# MEASUREMENT PRINCIPLES

Napson is the only vendor in the world, who manufactures and sells 2 kinds of resistance measurement equipment.
Contact types with 4 point probe and Non-contact types, such as eddy current measurement.
Here are the electrical resistance principles which can be measured by Napson resistance measurement systems.

## The definition of resistance measurement

Generally, electrical resistance (Resistance) is used as evaluation of the conductivity (Ease of electric conductance) of a substance or material.

“As a valuation basis of electrical resistance, the unit Ω(ohm)is used.”

### Electric Resistance ＝ Ω (Ohm)

R = V/I　*V= Voltage I= Current

The insulation resistance, for example, measured by a digital multi-meter (insulation resistance tester) is denoted by the unit, ohm.

The electrical resistance for a semiconductor or thin film measurement is defined by standards, such as SEMI (ASTM) and JIS.

### Resistivity＝ Ωcm (ohm_centimeter)

Resistivity is used for “volume resistance” for a substance.
[or Specific lectrical resistance, Volume resisance]

When it expresses the electrical resistance of a certain material, such as a silicon wafer, bulk or a conductive rubber plastic, this term is used.

Electrical resistance: When the electric resistivity is ρ, the length is L and cross-sectional area for a conductor is A
The R is givin by ;

R ＝ ρ × [L/A]

Where ρ is given by

ρ ＝ V/I × [A/L]

*When the unit is set to Ω-cm, the volume is shown by cubic measure, such as 1cm x 1cm x 1cm.
It may be shown by Ω-m (ohm meter) depending on the measuring object. ### Sheet resistance ＝ Ω/□ (ohm per square)

The “surface resistance” for a material

When it expresses the electrical resistance of a sheet (such as a thin film or a film-like substance), this term is used.

When it expresses three-dimensional conductivity, resistance is givin by

R ＝ ρ × L/A ＝ L/W ×ρs

When the length of a sample[L] and the width[W]are equal, the resistance[R] and he sheet resistance[ρ] will become equal.

“Moreover, Sheet resistance[ρs] is the value which divided resistivity[ρ] by thickness[t] .” ## Contact : 4 point probe measurement

This section provides an overview of the resistance measurement principle of 4 point probe method.
(details of the principle are explained in the document).

4 point probe method can measure resistance ranges from 1E-3 (1m) to 1E+9 (1G) Ω/sq level.
It is the basic measurement method for electrical resistance measurements in a wide range of fields.

The measurement method:
1) Four linearly aligned probes are set on the surface of a specimen.
2) A constant current is applied between the two outer probes.
3) The resistance is determined by measuring the potential difference between the two inner probes.

As shown in the picture below, this principle is applicable to both resistivity and sheet resistance.
Our 4 point measuring products are in compliance with JIS and ASTM standards.

### Measurement principle(Resistivity) ### Measurement principle(Sheet Resistance) http://www.monozukuri.org/mono/db-dmrc/pvdcvddb/outline/evaluation/fourprobeelectricalresistivity.html

The Napson 4 point probe method instrument complies with the following Japanese Industrial Standards (JIS)and American Society for Testing and Materials (ASTM).

Japan Industrial Standards Testing Method Of Resistivity For Silicon Crystals And Silicon Wafers With Four-point Probe Testing method for resistivity of conductive plastics with a four-point probe array Standard Test Method for Measuring Resistivity of Silicon Wafers With an In-line Four-Point Probe Standard Test Method for Sheet Resistance of Silicon Epitaxial, Diffused, Polysilicon and Ion-implanted Layers Using an In-Line Four-Point Probe with the Single-Configuration Procedure Standard Test Method for Sheet Resistance of Thin Metallic Films With an Collinear Four-Probe Array Standard Test Method for Sheet Resistance Uniformity Evaluation by In-Line Four-Point Probe with the Dual-Configuration Procedure

## Non-contact; Eddy current measurement

This describes the resistance measurement principle for a non- contact type (eddy current method).

The non-contact type (eddy current method) performs measurement of resistivity and sheet resistance by using the eddy current which occurs by electromagnetic induction within a specimen.

An eddy current is circular current which forms in a conductor due to electromagnetic induction [Lenz’s law], when the magnetic flux which passes along a conductor changes. The magnetic flux is changed by adding high frequency component between the probes (magnetic body), arranged on both

sides (upper and lower sides) between the fixed gap, where an eddy current flows through the sample inserted between gaps.
(*Napson can offer other models with one side probe version)

At this time, an eddy current flows into the direction which resists change of the magnetic flux by electromagnetic induction [Lenz’s law]. Pc = Et・I = Et(Io + Ie）

Pc : High-frequency consumed power
I : High-frequency drive current
Et : High-frequency voltage
Io : High-frequency drive current [Without sample]
Ie : High-frequency drive current [at the sample measurement]

The absorption of high-frequency power in the sample by the generated eddy current is lost as Joule heat.

The resistivity/sheet resistance of the sample can be measured with the non-contact method by measuring the absorption value of high-frequency power,

because this absorption and the conductivity (reciprocal of resistivity) and thickness of a sample have a direct relationship.
(*The Joule heat is so small that neither the sample nor the area is affected.)

Moreover, the influence of contact resistance in the case of a contact type can be eliminated.

Explanation of Non-contact (Dual probes ) and Non-destructive(Single probe)

http://www.monozukuri.org/mono/db-dmrc/pvdcvddb/outline/evaluation/eddycurrentelectricalresistivity.html

As mentioned above, the resistivity ( or sheet resistance) is measured by inserting a sample in the gap between the probes.

Therefore, restrictions on the form of a probe depend upon the thickness and corresponding size of a sample.

• Restrictions of the thickness of a sample : the gap between probes is usually 2 mm.
• Restrictions of the size of a sample :A large specimen has a limit on the measurement head. NAPSON offers a single-sided and hand probe technology for easy handling and measurement of large or thick samples, as shown on the left.

[Non-destructive(Single probe) type system : EC-80P]