# Simulation and Characterization of High-Frequency Performances of Advanced MIM Capacitors

J.Piquet(1), O.Cueto(2), F.Charlet(3), M.Thomas(4), C.Bermond(1),
A.Farcy(4), J. Torres(4), B.Fléchet(1)

*(1) LAHC, Université de Savoie, Bâtiment Le
Chablais, 73376 Le Bourget du lac cedex, France.
(2) CEA/DRT-LETI/D2NT-CEA/GRE, 17 rue des Martyrs, 38054 Grenoble Cedex 9, France.
(3) SILVACO. 55 rue Blaise Pascal 38330 Montbonnot St Martin France.
(4) STMicroelectronics, 850 rue Jean Monnet, 38926 Crolles cedex, France
jerome.piquet@etu.univ-savoie.fr, olga.cueto@cea.fr,
francois.charlet@silvaco.com, maryline.thomas@st.com*

Abstract:

High-frequency simulations and characterizations of advanced metal-insulator-metal
(MIM) capacitors with ultra thin 32 nm PECVD Si_{3}N_{4} dielectric
are presented. The frequency dependent behavior of capacitors is numerically
and experimentally extracted over a wide frequency bandwidth. Numerical results
are validated by comparison to experimental results. An equivalent circuit model
of capacitors including four parameters is developed for a better understanding
of the frequency dependent behavior. We focused on the impact of design on the
performances of MIM capacitors realized on Si substrates.

**Introduction**

The Metal-Insulator-Metal capacitor is a key passive component in Radio Frequency
(RF) and analog integrated circuits. MIM capacitors have attracted great attention
because of their high capacitance density that supplies small area, increases
circuit density, and further reduces the fabrication cost. They provide good
voltage linearity properties. Developments focus on capacitance density increase
through the introduction of high-k materials to replace Si_{3}N_{4}
(k ~ 7) and 3D high-density architectures.

The improvement of performances thanks to Cu introduction in interconnects
naturally leads to the integration of copper as a metal electrode for MIM capacitors.
The objective is to improve the quality factor by reducing parasitic resistances
and ensure the compatibility of MIM capacitor integration scheme with copper
interconnect one. The required damascene architecture was first presented for
TiN/Si_{3}N_{4}/TiN MIM capacitors [1]. Here, a Cu/Si_{3}N_{4}/TaN/Cu
stack is implemented between M5 (metal5) and M6 (metal6) levels. Such MIM capacitors
have been integrated among multilevel copper interconnects in a 120 nm technology
node, using Si_{3}N_{4} to reach 2 fF/µm^{2} capacitances.

Special attention is paid on high-frequency performances as RF and analog applications
are targeted. A new 3D electromagnetic simulator (** QUEST**)
is used to predict electrical performances of MIM capacitors. High frequency
characterizations coupled with

**results are carried out to evaluate the impact of both the introduction of copper and the design of electrodes on performances.**

*QUEST*

**Simulation and Characterization**

The goal of this paper is to present a complete methodology to analyze and predict MIM capacitors performances built on a reliable and efficient 3D simulation tool validated by comparison with measurements. An electrical model of MIM capacitors is extracted from scattering parameters to obtain a better understanding of the frequency behavior of the capacitors.

**Test Structure Description**

Dedicated MIM capacitor test structures were fabricated on 200 mm silicon substrates
with a resistivity of 5.5 S/m. After completion of M5 level, the MIM cavity
is etched in the V5 inter-level dielectric (SiO2) down to a M5 copper interconnect,
which is used as a bottom electrode. Next, a 32 nm thick Si_{3}N_{4}
film is deposited by PECVD (Plasma Enhanced Chemical Vapor Deposition) in the
cavity, before metallization with deposition of a TaN/Ta barrier, which acts
as a top electrode, and Cu filling. Materials in excess are then removed by
CMP (Chemical and Mechanical Polishing). Finally, V5 and M6 levels are completed.
The resulting Cu/Si_{3}N_{4}/TaN/Cu stack is connected through
M5 and M6 levels, as shown in Figure 1.

Figure 1. Schematic and MEB cross-sections of the
damascene MIM capacitor stack integrated between M5 and M6 levels. |

The design of such damascene capacitors has to meet copper density requirements.
Thus, specific designs with comb or grid electrodes were introduced. Figure
2 illustrates the structures particularly studied. Two structures have been
selected for this study. C_{1} and C_{2} are different designs
of grid electrodes with the same area (3 300 µm^{2}) leading to a capacitance
of 6.6 pF. Each elementary single line of the grid is 12 µm wide.

Figure 2. Top views of studied MIM capacitors. W1
= 66 µm, L1 = 66 µm, W2 = 120 µm, L2 = 39 µm. |

All MIM capacitors are integrated between M5 and M6 levels. As M6 is a thick level ensuring the lowest resistance, access lines are dissymmetric in spite of an identical width of 10 µm (Figure 3). These dissymmetrical Metal5 and Metal6 access lines are connected to RF pads.

Figure 3: 3D view of MIM capacitor, where TM6 ~ 800
nm, TM5 ~ 300 nm, and TMIM ~ 400 nm. |

High-frequency behavior of such MIM capacitors is poorly known. So, DC and RF electrical characterizations are carried out to evaluate capacitor performances. A general equivalent electrical model is defined and checked over a large range of frequency (typically from 40 MHz to 25 GHz). Moreover, the impact of MIM capacitor design on its performances is investigated.

Capacitor access lines are connected to RF pads in order to contact measurement probes. Capacitance is measured using a HP4274A multi-frequency LCR meter at frequencies ranging from 100 Hz to 100 KHz. Scattering parameters are extracted using an ANRITSU 37397C Vector Network Analyzer after a TRL (Thru Reflect Line) calibration de-embedding technique [2]. This technique enables to eliminate discontinuities fromcontact pads to access lines and places the reference planes at both ends of capacitors (P1-P2). Thus, only MIM capacitor characteristics are measured.

**3D Electromagnetic Simulation**

**Presentation of the new simulation tool**

**. This simulator calculates the electromagnetic parameters of micro-electronic 3D geometries in frequency domain. It can extract Z, Y, S matrices and quality factors of Nports general structures.**

*QUEST*** QUEST** is based on a 3D field solver elaborated by
SILVACO in collaboration with CEA-LETI [3][4]. It uses an original formulation
of the Quasi-Static Maxwell equations where the problem is separated in two
parts, an impedance and a capacitance part.

The impedance problem is written using a (A, ) formulation [5], where A is the magnetic potential vector, is an equivalent vector electric potential defined on the conductors surface, µ is the permeability and sS is a surfacic conductivity that approximates the volumic conductivity and takes into account the skin effect. With this formulation, A and are solution of :

The magnetic potential vector A is calculated using edge finite elements [6] on a 3D regular grid (Figure 4). The electric potential vector TS is calculated using scalar P1 elements on a triangle meshing of the conductors surfaces (Figure 2b)

Figure 4. a) Magnetic Potential vector (A) and b)
Density of Current |

The capacitance problem comes from the equation:

where , are the surface potential and the surface electric charge. is a local impedance given by the impedance problem. The capacitance problem is solved using a fast and accurate computation method so called « fictitious domain method » [3].

**Validation of the numerical results**

Figure 5. Module and phase of reflexion parameters
resulting from both measurement and QUEST simulator for C _{1} structure. |

Figure 6. Module and phase of transmission parameters
resulting from both measurement and QUEST simulator for C _{1} structure. |

Figure 7. Module and phase of reflexion parameters
resulting from both measurement and QUEST simulator for C _{2} structure. |

Figure 8. Module and phase of transmission parameters
resulting from both measurement and QUEST simulator for C _{2} structure. |

An excellent similitude between measurement and ** QUEST**
results is observed for C

_{1}and C

_{2}structures. Module and phase evolution resulting from measurement and

*simulation have nearly the same behavior. Thus,*

**QUEST****is an efficient and accurate tool to evaluate the high frequency behavior of MIM capacitors.**

*QUEST*To improve the study, impact of design on MIM capacitors electrical performances is then evaluated.

**Impact of Design on Capacitors Performances**

To investigate the MIM capacitor characteristics at RF regimes, scattering parameters and characteristic
impedance of access lines have first to be extracted. M5 level access lines
are thinner than M6 ones, leading to different propagation constant on the two
access ports. A dissymmetrical calibration de-embedding technique is performed.
However, the characteristic impedance of each level access line is calculated
and their values are identical. Then, for the following extraction, M5 and M6
access lines are considered to have the same complex characteristic impedance
Z_{0}. The complex impedance of MIM capacitor is also extracted.

As the longest MIM capacitor is 66 µm (in the direction of propagation), and the maximum frequency measurement is 25 GHz, corresponding to a wavelength of 4.5 mm, MIM capacitors are considered as localized elements (i.e. no propagation effect occurs among electrodes) characterized by the serial complex impedance ZS. Scattering parameters and Z0 impedance of measurement references planes (P1 and P2) are used to calculate the B element of the transfer matrix ABCD. Then, ZS MIM capacitor impedance is directly extracted as following equation shows:

As a next step, MIM capacitors impedance ZS is extracted from both measurements and QUEST.

**Modeling**

For a better understanding of MIM capacitor behavior in a high-frequency regime, an equivalent circuit model is established as shown in Figure 9 and discussed. The elements C and Rp figure the basic model for the capacitor, whereas additional series Rs and Ls represent the parasitic resistance and inductance due to the specific electrode design [7]-[11]. Notice that the shunt Rp is originated from dielectric losses that brings on power dissipation.

Figure 9. Equivalent electrical model of MIM capacitors
extracted at a high-frequency regime. Measurement plane references are
at the capacitor borders. |

Thus, impedance of this model was calculated and its real and imaginary parts
were clearly identified. Coupled with the Z_{S} MIM capacitor impedance, each element
of the equivalent circuit model is extracted using the entire frequency range.

This method is used to determine each of the four parameters, C, Rp, Rs and
Ls, that appears in the equivalent circuit model and their values can be seen
in Table 1.

Table 1. Element values of equivalent circuit model. |

The capacitance values of the two structures were verified by performing measurement
with a LCR meter, resulting in a 6.65 pF capacitance for C_{1} and C_{2}. Both accuracy
and repeatability of this extraction were demonstrated thanks to a gap capacitance
value less than 3 % between same area structures. It was also proved that static
results and extracted high-frequency results are similar.

Design of MIM capacitors doesn’t act upon resistive elements Rs and Rp. However, for the same area structures, so with an identical capacitance value, when the capacitor length (L) is divided by a factor two, the inductive element Ls is divided by the same factor.

This result shows the relationship between length capacitor and parasitic inductance
(Ls). Extraction results confirm that the best MIM capacitor grid design is
C2 for an area of 3300 µm^{2}. So, as a design recommendation, the length
of electrodes has to be minimized.

Extracted elements from measurements are very closed to extracted ones from
* QUEST*. Error percentage is less than 3% on C element
and 10% on Ls element.

This method represents a very good solution to evaluate the electrical performances of MIM capacitors. Coupled with the new 3D electromagnetic simulator, efficient and competitive design having best high frequency behavior, could be integrated among new generation of damascene MIM capacitors.

**Conclusions**

From previous results, high-frequency behavior of damascene MIM capacitors
integrating copper electrodes is simulated to investigate electrical performances
as a function of design and material parameters. Accuracy and efficiency of
a new 3D electromagnetic simulator called ** QUEST** is
established. With this simulator, impact of new high-k dielectrics and new designs
on MIM capacitor electrical performances can be predicted for future generations
of RF integrated circuits based on these results. New materials, like Ta

_{2}O

_{5}, will increase the capacitance value and new design will be required to reduce the parasitic serial inductance in order to enable high-performance MIM capacitor integration for high frequency applications.

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© 2005 IEEE. Reprinted, with permission, from ESSDERC-05 article entitled
“Simulation and Characterization of High-frequency Performance of Advanced
MIM Capacitors” by Jerome Piquet et al.