Extrinsic Semiconductor: n-type (Donor) and p-type (Acceptor)

Pure silicon is a poor conductor at room temperature — intrinsic carrier concentration ni ≈ 1×10¹⁰ cm⁻³ gives a resistivity in the hundreds of kΩ·cm range, useless for building devices. Every diode, BJT, and MOSFET starts from silicon deliberately contaminated with controlled impurity levels — doping — to set carrier type and concentration by many orders of magnitude. Understanding donor and acceptor doping is the prerequisite for everything downstream: p-n junctions, depletion regions, and transistor action all reduce to how n-type and p-type regions interact.

The Doping Mechanism

Silicon has 4 valence electrons and forms a covalent tetrahedral lattice, each atom bonded to 4 neighbors. Doping replaces a small fraction of lattice silicon atoms with atoms from adjacent columns of the periodic table:

• n-type (donor doping): Group V elements — phosphorus (P), arsenic (As), antimony (Sb) — have 5 valence electrons. Four form covalent bonds with the silicon lattice; the fifth is only loosely bound to the donor atom (ionization energy ~0.01–0.05 eV, far less than silicon's 1.12 eV bandgap). At room temperature, essentially all donor atoms are ionized, releasing a free electron into the conduction band and leaving a fixed, immobile positive donor ion behind.
• p-type (acceptor doping): Group III elements — boron (B), gallium (Ga), indium (In) — have only 3 valence electrons. One covalent bond is left incomplete, creating a hole. This hole readily accepts an electron from a neighboring Si–Si bond, and that electron vacancy propagates through the lattice as a mobile positive carrier. The acceptor atom, having captured an electron, becomes a fixed negative ion.

In both cases the dopant concentration is denoted Nd (donors, atoms/cm³) or Na (acceptors, atoms/cm³), typically in the range 10¹⁴–10²⁰ cm⁻³ — corresponding to roughly 1 dopant atom per ~5×10⁸ (500 million) silicon atoms up to about 1 per 500 silicon atoms — a range that changes conductivity by 5–6 orders of magnitude.

Majority and Minority Carriers

Doping breaks the symmetry between electron and hole populations that exists in intrinsic silicon (n = p = ni). Assuming full dopant ionization and low-to-moderate doping (Nd or Na ≫ ni):

n-type material:

n₀ ≈ Nd                (majority carriers: electrons)
p₀ ≈ ni² / Nd           (minority carriers: holes)

p-type material:

p₀ ≈ Na                (majority carriers: holes)
n₀ ≈ ni² / Na           (minority carriers: electrons)

These follow from the mass-action law, which holds in thermal equilibrium regardless of doping:

n₀·p₀ = ni²

This is the single most useful equation in extrinsic semiconductor analysis — it lets you find the minority carrier concentration once you know the majority concentration, without ever needing to solve band-diagram equations from scratch.

Worked Example

Silicon doped with Nd = 1×10¹⁷ cm⁻³ phosphorus, at T = 300 K where ni ≈ 1×10¹⁰ cm⁻³.

Step 1 — majority carrier (electron) concentration:

n₀ ≈ Nd = 1×10¹⁷ cm⁻³

Step 2 — minority carrier (hole) concentration:

p₀ = ni² / n₀ = (1×10¹⁰)² / 1×10¹⁷ = 1×10²⁰ / 1×10¹⁷ = 1×10³ cm⁻³

Step 3 — check mass action law:

n₀·p₀ = (1×10¹⁷)·(1×10³) = 1×10²⁰ = ni² ✓

The result: electrons outnumber holes by a factor of 10¹⁴ in this material. That ratio is why we can safely call electrons the majority carrier and ignore hole conduction entirely for most first-order n-type device calculations — but minority carriers are far from irrelevant. In a p-n junction or BJT, the minority carrier population on each side is exactly what diffuses across the junction and constitutes most of the forward current — this is the physical basis of diode and transistor action covered in later topics.

Fermi Level Position

Doping shifts the Fermi level EF away from mid-gap, which is where it sits in intrinsic silicon:

• n-type: EF moves up, closer to the conduction band edge Ec. Heavier donor doping pushes it closer still.
• p-type: EF moves down, closer to the valence band edge Ev.

Quantitatively, EF relative to the intrinsic level Ei:

n-type: EF − Ei = kT·ln(Nd/ni)
p-type: Ei − EF = kT·ln(Na/ni)

where kT ≈ 0.0259 eV at 300 K. For the example above: EF − Ei = 0.0259·ln(1×10¹⁷/1×10¹⁰) = 0.0259·ln(1×10⁷) ≈ 0.0259 × 16.1 ≈ 0.418 eV. The Fermi level sits 0.418 eV above mid-gap — well above Ei but still 0.14 eV below Ec (since the gap is 1.12 eV, Ec is 0.56 eV above Ei). This Fermi level offset is exactly what determines the built-in potential when n-type and p-type regions are joined to form a p-n junction.

Conductivity and Resistivity

Doping's practical payoff is controllable conductivity:

σ = q·(n·μn + p·μp)

For n-type material where n ≫ p, this simplifies to σ ≈ q·Nd·μn. Using electron mobility μn ≈ 1350 cm²/V·s for lightly-to-moderately doped silicon:

σ ≈ (1.6×10⁻¹⁹ C)(1×10¹⁷ cm⁻³)(1350 cm²/V·s) ≈ 21.6 (Ω·cm)⁻¹
ρ = 1/σ ≈ 0.046 Ω·cm

Compare this to intrinsic silicon resistivity of ~3.4×10⁵ Ω·cm (from ρi = 1/(q·ni·(μn+μp)) with ni≈1×10¹⁰ cm⁻³) — 7 orders of magnitude higher. This is the entire point of doping: it converts silicon from an insulator-like material into a conductor with a resistivity you can dial in by choosing Nd or Na, and it does so while keeping the type of carrier (electron vs. hole) under design control.

Doping Concentration vs. Carrier Type Summary

Practical Design Implications

• Device fabrication: ion implantation or diffusion sets Nd/Na profiles precisely — source/drain regions in a MOSFET, base/emitter/collector regions in a BJT, are all just adjacent, differently-doped extrinsic regions.
• Resistivity engineering: substrate and epitaxial layer doping levels are chosen to trade off breakdown voltage (lower doping, wider depletion region, higher breakdown) against on-resistance (higher doping, lower resistivity).
• Temperature sensitivity: minority carrier concentration depends on ni², which is exponential in temperature (ni² ∝ T³·exp(−Eg/kT)). This is why minority-carrier-dominated leakage currents (reverse-bias diode leakage, BJT collector leakage) roughly double every 8–10°C, while majority-carrier conductivity in moderately doped silicon is comparatively temperature-stable.
• Compensated/counter-doped regions: if both donors and acceptors are present (as in real fabrication where a region is counter-doped), the net doping |Nd − Na| determines the effective type and concentration — this is the basis of forming p-n junctions within a single crystal by selective counter-doping.

Key Takeaways

• n-type doping uses Group V donors (P, As, Sb) that contribute free electrons; p-type doping uses Group III acceptors (B, Ga, In) that contribute holes — both fully ionize at room temperature in typical doping ranges.
• Mass-action law n₀·p₀ = ni² always holds in equilibrium, letting you compute minority carrier concentration directly from the majority (dopant) concentration.
• Doping shifts the Fermi level toward Ec (n-type) or Ev (p-type), by an amount kT·ln(N/ni) — this offset is the origin of built-in potential in p-n junctions.
• Typical doping levels of 10¹⁴–10²⁰ cm⁻³ change resistivity by 5–7 orders of magnitude relative to intrinsic silicon, making conductivity a design parameter rather than a fixed material constant.
• Minority carriers, though vastly outnumbered, dominate diode/BJT current behavior and drive strong temperature dependence of leakage currents — never assume they're negligible just because they're the minority.