Sheet resistance

The (specific) sheet resistance describes the electrical resistance of an electrically conductive layer of such a small thickness that electrical current flows through it only parallel to the layer , i.e. H. the current enters at one end face and exits at the opposite end face.

The electrical component sheet resistance is a typical example, but also cover electrodes of photodiodes, solar cells or the metal layer structures of printed circuit boards and integrated circuits .

definition

Geometry to define the electr. Resistance (left) or sheet resistance (right). If the current flows through the layer parallel to the double arrow on the letter L, then the entry and exit areas are units of area. ${\displaystyle A=d\cdot B}$

The specific sheet resistance of a resistive layer of the thickness with an isotropic specific resistance is ${\displaystyle R_{\Box }}$ ${\displaystyle d}$   ${\displaystyle \rho }$

${\displaystyle R_{\Box }={\frac {\rho }{d}}}$

I.e. the thinner the layer ( small), the higher its sheet resistance (with constant specific resistance ). ${\displaystyle d}$ ${\displaystyle \rho }$

Since the following also applies:

${\displaystyle \rho ={R}\cdot {\frac {A_{el}}{L}}}$

With

• electrical resistance ${\displaystyle R}$
• Electrode areas (electrodes over the entire width of two opposite edges ) ${\displaystyle A_{el}=d\cdot B}$ ${\displaystyle B}$
• length ${\displaystyle L,}$

follows

${\displaystyle \Rightarrow R_{\Box }={R}\cdot {\frac {A_{el}}{L\cdot d}}={R}\cdot {\frac {d\cdot B}{d\cdot L}}={R}\cdot {\frac {B}{L}}}$

With the help of the specific sheet resistance of a resistor layer, the size of a resistor made from it can be determined based on its geometry:

${\displaystyle \Leftrightarrow R={R_{\Box }}\cdot {\frac {L}{B}}}$

This is true for a square layer:

Edge lengths (any size) ${\displaystyle B=L}$

the sheet resistance corresponds to the resistance:

${\displaystyle R_{\Box }=R}$

unit

Since the specific resistance has the unit Ωm, the unit of the sheet resistance is identical to the unit Ω ( Ohm ) of the electrical resistance: ${\displaystyle \rho }$

${\displaystyle \left[R_{\Box }\right]={\frac {\left[\rho \right]}{\left[d\right]}}={\frac {\Omega \cdot {\text{m}}}{\text{m}}}=\Omega }$

For a better differentiation, the sheet resistance is therefore often given in the unit . Such an indexing of physical units is not provided for in the standards DIN 1301 and ISO 31 . ${\displaystyle \Omega /\Box }$

Measurement

The sheet resistance of a layer can be measured, for example, with the help of the four-point method , the special Van der Pauw method or as a non-contact measurement with a special eddy current tester. Often you can also calculate back from the known geometry. With the four-point method, the influence of the contact resistance on the measurement is eliminated by generating a current flow between two contact points, while the voltage drop is measured across two further contact points. With the non-contact sheet resistance measurement / sheet resistance measurement with eddy current, an electromagnetic alternating field is generated in the material, the opposing field of which is evaluated by the measuring sensor.

example

The sheet resistance of a copper layer (ρ ≈ 1.72 · 10 ⁻⁸  Ωm) with a thickness of just under 35 µm (as is often used on electrical circuit boards ) is just under 0.5 mΩ.

application

The sheet resistance measurement is often used to assess the homogeneity of electrically conductive or semiconducting materials or layers. Typical applications can be found, for example, in the quality inspection of TCO , metallic layers or layers made of conductive nanomaterials on architectural glass, polymer films, displays, OLED and in the wafer or photovoltaic industry. The contacting four-point method is mostly used for individual testing of hard, insensitive materials, while the non-contact eddy current method is used for scanning entire layers, for inline monitoring of the coating process and for measuring sensitive or encapsulated layers.

literature

• Dieter K. Schroder: Semiconductor Material and Device Characterization . 3rd edition. Wiley-Interscience et al. a., Hoboken NJ 2006, ISBN 0-471-73906-5 .

Web links

• Sheet resistance measurement Measurement of sheet or sheet resistance of thin conductive layers on insulating substrates, e.g. B. Metallization / Wafers / ITO / CVD / PVD
• Contactless sheet resistance measurement of conductive and semiconducting layers

swell

1. ↑ Article copper
2. ↑ Article Specific Resistance