![Threshold formation nowatermark](https://upload.wikimedia.org/wikipedia/commons/4/43/Threshold_formation_nowatermark.gif)
The threshold voltage, commonly abbreviated as V
th or V
GS(th), of a
field-effect transistor
The field-effect transistor (FET) is a type of transistor that uses an electric field to control the flow of current in a semiconductor. FETs (JFETs or MOSFETs) are devices with three terminals: ''source'', ''gate'', and ''drain''. FETs contro ...
(FET) is the minimum gate-to-source
voltage
Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...
(V
GS) that is needed to create a conducting path between the source and drain terminals. It is an important scaling factor to maintain power efficiency.
When referring to a
junction field-effect transistor
The junction-gate field-effect transistor (JFET) is one of the simplest types of field-effect transistor. JFETs are three-terminal semiconductor devices that can be used as electronically controlled switches or resistors, or to build amplifiers. ...
(JFET), the threshold voltage is often called pinch-off voltage instead. This is somewhat confusing since ''pinch off'' applied to
insulated-gate field-effect transistor (IGFET) refers to the
channel pinching that leads to current saturation behaviour under high source–drain bias, even though the current is never off. Unlike ''pinch off'', the term ''threshold voltage'' is unambiguous and refers to the same concept in any field-effect transistor.
Basic principles
In
n-channel
The field-effect transistor (FET) is a type of transistor that uses an electric field to control the flow of current in a semiconductor. FETs ( JFETs or MOSFETs) are devices with three terminals: ''source'', ''gate'', and ''drain''. FETs cont ...
''enhancement-mode'' devices, a conductive channel does not exist naturally within the transistor, and a positive gate-to-source voltage is necessary to create one such. The positive voltage attracts free-floating electrons within the body towards the gate, forming a conductive channel. But first, enough electrons must be attracted near the gate to counter the dopant ions added to the body of the FET; this forms a region with no mobile carriers called a
depletion region
In semiconductor physics, the depletion region, also called depletion layer, depletion zone, junction region, space charge region or space charge layer, is an insulating region within a conductive, doped semiconductor material where the mobile ...
, and the voltage at which this occurs is the ''threshold voltage'' of the FET. Further gate-to-source voltage increase will attract even more electrons towards the gate which are able to create a conductive channel from source to drain; this process is called ''inversion''. The reverse is true for the p-channel "enhancement-mode" MOS transistor. When V
GS = 0 the device is “OFF” and the channel is open / non-conducting. The application of a negative gate voltage to the p-type "enhancement-mode" MOSFET enhances the channels conductivity turning it “ON”.
In contrast, n-channel ''depletion-mode'' devices have a conductive channel naturally existing within the transistor. Accordingly, the term ''threshold voltage'' does not readily apply to ''turning'' such devices on, but is used instead to denote the voltage level at which the channel is wide enough to allow electrons to flow easily. This ease-of-flow threshold also applies to
p-channel
The field-effect transistor (FET) is a type of transistor that uses an electric field to control the flow of Electric current, current in a semiconductor. FETs (JFETs or MOSFETs) are devices with three terminals: ''source'', ''gate'', and ''dra ...
''depletion-mode'' devices, in which a negative voltage from gate to body/source creates a depletion layer by forcing the positively charged holes away from the gate-insulator/semiconductor interface, leaving exposed a carrier-free region of immobile, negatively charged acceptor ions.
For the n-channel depletion MOS transistor, a negative gate-source voltage will deplete (hence its name) the conductive channel of its free electrons switching the transistor “OFF”. Likewise for a p-channel "depletion-mode" MOS transistor a positive gate-source voltage will deplete the channel of its free holes, turning it “OFF”.
In wide planar transistors the threshold voltage is essentially independent of the drain–source voltage and is therefore a well defined characteristic, however it is less clear in modern nanometer-sized MOSFETs due to
drain-induced barrier lowering
Drain-induced barrier lowering (DIBL) is a short-channel effect in MOSFETs referring originally to a reduction of threshold voltage of the transistor at higher drain voltages.
In a classic planar field-effect transistor with a long channel, the bo ...
.
In the figures, the source (left side) and drain (right side) are labeled ''n+'' to indicate heavily doped (blue) n-regions. The depletion layer dopant is labeled ''N
A−'' to indicate that the ions in the (pink) depletion layer are negatively charged and there are very few holes. In the (red) bulk the number of holes ''p = N
A'' making the bulk charge neutral.
If the gate voltage is below the threshold voltage (left figure), the "enhancement-mode" transistor is turned off and ideally there is no
current
Currents, Current or The Current may refer to:
Science and technology
* Current (fluid), the flow of a liquid or a gas
** Air current, a flow of air
** Ocean current, a current in the ocean
*** Rip current, a kind of water current
** Current (stre ...
from the drain to the source of the transistor. In fact, there is a current even for gate biases below the threshold (
subthreshold leakage) current, although it is small and varies exponentially with gate bias. Therefore, datasheets will specify threshold voltage according to a specified measurable amount of current (commonly 250 μA or 1 mA).
If the gate voltage is above the threshold voltage (right figure), the "enhancement-mode" transistor is turned on, due to there being many electrons in the channel at the oxide-silicon interface, creating a low-resistance channel where charge can flow from drain to source. For voltages significantly above the threshold, this situation is called strong inversion. The channel is tapered when because the voltage drop due to the current in the resistive channel reduces the oxide field supporting the channel as the drain is approached.
Body effect
The ''body effect'' is the change in the threshold voltage by an amount approximately equal to the change in the source-bulk voltage,
, because the body influences the threshold voltage (when it is not tied to the source). It can be thought of as a second gate, and is sometimes referred to as the ''back gate'', and accordingly the body effect is sometimes called the ''back-gate effect''.
For an enhancement-mode nMOS MOSFET, the body effect upon threshold voltage is computed according to the Shichman–Hodges model, which is accurate for older process nodes, using the following equation:
::
where;
is the threshold voltage when substrate bias is present,
is the source-to-body substrate bias,
is the surface potential,
is threshold voltage for zero substrate bias,
is the body effect parameter,
is oxide thickness,
is oxide
permittivity
In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' (epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in ...
,
is the permittivity of silicon,
is a doping concentration,
is
elementary charge
The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...
.
Dependence on oxide thickness
In a given technology node, such as the
90-nm CMOS process, the threshold voltage depends on the choice of oxide and on oxide thickness. Using the body formulas above,
is directly proportional to
, and
, which is the parameter for oxide thickness.
Thus, the thinner the oxide thickness, the lower the threshold voltage. Although this may seem to be an improvement, it is not without cost; because the thinner the oxide thickness, the higher the
subthreshold leakage current through the device will be. Consequently, the design specification for 90-nm gate-oxide thickness was set at 1 nm to control the leakage current. This kind of tunneling, called Fowler-Nordheim Tunneling.
::
where;
and
are constants,
is the electric field across the gate oxide.
Before scaling the design features down to 90 nm, a dual-oxide approach for creating the oxide thickness was a common solution to this issue. With a 90 nm process technology, a triple-oxide approach has been adopted in some cases. One standard thin oxide is used for most transistors, another for I/O driver cells, and a third for memory-and-pass transistor cells. These differences are based purely on the characteristics of oxide thickness on threshold voltage of CMOS technologies.
Temperature dependence
As with the case of oxide thickness affecting threshold voltage, temperature has an effect on the threshold voltage of a CMOS device. Expanding on part of the equation in the
body effect section
::
where;
is half the contact potential,
is the
Boltzmann constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, ...
,
is temperature,
is the
elementary charge
The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...
,
is a doping parameter,
is the intrinsic doping parameter for the substrate.
We see that the surface potential has a direct relationship with the temperature. Looking above, that the threshold voltage does not have a direct relationship but is not independent of the effects. This variation is typically between −4 mV/K and −2 mV/K depending on doping level. For a change of 30 °C this results in significant variation from the 500 mV design parameter commonly used for the 90-nm technology node.
Dependence on random dopant fluctuation
Random dopant fluctuation (RDF) is a form of process variation resulting from variation in the implanted impurity concentration. In MOSFET transistors, RDF in the channel region can alter the transistor's properties, especially threshold voltage. In newer process technologies RDF has a larger effect because the total number of dopants is fewer.
Research works are being carried out in order to suppress the dopant fluctuation which leads to the variation of threshold voltage between devices undergoing same manufacturing process.
[Asenov, A. Huan]
Suppression of random dopant-induced threshold voltage fluctuations in sub-0.1-μm MOSFET's with epitaxial and δ-doped channels
Electron Devices, IEEE Transactions, 46, Issue: 8
See also
*
MOSFET operation
*
Channel length modulation
Channel length modulation (CLM) is an effect in field effect transistors, a shortening of the length of the inverted channel region with increase in drain bias for large drain biases. The result of CLM is an increase in current with drain bias an ...
References
External links
Online lecture on: Threshold Voltage and MOSFET Capacitancesby Dr. Lundstrom
{{DEFAULTSORT:Threshold Voltage
Transistor modeling
Electrical parameters
MOSFETs
fr:Transistor à effet de champ à grille métal-oxyde#Tension de seuil