How a transistor switches: the gate voltage opens the channel

A transistor in a chip has no moving part. A voltage on one electrode, the gate, pulls a thin sheet of electrons into being beneath it, and that sheet is the wire the current flows along. Take the voltage away and the sheet thins out. It never quite vanishes.

What is being claimed

The device here is the MOSFET, the transistor that fills integrated circuits. Chenming Hu's textbook explains its name this way: “the gate turns the transistor (inversion layer) on and off with an electric field through the oxide.” The gate sits on a layer of oxide so thin that, in a micrograph his book reproduces, it is 1.2 nm, about four molecules of silicon dioxide. The claim of this page is narrower than “a transistor is a switch.” The current does follow the gate voltage, but it follows it along two different laws, one on each side of a voltage called the threshold, and the current never reaches zero.

Why it is worth knowing

Hu's description of what any transistor does is that it “presents a high input resistance to the signal source, drawing little input power, and a low resistance to the output circuit”. The gate is insulated, so in this simple picture it draws essentially no steady current, yet it controls a current between two other terminals. The part people get wrong is the off state. Hu's own numbers show why it matters: if each transistor leaks a “modest 100 nA” while off, a cell-phone chip with one hundred million of them “would consume 10 A even in standby.”

How the gate makes a channel

Take an N-channel MOSFET. Its body is P-type silicon, where the mobile charges are holes. Two heavily doped N-type regions, the source and the drain, sit either side of the gate. With no gate voltage there is no electron path between them. A positive gate voltage pushes holes away from the surface and draws electrons up to it. Past a certain voltage those electrons form an inversion layer: a film of electrons, which Hu puts at 1 to 2 nm thin, induced in P-type silicon. That film is the channel. The body was never doped N-type; the gate field makes the electrons appear there.

The threshold voltage V_t is where the channel becomes substantial. Hu gives “a practical and common definition”: it is the gate voltage at which the current reaches 100 nA times W/L, the channel's width divided by its length.

Above threshold: the square law

Once the channel is formed, a drain voltage pulls its electrons along it. When the drain voltage is large enough, the current stops depending on it. Hu compares this to “a mountain stream feeding into a waterfall”: the stream sets the flow, and “the height of the waterfall ... has no influence over the flow rate.” His Equation 6.6.6 gives that saturation current as a constant times (V_gs − V_t)², where V_gs is the gate-to-source voltage. That is the square law: double the voltage above threshold and the current quadruples. The constant contains the channel's W/L, the oxide capacitance, the electron mobility and a bulk-charge factor m, “typically around 1.2”. Hu's example device has W = L = 10 µm, a 4 nm oxide and V_t = 0.3 V, and its curves reach about 0.2 mA at a 2 V gate.

The square law is a model, and Hu names its limits. It is “the long-channel IV model”. In short modern channels the electrons hit a top speed, and velocity saturation reduces the current by a factor of 1 + V_ds/ε_satL, where V_ds is the drain voltage and ε_sat the field at which that speed limit sets in. The shorter the channel, the bigger the cut.

Below threshold: off is not zero

Read on its own, the square law says the current is zero at threshold and below it. The section of Hu's Chapter 7 on this is titled against that reading: “‘Off’ Is Not Totally ‘Off’”. Below V_t a few electrons still reach the surface, and on a log plot the current is “clearly a straight line, i.e., an exponential function” of the gate voltage. His Equation 7.2.5 puts it as 100 nA × W/L times e^{q(V_gs−V_t)/ηkT}. At room temperature the current falls tenfold for every η × 60 mV below threshold. That step is the subthreshold swing S. It scales with temperature, and Hu's η is 1 plus a ratio of two capacitances, so it cannot fall below 1. At room temperature, then, 60 mV per decade is a physical floor, not a design choice. His example, η = 1.5, gives 90 mV.

Our arithmetic, for his example device if its swing were 90 mV: at zero gate voltage the current is about 0.046 nA, some 4.3 million times less than at a 2 V gate. That is a large ratio, not an infinite one. Hu's Table 7-1 shows the same thing in production: a high-performance 90 nm transistor of 2003 carries 1100 µA per µm of width when on and 0.15 when off, a ratio of about 7,300 (our arithmetic).

In short

The gate's field draws a sheet of electrons into P-type silicon and the sheet carries the current. Above threshold the simple long-channel model says the current grows as the square of the voltage above V_t. Below threshold it falls tenfold for every 60 mV or more at room temperature. The threshold is where one behaviour hands over to the other. The current does not switch off there.