Cross section of a MOSFET operating in the saturation region
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 and a reduction of output resistance. It is one of several short-channel effects in MOSFET scaling. It also causes distortion in JFET amplifiers.[1]
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 drainjointly 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 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. 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:[2] where = drain current, = technology parameter sometimes called the transconductance coefficient, W, L = MOSFET width and length, = gate-to-source voltage, =threshold voltage, = drain-to-source voltage, , and λ = channel-length modulation parameter. In the classic Shichman–Hodges model, is a device constant, which reflects the reality of transistors with long channels.
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:[3]
,
where VE is a fitting parameter, although it is similar in concept to the Early Voltage for BJTs. For a 65 nm process, roughly VE ≈ 4 V/μm.[3] (A more elaborate approach is used in the EKV model.[4]). 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 (which tends to limit the increase in channel current with drain voltage, thereby increasing the output resistance) and ballistic transport (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.
The metal-oxide-semiconductor field-effect transistor is a type of field-effect transistor (FET), most commonly fabricated by the controlled oxidation of silicon. It has an insulated gate, the voltage of which determines the conductivity of the device. This ability to change conductivity with the amount of applied voltage can be used for amplifying or switching electronic signals. A metal-insulator-semiconductor field-effect transistor (MISFET) is a term almost synonymous with MOSFET. Another synonym is IGFET for insulated-gate 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.
A bipolar junction transistor (BJT) is a type of transistor that uses both electrons and electron holes as charge carriers. In contrast, a unipolar transistor, such as a field-effect transistor (FET), uses only one kind of charge carrier. A bipolar transistor allows a small current injected at one of its terminals to control a much larger current flowing between the terminals, making the device capable of amplification or switching.
In electronics, a common collector amplifier is one of three basic single-stage bipolar junction transistor (BJT) amplifier topologies, typically used as a voltage buffer.
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. Conceptually, an ideal current mirror is simply an ideal inverting current amplifier that reverses the current direction as well. Or it can consist of a current-controlled current source (CCCS). The current mirror is used to provide bias currents and active loads to circuits. It can also be used to model a more realistic current source.
Transconductance, also infrequently called mutual conductance, is the electrical characteristic relating the current through the output of a device to the voltage across the input of a device. Conductance is the reciprocal of resistance.
The threshold voltage, commonly abbreviated as Vth or VGS(th), of a field-effect transistor (FET) is the minimum gate-to-source voltage (VGS) that is needed to create a conducting path between the source and drain terminals. It is an important scaling factor to maintain power efficiency.
In electronics, a common-source amplifier is one of three basic single-stage field-effect transistor (FET) amplifier topologies, typically used as a voltage or transconductance amplifier. The easiest way to tell if a FET is common source, common drain, or common gate is to examine where the signal enters and leaves. The remaining terminal is what is known as "common". In this example, the signal enters the gate, and exits the drain. The only terminal remaining is the source. This is a common-source FET circuit. The analogous bipolar junction transistor circuit may be viewed as a transconductance amplifier or as a voltage amplifier.. As a transconductance amplifier, the input voltage is seen as modulating the current going to the load. As a voltage amplifier, input voltage modulates the current flowing through the FET, changing the voltage across the output resistance according to Ohm's law. However, the FET device's output resistance typically is not high enough for a reasonable transconductance amplifier, nor low enough for a decent voltage amplifier. As seen below in the formula, the voltage gain depends on the load resistance, so it cannot be applied to drive low-resistance devices, such as a speaker. Another major drawback is the amplifier's limited high-frequency response. Therefore, in practice the output often is routed through either a voltage follower, or a current follower, to obtain more favorable output and frequency characteristics. The CS–CG combination is called a cascode amplifier.
The cascode is a two-stage amplifier that consists of a common-emitter stage feeding into a common-base stage.
A power MOSFET is a specific type of metal–oxide–semiconductor field-effect transistor (MOSFET) designed to handle significant power levels. Compared to the other power semiconductor devices, such as an insulated-gate bipolar transistor (IGBT) or a thyristor, its main advantages are high switching speed and good efficiency at low voltages. It shares with the IGBT an isolated gate that makes it easy to drive. They can be subject to low gain, sometimes to a degree that the gate voltage needs to be higher than the voltage under control.
In mesoscopic physics, ballistic conduction is the unimpeded flow of charge carriers, or energy-carrying particles, over relatively long distances in a material. In general, the resistivity of a material exists because an electron, while moving inside a medium, is scattered by impurities, defects, thermal fluctuations of ions in a crystalline solid, or, generally, by any freely-moving atom/molecule composing a gas or liquid. Without scattering, electrons simply obey Newton's second law of motion at non-relativistic speeds.
A buck converter or step-down converter is a DC-to-DC converter which steps down voltage from its input (supply) to its output (load). It is a class of switched-mode power supply. Switching converters provide much greater power efficiency as DC-to-DC converters than linear regulators, which are simpler circuits that lower voltages by dissipating power as heat, but do not step up output current. The efficiency of buck converters can be very high, often over 90%, making them useful for tasks such as converting a computer's main supply voltage, which is usually 12V, down to lower voltages needed by USB, DRAM and the CPU, which are usually 5, 3.3 or 1.8V.
A Wilson current mirror is a three-terminal circuit that accepts an input current at the input terminal and provides a "mirrored" current source or sink output at the output terminal. The mirrored current is a precise copy of the input current. It may be used as a Wilson current source by applying a constant bias current to the input branch as in Fig. 2. The circuit is named after George R. Wilson, an integrated circuit design engineer who worked for Tektronix. Wilson devised this configuration in 1967 when he and Barrie Gilbert challenged each other to find an improved current mirror overnight that would use only three transistors. Wilson won the challenge.
The Early effect, named after its discoverer James M. Early, is the variation in the effective width of the base in a bipolar junction transistor (BJT) due to a variation in the applied base-to-collector voltage. A greater reverse bias across the collector–base junction, for example, increases the collector–base depletion width, thereby decreasing the width of the charge carrier portion of the base.
The term contact resistance refers to the contribution to the total resistance of a system which can be attributed to the contacting interfaces of electrical leads and connections as opposed to the intrinsic resistance. This effect is described by the term electrical contact resistance (ECR) and arises as the result of the limited areas of true contact at an interface and the presence of resistive surface films or oxide layers. ECR may vary with time, most often decreasing, in a process known as resistance creep. The idea of potential drop on the injection electrode was introduced by William Shockley to explain the difference between the experimental results and the model of gradual channel approximation. In addition to the term ECR, interface resistance, transitional resistance, or just simply correction term are also used. The term parasitic resistance is used as a more general term, of which it is usually assumed that contact resistance is a major component.
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 bottleneck in channel formation occurs far enough from the drain contact that it is electrostatically shielded from the drain by the combination of the substrate and gate, and so classically the threshold voltage was independent of drain voltage. In short-channel devices this is no longer true: The drain is close enough to gate the channel, and so a high drain voltage can open the bottleneck and turn on the transistor prematurely.
Hybrid-Pi is a popular circuit model used for analyzing the small signal behavior of bipolar junction and field effect transistors. Sometimes it is also called Giacoletto model because it was introduced by L.J. Giacoletto in 1969. The model can be quite accurate for low-frequency circuits and can easily be adapted for higher frequency circuits with the addition of appropriate inter-electrode capacitances and other parasitic elements.
A carbon nanotube field-effect transistor (CNTFET) is a field-effect transistor that utilizes a single carbon nanotube or an array of carbon nanotubes as the channel material instead of bulk silicon in the traditional MOSFET structure. First demonstrated in 1998, there have been major developments in CNTFETs since.
In the theory of electrical networks, a dependent source is a voltage source or a current source whose value depends on a voltage or current elsewhere in the network.
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 are devices with three terminals: source, gate, and drain. FETs control the flow of current by the application of a voltage to the gate, which in turn alters the conductivity between the drain and source.
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