Substrates Van der Pauw Method 

UniversityWafer, Inc. supplies semiconductor wafers, fused quartz substrates, gallium phosphide wafers, thin-film materials, and research-grade substrates used for Van der Pauw resistivity, Hall effect, carrier concentration, and mobility measurements. These substrates support electrical characterization of thin films, amorphous silicon coatings, high-resistivity materials, and uniformly doped semiconductor samples for university, laboratory, and device research.

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GFused Quartz van der Pauw Measurements

A PhD candidate studying materials engineering requested the following quote.

Do you have amorphous p-doped Si wafers, or amorphous p-doped thin films deposited on wafers? What are the prices and lead times, because we would also need carrier concentrations.

We need a carrier concentration of 1015/cm3. We need the material to be fully amorphous, and we do not need it to be a wafer. A 10µm film deposited on a substrate like glass or fused quartz is OK too – we just need the film to 100% amorphous. We need around a 2inch wafer, and we need highly uniform carrier concentrations, preferably with Hall/van der Pauw measurements confirming the values.

The substrate can definitely be fused quartz, but the film on top of it must at least be a 10µm thick coating of p-type doped amorphous silicon.

Reference #213346 for specs and pricing.

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Measuring Resistivity of Gallium Phosphide Subsstrates

A staff scientist requested a quote for the following.

I see your sites have ZnSe and GaP wafers. I am not using them for THz applications. I am looking for thin, highly electrical resistive (undoped or semi-insulating), double side polished. Your site has some resistivity info on GaP, however, I cannot find any electrical parameters on ZnTe (mostly looking for resistivity). Could you provide price estimates and lead time info?

Question:

About general resistivity of the following wafer spec, how are they normally measured with these wafers? With probes on certain point of the wafer? (what kind of probes?) Or with electrical coatings on both sides?

Item Qty. Description
IM18. 1/2/4 2 are Prime Grade, 1 with a scratch on the back, 1 with a scratch on the top Gallium Phosphide wafers, Prime Grade, P/E 2"Ø×370±20µm, SI GaP:Cr[100], Ro=2E10 Ohmcm,
Nc=4.1E06/cc, u=75cm²/Vs, EPD<5E4/cm², One-side-polished, back-side matte etched, SEMI Flats, Sealed under nitrogen in single wafer cassette.

Answer:

The resistivity is measured on square shaped witness wafers with the 4-point Van der Pauw method.

Reference #317823 for specs and pricing.

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What Is The van der Pauw Method?

The van der Pauw method is a widely used technique for measuring the electrical resistivity and Hall effect of thin, flat, uniformly thick materials, typically semiconductors or conductive thin films. Named after Dutch physicist Leo J. van der Pauw, this method is especially useful for materials that do not have a simple rectangular or regular shape, such as circular or irregularly shaped samples.

Key Concepts and Procedure

  1. Sample Requirements:

    • The sample must be uniformly thick.
    • The sample should have a homogeneous material composition.
    • It should have no holes or other interruptions in continuity.
    • The sample must be thin enough that current flows primarily in the plane of the material.

  2. Electrode Placement:

    • Four ohmic contacts are placed on the periphery (typically near the edges) of the sample, spaced equally as much as possible.
    • The method requires only that contacts be on the boundary, not necessarily in specific locations, which is helpful for irregularly shaped samples.

  3. Resistivity Measurement:

    • Current is passed between two adjacent contacts, and the resulting voltage is measured across the opposite two contacts.
    • This process is repeated in different configurations (often four measurements in total with different pairs of contacts) to compute the sample's resistivity.

  4. Resistivity Calculation:

    • The resistivity is calculated using the van der Pauw formula, which accounts for the different measured voltages and the geometry of the sample:e−πRAB,CD/Rs+e−πRBC,DA/Rs=1where Rs is the sheet resistance, and RAB,CD and RBC,DA are the resistances measured across the different configurations.
    • This formula requires solving for Rs, often through iteration or approximation.

  5. Hall Effect Measurement (optional):

    • If a magnetic field is applied perpendicular to the sample, the van der Pauw method can also be used to measure the Hall voltage, enabling the calculation of the carrier concentration and mobility of the material.

Advantages of the van der Pauw Method

  • Versatile: Applicable to samples with irregular shapes.
  • Minimal Contact Area Required: Only four small contacts are needed, simplifying sample preparation.
  • Non-destructive: Generally does not require modification of the sample structure.

Applications

The van der Pauw method is widely used in semiconductor research, materials science, and MEMS device fabrication (such as the optical MEMS work you’re involved in) because it allows for accurate resistivity measurements in small or irregularly shaped samples.

Van der Pauw electrical measurement method schematic for semiconductor wafer sheet resistance testing