What is a Subsrate Sheet Resistance?

university wafer substrates

What is the Sheet Resistance of My Wafers?

A senior engineer requested the following wafer on the silicon wafers that they purchased from us.

I interested in a quote for silicon wafers. Common specs for all varieties: Bare (no thermal oxide), 200mm diameter, 725-1200um thick, SSP, what is your typical spec on miscut degree range? Varieties: 1. Si(100) with <100> notch orientation with no doping (more accurately, looking for high wafer sheet resistance, say greater than 100 ohms). 2. Si(110) with fixed notch orientation (whatever is most common). Can you quote with common doping (lowest cost) and undoped for high wafer resistance? 3. Si(111) with fixed notch orientation (whatever is most common). Can you quote with common doping (lowest cost) and undoped for high wafer resistance?

What is the sheet resistance of the following?

Si(110) with fixed notch orientation Bare (no thermal oxide), 200mm diameter, 725-1200um thick, SSP. Qty. 25pcs   

UniversityWafer, Inc. Quoted:

Sheet resistance is <100 Ohm.cm and on-axis +/-1deg.

Reference  279206 for specs and quantity.

Get Your Quote FAST! Or, Buy Online and Start Saving Today!

How to Calculate Sheet Resistance

  1. Understand the Formula:

    Sheet resistance is calculated as:

    Rs = ρ / t

    Where:

    • Rs: Sheet resistance (Ω/□)
    • ρ: Resistivity of the material (Ω·cm)
    • t: Thickness of the thin film (cm)
  2. Obtain Material Resistivity (ρ):

    Use a four-point probe or other methods to measure the resistivity of the material. Resistivity depends on material properties, doping concentration, and temperature.

  3. Measure Film Thickness (t):

    Use techniques such as ellipsometry, profilometry, or cross-sectional scanning electron microscopy (SEM). Ensure the thickness is uniform across the film.

  4. Plug Values into the Formula:

    Divide the resistivity by the thickness to calculate Rs. Example:

    If ρ = 1 Ω·cm and t = 0.001 cm:
Rs = ρ / t = 1 / 0.001 = 1000 Ω/□
  5. Alternative Method: Four-Point Probe:

    Place four probes in a line on the thin film. Measure the voltage drop (V) and the current (I) through the film. Calculate the sheet resistance using:

    Rs = (π / ln(2)) × (V / I) ≈ 4.532 × (V / I)

    This method accounts for film uniformity and eliminates contact resistance errors.

  6. Account for Temperature Effects:

    Resistivity can change with temperature, so ensure measurements are done under controlled conditions.

By following these steps, you can accurately calculate sheet resistance for semiconductor and thin-film applications.

 

What is Sheet Resistance?

Sheet resistance is a measure of resistance for thin films of uniform thickness and is often used in the context of semiconductor and thin-film materials. It describes the resistance of a square-shaped segment of the film and is expressed in ohms per square (Ω/□).

Key Points:

  1. Definition:

    • Sheet resistance is the resistance between opposite edges of a square of the material, independent of the size of the square. It's defined as: Rs=ρtR_s = \frac{\rho}{t} Where:
      • RsR_s is the sheet resistance in ohms per square (Ω/□),
      • ρ\rho is the resistivity of the material (Ω·cm),
      • tt is the thickness of the film (cm).

  2. Unit:

    • The unit is ohms per square (Ω/□). It's not simply "ohms" because the value depends on the geometry (the "square" reference).

  3. Why It's Useful:

    • In thin films, measuring bulk resistivity (ρ\rho) is impractical since the film is very thin. Sheet resistance simplifies the characterization of thin materials.
    • It is widely used in semiconductor manufacturing (e.g., characterizing doped layers, metallic interconnects, or transparent conductive coatings).

  4. Applications:

    • Semiconductors: To measure doping levels in layers of silicon.
    • Thin Films: To evaluate metallic or resistive layers in electronic devices.
    • Solar Panels: To analyze transparent conductive coatings.

  5. Measurement Techniques:

    • The four-point probe method is commonly used to measure sheet resistance. It eliminates the effects of contact resistance, which can distort readings when using a simple two-probe method.

Example:

If a thin silicon layer has a resistivity of 1 Ω⋅cm and a thickness of 0.01 cm the sheet resistance would be:

Rs = p/t = 1  Ω/0.01 cm = 100  Ω/□

Sheet resistance is a critical parameter for designing and analyzing electronic and photonic devices where thin layers are involved.