Semiconductor Fabrication: From Sand to Chip · Module 1
Semiconductors and the Transistor
Every chip rests on one kind of material and one kind of device. This module explains both. No earlier course is needed.
What you will learn
- What makes a semiconductor different from a metal and from an insulator
- How doping sets the number and the type of charge carriers
- How a MOS transistor works as a switch
- Why the industry has spent sixty years making transistors smaller
In plain language
A copper wire always conducts electricity. A piece of glass does not. A semiconductor sits between the two, and its real value is that we can control how well it conducts. Adding a tiny amount of another element, applying a voltage, or shining light on it can change its conductivity by a factor of a million or more. Silicon is the semiconductor used in almost every chip.
A transistor uses this control to make a switch with no moving parts. A small voltage on one terminal, called the gate, decides whether current flows between two other terminals. A switch that is on or off can stand for a 1 or a 0. Billions of these switches wired together can add numbers, store photos, and run software.
A modern processor holds tens of billions of transistors in an area about the size of a fingernail. The rest of this course explains how they are made.
Core lesson
Conductors, insulators, and semiconductors
Electrons in a solid can only have energies inside certain ranges called bands. The highest band that is filled with electrons is the valence band. The next band above it, where electrons are free to move through the crystal, is the conduction band. The energy difference between the two is the band gap.
In a metal there is no gap, so electrons move freely. In an insulator such as silicon dioxide the gap is about 9 electron volts (eV), far too large for electrons to cross under normal conditions. Silicon has a band gap of 1.12 eV at room temperature. That is small enough for heat alone to lift a few electrons into the conduction band. Each electron that leaves the valence band leaves behind an empty state called a hole, which behaves like a positive charge that can also move.
Pure silicon at room temperature has about 1010 free electrons in each cubic centimeter, among 5 × 1022 silicon atoms. That is roughly one free electron for every five trillion atoms, which is why pure silicon conducts poorly.
| Material | Class | Resistivity (Ω·cm) |
|---|---|---|
| Copper | Conductor | about 2 × 10−6 |
| Doped silicon | Semiconductor | 10−3 to 102, set by doping |
| Pure silicon | Semiconductor | about 2 × 105 |
| Silicon dioxide | Insulator | above 1014 |
Doping
Each silicon atom has four outer electrons and bonds to four neighbors. If we replace one silicon atom with phosphorus, which has five outer electrons, the fifth electron has no bond to fill and is free to move. Silicon doped this way is called n-type because its carriers are negative electrons. If we use boron, which has three outer electrons, one bond is left incomplete. That missing electron is a hole, and silicon doped with boron is called p-type because its carriers are positive.
Very little dopant is needed. One phosphorus atom for every million silicon atoms gives 5 × 1016 electrons per cubic centimeter. That is about five million times more than in pure silicon, and it lowers the resistivity from about 2 × 105 Ω·cm to about 0.1 Ω·cm.
The same sensitivity explains why chip factories are so clean. If one intended atom in a million changes the material this much, a few unwanted atoms in a billion can ruin a device. Module 3 covers how fabs control contamination.
The p-n junction
Where p-type silicon meets n-type silicon, a junction forms that lets current pass easily in one direction and blocks it in the other. Junctions do two jobs in a chip. They are devices in their own right, called diodes, and they electrically separate the parts of a transistor from the silicon around them.
The MOS transistor
The transistor in nearly all chips today is the MOSFET, short for metal-oxide-semiconductor field-effect transistor. It has a source, a drain, and a gate. In an n-channel transistor, the source and the drain are two n-type regions made in p-type silicon. The gate sits above the gap between them, separated from the silicon by a very thin insulating layer.
With no voltage on the gate, there is no conducting path from source to drain, and the switch is off. A positive voltage on the gate attracts electrons to the silicon surface just under the insulator. Once the gate voltage passes a value called the threshold voltage, these electrons form a thin conducting layer, the channel, that joins source and drain. The switch is now on.
ANNLab, University of Arizona
Figure 1. Cross-section of an n-channel MOS transistor. With no gate voltage there is no path between source and drain. A gate voltage above threshold draws electrons to the surface and forms a channel.
A water tap is a fair picture of this. The source is the supply pipe, the drain is the outlet, and the gate is the handle. The difference is that the gate is insulated from the channel, so almost no current flows into it. Holding the switch on or off costs very little power.
Chips combine n-channel transistors with p-channel transistors, which work the same way with holes and a negative gate voltage. This pairing is called CMOS, for complementary MOS. In a CMOS logic gate, one transistor of each pair is off whenever the other is on, so the circuit draws power mainly at the moment it switches. That low standby power is the reason CMOS became the standard technology for digital chips.
Why smaller is better
A transistor with a shorter channel switches faster, uses less energy each time it switches, and takes up less area. In 1965 Gordon Moore observed that the number of components on a chip was doubling about every year, and in 1975 he revised the pace to about every two years. The trend held for decades. The first microprocessor, the Intel 4004 of 1971, had about 2,300 transistors. Leading processors today have tens of billions.
Shrinking a flat transistor eventually stops working, because the gate loses control of a very short channel. Since about 2011, leading manufacturers have built the channel as a vertical fin with the gate wrapped over three sides, a design called the FinFET. The newest generation stacks thin sheets of silicon and wraps the gate all the way around each one. Names such as “3 nm” now label a technology generation and no longer measure any single feature on the chip.
Every one of these advances came from better fabrication. The modules that follow take each fabrication step in turn.
Going deeper
These three sections add the equations behind the core lesson, each with a worked example. They assume first-year algebra and can be skipped without losing the thread of the course.
In silicon at equilibrium, the electron concentration n and the hole concentration p are linked by a simple rule.
n × p = ni2
Here ni is the intrinsic carrier concentration, about 1 × 1010 cm−3 for silicon at 300 K. Raising one carrier type lowers the other.
Worked example
Silicon is doped with 1 × 1016 phosphorus atoms per cm3. At room temperature nearly every phosphorus atom gives up its extra electron, so n ≈ 1 × 1016 cm−3. The hole concentration is then p = ni2 / n = 1020 / 1016 = 1 × 104 cm−3. Electrons outnumber holes by a factor of 1012. Electrons are therefore called the majority carriers and holes the minority carriers.
Conductivity depends on how many carriers there are and how easily they move. The ease of movement is the mobility, written μ.
σ = q (n μn + p μp) and ρ = 1 / σ
Here q is the electron charge, 1.6 × 10−19 C, and ρ is the resistivity.
Worked example
Take the same n-type silicon with n = 1 × 1016 cm−3. The electron mobility at this doping is about 1,200 cm2/V·s, and the hole term is far too small to matter. Then σ = 1.6 × 10−19 × 1016 × 1,200 ≈ 1.9 S/cm, and ρ ≈ 0.5 Ω·cm. Pure silicon is about 2 × 105 Ω·cm, so this light doping has lowered the resistivity by a factor of about 400,000.
For a transistor with a long channel that is fully on, a first estimate of the drain current is
ID = (W / 2L) μ Cox (VG − VT)2
W and L are the width and the length of the channel, VG is the gate voltage, and VT is the threshold voltage. Cox is the capacitance of the gate insulator per unit area, equal to its permittivity divided by its thickness. A shorter channel or a thinner insulator gives more current, which is the basic reason for scaling.
Worked example
A silicon dioxide gate insulator is 2 nm thick. The permittivity of silicon dioxide is 3.9 × 8.85 × 10−14 F/cm = 3.45 × 10−13 F/cm. Dividing by 2 × 10−7 cm gives Cox ≈ 1.7 × 10−6 F/cm2. Halving the thickness would double this value and the current with it.
This equation overestimates the current in very short transistors, where electrons reach a maximum speed. The trends still hold. Module 5 explains why manufacturers replaced silicon dioxide with insulators that give the same capacitance at a larger thickness.
Check your understanding
Try each question before opening the answer. The last question uses the Going deeper material.
Silicon has a band gap of 1.12 eV. This is small enough for a few electrons to reach the conduction band at room temperature, and for doping or a gate voltage to change the number of carriers by many orders of magnitude. A metal has no gap, and an insulator has a gap too large to cross.
It is n-type. Phosphorus has five outer electrons, one more than silicon needs for its four bonds. The extra electron is free to move, so electrons are the majority carriers.
The positive gate voltage attracts electrons to the silicon surface under the gate insulator. They form a conducting channel between the n-type source and the n-type drain, and the transistor turns on.
Each logic gate pairs an n-channel transistor with a p-channel transistor. In either steady state one of the two is off, so there is no direct path from the supply to ground. The gates are also insulated, so almost no current flows into them. Power is drawn mainly during switching.
Boron makes the silicon p-type, so p ≈ 1 × 1017 cm−3. From the mass action law, n = ni2 / p = 1020 / 1017 = 1 × 103 cm−3.
Key terms
- Band gap. The energy an electron needs to move from the valence band to the conduction band
- Carrier. A mobile charge that carries current, either an electron or a hole
- Hole. An empty electron state in the valence band that behaves like a mobile positive charge
- Doping. Adding a small, controlled amount of another element to change the carrier concentration
- n-type and p-type. Silicon doped so that electrons (n-type) or holes (p-type) are the majority carriers
- p-n junction. The boundary between p-type and n-type regions, which passes current in one direction
- MOSFET. Metal-oxide-semiconductor field-effect transistor, the switch used in nearly all chips
- Gate. The terminal whose voltage turns the transistor on or off
- Channel. The thin conducting layer under the gate that joins source and drain when the transistor is on
- Threshold voltage. The gate voltage at which the channel forms
- CMOS. Complementary MOS, a circuit style that pairs n-channel and p-channel transistors
In the fab
Process engineers, device engineers, and test technicians use these ideas every day. When an electrical test shows a transistor with the wrong threshold voltage or too little current, they trace the result back to a doping step, an insulator thickness, or a channel length.
Further reading
J. D. Plummer and P. B. Griffin, Integrated Circuit Fabrication: Science and Technology, Cambridge University Press. The authors offer a prepublication version that is free to read on the Stanford book site (opens in a new tab).
For hands-on practice, see the Semiconductor Processing Laboratory Online Modules on our Training page.
Course homeNext: Module 2, From Sand to Wafer
Created by Prof. Zafer Mutlu, ANNLab, University of Arizona.