7.2 Extrinsic semiconductors

Extrinsic semiconductors are intrinsic semiconductors that have been intentionally doped with impurity atoms to control their electrical properties. Doping lets engineers tune carrier concentrations, conductivity, and optical behavior with remarkable precision. This is what makes nearly every modern electronic device possible.

This topic covers the two main types of extrinsic semiconductors (n-type and p-type), how doping works at the atomic level, the resulting changes in carrier concentration and energy levels, and the key techniques used to characterize these materials.

Types of extrinsic semiconductors

Doping introduces specific impurity atoms into an intrinsic semiconductor's crystal lattice. These impurities modify the band structure by adding new energy levels near the band edges, which dramatically changes the number of free carriers available for conduction.

N-type semiconductors

N-type semiconductors are created by doping with donor impurities, atoms from group V of the periodic table (phosphorus, arsenic, antimony). In a silicon lattice, each host atom forms four covalent bonds. A group V atom also forms four bonds but has one extra valence electron left over. This extra electron is only weakly bound to the donor atom, so at room temperature it easily ionizes into the conduction band.

• Majority carriers: electrons
• Minority carriers: holes
• The Fermi level shifts upward, closer to the conduction band, reflecting the increased electron population
• Conductivity increases because there are far more free electrons than in the undoped material

P-type semiconductors

P-type semiconductors are formed by doping with acceptor impurities, atoms from group III (boron, gallium, indium). A group III atom has only three valence electrons, so when it sits in the silicon lattice it leaves one bond incomplete. This missing electron acts as a hole that can accept an electron from a neighboring bond, effectively creating a mobile positive charge carrier in the valence band.

• Majority carriers: holes
• Minority carriers: electrons
• The Fermi level shifts downward, closer to the valence band
• Hole-based conduction dominates the electrical transport

Doping process

Doping alters the electronic structure of a semiconductor in a controlled way. The choice of dopant species, concentration, and incorporation method all affect device performance, so precise control over the doping process is essential.

Substitutional doping

In substitutional doping, dopant atoms replace host atoms at regular lattice sites. This is the most common approach for silicon-based devices.

• Group V elements (P, As, Sb) substitute for Si to create n-type material
• Group III elements (B, Ga, In) substitute for Si to create p-type material
• The dopant atom must have a similar atomic radius to the host atom to minimize lattice distortion
• Each dopant introduces a shallow energy level near a band edge; the ionization energy (typically 10–50 meV in Si) determines how easily the dopant releases or captures a carrier

Interstitial doping

In interstitial doping, dopant atoms sit in the spaces between host atoms rather than replacing them. This is more common in compound semiconductors like GaAs and InP.

• Interstitial dopants can introduce lattice strain, which affects both electronic and optical properties
• Diffusion coefficients for interstitial dopants are typically much higher than for substitutional dopants, meaning they move through the lattice more easily during processing
• This faster diffusion can be an advantage (rapid doping) or a disadvantage (unwanted dopant migration during thermal steps)

Donor and acceptor levels

When dopant atoms are incorporated into a semiconductor, they introduce discrete energy levels within the band gap. The position of these levels relative to the band edges determines how effectively the dopants contribute carriers at a given temperature.

Energy band diagrams

• Donor levels sit just below the conduction band edge (typically within ~50 meV for shallow donors in Si). At room temperature, most donors are ionized, and their extra electrons occupy conduction band states.
• Acceptor levels sit just above the valence band edge. At room temperature, electrons from the valence band fill these levels, leaving behind mobile holes.
• The band gap itself remains essentially unchanged by moderate doping.
• At very high doping concentrations (above roughly $10^{18} \text{ cm}^{-3}$ in Si), individual impurity levels can broaden into an impurity band that merges with the nearest band edge, fundamentally changing the electronic structure.

Fermi level shifts

In an intrinsic semiconductor, the Fermi level $E_F$ sits near the middle of the band gap. Doping moves it:

• N-type: $E_F$ shifts toward the conduction band. The higher the donor concentration $N_D$, the closer $E_F$ gets to $E_C$.
• P-type: $E_F$ shifts toward the valence band. Higher acceptor concentration $N_A$ pushes $E_F$ closer to $E_V$.
• The occupation of all energy states is governed by Fermi-Dirac statistics: $f(E) = \frac{1}{1 + \exp\left(\frac{E - E_F}{k_B T}\right)}$
• When doping is so heavy that $E_F$ enters the conduction band (n-type) or valence band (p-type), the semiconductor is called degenerate and starts to behave more like a metal.

Carrier concentration

Doping can increase the majority carrier concentration by many orders of magnitude compared to the intrinsic value. For silicon at room temperature, the intrinsic carrier concentration is about $n_i \approx 1.5 \times 10^{10} \text{ cm}^{-3}$. A typical doping level of $10^{16} \text{ cm}^{-3}$ raises the majority carrier concentration by a factor of roughly $10^6$.

Temperature dependence

The carrier concentration in an extrinsic semiconductor passes through three distinct regimes as temperature increases:

1. Freeze-out region (low $T$): Thermal energy is insufficient to ionize all dopants. Carrier concentration rises steeply with temperature as more dopants become ionized.
2. Saturation (extrinsic) region (intermediate $T$): Essentially all dopants are ionized, so carrier concentration plateaus at approximately $N_D$ (or $N_A$). This is the normal operating range for most devices.
3. Intrinsic region (high $T$): Thermally generated electron-hole pairs across the band gap begin to outnumber the dopant-supplied carriers. The material behaves increasingly like an intrinsic semiconductor.

Doping concentration effects

• Increasing dopant concentration raises the majority carrier concentration, but the relationship saturates at very high levels due to solid solubility limits and self-compensation effects.
• Heavy doping (above ~$10^{18} \text{ cm}^{-3}$ in Si) causes impurity band formation and band gap narrowing.
• Degenerate doping occurs when the dopant concentration is so high that $E_F$ enters a band. The material no longer follows classical semiconductor statistics and must be treated with full Fermi-Dirac statistics.
• Compensation from unintentional impurities of the opposite type can reduce the effective carrier concentration (more on this below).

Electrical properties

Conductivity vs. temperature

The conductivity of an extrinsic semiconductor depends on both carrier concentration and carrier mobility, following $\sigma = nq\mu_e + pq\mu_h$, where $n$ and $p$ are electron and hole concentrations and $\mu_e$, $\mu_h$ are their mobilities.

The temperature dependence mirrors the three carrier concentration regimes:

1. Low $T$: Conductivity rises as dopants ionize. Mobility is relatively high because phonon scattering is weak, but the carrier supply is limited.
2. Intermediate $T$: Carrier concentration is saturated. Conductivity actually decreases somewhat because mobility drops due to increasing phonon scattering (lattice vibrations scatter carriers more effectively at higher temperatures).
3. High $T$: Intrinsic carriers flood in, and conductivity rises again despite continued mobility reduction.

This non-monotonic behavior is a distinctive signature of extrinsic semiconductors.

Hall effect in extrinsics

The Hall effect is one of the most powerful tools for characterizing extrinsic semiconductors. When a current-carrying sample is placed in a perpendicular magnetic field, a transverse voltage (the Hall voltage) develops.

• The Hall coefficient is $R_H = \frac{1}{nq}$ for a single carrier type, so it's inversely proportional to carrier concentration.
• The sign of $R_H$ tells you the carrier type: negative for n-type (electrons), positive for p-type (holes).
• Hall mobility $\mu_H = |R_H| \sigma$ provides information about scattering mechanisms and crystal quality.
• In practice, mixed conduction (both electrons and holes contributing) and magnetoresistance effects can complicate the analysis.

Optical properties

Doping changes how a semiconductor interacts with light, which matters for designing LEDs, lasers, photodetectors, and solar cells.

Absorption spectrum changes

• Dopants introduce sub-band-gap absorption features corresponding to transitions involving impurity levels.
• Free carrier absorption increases with doping concentration, particularly in the infrared. This absorption scales roughly as $\lambda^2$ (wavelength squared).
• At high doping levels, band gap narrowing shifts the absorption edge to lower energies. This is significant in heavily doped emitter regions of solar cells and bipolar transistors.
• Urbach tails appear as exponential tails below the band edge in the absorption spectrum, caused by disorder and electric field fluctuations from randomly distributed dopants.

Photoluminescence in extrinsics

Photoluminescence (PL) spectroscopy reveals the radiative recombination pathways introduced by doping:

• Donor-acceptor pair (DAP) recombination: An electron on a donor recombines with a hole on an acceptor, producing sharp emission lines whose energy depends on the pair separation.
• Band-to-impurity transitions: Conduction band electrons recombining with acceptor-bound holes (or donor-bound electrons with valence band holes) produce broader emission peaks.
• Non-radiative recombination through deep-level defects competes with luminescence and can significantly quench PL intensity, which is why material purity and crystal quality matter for light-emitting devices.

Applications of extrinsic semiconductors

Transistors and diodes

• Bipolar junction transistors (BJTs) use alternating n-type and p-type regions (npn or pnp) to amplify current. The doping profile of each region controls gain and switching speed.
• Field-effect transistors (FETs) use a doped semiconductor channel whose conductivity is modulated by a gate voltage. MOSFETs, the backbone of digital logic, rely on precisely controlled doping in the source, drain, and channel regions.
• P-n junction diodes form when n-type and p-type regions meet. The built-in potential at the junction enables rectification (passing current in one direction only).
• Zener diodes use heavily doped p-n junctions that undergo controlled reverse breakdown, making them useful for voltage regulation.

Solar cells and LEDs

• Solar cells use the electric field at a p-n junction to separate photogenerated electron-hole pairs. Optimizing the doping profile (concentration and depth) is critical for maximizing efficiency.
• LEDs rely on radiative recombination when electrons and holes are injected into a doped active region. The semiconductor's band gap determines the emission wavelength (color).
• Modern LEDs often use quantum well structures within the active region to confine carriers and enhance recombination efficiency, allowing precise color tuning.

Characterization techniques

Hall measurements

Hall measurements are the standard method for determining carrier type, concentration, and mobility in a single experiment.

• The van der Pauw technique is widely used because it works on samples of arbitrary shape, requiring only four contacts at the perimeter.
• Temperature-dependent Hall measurements are particularly valuable: by tracking carrier concentration vs. temperature, you can extract the ionization (activation) energy of dopants from an Arrhenius plot.
• At high magnetic fields, magnetoresistance effects can introduce errors that need to be accounted for in the analysis.

DLTS and photoconductivity

• Deep Level Transient Spectroscopy (DLTS) is the go-to technique for identifying deep-level traps and defects in semiconductors. It works by monitoring capacitance transients in a reverse-biased junction as trapped carriers are thermally emitted.
• DLTS provides the activation energy, capture cross-section, and concentration of each trap level.
• Photoconductivity measurements probe how carrier generation and recombination respond to illumination. The spectral dependence of photoconductivity reveals absorption thresholds associated with impurity levels and band-to-band transitions.

Extrinsic vs. intrinsic semiconductors

Carrier concentration comparison

Temperature sensitivity differences

• Intrinsic semiconductors are highly sensitive to temperature because their carrier concentration depends exponentially on $-E_g / 2k_BT$.
• Extrinsic semiconductors show much more stable electrical properties in the saturation region, which is why they're preferred for devices that need to operate reliably across a temperature range.
• At sufficiently high temperatures, both types converge to intrinsic behavior as thermally generated carriers overwhelm the dopant contribution.
• At very low temperatures, extrinsic semiconductors experience dopant freeze-out, while intrinsic semiconductors simply have vanishingly small carrier concentrations.

Compensation in semiconductors

Compensation occurs when both donor and acceptor impurities are present in the same semiconductor. Their effects partially cancel, and the net electrical behavior depends on the difference between the two concentrations.

Donor-acceptor compensation

• If $N_D > N_A$, the material is n-type with a net electron concentration of approximately $N_D - N_A$.
• If $N_A > N_D$, the material is p-type with a net hole concentration of approximately $N_A - N_D$.
• Compensation can be intentional (used to create semi-insulating substrates, such as Cr-doped GaAs) or unintentional (background impurities from growth partially neutralize the intended dopant).

Effects on carrier concentration

• The effective carrier concentration is always less than the total dopant concentration due to compensation.
• Heavily compensated semiconductors can have very high resistivity even though they contain large numbers of both donor and acceptor atoms. This is exploited in semi-insulating substrates for high-frequency devices.
• The temperature dependence of carrier concentration becomes more complex in compensated materials because the ionization of donors and acceptors proceeds at different rates.
• Compensation also affects where the Fermi level sits and delays the onset of degenerate behavior to higher total dopant concentrations.