6.2 n-type and p-type doping

Doping is the process of intentionally adding impurity atoms to an intrinsic semiconductor to control its electrical properties. This single technique underlies nearly every semiconductor device, from diodes and transistors to solar cells, because it lets you determine whether electrons or holes carry most of the current.

Doping in semiconductors

An intrinsic semiconductor (pure Si or Ge) has equal numbers of electrons and holes, all generated by thermal excitation across the bandgap. By introducing specific impurity atoms, you create an extrinsic semiconductor where one type of carrier dominates. The species and concentration of the dopant determine whether the material becomes n-type or p-type, and how strongly its conductivity changes.

n-type vs p-type doping

• n-type doping introduces atoms with more valence electrons than the host (donor impurities). Each donor contributes roughly one free electron to the conduction band, making electrons the majority carriers.
• p-type doping introduces atoms with fewer valence electrons than the host (acceptor impurities). Each acceptor captures an electron from the valence band, leaving behind a hole. Holes become the majority carriers.

The minority carrier in each case is the opposite type: holes in n-type, electrons in p-type.

Intrinsic vs extrinsic semiconductors

In an intrinsic semiconductor like pure silicon, every electron that reaches the conduction band leaves behind a hole, so $n = p = n_i$. Doping breaks that symmetry. Even a small dopant concentration (say $10^{15}\,\text{cm}^{-3}$) vastly outnumbers silicon's intrinsic carrier concentration ($n_i \approx 1.0 \times 10^{10}\,\text{cm}^{-3}$ at 300 K), so the majority carrier type is almost entirely set by the dopant.

Donor and acceptor impurities

Silicon sits in group IV with four valence electrons. That's the reference point:

• Donors come from group V (phosphorus, arsenic, antimony). They have five valence electrons. Four form covalent bonds with neighboring Si atoms; the fifth is loosely bound and easily freed into the conduction band.
• Acceptors come from group III (boron, aluminum, gallium). They have three valence electrons. They bond with only three neighbors, creating an empty state (hole) that a nearby valence electron can fill.

Fermi level shifts from doping

The Fermi level $E_F$ is the energy at which the occupation probability is 50% at thermal equilibrium. In an intrinsic semiconductor, $E_F$ sits roughly at the middle of the bandgap.

• n-type doping shifts $E_F$ upward, closer to the conduction band edge $E_C$. The higher the donor concentration, the closer $E_F$ moves to $E_C$.
• p-type doping shifts $E_F$ downward, closer to the valence band edge $E_V$.

This shift directly reflects the change in carrier concentrations and governs how the semiconductor behaves when it contacts other materials.

Characteristics of n-type semiconductors

An n-type semiconductor is formed by doping with donor impurities. The extra electrons from the donors raise the free electron concentration well above the intrinsic level, making electrons the majority carriers and holes the minority carriers.

Majority carriers in n-type

Electrons dominate conduction. If you dope silicon with $N_D = 10^{16}\,\text{cm}^{-3}$ phosphorus atoms (and assume full ionization), the electron concentration is approximately $n \approx 10^{16}\,\text{cm}^{-3}$. The hole concentration drops to $p = n_i^2 / n \approx 10^4\,\text{cm}^{-3}$, which is negligible by comparison.

Electron energy levels in n-type

Each donor atom introduces a discrete energy level just below the conduction band edge. For phosphorus in silicon, this donor level sits about 45 meV below $E_C$. Since thermal energy at room temperature is $k_BT \approx 26\,\text{meV}$, most donors are ionized at 300 K, and their electrons populate the conduction band.

Conductivity changes in n-type

More free electrons means higher conductivity. The relationship is:

$\sigma = q n \mu_e$

where $q$ is the elementary charge ($1.6 \times 10^{-19}\,\text{C}$), $n$ is the electron concentration, and $\mu_e$ is the electron mobility. Increasing the donor concentration raises $n$, though at very high doping levels the mobility drops due to impurity scattering (more on this below).

Examples of n-type dopants

• Silicon: phosphorus (P), arsenic (As), antimony (Sb). Phosphorus is the most common for standard doping; arsenic is preferred when a shallow, tightly controlled profile is needed (e.g., in MOSFET source/drain regions) because of its lower diffusivity.
• Gallium arsenide (GaAs): silicon (Si) substituting on a Ga site, or tellurium (Te) substituting on an As site.

Characteristics of p-type semiconductors

A p-type semiconductor is formed by doping with acceptor impurities. The acceptors create holes in the valence band, making holes the majority carriers and electrons the minority carriers.

Majority carriers in p-type

Holes dominate conduction. With $N_A = 10^{16}\,\text{cm}^{-3}$ boron atoms in silicon, the hole concentration is $p \approx 10^{16}\,\text{cm}^{-3}$, and the electron concentration falls to $n = n_i^2 / p \approx 10^4\,\text{cm}^{-3}$.

Electron energy levels in p-type

Acceptor atoms create energy levels just above the valence band edge. For boron in silicon, the acceptor level is about 45 meV above $E_V$. At room temperature, electrons from the valence band are thermally excited into these acceptor levels, leaving mobile holes behind.

Conductivity changes in p-type

The conductivity expression mirrors the n-type case but uses hole quantities:

$\sigma = q p \mu_h$

Because hole mobility in silicon ($\mu_h \approx 450\,\text{cm}^2/\text{Vs}$) is lower than electron mobility, a p-type sample needs a higher carrier concentration than an n-type sample to reach the same conductivity.

Examples of p-type dopants

• Silicon: boron (B) is by far the most common. Aluminum (Al) and gallium (Ga) are also group III acceptors but used less frequently.
• Gallium arsenide (GaAs): zinc (Zn) and carbon (C) on an As site.

Charge carrier concentrations

The concentrations of electrons and holes determine a semiconductor's electrical behavior. Doping gives you direct control over these numbers.

Intrinsic carrier concentration

The intrinsic carrier concentration $n_i$ is the electron (or hole) density in a pure semiconductor at thermal equilibrium:

$n_i = \sqrt{N_c N_v}\,\exp\!\left(\frac{-E_g}{2k_BT}\right)$

• $N_c$ and $N_v$ are the effective densities of states in the conduction and valence bands.
• $E_g$ is the bandgap energy (1.12 eV for Si at 300 K).
• $k_B$ is Boltzmann's constant.

For silicon at room temperature, $n_i \approx 1.0 \times 10^{10}\,\text{cm}^{-3}$. This is a small number compared to typical doping levels, which is exactly why doping is so effective.

Majority and minority carrier densities

The mass action law holds at thermal equilibrium:

$np = n_i^2$

This is true regardless of doping. So if you increase $n$ by adding donors, $p$ must decrease, and vice versa. For an n-type semiconductor with $n \approx N_D$, the minority hole concentration is simply $p = n_i^2 / N_D$.

Temperature dependence of carrier concentrations

• $n_i$ rises exponentially with temperature because more electrons gain enough thermal energy to cross the bandgap.
• The majority carrier concentration in a doped semiconductor stays roughly constant over a wide temperature range (the "extrinsic region"), since it's pinned by the dopant concentration.
• At very high temperatures, $n_i$ can grow large enough to rival the doping level. At that point the material behaves intrinsically again. This sets an upper operating temperature limit for semiconductor devices.
• The minority carrier concentration tracks $n_i^2 / N_D$ (or $n_i^2 / N_A$), so it's much more temperature-sensitive than the majority concentration.

Charge neutrality in doped semiconductors

A semiconductor must remain electrically neutral overall. The charge neutrality condition is:

$n + N_A^- = p + N_D^+$

For a purely n-type semiconductor ($N_A = 0$) with full ionization: $n \approx N_D$. For a purely p-type semiconductor ($N_D = 0$) with full ionization: $p \approx N_A$. When both donors and acceptors are present (compensation doping), the net carrier type depends on which dopant has the higher concentration.

Mobility of charge carriers

Mobility ($\mu$) quantifies how fast a carrier drifts per unit electric field. It has units of $\text{cm}^2/\text{Vs}$. Higher mobility means carriers respond more readily to an applied field, which translates directly to higher conductivity and faster devices.

Electron and hole mobilities

In most semiconductors, electrons are more mobile than holes because electrons have a smaller effective mass. Typical values for intrinsic silicon at 300 K:

• Electron mobility: $\mu_e \approx 1400\,\text{cm}^2/\text{Vs}$
• Hole mobility: $\mu_h \approx 450\,\text{cm}^2/\text{Vs}$

This roughly 3:1 ratio is one reason n-channel MOSFETs are preferred over p-channel in many circuit designs.

Factors affecting carrier mobility

Four main scattering mechanisms limit mobility:

1. Lattice (phonon) scattering: Thermal vibrations of the crystal lattice deflect carriers. Dominates at moderate-to-high temperatures.
2. Ionized impurity scattering: Coulomb interactions between carriers and charged dopant ions. Dominates at high doping concentrations and low temperatures.
3. Carrier-carrier scattering: Becomes significant at very high carrier densities.
4. Defect/surface scattering: Crystal imperfections and interfaces scatter carriers, especially relevant in thin films and nanoscale devices.

Mobility changes from doping concentration

At low doping ($< 10^{15}\,\text{cm}^{-3}$), mobility is close to the intrinsic value because phonon scattering dominates. As doping increases beyond $\sim 10^{17}\,\text{cm}^{-3}$, ionized impurity scattering becomes significant and mobility drops noticeably. For heavily doped silicon ($> 10^{19}\,\text{cm}^{-3}$), electron mobility can fall below $100\,\text{cm}^2/\text{Vs}$.

This trade-off matters: higher doping raises carrier concentration but lowers mobility. Conductivity still increases with doping overall, but not as steeply as you might expect from the carrier concentration alone.

Conductivity relation to mobility and carrier density

The general conductivity expression for a semiconductor with both carrier types is:

$\sigma = q(n\mu_e + p\mu_h)$

In practice, one term usually dominates. For n-type: $\sigma \approx qn\mu_e$. For p-type: $\sigma \approx qp\mu_h$. Optimizing a device often means balancing doping level against the resulting mobility to hit a target conductivity or switching speed.

Applications of doped semiconductors

Controlled doping is what makes semiconductor technology possible. By placing n-type and p-type regions next to each other, you create junctions with unique electrical behavior.

p-n junctions and diodes

When p-type and n-type regions meet, electrons diffuse from the n-side into the p-side and holes diffuse the other way. This leaves behind a depletion region of exposed, immobile dopant ions and a built-in electric field that opposes further diffusion.

• Forward bias (positive voltage on p-side) shrinks the depletion region and allows large current flow.
• Reverse bias widens the depletion region and blocks current (only a tiny leakage current flows).

This rectifying behavior is the basis of the semiconductor diode.

Bipolar junction transistors (BJTs)

A BJT stacks two p-n junctions back-to-back in either an npn or pnp configuration, forming three regions: emitter, base, and collector. The base is intentionally thin and lightly doped.

A small base current controls a much larger collector current, giving the BJT its amplification ability. The current gain ($\beta$) can range from roughly 20 to several hundred depending on the design. BJTs are used in analog amplifiers, oscillators, and some digital logic families.

Field effect transistors (FETs)

FETs control current through a semiconductor channel using a voltage applied to a gate terminal, rather than a current. The two main types:

• JFETs use a reverse-biased p-n junction to modulate the channel width.
• MOSFETs use a metal-oxide-semiconductor gate stack. Applying a gate voltage creates (or depletes) a conducting channel between the source and drain.

MOSFETs are the building blocks of modern integrated circuits. Their high input impedance and scalability make them dominant in microprocessors, memory, and power electronics.

Photovoltaic solar cells

A solar cell is essentially a large-area p-n junction optimized for light absorption. The process works in three steps:

1. A photon with energy $\geq E_g$ is absorbed, creating an electron-hole pair.
2. The built-in electric field at the junction separates the electron and hole before they can recombine.
3. The separated carriers flow through an external circuit, delivering electrical power.

Doping profiles are carefully engineered to maximize carrier collection. A typical silicon solar cell uses a heavily doped n-type emitter on top of a lightly doped p-type base. Commercial silicon cells currently achieve efficiencies of around 20-26%.