Semiconductors Conductivity Control: True or False?

Yes, the true statement is that a semiconductor’s conductivity can be controlled. This is the defining property that separates semiconductors from conductors and insulators, and it is the basis for every transistor, diode, and integrated circuit. By introducing impurities (doping), applying voltage, or exposing the material to light, you can change its electrical resistance by orders of magnitude, from nearly insulating to nearly conducting.

Formula

The conductivity (σ) of a semiconductor is given by:

σ = q × (n × μ_e + p × μ_h)

where:

• q = elementary charge (1.6 × 10^-19 C)
• n = electron concentration (cm^-3)
• p = hole concentration (cm^-3)
• μ_e = electron mobility (cm²/V·s)
• μ_h = hole mobility (cm²/V·s)

For intrinsic silicon at room temperature, n = p ≈ 1.5 × 10¹⁰ cm^-3, μ_e ≈ 1350 cm²/V·s, and μ_h ≈ 480 cm²/V·s, giving σ ≈ 4.4 × 10^-4 S/m. The calculator above models the exponential temperature dependence and the linear effect of doping, using a simplified activation energy of 0.05 eV for illustration.

Worked Example

Using the default values (T = 25°C, dopant concentration = 10¹⁵ cm^-3):

1. Convert temperature to Kelvin: 25 + 273.15 = 298.15 K
2. Compute the intrinsic term: 1.6e-3 × exp(-0.05 / (8.617e-5 × 298.15)) = 1.6e-3 × exp(-1.947) ≈ 1.6e-3 × 0.1427 ≈ 2.28 × 10^-4 S/m
3. Add the doping term: 1.6e-3 × (10¹⁵ / 10¹⁵) = 1.6e-3 S/m
4. Total conductivity: 2.28e-4 + 1.6e-3 ≈ 1.83 × 10^-3 S/m
5. The calculator rounds to 4 decimal places, giving 0.0018 S/m (or 1.8 × 10^-3 S/m).

This matches the headline output. The resistivity is the reciprocal: 1 / 0.0018 ≈ 556 Ω·m.

What Makes a Semiconductor a Semiconductor?

Semiconductors are materials with a band gap—an energy range where no electron states exist—that is neither too wide (like insulators) nor absent (like metals). In silicon, the gap is about 1.12 eV at room temperature. At absolute zero, the valence band is full and the conduction band is empty, so the material behaves as an insulator. As temperature rises, some electrons gain enough thermal energy to jump the gap, creating free electrons and holes, and conductivity increases exponentially. This is why the calculator includes a temperature term.

The key difference from a metal is that in a metal, the valence and conduction bands overlap, so there are always free electrons regardless of temperature. In an insulator, the gap is so large (e.g., diamond at 5.5 eV) that thermal excitation is negligible at ordinary temperatures. Semiconductors sit in between, allowing external stimuli to tip the balance.

How Doping Controls Conductivity

Doping is the deliberate introduction of impurity atoms into the crystal lattice. For silicon (group IV), a phosphorus atom (group V) donates an extra electron, creating an n-type semiconductor. A boron atom (group III) accepts an electron, leaving a hole, creating a p-type semiconductor. The conductivity increases roughly linearly with dopant concentration, as shown in the calculator’s doping term.

For example, a doping concentration of 10¹⁶ cm^-3 increases conductivity by a factor of 10 compared to 10¹⁵ cm^-3. Modern transistors use doping levels ranging from 10¹⁴ to 10²⁰ cm^-3, allowing precise control over whether a region conducts or not. This is how a transistor can act as a switch: by applying a voltage to the gate, you create an electric field that either attracts or repels charge carriers in the channel, turning the device on or off.

Field Effect: The Transistor Revolution

The most important method of controlling conductivity in practice is the field effect. In a metal-oxide-semiconductor field-effect transistor (MOSFET), a voltage applied to the gate electrode creates an electric field that penetrates the semiconductor. If the voltage exceeds a threshold, it inverts the region under the gate, forming a conductive channel between source and drain. This allows current to flow. Remove the voltage, and the channel disappears, blocking current.

This is why digital electronics work: billions of tiny switches (transistors) can be turned on and off by applying voltages, representing 1s and 0s. The control is not just binary—by varying the gate voltage, you can also modulate the channel’s resistance continuously, which is how analog amplifiers work. The field effect is purely electrostatic, so it consumes almost no power to control, which is why CMOS (complementary MOS) circuits are so energy-efficient.

Other Ways to Control Conductivity

Besides doping and field effect, conductivity can be controlled by:

• Light: Photons with energy greater than the band gap create electron-hole pairs, increasing conductivity. This is the principle behind photodetectors and solar cells.
• Temperature: As shown in the calculator, conductivity increases with temperature for intrinsic semiconductors, but for doped semiconductors, mobility decreases with temperature, so the net effect depends on the doping level.
• Mechanical strain: Piezoresistive effect changes the band gap and carrier mobility, used in pressure sensors and accelerometers.
• Magnetic field: The Hall effect creates a transverse voltage, used for magnetic field sensing.

These mechanisms are exploited in a wide range of sensors and devices, from thermistors to strain gauges.

Common Misconceptions

One common misconception is that semiconductors are “half conductors”—that they conduct half as well as metals. In reality, their conductivity can vary by more than 10 orders of magnitude depending on doping and temperature. Pure silicon is a poor conductor, but heavily doped silicon can approach metallic conductivity.

Another misconception is that “semiconductor” refers to a specific material. In fact, many materials are semiconductors: silicon, germanium, gallium arsenide, silicon carbide, and organic polymers, each with different band gaps and properties. The term describes the behavior, not a specific substance.

Also, people often confuse semiconductor with conductor in everyday language. A semiconductor is not a conductor; it is a material whose conductivity can be controlled, which is exactly what the question asks. This control is what enables the entire digital age.

Limits and Real-World Considerations

The simple formula in the calculator assumes a uniform, non-degenerate semiconductor. At very high doping levels (above 10¹⁸ cm^-3), the material becomes degenerate, and the band gap narrows, causing the conductivity to deviate from the linear model. At high electric fields, carrier velocity saturates, limiting the maximum current. Thermal runaway is also a risk: as temperature increases, conductivity increases, which can lead to more current and more heating—a positive feedback loop that can destroy the device.

In practice, engineers must consider these effects when designing circuits. For instance, a silicon diode has a forward voltage drop of about 0.7 V, which is a consequence of the band gap. This is why LEDs require a minimum voltage to turn on. The calculator above is a useful approximation for educational purposes, but real devices require more complex models.

Frequently Asked Questions

Is silicon the only semiconductor?

No, silicon is the most widely used, but germanium was used in early transistors, and gallium arsenide (GaAs) is used in high-frequency and optoelectronic applications. Silicon carbide (SiC) and gallium nitride (GaN) are used for high-power and high-temperature devices. Each material has its own band gap and carrier mobilities.

Why does temperature affect conductivity?

In an intrinsic semiconductor, higher temperature provides more thermal energy, allowing more electrons to jump the band gap, creating more charge carriers, so conductivity increases. In doped semiconductors, the carrier concentration is fixed by doping, but higher temperature increases lattice vibrations, which scatter carriers and reduce mobility, so conductivity may decrease slightly.

What is the difference between n-type and p-type?

N-type semiconductors have an excess of electrons (negative charge carriers), created by doping with donor atoms like phosphorus. P-type semiconductors have an excess of holes (positive charge carriers), created by doping with acceptor atoms like boron. In a p-n junction, the interface between these two types forms a diode.

Can a semiconductor conduct electricity without doping?

Yes, pure (intrinsic) semiconductors do conduct, but very poorly at room temperature. For silicon, the intrinsic carrier concentration is about 10¹⁰ cm^-3, which gives a conductivity of around 10^-4 S/m—many orders of magnitude lower than a metal. Doping increases this dramatically.

How does a transistor use conductivity control?

A field-effect transistor has three terminals: source, drain, and gate. The gate is separated from the semiconductor by an insulating layer. Applying a voltage to the gate creates an electric field that either attracts electrons (forming an n-channel) or repels them (forming a p-channel), thus controlling the conductivity between source and drain. This allows the transistor to act as a switch or amplifier.

What is the band gap and why does it matter?

The band gap is the energy difference between the valence band (where electrons are bound) and the conduction band (where electrons are free to move). It determines the intrinsic carrier concentration and the wavelength of light the material can absorb or emit. Silicon’s band gap of 1.12 eV corresponds to infrared light, which is why silicon solar cells are not efficient at capturing visible light.

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in t | Temperature | °C | 25 | -273
in d | Dopant concentration | atoms/cm³ | 1e15 | 0
out sigma | Conductivity | S/m | 1.6e-3 * exp(-0.05 / (8.617e-5 * (t + 273.15))) + 1.6e-3 * d / 1e15 | 4
out rho | Resistivity | Ω·m | 1 / sigma | 4