English
Menu

Intrinsic vs Extrinsic Semiconductor: Carriers, Fermi Level and Temperature Compared

An intrinsic semiconductor is a pure semiconductor with almost no impurities. It contains equal numbers of electrons, lifted by heat from the valence band into the conduction band, and the holes they leave behind. An extrinsic semiconductor has donors or acceptors deliberately added, so either electrons or holes become the majority carriers. The intrinsic carrier density of silicon at room temperature is only about 1×10¹⁰ cm⁻³, so real devices add impurities to set the carrier density and conductivity type.

AspectIntrinsic semiconductorExtrinsic semiconductor (n-type, p-type)
ImpuritiesNone added on purpose (ideally perfectly pure)Donors (phosphorus, arsenic, etc.) or acceptors (boron, etc.) are added
Origin of carriersOnly thermal generation of electron–hole pairsMainly ionization of impurities, plus a small amount of thermal pair generation
Electrons vs holesEqual (n = p = ni)One type dominates: n ≈ ND in n-type, p ≈ NA in p-type
Carrier density (silicon at room temperature)About 1×10¹⁰ cm⁻³Set mostly by the impurity concentration; can be many orders of magnitude above the intrinsic density
Product of electron and hole densitiesn × p = ni²Also n × p = ni² in thermal equilibrium. Minority carrier density is ni² / impurity concentration
Fermi levelNear the middle of the band gap (intrinsic Fermi level)Shifts toward the conduction band in n-type and toward the valence band in p-type
Resistivity (silicon at room temperature)High (on the order of 10⁵ Ω·cm)Low; drops by orders of magnitude depending on impurity concentration
As temperature risesCarriers increase exponentially and resistivity falls sharplyCarrier density is nearly constant over a middle temperature range that includes room temperature. At very low temperatures impurities stop ionizing and carriers decrease (freeze-out); at high temperatures thermally generated carriers take over and it behaves like an intrinsic semiconductor
How it is usedRarely used in devices as is; it is the high-purity crystal that doping starts fromNearly every device: transistors, diodes, wells, sources and drains

Figures are typical orders of magnitude and vary by process generation and product.

When to use which

Intrinsic semiconductor
As a reference for understanding material properties. Through n × p = ni², the intrinsic carrier density ni sets the minority carrier density in doped semiconductors and the leakage current of PN junctions.
Extrinsic semiconductor
When building devices. The type and concentration of impurities set the conductivity type and resistivity, and n-type and p-type regions are combined to make PN junctions and transistors.
Caution at high temperature
As temperature rises, the intrinsic carrier density increases rapidly and the properties set by doping are gradually lost. SiC and GaN, with their wide band gaps, have very small intrinsic carrier densities, so they can operate at higher temperatures than silicon.

FAQ

Does current flow in an intrinsic semiconductor?

Yes. Even at room temperature, heat creates electron–hole pairs, so it conducts slightly. In silicon, however, the intrinsic carrier density of about 1×10¹⁰ cm⁻³ is tiny compared with the atomic density (about 5×10²² cm⁻³), so the resistivity is high.

Why is a doped semiconductor called "extrinsic"?

Because most of its carriers come not from the semiconductor itself but from impurities added from outside, in contrast to an intrinsic semiconductor, whose carriers are generated thermally in the pure crystal.

How much doping does it take to change the carrier density?

Silicon's intrinsic carrier density is about 1×10¹⁰ cm⁻³, so once donors or acceptors are added well above that level, the carrier density is set almost entirely by the impurity concentration. For example, phosphorus at 1×10¹⁶ cm⁻³ is only about 1 atom in 5 million silicon atoms, yet it makes the electron density 1 million times the intrinsic value.

What happens when you heat an extrinsic semiconductor?

In silicon, over a middle temperature range that includes room temperature, the carrier density stays nearly constant and roughly equal to the impurity concentration. If the temperature rises further and the intrinsic carrier density approaches the impurity concentration, thermally generated carriers increase, the material behaves like an intrinsic semiconductor, and PN junctions and similar structures stop working properly.

Check your understanding

What happens to the intrinsic carrier density when the temperature of an intrinsic semiconductor is raised?

  1. AIt increases
  2. BIt decreases
  3. CIt does not change
Show answer and explanation

Answer: A. It increases

As temperature rises, valence electrons more easily cross the band gap with thermal energy, creating more electron-hole pairs. The intrinsic carrier density follows ni ∝ T^(3/2)·exp(−Eg/2kT), and in silicon near room temperature it roughly doubles for every 10 °C rise. This steep increase is why PN-junction reverse leakage grows at high temperature, and why wide-bandgap SiC and GaN handle high-temperature operation well.

Which correctly describes how the resistivity of an intrinsic semiconductor depends on temperature?

  1. AResistivity decreases as temperature rises
  2. BResistivity increases as temperature rises
  3. CResistivity is constant regardless of temperature
Show answer and explanation

Answer: A. Resistivity decreases as temperature rises

In an intrinsic semiconductor, the number of carriers excited across the band gap rises exponentially with temperature, so resistivity falls (a negative temperature coefficient). In metals the carrier count is nearly fixed and lattice-vibration scattering increases, so resistivity rises. NTC thermistors exploit this behavior. Note that in doped silicon near room temperature the carrier count is roughly constant, so there is a range where resistance actually rises as mobility drops.

In a semiconductor in thermal equilibrium, what is the product of electron density n and hole density p (n×p)? (ni: intrinsic carrier density)

  1. AIt is always 0
  2. BIt equals ni squared
  3. CIt equals the square of the impurity concentration
Show answer and explanation

Answer: B. It equals ni squared

In thermal equilibrium, n × p = ni² holds even with doping (the law of mass action): adding electrons gives holes more partners to recombine with, so holes decrease correspondingly. For example, adding 1×10¹⁶ cm⁻³ donors to silicon (ni ≈ 1×10¹⁰ cm⁻³) gives a hole density of 1×10⁴ cm⁻³. It does not hold out of equilibrium, such as under illumination or current injection, where np > ni².

  1. What is the approximate hole density in n-type silicon with a donor concentration of 1×10¹⁶ cm⁻³ (all donors ionized, intrinsic carrier density ni = 1×10¹⁰ cm⁻³)?
  2. Silicon contains both donors at 5×10¹⁶ cm⁻³ and acceptors at 2×10¹⁶ cm⁻³ (room temperature, all ionized). Which describes it correctly?
  3. Why does the carrier density of n-type silicon drop sharply when it is cooled to cryogenic temperatures?

Practice Semiconductor physics questions

Key terms explained

Intrinsic carrier density
The density of thermally generated electrons and holes in an undoped semiconductor, written ni. For silicon it is about 1×10¹⁰ cm⁻³ at room temperature and rises steeply with temperature. In equilibrium, n × p = ni².
Donor
An impurity that supplies electrons to a semiconductor. For silicon, group V elements such as phosphorus (P) and arsenic (As) act as donors and make n-type semiconductors.
Acceptor
An impurity that accepts electrons from a semiconductor and creates holes. For silicon, group III elements such as boron (B) act as acceptors and make p-type semiconductors.
Fermi level
The energy at which the probability of an electron occupying a state is exactly one half. It lies closer to the conduction band in n-type material and closer to the valence band in p-type.
Degenerate semiconductor
A semiconductor doped so heavily that the Fermi level lies inside the conduction or valence band. It behaves almost like a metal and is used in tunnel diodes and low-resistance contacts.

Related comparisons