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MOS Capacitors

MOS Capacitor: A Detailed Overview

Introduction

A MOS (Metal-Oxide-Semiconductor) capacitor is one of the fundamental building blocks in semiconductor devices and forms the basis of MOSFETs (Metal-Oxide-Semiconductor Field-Effect Transistors). It consists of a metal gate, an insulating oxide layer, and a semiconductor substrate. Understanding the MOS capacitor is critical to grasp modern electronic device operation.

Structure

A typical MOS capacitor consists of three layers:

  1. Metal Gate: Traditionally aluminum, but modern devices often use heavily-doped polysilicon due to its process compatibility and work function tunability.
  2. Oxide Layer: An insulating layer, typically silicon dioxide (SiO₂), though modern devices may use high-k dielectrics like HfO₂ to reduce leakage current.
  3. Semiconductor: Usually silicon substrate, which can be p-type or n-type depending on doping. The doping concentration affects the threshold voltage and capacitance characteristics.

Diagram

Below is an example diagram of a MOS capacitor structure:

MOS Capacitor Diagram

Working Principle

The MOS capacitor operation depends on the gate voltage (Vgs) relative to the substrate. The behavior can be classified into four distinct regimes:

1. Accumulation

Accumulation occurs in a Metal-Oxide-Semiconductor (MOS) capacitor when a voltage is applied to the gate such that it attracts majority carriers to the semiconductor-oxide interface. This happens when the gate voltage (Vgb with respect to body/substrate voltage​) is more negative for a p-type semiconductor or more positive for an n-type semiconductor

  • Condition: Vgb < 0 for p-type substrate and Vgb > 0 for n-type substrate.
  • Effect: Majority carriers (holes in p-type and electrons in n-type) accumulate below the oxide-semiconductor interface
  • Characteristics: Maximum capacitance between gate and substrate, equal to Cox

2. Flat-band

The flat-band voltage (Vfb) in a Metal-Oxide-Semiconductor (MOS) capacitor is the voltage applied to the gate that ensures the energy bands in the semiconductor are flat, meaning there is no band bending at the semiconductor-oxide interface. This condition occurs when there is no net charge in the semiconductor, and the surface potential ϕs(potential of semiconductor just under the oxide) is zero.

  • Condition: Vgb = Vfb
  • Effect: No band bending, no net charge in semiconductor
  • Characteristics: Represents the reference point for voltage measurements

3. Depletion

  • Condition: Vfb < Vgb < Vth (Threshold voltage)
  • Effect:
    • Majority carriers are repelled, forming a depletion region
    • Width of depletion region increases with gate voltage
    • Total capacitance decreases due to series combination of Cox and depletion capacitance

4. Inversion

  • Condition: Vgb > Vth
  • Effect:
    • Strong band bending attracts minority carriers
    • Forms an inversion layer of minority carriers from substrate of electrons (for p-type) and holes (for n-type substrate).
    • At inversion, magnitude of carrier concentration in version layer is same as the majority carrier in the bulk.
    • Depletion width reaches maximum
  • Characteristics:
    • Low frequency: Capacitance returns to Cox
    • High frequency: Capacitance remains at minimum due to minority carrier response limitations

WORK FUNCTIONS

Work Function in MOS Capacitors

Introduction

The work function (φ) is a fundamental property of materials that represents the minimum energy required to remove an electron from the Fermi level to vacuum. It plays a crucial role in Metal-Oxide-Semiconductor (MOS) capacitors and transistors.

Definition

The work function of a material is given by:

where:

  • Evac is the vacuum energy level (the energy needed to remove an electron completely from the material).
  • Ef is the Fermi level (the energy at which the probability of finding an electron is 50% at thermal equilibrium).

Work Function in MOS Capacitors

In a MOS structure, there are three key work functions:

  1. Metal Work Function Φm: The work function of the gate material (e.g., aluminum, polysilicon, or high-k metal gates).
  2. Semiconductor Work Function Φs: The work function of the semiconductor, dependent on doping concentration.
  3. Oxide Work Function: Insulating layer (e.g., SiO₂) does not contribute to work function directly, but influences charge behavior.

The metal-semiconductor work function difference is critical for determining the flat-band voltage:

Φms = Φm- Φs

Effect on MOS Behavior

The work function influences the threshold voltage (Vth) of a MOSFET, which is given by:

where:

  • Vfb is the flat-band voltage
  • Φf is the Fermi potential of the semiconductor
  • Qd is the depletion charge
  • Cox is the oxide capacitance

Typical Work Function Values

Material Work Function (eV)
Aluminum (Al) 4.1 - 4.3
Polysilicon (p-type) ~5.0
Polysilicon (n-type) ~4.1
Silicon (Intrinsic) ~4.6
Silicon Dioxide (SiO₂) ~0 (insulator)
High-k metals (e.g., TiN, TaN) 4.5 - 5.2

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Applications

  1. MOSFETs: MOS capacitors form the gate structure in MOSFETs.
  2. Dynamic RAM: Used to store charge in memory cells.
  3. Sensors: MOS structures are used in gas sensors and other semiconductor-based sensors.

Introduction to MOSFET

Inversion channel formed when Vgb >= Vth, will allow carriers to flow if a voltage difference is applied between the two ends of inversion channel. By controlling the Gate voltage, we control the inversion channel and hence, the carriers flowing in it. We can also control this current through the potential applied across the ends of inversion layer. This forms the basis of MOS based field effect transistors (FET). Two terminals Source and Drain are fabricated respectively such that inversion layer from a conducting channel between them. The voltage in MOSFET are measured w.r.t. reference terminal ’Source’. Hence, the two controlling voltages are Vgs and Vds and output controlled is the channel (inversion channel to be more specific) current also called the drain current Id. Characteristics: As expected, increasing Gate voltage (in the direction enhancing the inversion layer) will increase the channel current Id and increasing the drain-source voltage (Vds) also increases the channel current Id.

Summary

The MOS capacitor is a simple yet versatile device critical for modern electronics. It showcases how electric fields control charge distribution, forming the foundation for transistors and memory devices. Mastering its working is a stepping stone for understanding semiconductor physics and device engineering.

References

  • "Semiconductor Device Fundamentals" by Robert F. Pierret.
  • Online materials from IEEE Xplore and similar educational sources.