N-Type Doping

Part of Semiconductors

Adding donor atoms to create electron-rich semiconductor material for device fabrication.

Why This Matters

Pure semiconductor is not very useful: it has equal numbers of electrons and holes, and its conductivity varies dramatically with temperature. Doping — intentionally introducing trace amounts of impurity atoms — gives semiconductor material controlled, stable electrical properties. N-type doping adds atoms with one extra valence electron (donors), creating material where electrons are the majority carriers.

Understanding n-type doping from first principles enables you to choose the right dopant, calculate the doping level needed for a specific resistivity, troubleshoot unexpected conductivity, and combine n-type and p-type regions into functional devices. These are not abstract concepts — they directly determine whether your transistors have the right current gain, whether your diodes have adequate breakdown voltage, and whether your resistors have reproducible values.

For a rebuilding civilization, mastering doping also means mastering the supply chain for dopant materials. Which donors are chemically accessible? Which can be introduced into semiconductors with available equipment? Knowing the full menu of options allows improvisation when the ideal material is unavailable.

Donor Atoms and the Mechanism

Silicon and germanium are Group IV elements: each atom has 4 valence electrons, forming 4 covalent bonds with neighbors. When a Group V atom (5 valence electrons) replaces a lattice atom, four of its electrons participate in bonding, but the fifth has no bond to fill. This fifth electron is loosely bound — only 0.01-0.05 eV below the conduction band edge. At room temperature (thermal energy ~0.026 eV), it is easily excited into the conduction band, leaving behind a fixed positive ion.

This is n-type doping: each donor atom contributes one free electron. The number of free electrons (n) ≈ donor concentration (N_D) at room temperature, because virtually all donors are ionized.

Common n-type dopants for silicon:

• Phosphorus (P): Most common. Ionization energy 0.045 eV, easily fully ionized at room temperature. Introduced by POCl3 diffusion, ion implantation, or phosphine (PH3) gas.
• Arsenic (As): Lower diffusivity than phosphorus — useful when you need a sharp, stable junction that won’t move during subsequent high-temperature steps. Toxic as arsine gas and arsenic trioxide.
• Antimony (Sb): Very low diffusivity. Slow-moving in silicon, used for deep buried layers. Less common.

Common n-type dopants for germanium:

• Antimony (Sb): Standard n-type dopant for germanium. Used in early transistors.
• Arsenic (As): Also works.
• Phosphorus (P): Less commonly used in germanium.

Practically: phosphorus for most silicon work (accessible, well-characterized), antimony for germanium work.

Resistivity and Doping Concentration

Resistivity is the measurable quantity that maps to doping concentration. For n-type material: ρ = 1 / (q × n × µ_n) ≈ 1 / (q × N_D × µ_n)

For silicon at room temperature (µ_n ≈ 1350 cm²/V·s for lightly doped material):

• N_D = 10^14 cm^-3 → ρ ≈ 46 Ω·cm (lightly doped, near-intrinsic)
• N_D = 10^15 cm^-3 → ρ ≈ 4.6 Ω·cm
• N_D = 10^16 cm^-3 → ρ ≈ 0.46 Ω·cm
• N_D = 10^17 cm^-3 → ρ ≈ 0.046 Ω·cm
• N_D = 10^20 cm^-3 → ρ ≈ 0.001 Ω·cm (near-metallic, “degenerate” semiconductor)

Note: mobility decreases with increasing doping (impurity scattering), so resistivity doesn’t scale exactly with 1/N_D at high doping.

Measuring resistivity: Four-point probe measurement. Four equally-spaced probes in a line are pressed onto the semiconductor surface. Current passes between outer probes; voltage is measured between inner probes. Resistivity: ρ = (π/ln2) × (V/I) × t (for thin wafer, where t is wafer thickness). Simple to construct: four needle probes spaced 1 mm apart, fixed in a row in a wooden block. With a known current (e.g., 1 mA) and measured voltage, calculate resistivity in minutes.

Alternatively, van der Pauw method: four contacts at the periphery of a square sample. Two configurations of current and voltage measurement yield sheet resistance, then resistivity with known thickness.

Doping Techniques for Primitive Fabrication

Zone leveling: During zone refining, controlled amounts of dopant are added to the molten zone to set the final doping level of the refined crystal. Add a weighed amount of phosphorus (as red phosphorus powder, not the toxic white form) to the starting charge before refining. After refining, the crystal has the desired n-type doping with good uniformity along most of its length.

Calculation: to achieve N_D = 10^15 cm^-3 in germanium (density 5.35 g/cm³, atomic weight 72.6), a 10-gram germanium charge contains 8.28×10^-2 mol = 5×10^22 Ge atoms. To get 10^15 Sb atoms per cm^3 in 1.87 cm³ volume = 1.87×10^15 Sb atoms needed. This is 3.1×10^-9 mol Sb = 0.38 µg Sb. Measuring sub-microgram quantities requires a chemical balance with milligram precision and weighing by difference from a small solution.

Diffusion doping: Heat semiconductor in atmosphere containing dopant vapor at controlled temperature and time. As described in Junction Formation — this is the standard industrial method.

Alloying with doped material: Melt together high-purity semiconductor with a weighed quantity of a heavily doped master alloy. The master alloy is pre-prepared at known doping level; diluting it into a large semiconductor charge achieves the desired final concentration. Allows reasonably precise doping without gas-phase chemistry.

Compensation and Net Doping

Real semiconductor material may contain both donors and acceptors (from deliberate doping and residual impurities from purification). The net doping is:

• If N_D > N_A: n-type with effective donor concentration N_D - N_A
• If N_A > N_D: p-type with effective acceptor concentration N_A - N_D
• If N_D = N_A: compensated, near-intrinsic semiconductor

This has a practical consequence: measuring p-type material? Add known amount of phosphorus until resistivity stops decreasing and starts increasing again. The turning point gives you the original acceptor concentration. This is the Hall effect measurement principle — but the compensation titration approach works without Hall equipment.

Compensation also means that a partially-purified semiconductor material with residual contamination has lower net carrier concentration (and higher resistivity) than either impurity type alone. If your “purified” germanium has higher-than-expected resistivity, it may not be undoped intrinsic — it may be compensated with background donors and acceptors nearly canceling. Test with Hall effect measurement to determine true type and concentration.

Quality Control and Specification

Before fabricating devices, measure and record the n-type doping of each wafer or ingot lot:

1. Resistivity (four-point probe): confirm target range for application.
2. Carrier type (thermoelectric probe): touch one probe at room temperature, one at ~70°C. Voltage polarity indicates type: for n-type, the hot probe is negative (electrons diffuse from hot to cold region, leaving positive charge at hot probe).
3. Minority carrier lifetime (photoconductance decay): illuminate the sample with a brief flash of light. Excess carriers generated by light recombine over time τ. Measure decay of photoconductance to extract τ. For transistor base material: τ > 10 µs is good; τ < 1 µs indicates contamination.
4. Mobility (Hall measurement): apply magnetic field perpendicular to current flow; measure transverse Hall voltage. Hall factor gives carrier concentration and mobility independently. Requires a magnet and four contacts — more elaborate setup but provides the most complete characterization.

Match wafer specifications to device requirements: transistor collector regions need light doping (high breakdown voltage); base regions need moderate doping (controlled width and carrier concentration); heavily doped emitter regions need high doping regardless of type.