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MOSFET#

A metal-oxide-semiconductor field-effect transistor is a field-effect transistor which functions by exploiting the properties of MOS capacitors and p-n junctions.

Enhancement-Mode MOSFET#

Structure#

An enhancement-mode MOSFET has the same structure as a MOS capacitor except that the substrate is embedded with two regions of heavily doped semiconductor of the opposite type which are lateral to the gate:

Each of the lateral regions is connected to a terminal, either the source or the drain.

Enh MOSFET Structure

The most important dimensional parameters of a MOSFET are the physical distance (channel length) \(L\) between the source and the drain, the width \(W\) and the thickness \(t_{\text{ox}}\) of the insulator layer.

We want \(L\) to be as small as possible, usually being around 60 nm - 70 nm. The value of \(t_{\text{ox}}\) is usually around 50 times smaller than \(L\), i.e. between 1.5 nm and 2 nm. The width \(W\) can vary widely, ranging from a couple hundred nanometers to tens of micrometers.

Notation

The following symbols are used for enhancement-mode MOSFETs to explicitly indicate that the bulk and source are connected:

NMOS PMOS
Enh NMOS Symbol Bulk to Source Enh PMOS Symbol Bulk to Source

The following symbols are used for enhancement-mode MOSFETs to explicitly indicate that the bulk and source are not connected:

NMOS PMOS
Enh NMOS Symbol Bulk Open Enh PMOS Bulk Open

The following symbols are also used for enhancement-mode MOSFETs but give no information whether the bulk and source are connected or not:

NMOS PMOS
Enh NMOS No Bulk Symbol 1 Enh PMOS No Bulk Symbol 1
Enh NMOS No Bulk Symbol 2 Enh PMOS No Bulk Symbol 2

The combination of NMOS and PMOS for the implementation of digital circuits is known as complementary MOS (CMOS).

Physical Characteristics#

Each enhancement-mode MOSFET is characterized by a few fixed constants which stem from the physical properties of its elements and their configuration:

Constant Description
\(\varepsilon_{\text{ox}}\) The relative electric permittivity \(\varepsilon_{\text{ox}}\) of the insulation layer.
\(\mu\) (usually \(\mu_n\) for NMOS and \(\mu_p\) for NMOS) Measures how easily charge carriers can move around.
\[\mu_n \approx 3 \mu_p\]
\[C_{\text{ox}} = \frac{\varepsilon_{\text{ox}}\varepsilon_{0}}{t_{\text{ox}}}\]

The process transconductance parameter:

\[k' = \mu C_{\text{ox}} = \frac{\mu \cdot \varepsilon_{\text{ox}} \cdot \varepsilon_0}{t_{\text{ox}}}\]

The total gate capacitance:

\[C_{\text{G}} = \frac{\varepsilon_{\text{ox}}\cdot \varepsilon_0 \cdot W \cdot L}{t_{\text{ox}}}\]

The threshold voltage \(V_{\text{th}}\) - positive for NMOS and negative for PMOS.

Operation#

The following variables are used to characterize the operation of an enhancement-mode MOSFET:

  • the voltage \(V_{\text{GS}}\) between the gate and the source: \(V_{\text{GS}} = \phi_{\text{G}} - \phi_{\text{S}}\);
  • the voltage \(V_{\text{DS}}\) between the drain and the source: \(V_{\text{DS}} = \phi_{\text{D}} - \phi_{\text{S}}\);
  • the current \(I_\text{D}\) flowing from the drain to the source.

Enh MOSFET Variables

In an NMOS, the source is always at a lower potential than the drain: \(\phi_{\text{S}} \lt \phi_{\text{D}}\).

In a PMOS, the source is always at a higher potential than the drain: \(\phi_{\text{S}} \gt \phi_{\text{D}}\).

This, combined with the above convention, which is used for both PMOS and NMOS, ultimately determines the algebraic signs of the aforementioned quantities:

NMOS PMOS
\(V_{\text{GS}}\) \(\gt 0\) \(\lt 0\)
\(V_{\text{DS}}\) \(\gt 0\) \(\lt 0\)
\(I_{\text{D}}\) \(\gt 0\) \(\lt 0\)

The operation of a MOSFET is divided into three modes or regions depending on the relationship between \(V_{\text{GS}}\), \(V_{\text{DS}}\) and \(V_{\text{th}}\):

  • \(|V_{\text{GS}}| \lt |V_{\text{th}}|\) (cutoff region);
  • \(|V_{\text{GS}}| \gt |V_{\text{th}}|\) and \(|V_{\text{DS}}| \lt |V_{\text{GS}}| - |V_{\text{th}}|\) (triode region or linear region);
  • \(|V_{\text{GS}}| \gt |V_{\text{th}}|\) and \(|V_{\text{DS}}| \ge ​|V_{\text{GS}}|-|V_{\text{th}}|\) (saturation region).

The most common theoretical model for the dependence of \(I_{\text{D}}\) on \(V_{\text{GS}}\) and \(V_{\text{DS}}\) is the following:

\[I_{\text{D}, \text{NMOS}} = \begin{cases}0, & 0 \le V_{\text{GS}} \lt V_{\text{th}} \text{ and } V_{\text{DS}} \ge 0 & \text{(cutoff)} \\ \beta \left(V_{\text{GS}} - V_{\text{th}} - \frac{V_{\text{DS}}}{2}\right)V_{\text{DS}}, & V_{\text{GS}} \gt V_{\text{th}} \text{ and } 0 \lt V_{\text{DS}} \lt V_{\text{GS}} - V_{\text{th}} & \text{(linear)} \\ \frac{\beta}{2}(V_{\text{GS}}-V_{\text{th}})^2, & V_{\text{GS}} \gt V_{\text{th}} \text{ and } V_{\text{DS}} \gt V_{\text{GS}} - V_{\text{th}} & \text{(saturation)}\end{cases}\]
\[I_{\text{D}, \text{PMOS}} = \begin{cases}0, & 0 \ge V_{\text{GS}} \gt V_{\text{th}} \text{ and } V_{\text{DS}} \le 0 & \text{(cutoff)} \\ -\beta \left(V_{\text{GS}} - V_{\text{th}} - \frac{V_{\text{DS}}}{2}\right)V_{\text{DS}}, & V_{\text{GS}} \lt V_{\text{th}} \text{ and } 0 \gt V_{\text{DS}} \gt V_{\text{GS}} - V_{\text{th}} & \text{(linear)} \\ -\frac{\beta}{2}(V_{\text{GS}}-V_{\text{th}})^2, & V_{\text{GS}} \lt V_{\text{th}} \text{ and } V_{\text{DS}} \lt V_{\text{GS}} - V_{\text{th}} & \text{(saturation)}\end{cases}\]
\[\beta = \frac{\mu C_{G}}{L^2} = k_n'\frac{W}{L}\]

Transfer Characteristic#

The voltage \(V_{\text{GS}}\) between the gate and the source controls the resistance between the drain and the source.

The transfer characteristic of an enhancement-mode MOSFET describes the relationship between the current \(I_D\) and \(V_{\text{GS}}\) for a fixed \(V_{\text{DS}}\). It is divided into three regions.

In the cutoff region (\(|V_{\text{GS}}| \lt |V_{\text{th}}|\)), the two p-n junctions cause very high resistance and the current \(I_{\text{D}}\) is effectively zero (\(I_D \approx 0\)).

Enh MOSFET Cutoff

In the saturation region (\(V_{\text{th}} \lt V_{\text{GS}} \lt V_{\text{th}} + V_{\text{DS}}\)), the MOS structure enters inversion mode and the drain and the source become connected by a channel which contains the same type of mobile charge carriers as them, effectively bypassing the p-n junctions. This causes the resistance between the drain and the source to drop, since current \(I_D\) can now flow between the drain to the source via this channel. The current \(I_D\) increases quadratically with \(V_{\text{DS}}\).

MOSFET Conducting

In the triode region or linear region (\(|V_{\text{GS}}| \gt |V_{\text{DS}}| + |V_{\text{th}}|\)), the current \(I_D\) increases linearly with \(V_{\text{DS}}\).

Enh MOSFEET Linear Region

Output Characteristic#

The output characteristic or drain characteristic of an enhancement-mode MOSFET describes the relationship between the current \(I_D\) and \(V_{\text{DS}}\) for a fixed \(V_{\text{GS}}\).

When the MOSFET is in the cutoff region (\(V_{\text{GS}} \lt V_{\text{th}}\)), the current \(I_D\) is effectively zero, regardless of \(V_{\text{DS}}\).

When the MOSFET is in the triode region (\(V_{\text{GS}} \gt V_{\text{th}}\) and \(V_{\text{DS}} \lt V_{\text{GS} - V_{\text{th}}}\)), the dependence between \(I_D\) and \(V_{\text{DS}}\) is linear.

When the MOSFET is in the saturation region (\(V_{\text{GS}} \gt V_{\text{th}}\) and \(V_{\text{DS}} \ge V_{\text{GS} - V_{\text{th}}}\)), the current \(I_D\) remains constant, regardless of how much \(V_{\text{DS}}\) increases.