Metal-Insulator-Metal Capacitor

A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator). When there is a potential difference (voltage) across the conductors, a static electric field develops across the dielectric, causing positive charge to collect on one plate and negative charge on the other plate as depicted in Figure 2.11 [26, 27]. Energy is stored in the electrostatic field. An ideal capacitor is characterized by a single constant value, capacitance, measured in farads.

This is the ratio of the electric charge on each conductor to the potential difference between them. Capacitors are widely used in electronic circuits for blocking direct current while allowing alternating current to pass, in filter networks, for smoothing the output of power supplies, in the resonant circuits that tune radios to particular frequencies and for many other purposes.

A very important characteristic of a capacitor is its capacitance which is a measure of how much electrical charge it can store for a given voltage applied across the two metal layers. The capacitance of a parallel-plate MIM capacitor can be calculated by Equation 2.1[28]

(2.1)

Equation 2.1 shows that the capacitance depends on the dimensions of the capacitor and the properties of the insulator material. The important dimensions are the area of the capacitor (A) and the thickness of the insulator layer (d).

22

Figure 2.11 Schematic of Metal-Insulator-Metal structured capacitor. [Cited from http://en.wikipedia.org/wiki/Capacitor]

The capacitance increases if the area, A, is increased or if the insulator thickness, t, is reduced. The capacitance also depends on a physical constant, 𝜺0, which does not change with technology, and a property of the insulator material called the dielectric constant, k. The value of k for the most commonly used dielectric, silicon dioxide, is approximately 3.9. With each new generation of technology there is a demand to reduce the size of the components to fit more of them into a single IC.

2.5.2 Leakage Current

Recently, there are many researches for examining the leakage current of MOS capacitor devices with high dielectric gate oxide. In the MOS structure there are several conduction mechanisms that have been proposed to describe the leakage current conduction in dielectric films [29]. Leakage current is the unintended loss of electrical current or electrons. In fact, leakage is a problem that inhibits faster advancements in computer performance. The term also applies to electronics and consumer electronics devices. Semiconductors make use of millions of transistors to perform calculations and store data in computer microprocessors. Transistors are devices used to amplify and switch electronic signals. Leakage current in

23

semiconductors occurs at the transistor level. As semiconductor manufacturers continue to make transistors smaller to squeeze more onto a chip, leakage current problems increase. The small size of transistor, having thin insulating layer may cause more leakage current. Leakage in transistors causes semiconductors to require more power to operate, as they must replace the current lost to leakage [30].

Figure 2.12 Schematic plot of the trap generation in the gate oxide. The presence of traps in the energy barrier yields the Trap Assisted Tunneling mechanism. [Cited from ref. 30]

The leakage current of an electrolytic capacitor is based on the physical properties that lead to electrical losses. These are as follows: (i) Energy required to building up oxide layers (ii) Weaknesses in the dielectric which result in a low current flow and (iii) Tunnel effects. The corresponding configuration for the measurement of each current is illustrated in Figure 2.12. The conduction mechanism for three current components indicates that the electron tunneled through the traps to the substrate, produces the problem of leakage current. Therefore authors focus on the role of those carriers for the generation of oxide traps and hence leakage current problems in electronic devices.

24

2.5.3 Traps Influenced Current-Transport Mechanism

Recently, high-k dielectrics have been investigated widely in order to replace conventional SiO2 for reducing gate leakage current. However, because of the high density of bulk traps, device with high-k based dielectric also suffers mobility degradation and poor reliability as sketched viewed in Figure 2.13. In addition, it has been reported that the bulk traps significantly enhance the gate induced drain leakage (GIDL) current in high-k devices [31].

Figure 2.13 Schematic pictures to represent the traps over film surface. [Cited from ref. 31]

The Poole–Frenkel emission [32], is a means by which an electrical insulator can conduct electricity. It is named after Y. Frenkel, who published on it in 1938, [33] and also after H. H. Poole (Horace Hewitt Poole, 1886-1962), Ireland. Electrons can move (slowly) through an insulator by the following method. The electrons are generally trapped in localized states (loosely speaking, they are "stuck" to a single atom, and not free to move around the crystal). Occasionally, random thermal fluctuations will give that electron enough energy to get out of its localized state, and move to the conduction band. Once there, the electron can move through the crystal, for a brief

25

amount of time, before relaxing into another localized state (in other words, "sticking"

to a different atom). The Poole–Frenkel effect describes how, in a large electric field,

Figure 2.14(a) Schematic energy band diagram for HfO2 film to explain Pool–Frenkel effect, and (b) Schematic energy band diagram to explain the Schottky–Richardson emission. [Cited from refs. 35 & 36]

the electron doesn't need as much thermal energy to get into the conduction band (since part of this energy comes from being pulled by the electric field), so it does not need as large a thermal fluctuation and will be able to move more frequently. Taking everything into account (both the frequency with which electrons get excited into the conduction band, and their motion once they're there), the standard quantitative expression for the Poole–Frenkel effect [34] is described by the equation

^

26

Figure 2.14 (a), for HfO₂ film showed the energy band affected because of partial traps remained and procure poorer dielectric properties [35]. Further curing treatment to reduce the surface traps, the Poole–Frenkel emission is gradually restrained. Finally, the current transport mechanism is replaced by Schottky–Richardson emission. For standard Schottky–Richardson emission [36], can be expressed as

^ conduction mechanism. The conversion of current transport mechanism from trap-assisted tunneling to Schottky–Richardson emission demonstrates theoretically that the traps were really terminated during the thermal or passivation curing process.

2.5.4 Capacitance and Dielectric Constant

Capacitance is a property that exists between any two conductive surfaces within some reasonable proximity (Figure 2.15). A change in the distance between the surfaces changes the capacitance. It is this change of capacitance that capacitive sensors use to indicate changes in position of a target. Capacitance (symbol ‘C’) is a measure of a capacitor's ability to store charge. A large capacitance means that more charge can be stored. Capacitance is measured in farads, denoted by symbol ‘F’.

27

Figure 2.15 The plates are metallic and they are separated by a distance (d). [Cited from ref. 37]

A substance in which an electric field may be maintained with zero or near-zero power dissipation, i.e., the electrical conductivity is zero or near zero. A dielectric material is an electrical insulator, when a dielectric is placed in an electric field; electric charges do not flow through the material, as in a conductor, but only slightly shift from their average equilibrium positions causing dielectric polarization. Because of dielectric polarization, positive charges are displaced toward the field and negative charges shift in the opposite direction. This creates an internal electric field which reduces the overall field within the dielectric itself. If a dielectric is composed of weakly bonded molecules, those molecules not only become polarized, but also reorient so that their symmetry axis aligns to the field [37]. The latter is expressed by a number called the dielectric constant. A common, yet notable example of a dielectric is the electrically insulating material between the metallic plates of a capacitor.