Lecture date: Friday, 2014.09.05 (lecture recording)
This lecture combines ideas about doping and charge carrier distribution to introduce the concept of the Metal Oxide Semiconductor Field Effect Transistor (MOSFET)—a simple electronic switch that forms the basis for modern electronics.
The Field Effect
Electric fields can be used to modify the distribution of charge carriers in a semiconductor. This is called the field effect.
When a voltage is applied to a conductive (e.g. metal) 'gate' electrode that is insulated from a semiconductor (e.g. silicon) by a dielectric (e.g. silicon dioxide), the electric field bends the valence and conduction bands in the semiconductor.
In the examples below, we consider a semiconductor that has been lightly-doped with a Group IV p-type acceptor dopant such as boron so that the principle charge carriers are holes. This lightly-doped p-type region could be used as the channel in an N-channel MOSFET (described in detail below).
Sub-Threshold Gate Voltage
At gate voltages—V(GS)—below the device-specific threshold voltage—V(th)—the semiconductor valence band is lowered in energy, causing this band to fill with electrons and depleting the semiconductor of holes. This leaves immobile, negatively-charged acceptor dopant ions near the semiconductor–dielectric interface, in the so-called depletion region. The depletion region is depleted of its positive charge carriers, so its conductivity decreases.
The depletion region grows into the semiconductor until the exposed negatively-charged acceptor ion charge balances the positive charge imposed on the insulator surface by the gate electrode. As the voltage on the gate is increased, the valence band is bent further and the depletion layer deepens.
Threshold Gate Voltage and Above
The conduction band is also lowered in energy by a positive gate voltage. At lower voltages, this effect is minimal and the conduction band is not significantly populated. However, conduction band population increases exponentially as the voltage is increased, and at some threshold voltage the density of electrons exceeds the density of holes in the bulk material—an inversion layer is formed. Above this threshold voltage, increases in the imposed positive charge are counteracted almost entirely by addition of electrons to the increasingly-bent conduction band, and the depletion region doesn't grow any deeper. This inversion layer can now freely conduct charge via electrons.
Where do the Electrons Come From?
Excerpted from "Modern Semiconductor Devices for Integrated Circuits", by Chenming Hu (inventor of the FINFET):
"In this section, we have assumed that electrons will appear in the inversion layer whenever the closeness between Ec and Ef suggests their presence. However, there are few electrons in the P-type body, and it can take minutes for thermal generation to generate the necessary electrons to form the inversion layer. The MOS transistor structure shown in Fig. 5–2 solves this problem. The inversion electrons are supplied by the N+ junctions, as shown in Fig. 5–10a. The inversion layer may be visualized as a very thin N layer (hence the term inversion of the surface conductivity type) as shown in Fig. 5–10b."
The MOSFET is essentially a switch/amplifier in which the source-to-drain current is controlled by the gate-source and drain-source voltages.
In an N-channel MOSFET, the source and drain are N+ (heavily N) doped and the channel is P- (lightly P) doped. Operation is as follows:
- At neutral gate voltage, electrons from the source are unable to flow through the P-type channel to the drain.
- At sub-threshold voltages, the channel is depleted of holes and becomes even less conductive.
- Above the threshold voltage, the electric field induces the formation of an electron-rich inversion layer in the channel; electrons are now free to flow from the source through the channel to the drain.
Conductance of the channel increases with increasing gate voltage, increasing the flow of current from source to drain for a given source-drain voltage; this is called linear, Ohmic, or triode (in reference to the triode Vacuum Tube) operation, and the MOSFET is basically acting as a variable resistor controlled by the gate. MOSFETs operating in the linear region are occasionally used as voltage-controlled precision resistors.
When V(GS) > V(th) (i.e. gate-source bias is above the device's threshold voltage) and V(DS) ≥ V(GS)–V(th) (i.e. drain-source bias is sufficiently higher than the gate-source bias), current flow through the MOSFET becomes independent of the drain-source voltage applied across it but remains dependent on the gate-source voltage. This is termed saturation or active operation.
Saturation occurs due to channel pinch-off and channel length modulation—the electric field exerted by the drain causes the drain-side depletion region to expand, 'pinching off' the conductive inversion channel so that it no longer reaches the drain. Conduction continues because high-velocity electrons traversing the channel are 'injected' into this depletion region and swept into the drain by the strong electric field.
MOSFETs operating in the saturation region act as voltage-controlled current sources and are used as amplifiers and on-off switches.
In digital devices, N– and P–type devices are used together to construct integrated circuits using a technology called Complementary Metal-Oxide-Semiconductor (CMOS). By configuring arrays of complementary N– and P–type MOSFETs in certain topologies, the logic functions—AND, OR, NOT, &etc—can be constructed. Logic functions are further composed to build topologies with higher-order behaviours—registers, adders, subtractors, multiplexers, encoders, decoders—in a process called logic synthesis.
- Transistor size is often described by a single number, e.g. "22nm"; this refers to the critical dimension (CD), which for a MOSFET is typically the channel length.
- By shrinking the transistor's physical dimensions, the transistor's speed can be increased.
- Gordon Moore, co-founder of Intel, formulated "Moore's Law" from observation in 1965: "the number of transistors in a dense integrated circuit doubles approximately every two years". This was adopted as an industry benchmark and became a self-fulfilling prophecy.
- In the 70's, MOSFET construction switched from metal gates to heavily-doped Si gates; in the 2000's, many manufacturers switched back to metal gates.
- SiO₂ is no longer used as the gate dielectric; so-called high-κ materials (e.g. halfnium oxide) are used instead to increase the MOSFET capacitor charge per volt applied at the gate and reduce leakage currents, reducing device heating and increasing efficiency.
- Modern CPUs contain billions of transistors.
- Graphics Processing Units (GPUs) have more transistors than CPUs; they are specially designed for massively-parallel matrix and vector calculations, and are increasingly being used by scientists and engineers to run simulations and optimizations.
- Devices are often manufactured, tested, and then 'binned' based on their performance. Product binning is extremely common in the semiconductor industry.
- Germanium (Ge) has significantly higher electron and hole mobilities than Si, but growing defect-free oxides on Ge is much more difficult.
Drs. Vivek Subramanian and Michel Maharbiz created this video for EE40: EE40 - MOSFET device physics