metal finger capacitors.

Drawbacks of prior art.

Existing metal finger capacitor models do not have certain capacitance components. For some of those covered capacitance components, there is no correct extraction capacitance expressions. So, the statistical behavior of the existing VNCAP model is questionable. And, the existing VNCAP models do not give correct capacitance density relations among various metal level combinations.

New method is this disclosure:
I. Capacitance extraction formulas are given below for each of important capacitance components.

1.

Nea

r-

parallel-

plate capacitance component. For a finger gap associated with a give metal level

(say, Mx level), its capacitance per unit length is

tan

tan

ε

α

=

0

ε

C x −

s

+

t

1 α

ln

2

α

s

t

              ^, (1) which takes a limiting value

.

tan

,

0

t

C x <<

ε

ε

1 s

t

= α

(2)

In Eqs. (1) and (2), ε

0

is the electric dielectric constant of vacuum, ε

x

s

is an effective relative

                     is the finger-to-finger space at half height, t is the thickness of Mx level fingers, and α is half of the angle (in arc) between the two side walls of Mx fingers.

2. Capacitance component associated with a via space [say, the related via level is Vx and Vx is between metal levels Mx and M(x+1)]. This can be a weighted average o...