Density of States Near the Conduction and Valence Bands

Effective Density of States in Silicon

The effective density of states describes the number of available electron states near the conduction-band minimum or hole states near the valence-band maximum. These values are important when calculating carrier concentration, intrinsic semiconductor behavior, Fermi-level position, and the electrical properties of silicon wafers.

A PhD candidate requested information about the effective density of states for n-type silicon, p-type silicon, and intrinsic silicon wafers.

Conduction- and Valence-Band Density of States

For crystalline silicon at approximately 300 K, the commonly used effective density-of-states values are:

• Conduction band, N_C: approximately 2.8 × 10¹⁹ cm⁻³
• Valence band, N_V: approximately 1.04 × 10¹⁹ cm⁻³

N_C represents the effective number of available electron states near the conduction-band minimum, while N_V represents the effective number of available hole states near the valence-band maximum.

These parameters depend primarily on carrier effective mass and temperature. They are material properties and are not determined directly by whether the wafer is n-type, p-type, or intrinsic. Doping changes the carrier concentration and Fermi-level position rather than fundamentally redefining N_C or N_V.

Density of States and Carrier Concentration

Under nondegenerate conditions, electron and hole concentrations may be estimated using:

n = N_C exp[−(E_C − E_F)/kT]

p = N_V exp[−(E_F − E_V)/kT]

Where:

• n is the electron concentration
• p is the hole concentration
• E_C is the conduction-band edge
• E_V is the valence-band edge
• E_F is the Fermi level
• k is the Boltzmann constant
• T is absolute temperature

For intrinsic silicon, the electron and hole concentrations are equal. The intrinsic carrier concentration can be estimated from N_C, N_V, and the silicon band-gap energy.

The commonly used approximation is:

n_i = √(N_CN_V) exp(−E_g/2kT)

Because the density of states varies with temperature, calculations performed significantly above or below room temperature should use temperature-adjusted values.

Reference #250233 for additional information, wafer specifications, and pricing.

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Which N-Type Silicon Wafer Has the Highest Conductivity?

There is no single dopant that automatically produces the highest conductivity in every n-type silicon wafer. Electrical conductivity depends on several connected factors:

• Dopant species
• Active dopant concentration
• Electron mobility
• Crystal quality
• Compensation by unwanted impurities
• Thermal processing history
• Wafer temperature during measurement

For n-type silicon, the most common donor dopants are phosphorus, arsenic, and antimony. Heavily doped wafers generally have lower resistivity and higher conductivity, but very high dopant concentrations can reduce carrier mobility because of ionized-impurity scattering.

Phosphorus-Doped Silicon

Phosphorus-doped silicon is widely used because it provides a practical balance of conductivity, dopant activation, availability, and process compatibility. It is common in integrated circuits, solar cells, sensors, MEMS, and general semiconductor research.

Arsenic-Doped Silicon

Arsenic-doped silicon can provide highly conductive n-type material and is frequently selected when a relatively shallow and stable donor profile is required. Arsenic diffuses more slowly in silicon than phosphorus, which can help preserve abrupt junction profiles during thermal processing.

Common applications include:

• Low-resistance device regions
• Source and drain structures
• High-speed integrated circuits
• Ohmic contacts
• Heavily doped silicon substrates

Antimony-Doped Silicon

Antimony-doped silicon is valued for its low diffusion coefficient. It may be selected when maintaining a stable dopant distribution during high-temperature processing is more important than maximizing dopant solubility.

Potential applications include:

• Buried layers
• High-temperature processing
• Precision dopant-profile research
• Power-device development
• Sensor fabrication

How Silicon Wafer Conductivity Is Evaluated

Conductivity should be evaluated from measured resistivity, carrier concentration, and mobility rather than from dopant identity alone. The relationship is commonly written as:

σ = q(nμ_n + pμ_p)

For a strongly n-type wafer, electron conduction dominates, so the expression is often approximated as:

σ ≈ qnμ_n

A four-point probe can be used to measure sheet resistance or resistivity while minimizing the effect of contact resistance.

The best wafer should therefore be chosen by specifying the required resistivity, carrier concentration, dopant, thermal budget, crystal orientation, and device process—not by assuming one dopant is always the most conductive.

Reference #270670 for n-type silicon wafer specifications and pricing.