Metal Oxide Semiconductor Field Effect Transistor (MOSFET) Capacitor (Part - 1) Electrical Engineering (EE) Notes | EduRev

VLSI System Design

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Electrical Engineering (EE) : Metal Oxide Semiconductor Field Effect Transistor (MOSFET) Capacitor (Part - 1) Electrical Engineering (EE) Notes | EduRev

The document Metal Oxide Semiconductor Field Effect Transistor (MOSFET) Capacitor (Part - 1) Electrical Engineering (EE) Notes | EduRev is a part of the Electrical Engineering (EE) Course VLSI System Design.
All you need of Electrical Engineering (EE) at this link: Electrical Engineering (EE)

 Objectives

  In this course you will learn the following

  • MOS as Capacitor
  • Modes of operation
  • Capacitance calculation of MOS capacitor


4.1 MOS as Capacitor

Refering to fig. 4.1, we can see there is an oxide layer below the Gate terminal. Since oxide is a very good insulator, it contributes to an oxide capacitance in the circuit.

Metal Oxide Semiconductor Field Effect Transistor (MOSFET) Capacitor (Part - 1) Electrical Engineering (EE) Notes | EduRev

Fig 4.1: Cross-section view of MOS Capacitor

Normally, the capacitance value of a capacitor doesn't change with values of voltage applied across its terminals. However, this is not the case with MOS capacitor. We find that the capacitance of MOS capacitor changes its value with the variation in Gate voltage. This is because application of gate voltage results in band bending in silicon substrate and hence variation in charge concentration at Si-SiO2 interface.


4.2 Modes of operation

Depending upon the value of gate voltage applied, the MOS capacitor works in three modes :

Metal Oxide Semiconductor Field Effect Transistor (MOSFET) Capacitor (Part - 1) Electrical Engineering (EE) Notes | EduRev                                                                      Metal Oxide Semiconductor Field Effect Transistor (MOSFET) Capacitor (Part - 1) Electrical Engineering (EE) Notes | EduRev

Fig 4.2a: Accumulation mode (grey layer - strong hole concentration)   Fig 4.2b: Depletion Mode (light grey layer - depletion region)

1. Accumulation: In this mode, there is accumulation of holes (assuming n-MOSFET) at the Si-SiO2 interface. All the field lines emanating from the gate terminate on this layer giving an effective dielectric thickness as the oxide thickness (shown in Fig. 4.2a). In this mode, Vg <0

2. Depletion: As we move from negative to positive gate voltages the holes at the interface are repelled and pushed back into the bulk leaving a depleted layer. This layer counters the positive charge on the gate and keeps increasing till the gate voltage is below threshold voltage. As shown in Fig. 4.2b we see a larger effective dielectric length and hence a lower capacitance.

Metal Oxide Semiconductor Field Effect Transistor (MOSFET) Capacitor (Part - 1) Electrical Engineering (EE) Notes | EduRev

Fig 4.2c: Strong Inversion mode (grey layer - strong electron concentration, light grey - depletion region)

3. Strong Inversion: When Vg crosses threshold voltage, the increase in depletion region width stops and charge on layer is countered by mobile electrons at Si-SiO2 interface. This is called inversion because the mobile charges are opposite to the type of charges found in substrate. In this case the inversion layer is formed by the electrons. Field lines hence terminate on this layer thereby reducing the effective dielectric thickness as shown in Fig. 4.2c)


4.3 Capacitace calculation of MOS Capacitor

In the last chapter, we gave you an introduction of MOS as capacitor. In this chapter, we will see how MOS works as a capacitor with derivation of some related equations.

Metal Oxide Semiconductor Field Effect Transistor (MOSFET) Capacitor (Part - 1) Electrical Engineering (EE) Notes | EduRev

Fig 4.3: Gate and Depeletion charge of MOS Capacitor

By Gauss's Law:  Metal Oxide Semiconductor Field Effect Transistor (MOSFET) Capacitor (Part - 1) Electrical Engineering (EE) Notes | EduRev

Also by thermal equilibrium: Metal Oxide Semiconductor Field Effect Transistor (MOSFET) Capacitor (Part - 1) Electrical Engineering (EE) Notes | EduRev

where p and are hole and electron concentrations of substrate and ni is hole or electron concentration of the corresponding intrinsic seminconductor.

We see that if we keep making VGS more and more -ve, the charges Qs and Qm keep increasing. Thus, it is acting like a good parallel plate capacitor. Its capacitance can be given as-

Metal Oxide Semiconductor Field Effect Transistor (MOSFET) Capacitor (Part - 1) Electrical Engineering (EE) Notes | EduRev

For +ve bias voltage on gate, increasing VGS will increase Qm and Qs.

Using the depletion approximation, we can write depletion width  Metal Oxide Semiconductor Field Effect Transistor (MOSFET) Capacitor (Part - 1) Electrical Engineering (EE) Notes | EduRev as a function of Metal Oxide Semiconductor Field Effect Transistor (MOSFET) Capacitor (Part - 1) Electrical Engineering (EE) Notes | EduRev as

Metal Oxide Semiconductor Field Effect Transistor (MOSFET) Capacitor (Part - 1) Electrical Engineering (EE) Notes | EduRev

where Na is the substrate acceptor density,∈s is dielectric constant of substrate and Metal Oxide Semiconductor Field Effect Transistor (MOSFET) Capacitor (Part - 1) Electrical Engineering (EE) Notes | EduRev is the surface potential at substrate.

The depletion region grows with increased voltage across the capacitor until strong inversion is reached. After that, further increase in the voltage results in inversion rather than more depletion. Thus the maximum depletion width is:

Metal Oxide Semiconductor Field Effect Transistor (MOSFET) Capacitor (Part - 1) Electrical Engineering (EE) Notes | EduRev

Also, Metal Oxide Semiconductor Field Effect Transistor (MOSFET) Capacitor (Part - 1) Electrical Engineering (EE) Notes | EduRev

Therfore atMetal Oxide Semiconductor Field Effect Transistor (MOSFET) Capacitor (Part - 1) Electrical Engineering (EE) Notes | EduRev

But by Gauss's law, electrons must compensate for increasing Qs.

So, Metal Oxide Semiconductor Field Effect Transistor (MOSFET) Capacitor (Part - 1) Electrical Engineering (EE) Notes | EduRev

where charge Qi is due to electrons in the inversion layer.

Earlier due to low electric field, the electron-hole pairs formed below the oxide interface recombine. However, once the electric field increases, the electron-hole pairs formed are not able to recombine. So the free electron concentration increases.

By Kirchoff's law, VGS  is given by:Metal Oxide Semiconductor Field Effect Transistor (MOSFET) Capacitor (Part - 1) Electrical Engineering (EE) Notes | EduRev

Metal Oxide Semiconductor Field Effect Transistor (MOSFET) Capacitor (Part - 1) Electrical Engineering (EE) Notes | EduRev

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