Measuring Substrate Fermi Level

Understanding and measuring a substrate's Fermi level is critical for semiconductor research, device fabrication, graphene characterization, and electronic materials analysis. This guide explains what the Fermi level is, how it affects silicon, gallium arsenide (GaAs), silicon carbide (SiC), graphene, sapphire, and glass substrates, and the most common measurement techniques including Kelvin Probe Force Microscopy (KPFM), scanning tunneling microscopy (STM), and photoemission spectroscopy. Learn how doping, resistivity, and band structure influence Fermi level position in advanced semiconductor materials.

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What Is the Fermi Level of Graphene?

A PhD candidate requested the following information:

I would like to know some details about suspended monolayer graphene on cavities:

  1. Is this graphene produced by CVD or exfoliation? Do you have information about its mobility and Fermi level?
  2. What supporting substrates can be used? Is SiO2/Si suitable?
  3. Can the cavity geometry and dimensions be customized?

UniversityWafer, Inc. Response

The graphene supplied for this application is CVD-grown graphene. Standard supporting substrates can include copper, SiO2/Si, quartz, and PET, depending on the product and transfer requirements.

For suspended monolayer graphene on cavities, substrate and cavity requirements should be confirmed for each project. Previously specified process requirements include:

  • Substrate size up to approximately 1.5 cm × 1.5 cm
  • Substrate capable of withstanding the required transfer-process temperature
  • Cavity dimensions selected to provide adequate suspended-graphene yield
  • Cavity depth compatible with the transfer and suspension process

The Fermi level of graphene should not be treated as a single fixed value for all graphene samples. In ideal, charge-neutral monolayer graphene, the Fermi level is at the Dirac point. In real samples, however, the Fermi level can shift above or below the Dirac point because of electron or hole doping.

The Fermi-level position can be affected by carrier concentration, substrate interactions, adsorbed molecules, residues from fabrication or transfer, defects, electrostatic gating, and environmental conditions. Therefore, a Fermi-level value should be associated with the specific graphene sample and measurement conditions.

Graphene's work function is related to the position of its Fermi level relative to the vacuum level, but the two terms should not be used interchangeably. Work-function measurements, together with appropriate information about the electronic structure and measurement conditions, can help characterize the electronic properties of a graphene sample.

Carrier mobility is likewise sample dependent and can vary with graphene quality, carrier density, substrate, contamination, defects, temperature, and measurement method.

Reference #222239 for specs and pricing.

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Gallium Arsenide (GaAs) Substrates and the Fermi Level

An associate professor of physics requested the following information:

Looking for semiconductor samples for undergraduate students to use scanning tunneling microscopy to investigate the band gap at room temperature. I thought Gallium Arsenide (GaAs) could be an option because it can be cleaved. I would also be interested in Si samples if they were pre-cut to approximately 5 mm × 5 mm.

Can you confirm that these materials have a measurable band gap? The objective is for students to investigate the electronic structure using STM or scanning tunneling spectroscopy (STS).

Does GaAs Have a Band Gap?

Yes. Crystalline gallium arsenide is a direct-band-gap III-V semiconductor. At room temperature, its band gap is approximately 1.42 eV.

Silicon is an indirect-band-gap semiconductor with a room-temperature band gap of approximately 1.12 eV.

However, the existence of a bulk band gap does not by itself guarantee that a particular STM/STS experiment will reproduce the bulk band-gap value directly.

STM and STS measurements are highly sensitive to the electronic properties of the surface. Results can be affected by surface preparation, surface states, reconstruction, contamination, doping, sample conductivity, tip condition, tip-induced band bending, temperature, and measurement parameters.

Highly resistive semiconductor samples can also present practical difficulties for STM because tunneling measurements require a suitable electrical conduction path. The appropriate substrate resistivity and doping should therefore be selected according to the experimental setup.

Does Higher Resistivity Determine the Fermi Level?

No. Resistivity alone does not uniquely determine the Fermi-level position.

For a semiconductor, resistivity depends on carrier concentrations and mobilities:

ρ = 1 / [q(nμn + pμp)]

where q is the elementary charge, n and p are the electron and hole concentrations, and μn and μp are the corresponding carrier mobilities.

In ordinary nondegenerate p-type silicon, acceptor doping shifts the Fermi level toward the valence band. In n-type silicon, donor doping shifts it toward the conduction band. The exact position depends on dopant concentration, compensation, temperature, and material properties.

Therefore, it is not scientifically safe to infer a unique Fermi-level position simply from a statement that one wafer has higher resistivity than another.

Reference #263351 for specs and pricing.

Where Is the Fermi Level in Different Substrate Materials?

The Fermi level (EF) is the electron chemical potential of a material. Its position relative to the electronic bands depends on the material and can also depend on doping, defects, stoichiometry, temperature, interfaces, surface charge, and other conditions.

For semiconductors, it is particularly useful to describe the Fermi level relative to the valence-band maximum and conduction-band minimum.

Borofloat and Borosilicate Glass

Borofloat borosilicate glass is an electrical insulator with a large energy gap.

Insulators can still be described using an electron chemical potential, so it is misleading to say that glass simply “does not have a Fermi level.” However, assigning a precise Fermi-level position within the energy gap is generally more complicated than for a well-characterized crystalline semiconductor and can depend strongly on defects, composition, charge states, surfaces, and interfaces.

Silicon

For intrinsic crystalline silicon , the Fermi level lies near the intrinsic energy level, which is close to the middle of the band gap but is not necessarily exactly at midgap.

In n-type silicon, donor doping shifts the Fermi level toward the conduction band. In p-type silicon , acceptor doping shifts it toward the valence band.

With sufficiently heavy degenerate doping, the Fermi level can enter the conduction band in n-type material or the valence band in p-type material.

Gallium Arsenide (GaAs)

Gallium Arsenide (GaAs) is a direct-band-gap III-V semiconductor.

In intrinsic GaAs, the Fermi level lies near the intrinsic level within the band gap. It should not automatically be described as being exactly at the center of the gap.

Donor doping shifts the Fermi level toward the conduction band, while acceptor doping shifts it toward the valence band. The exact position depends on carrier concentration, dopant concentration, compensation, temperature, and material properties.

Sapphire (Al2O3)

Sapphire is a wide-band-gap electrical insulator rather than a conventional semiconductor.

As with glass, an electron chemical potential can still be defined. However, it is not scientifically appropriate to assume that the Fermi level of every sapphire substrate lies exactly at the middle of its energy gap. Defects, impurities, surfaces, interfaces, and charge states can affect its effective position.

Silicon Carbide (SiC)

Silicon Carbide (SiC) is a wide-band-gap semiconductor available in several polytypes, including technologically important 4H-SiC and 6H-SiC.

The band structure and band-gap energy depend on the SiC polytype. In n-type SiC, the Fermi level shifts toward the conduction band; in p-type SiC, it shifts toward the valence band.

A precise Fermi-level position requires information such as polytype, dopant species, dopant or carrier concentration, compensation, defects, and temperature.

Can a Wafer's Fermi Level Be Specified by Material Name Alone?

Generally, no. Saying that a substrate is silicon, GaAs, SiC, graphene, sapphire, or glass is usually not enough to assign a precise Fermi-level energy.

For semiconductor wafers, useful information can include:

  • Material and crystal structure or polytype
  • N-type, p-type, semi-insulating, or nominally undoped specification
  • Dopant species
  • Dopant or carrier concentration
  • Resistivity
  • Temperature
  • Compensation and defect concentration
  • Surface and interface conditions

With appropriate material parameters, the Fermi-level position can often be estimated theoretically. Experimental techniques can also characterize quantities related to the Fermi level, work function, carrier concentration, and electronic band structure.

What Is the Fermi Level?

The Fermi level (EF) is the electron chemical potential of a material and serves as an energy reference for describing the occupation of electronic states. Energy band diagram illustrating the Fermi level in a semiconductor

At thermal equilibrium and at a finite temperature, the probability that an available electronic state at energy E is occupied by an electron is described by the Fermi-Dirac distribution:

f(E) = 1 / [1 + exp((E - EF)/kBT)]

When E = EF and T > 0 K, the occupation probability is 50%.

At absolute zero, the Fermi-Dirac distribution approaches a step function: available states below the Fermi energy are occupied and available states above it are empty. Therefore, defining the Fermi level simply as a state with a 50% occupation probability at absolute zero is misleading.

This distinction is particularly important for semiconductors and insulators because the Fermi level can lie inside a band gap where an ideal crystal has no allowed bulk electronic states.

Fermi Level of Silicon Carbide (SiC)

A doctoral student working in materials research requested information about heavily doped n-type 4H-SiC for divacancy-qubit research.

Could UniversityWafer supply n-type 4H-SiC, on-axis (0001), with resistivity of approximately 0.015–0.028 Ω·cm? We would also like information about dopant concentration and wafer source because residual defects and Fermi-level position can affect divacancy studies.

Example material previously quoted:

  • 2" n-type 4H-SiC, on-axis (0001), 0.015–0.028 Ω·cm, approximately 0.33 mm thick
  • 3" n-type 4H-SiC, on-axis (0001), 0.015–0.028 Ω·cm, approximately 0.35 mm thick
  • 4" n-type 4H-SiC, on-axis (0001), 0.015–0.028 Ω·cm, approximately 0.35 mm thick

The referenced material was specified as nitrogen-doped n-type 4H-SiC, with a reported concentration on the order of 1018–1019 cm−3.

For a specific SiC wafer, the Fermi-level position should not be inferred from material name alone. It depends on factors including dopant concentration, dopant ionization, compensation, defects, temperature, and the SiC polytype.

For defect and quantum applications, the charge state of defects such as vacancies and divacancies can depend on the Fermi-level position and local electronic environment. Lot-specific characterization is therefore important when these properties are critical to an experiment.

Reference #277893 for specs and pricing.

How Can a Material's Fermi Level Be Determined?

There is no single universal measurement that directly provides an absolute Fermi-level position for every material. The appropriate method depends on whether the sample is a metal, semiconductor, insulator, two-dimensional material, or heterostructure and on which energy reference is required.

Experimental measurements often determine quantities related to the work function, band-edge positions, carrier concentration, or electronic density of states. These measurements can then be combined with known material parameters to determine or estimate the Fermi-level position.

Photoelectron Spectroscopy

Techniques such as ultraviolet photoelectron spectroscopy (UPS) and X-ray photoelectron spectroscopy (XPS) can provide information about occupied electronic states and their energies relative to the Fermi level. UPS is particularly useful for characterizing valence-band structure and work function.

Kelvin Probe and Kelvin Probe Force Microscopy

Kelvin probe measurements determine the contact potential difference between a sample and a reference probe. If the probe work function is known, the sample work function can be determined.

Kelvin probe force microscopy (KPFM) provides spatially resolved measurements of contact potential difference and can reveal local work-function variations across a surface.

These techniques measure quantities related to the work function; they should not be described as simply measuring the Fermi level directly without an energy reference or additional material information.

Electrical and Semiconductor Measurements

For a semiconductor with known band parameters, measurements of carrier concentration and temperature can be used to estimate the Fermi-level position.

Techniques such as Hall-effect measurements can provide carrier type, carrier concentration, and mobility. Capacitance-voltage measurements and other semiconductor-device characterization techniques can also provide information about doping and electrostatic potentials.

Fermi Level of Degenerately Doped Silicon Wafers

A researcher asked:

What does degenerately doped silicon mean? Does it refer to the Fermi level being very close to the valence-band edge or conduction-band edge?

A degenerately doped semiconductor contains a sufficiently high concentration of electrically active dopants that ordinary nondegenerate Maxwell-Boltzmann approximations are no longer adequate. Fermi-Dirac statistics must then be considered.

In heavily doped n-type silicon, the Fermi level moves toward the conduction band and, with sufficiently strong degeneracy, can lie within the conduction band.

In heavily doped p-type silicon, the Fermi level moves toward the valence band and can enter the valence band under sufficiently degenerate conditions.

There is no single universal carrier-concentration or resistivity value that defines degeneracy for every semiconductor. The condition depends on temperature, effective density of states, band structure, dopant concentration, and other material properties.

Very low resistivity can be a practical indication of heavy doping, but resistivity alone is not the fundamental definition of a degenerate semiconductor.

Reference #224057 for specs and pricing.

How Does the Fermi Level Depend on Temperature?

Temperature affects both the Fermi-Dirac occupation distribution and, in many materials, the position of the Fermi level itself.

As temperature increases, the Fermi-Dirac distribution broadens. Electronic states somewhat above EF acquire a greater probability of occupation, while states somewhat below EF acquire a greater probability of being empty.

In a semiconductor, the Fermi level should not be assumed to remain fixed as temperature changes. Its position can shift because carrier concentrations, dopant ionization, intrinsic carrier generation, and band-edge energies are temperature dependent.

For example, in an n-type semiconductor the Fermi level is generally closer to the conduction band than the intrinsic level over the extrinsic temperature range. At sufficiently high temperature, thermally generated electron-hole pairs become increasingly important, and the Fermi level tends toward the intrinsic level.

Similarly, the Fermi level of ordinary p-type material lies closer to the valence band than the intrinsic level, but it also tends toward the intrinsic level when intrinsic carrier generation becomes dominant.

Where Is the Fermi Level in an N-Type Semiconductor?

In an n-type semiconductor, donor doping increases the electron concentration and shifts the Fermi level toward the conduction-band edge relative to the intrinsic Fermi level.

Under nondegenerate conditions, the electron concentration can be related approximately to the Fermi-level position by:

n ≈ NC exp[-(EC - EF)/kBT]

where NC is the effective density of states in the conduction band and EC is the conduction-band edge.

Increasing donor concentration generally moves EF closer to EC. At sufficiently high doping, the semiconductor becomes degenerate and the nondegenerate approximation above is no longer valid.

Where Is the Fermi Level in a P-Type Semiconductor?

In a p-type semiconductor, acceptor doping increases the hole concentration and shifts the Fermi level toward the valence-band edge.

Under nondegenerate conditions:

p ≈ NV exp[-(EF - EV)/kBT]

where NV is the effective density of states in the valence band and EV is the valence-band edge.

Increasing acceptor concentration generally moves EF closer to EV. In sufficiently heavily doped p-type material, the Fermi level can enter the valence band.

What Is Fermi-Level Pinning?

Fermi-level pinning occurs when the electronic properties of a semiconductor surface or interface cause the local Fermi-level position and associated band bending to become relatively insensitive to changes that would otherwise shift the expected interface energy alignment.

This behavior is commonly associated with a high density of surface or interface electronic states. These states can accept or donate charge and strongly influence the electrostatic potential near the semiconductor surface.

Fermi-level pinning is particularly important at metal-semiconductor contacts because it can cause the actual Schottky-barrier height to depend less strongly on the metal work function than an ideal interface model would predict.

Pinning can also affect band bending, contact resistance, surface carrier concentration, transistor behavior, sensors, and other semiconductor devices.

The term does not mean that the Fermi level throughout the entire semiconductor becomes completely fixed regardless of doping. It primarily describes electronic behavior associated with a particular surface or interface.

What Is the Fermi Level of (Sr1−xLax)TiO3?

In La-doped strontium titanate, (Sr1−xLax)TiO3, substitution of La3+ for Sr2+ can provide additional electrons and produce n-type electronic behavior.

Increasing electrically active La doping generally increases the electron concentration and can move the chemical potential toward or into conduction-band states.

However, a specific numerical Fermi-level value cannot be determined from x alone. It can also depend on temperature, oxygen stoichiometry, defects, compensation, strain, carrier concentration, and the electronic structure of the particular sample.

Fermi Level vs. Band Gap

The Fermi level and band gap describe different properties.

The band gap (Eg) is the energy difference between the valence-band maximum and conduction-band minimum:

Eg = EC - EV

The Fermi level (EF) is the electron chemical potential and determines the statistical occupation of available electronic states.

In a semiconductor, EF can lie within the band gap even though an ideal crystal has no allowed bulk electronic states at that exact energy.

Why Is the Fermi Level Important?

The Fermi level is fundamental to semiconductor physics because its position helps determine equilibrium electron and hole concentrations and the electronic behavior of materials, surfaces, junctions, and contacts.

Understanding the Fermi level is important when studying:

  • N-type and p-type semiconductor doping
  • Carrier concentration
  • PN junctions
  • Metal-semiconductor contacts and Schottky barriers
  • MOS structures and transistors
  • Surface and interface band bending
  • Heterojunctions
  • Graphene and two-dimensional materials
  • Semiconductor defect charge states
  • Photovoltaic and optoelectronic devices

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