Channel length modulation
Encyclopedia
To understand the effect, first the notion of pinch-off of the channel is introduced. The channel is formed by attraction of carriers to the gate, and the current drawn through the channel is nearly a constant independent of drain voltage in saturation mode. However, near the drain, the gate and drain jointly determine the electric field pattern. Instead of flowing in a channel, beyond the pinch-off point the carriers flow in a subsurface pattern made possible because the drain and the gate both control the current. In the figure at the right, the channel is indicated by a dashed line and becomes weaker as the drain is approached, leaving a gap of uninverted silicon between the end of the formed inversion layer and the drain (the pinch-off region).
As the drain voltage increases, its control over the current extends further toward the source, so the uninverted region expands toward the source, shortening the length of the channel region, the effect called channel-length modulation. Because resistance is proportional to length, shortening the channel decreases its resistance, causing an increase in current with increase in drain bias for a MOSFET
MOSFET
The metal–oxide–semiconductor field-effect transistor is a transistor used for amplifying or switching electronic signals. The basic principle of this kind of transistor was first patented by Julius Edgar Lilienfeld in 1925...
operating in saturation. The effect is more pronounced the shorter the source-to-drain separation, the deeper the drain junction, and the thicker the oxide insulator.
In the weak inversion region, the influence of the drain analogous to channel-length modulation leads to poorer device turn off behavior known as drain-induced barrier lowering, a drain induced lowering of threshold voltage.
In bipolar devices a similar increase in current is seen with increased collector voltage due to base-narrowing, known as the Early effect
Early Effect
The Early effect is the variation in the width of the base in a bipolar junction transistor due to a variation in the applied base-to-collector voltage, named after its discoverer James M. Early...
. The similarity in effect upon the current has led to use of the term "Early effect" for MOSFETs as well, as an alternative name for "channel-length modulation".
Shichman–Hodges model
In textbooks, channel length modulation in active mode usually is described using the Shichman–Hodges model, accurate only for old technology:
where
= drain current, 
=technology parameter sometimes called the transconductance coefficient, W ,L = MOSFET width and length,
= gate-to-source voltage, 
=threshold voltageThreshold voltage
The threshold voltage of a MOSFET is usually defined as the gate voltage where an inversion layer forms at the interface between the insulating layer and the substrate of the transistor. The purpose of the inversion layer's forming is to allow the flow of electrons through the gate-source junction...
,
= drain-to-source voltage and λ = channel-length modulation parameter. The threshold voltage Vth in this formula is subject to drain-induced barrier lowering, and accurate results require computer models.Output resistance
Channel-length modulation is important because it decides the MOSFET output resistance, an important parameter in circuit design of current mirrorCurrent mirror
A current mirror is a circuit designed to copy a current through one active device by controlling the current in another active device of a circuit, keeping the output current constant regardless of loading. The current being 'copied' can be, and sometimes is, a varying signal current...
s and amplifiers.
In the Shichman–Hodges model used above, output resistance is given as:
-
,
where
= drain-to-source voltage, 
= drain current and 
= channel-length modulation parameter. Without channel-length modulation (for λ = 0), the output resistance is infinite. The channel-length modulation parameter usually is taken to be inversely proportional to MOSFET channel length L, as shown in the last form above for rO:-
≈ 
,
where VE = is a fitting parameter, although it is similar in concept to the Early Voltage
Early Effect
The Early effect is the variation in the width of the base in a bipolar junction transistor due to a variation in the applied base-to-collector voltage, named after its discoverer James M. Early...
for BJTs. For a 65 nm process, roughly VE ≈ 4 V/μm. (A more elaborate approach is used in the EKV model.). However, no simple formula used for λ to date provides accurate length or voltage dependence of rO for modern devices, forcing use of computer models, as discussed briefly next.
The effect of channel-length modulation upon the MOSFET output resistance varies both with the device, particularly its channel length, and with the applied bias. The main factor affecting the output resistance in longer MOSFETs is channel length modulation as just described. In shorter MOSFETs additional factors arise such as: drain-induced barrier lowering (which lowers the threshold voltage, increasing the current and decreasing the output resistance), velocity saturation
Velocity saturation
In semiconductors, when a strong enough electric field is applied, the carrier velocity in the semiconductor reaches a maximum value, saturation velocity. When this happens, the semiconductor is said to be in a state of velocity saturation...
(which tends to limit the increase in channel current with drain voltage, thereby increasing the output resistance) and ballistic transport
Ballistic transport
Ballistic transport is the transport of electrons in a medium with negligible electrical resistivity due to scattering. Without scattering, electrons simply obey Newton's second law of motion at non-relativistic speeds....
(which modifies the collection of current by the drain, and modifies drain-induced barrier lowering so as to increase supply of carriers to the pinch-off region, increasing the current and decreasing the output resistance). Again, accurate results require computer models.
See also
- Threshold voltageThreshold voltageThe threshold voltage of a MOSFET is usually defined as the gate voltage where an inversion layer forms at the interface between the insulating layer and the substrate of the transistor. The purpose of the inversion layer's forming is to allow the flow of electrons through the gate-source junction...
- Short channel effectShort channel effectIn electronics, a short-channel effect is an effect whereby a MOSFET, in which the channel length is the same order of magnitude as the depletion-layer widths of the source and drain junction, behaves differently from other MOSFETs....
- Drain-induced barrier lowering
- MOSFET operation
- Hybrid-pi modelHybrid-pi modelThe hybrid-pi model is a popular circuit model used for analyzing the small signal behavior of bipolar junction and field effect transistors. The model can be quite accurate for low-frequency circuits and can easily be adapted for higher frequency circuits with the addition of appropriate...
- Transistor modelsTransistor modelsTransistors are simple devices with complicated behavior. In order to ensure the reliable operation of circuits employing transistors, it is necessary to scientifically model the physical phenomena observed in their operation using transistor models. There exists a variety of different models that...