In the previous installment we met a three-terminal device for the first time: the junction transistor (BJT). Its structure was such that a small current into the base makes a large current flow through the collector. It was the first way of moving something big with something small.
That way, however, carries a price. Control costs current. The current fed into the base is not a signal; it is spent opening the device and vanishes. Put not one device but hundreds of millions on a single chip, and that price turns directly into heat and power.
The question this installment answers is this. Can a device be opened without using current? The answer is yes, and a device that does so is called a field-effect transistor (FET).
The operating values in this text are examples meant to show how a calculation goes, not the specifications of any particular company. Every figure quoted here was confirmed in published literature, and the sources are listed at the end.
Renaming the Terminals from Scratch
The English Wikipedia "Field-effect transistor" article defines the FET as a transistor that uses an electric field to control the current within a semiconductor. And it names the three terminals as follows.
- Source — where carriers enter the channel.
- Drain — where carriers leave the channel.
- Gate — the terminal that modulates the conductivity of the channel. A voltage applied here controls the drain current.
The "Field-effect transistor" article states that these three correspond roughly to the emitter, collector and base of a BJT. And most FETs have a fourth terminal as well: the body. It refers to the piece of semiconductor on which source, gate and drain sit, and it is used to set the device's operating point.
The path along which carriers travel between source and drain is the channel.
The "Field-effect transistor" article explains that the gate may be thought of as an actual door being opened and closed. The gate lets electrons through or blocks them by creating or removing the channel. Where the base of a BJT was a terminal that intervenes in a flow, the gate of a FET is a terminal that lays down or erases the road itself.
One more property that separates it from the BJT emerges here. The "Field-effect transistor" article states that, unlike the BJT, most FETs are electrically symmetric, so that swapping the source and drain connections does not change the behaviour. Emitter and collector, differing in doping concentration, could not be exchanged. In a FET, that distinction is settled merely by which side the circuit puts the higher voltage on.
No Contact — What the Name "Field Effect" Means
The heart of the FET lies in one place in its structure. The gate does not touch the channel. A thin insulating film sits between them.
The Wikipedia "MOSFET" article describes the gate as separated from the channel by a thin insulating layer, traditionally of silicon dioxide. And the FET article states that one of the criteria dividing FETs is what insulates the channel from the gate. Insulation is not a side detail but an axis of classification.
If there is no contact, how does control happen? The MOSFET article answers. Apply a voltage between gate and source and the electric field it creates penetrates the oxide and forms a channel at the surface where semiconductor meets insulator.
What crossed over was the electric field, not charge. Place a magnet on a sheet of paper and the iron filings beneath the paper move. The magnet never touched the filings. What the gate does to the channel is just like that, and hence the name field effect.
No Current Flows Through the Gate
Since there is an insulating film, a natural consequence follows. The MOSFET article states the great advantage of the MOSFET in digital switching this way — the oxide between gate and channel prevents direct current from flowing into the gate, further reducing power consumption and giving a very large input impedance. The FET article likewise describes the FET as showing an extremely high input impedance at low frequencies.
This stands in direct contrast to the BJT. A BJT must keep base current flowing the whole time it is on. A FET stays open once the voltage has been applied. There is no steady current needed to hold it open.
The FET article notes that the FET is also called a unipolar transistor, because it uses only one kind of carrier — electrons (n-channel) or holes (p-channel). The BJT enlisted both, and so was "bipolar."
The idea is older than the BJT. US 1,745,175 (Julius Edgar Lilienfeld, filed 1926, granted 1930), published on Google Patents, contains the statement that because the thickness of the film is very small, applying an electrostatic force to it affects the electrical conductivity of that film. The conception ran more than 20 years ahead of the point-contact transistor of 1947.
MOS — The Capacitor of the Previous Installment Is Here
Gate, insulator, semiconductor. These three layers have a settled name. Taking the initials of metal, oxide and semiconductor, it is called the MOS structure. A field-effect transistor built with this structure is a MOSFET.
The MOSFET article describes the MOS structure as obtained by growing a layer of silicon dioxide on a silicon substrate and depositing metal or polycrystalline silicon on top of it. And the following sentence is the heart of this installment.
Since silicon dioxide is a dielectric, this structure is equivalent to a planar capacitor with one of its electrodes replaced by a semiconductor.
We can carry over the formula from the previous installment unchanged.
C = ε A / d
The correspondence lines up like this.
- ε — the permittivity of the gate insulator. Only the dielectric inserted between the plates has become an oxide.
- A — the area over which the gate faces the channel.
- d — the thickness of the insulating film. The role once played by the depletion layer is now played by the oxide.
The junction capacitance of the previous installment was a capacitance that came along whether you wanted it or not. The capacitance of a MOS is made on purpose, and the device is operated by it. The same formula is an obstacle in one place and a component in another.
Putting Numbers In Once
Capacitance per unit area is given its own name, oxide capacitance, and written with a lower-case letter. Engineering LibreTexts' "Basic MOS Structure" states that the gate and the substrate form a kind of parallel-plate capacitor with the oxide as the insulating layer, and defines the capacitance per unit area as follows.
cox = εox / xox
Let us carry over the example values given in "Basic MOS Structure" and work the calculation through. This article assumes the two values below as the example from "Basic MOS Structure" and calculates with them.
- the permittivity of silicon dioxide εox ≈ 3.3 × 10−13 F/cm
- the oxide thickness xox = 250 Å = 2.5 × 10−6 cm
Dividing gives cox ≈ 1.30 × 10−7 F/cm2. That is the same as the value the literature records.
That the denominator here is thickness explains the whole history of the device. The MOSFET article describes how shrinking a device very small requires the gate dielectric layer to be made very thin, around 1 nm in the latest technology. Keeping the same permittivity and changing only the thickness to 1 nm (= 1 × 10−7 cm), dividing again gives cox ≈ 3.3 × 10−6 F/cm2. Since 250 Å is 25 nm, the thickness becomes 1/25 and the capacitance per unit area becomes 25 times larger.
A large capacitance means that the same gate voltage draws more charge into the channel. That is why making the insulating film thin is the same work as making the device strong. The same thing can be aimed at through materials. The table in the Wikipedia "Relative permittivity" article gives the relative permittivity of silicon dioxide as 3.9 and that of silicon as 11.68. It means there is also a road to enlarging ε, the numerator.
What Gate Voltage Does to the Channel — Three States
Now let us apply a voltage to this capacitor. Take the body to be p-type, with holes as the majority carriers. Depending on the voltage applied, the region near the interface falls into one of three states. Engineering LibreTexts' "MOS Fundamentals" divides these three into accumulation, depletion and inversion.
Accumulation — the voltage is applied in the direction that draws majority carriers toward the interface. "MOS Fundamentals" describes this state as one in which the majority carrier concentration is higher near the oxide–semiconductor interface than in the bulk. For p-type, holes pile up thickly at the interface.
Depletion — a little voltage is applied in the opposite direction. The MOSFET article states that applying a positive voltage from the gate to a p-type body pushes the positively charged holes away from the interface, leaving a carrier-free region containing only immobile negative acceptor ions. The same kind of layer as the depletion layer seen in #03 appears here too.
Inversion — the positive voltage is raised further. The MOSFET article describes how, once the gate voltage is high enough, negative carriers gather at high concentration in a thin layer right beside the surface where insulator meets semiconductor, forming an inversion layer. The surface of the p-type body has been turned over into a layer in which electrons are the majority. Hence "inversion."
This inversion layer is precisely the channel. The MOSFET article states that the inversion layer provides a path along which current can pass between source and drain. Source and drain were n-type and the body between them p-type, so until inversion occurred there was no road between the two. The gate voltage lays down a road that was not there.
Threshold Voltage — Only the Name Here
The voltage at which that road begins to appear has a name. The Wikipedia "Threshold voltage" article defines the threshold voltage (Vth) as the minimum gate-to-source voltage needed to create a conducting path between source and drain. The MOSFET article records the same value as the gate voltage at which the electron density in the inversion layer equals the hole density in the body. The wording differs, but the point they indicate is the same.
Almost the whole character of a single device is contained in this number, and there is a body of discussion devoted solely to measuring and extracting it. In this series we leave it at the name and its meaning and move on.
Enhancement Mode and Depletion Mode
Devices split into two branches according to when the channel exists. The FET article and the Threshold voltage article record the same content.
Enhancement-mode devices have no conducting channel originally present inside them. For an n-channel, a positive gate-to-source voltage must be applied before a channel appears. With no voltage applied, it is off. The MOSFET article sums up the enhancement mode by saying that the voltage applied to the gate increases the conductivity of the device.
Depletion-mode devices are the opposite. The Threshold voltage article states that an n-channel depletion-mode device has a conducting channel present from the outset, and describes a negative voltage as required to turn it off. The MOSFET article likewise records that in depletion mode the voltage applied to the gate decreases the conductivity.
For use as a switch, enhancement mode is the convenient one. A device that is off when nothing is applied is the safer one.
MOSFET and TFT — The Same Principle, a Different Place
Everything said so far presumed that the semiconductor was the silicon wafer itself. The channel formed on the surface of that wafer. But when a display is to be made, the circumstances change. A sheet of glass cannot be turned into a silicon wafer.
The Wikipedia "Thin-film transistor" article defines the thin-film transistor (TFT) as a special kind of field-effect transistor made by thin-film deposition, and states that it is grown on a substrate that is supporting but non-conducting, such as glass. And it specifies that this is what distinguishes it from the bulk MOSFET, in which the semiconductor material is the substrate.
Reduced to a single sentence: the MOSFET carves its semiconductor, the TFT lays one on.
Laying one on changes even the mode of operation. A study of InGaZnO thin-film transistors published in the journal Scientific Reports (DOI 10.1038/srep22567) describes it thus — the silicon MOSFET conducts in inversion mode, whereas the TFT operates in carrier accumulation mode regardless of the channel material. The Scientific Reports paper adds that in accumulation-mode devices the polarity of the induced carriers is not inverted.
What differs is which of the three states seen above is used.
- MOSFET — an electron layer is created on a p-type body by inversion and used. From the body's point of view the carriers in the channel are minority carriers. The FET article likewise records that the inversion layer confines a flow of minority carriers.
- TFT — carriers of the same kind are accumulated in the deposited semiconductor film and used. Because the polarity is not inverted, the kind of carrier does not change.
What gets laid on is open. The TFT article lists amorphous silicon and polycrystalline silicon as having been used, along with metal oxides such as indium gallium zinc oxide (IGZO), organic semiconductors and carbon nanotubes. The switch in the single pixel seen in the previous installment is this device.
Summary
- The gate of a FET does not touch the channel. An insulating film lies between them, and what crosses over is not charge but the electric field. That is why the name is "field effect."
- Consequently no direct current flows through the gate. The input impedance is very large, and no steady current is needed to hold the device on. This is the point at which it parts from the BJT, which controlled with current.
- The MOS structure of gate, oxide and semiconductor is a planar capacitor with one electrode replaced by a semiconductor. C = εA/d applies unchanged, and the capacitance per unit area is cox = εox/xox. Because thickness is the denominator, making the insulating film thin is the same work as making the device strong.
- Gate voltage drives the interface into the three states of accumulation, depletion and inversion. The voltage at which the channel begins to appear is the threshold voltage.
- The MOSFET carves the wafer and opens by inversion; the TFT lays a semiconductor on glass and opens by accumulation. They are two devices that use the same principle in different places.
Up to here we have seen how a device is opened. The next installment moves on to what happens after it is open — what curve the drain current traces as the gate voltage is raised bit by bit, and which stretch of that curve is used for switching and which for amplification.
References
- Field-effect transistor — Wikipedia : the definition of the FET (controlling current with an electric field), the roles of source, drain, gate and body and their correspondence with BJT terminals, the symmetry of source and drain, unipolar operation and high input impedance, the point that the method of insulation is one of the criteria of classification
- MOSFET — Wikipedia : the point that the gate is separated from the channel by a thin insulating layer, the statement that the MOS structure "is equivalent to a planar capacitor with one of its electrodes replaced by a semiconductor," the point that the electric field penetrates the oxide and creates the inversion layer and channel, the formation of depletion and inversion and the definition of the threshold voltage, the point that the oxide blocks gate direct current, the 1 nm gate dielectric
- Thin-film transistor — Wikipedia : the definition of the TFT (a FET made by thin-film deposition), the point that it is grown on a non-conducting substrate such as glass, the statement that it differs from the bulk MOSFET in which the semiconductor is the substrate, the channel materials (amorphous and polycrystalline silicon, IGZO and others)
- Threshold voltage — Wikipedia : the definition of the threshold voltage as the minimum gate-to-source voltage that creates a conducting path between source and drain, the statement that the enhancement mode has no channel originally while the depletion mode does
- Capacitor — Wikipedia : the capacitance of a parallel-plate capacitor, C = εA/d
- Relative permittivity — Wikipedia : the table of relative permittivities — silicon dioxide 3.9, silicon 11.68
- Basic MOS Structure — Introduction to Physical Electronics (Wilson), Engineering LibreTexts : the statement that the gate and substrate form a parallel-plate capacitor, the definition of cox = εox/xox and the example calculation (3.3 × 10−13 F/cm, 250 Å → 1.30 × 10−7 F/cm2)
- Metal-Oxide-Semiconductor (MOS) Fundamentals — Engineering LibreTexts : the division into the three regions of accumulation, depletion and inversion, the statement that in accumulation the majority carrier concentration is higher near the interface than in the bulk
- Conduction Threshold in Accumulation-Mode InGaZnO Thin Film Transistors, Scientific Reports (2016), DOI 10.1038/srep22567 : the statement that the silicon MOSFET conducts in inversion mode while the TFT operates in accumulation mode regardless of channel material, with no polarity inversion of the induced carriers
- US 1,745,175 — Method and apparatus for controlling electric currents (J. E. Lilienfeld, filed 1926 · granted 1930), Google Patents : the statement that because the thickness of the film is very small, applying an electrostatic force affects the electrical conductivity of that film
- ※ The portions quoted above from Wikipedia articles are licensed under CC BY-SA 4.0.