Four point probe

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??????? Semiconductor Materials and Device
Characterization Topic 1 resistivity and Four
point Probe Instructor Dr. Yi-Mu
Lee Department of Electronic Engineering Nationa
l United University
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Resistivity Four point probe
Features two probes carry current two probes
sense the voltage First proposed by Wenner in
1916 Target from resistivity to S.C. doping
profile
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Four point probe
Voltage probes are very high impedence (1012
ohms) Negligible why? (due to a very small
current) Rc (contact resistance) Rp (probe
resistance) Rsp (spreading resistance) Rsp
occurs when current flows from the probe to S.C
and from S.C to probe Special Features ?
2?s (V/I) 1. S 1.588mm, 2?s 1 2. Smaller
probe spacings allow measurements closer to wafer
edges
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Four point probe
Special Features ? 2?s (V/I) 1. S 1.588mm,
2?s 1 2. Smaller probe spacings allow
measurements closer to wafer edges
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Figure Scaling
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Linear and Log Scaling
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Four Point Probe principle and equation
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Resistivity and Conductivity
Non-uniform doped sample
D. K. Schroder, p. 10
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Doping Profile and depth --How to determine
Na-depth(x)?
D. K. Schroder, p. 29
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How to determine Na-depth(x)?
Using eq. (1.38)
?s ?/t ?
D. K. Schroder, p. 30
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Identifying flats on silicon wafers
D. K. Schroder, p. 42
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Current flow through a metal-S.C junction
(1) Rectification contact
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n-type substrate
Rectifying contact
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Current flow through a metal-S.C junction
(2) Ohmic contact
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Ohmic contact with n-type S.C
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Ohmic contact with p-type S.C
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Determine conductivity type using 4-point probe
Rectification method
Current meter
n-type silicon --When ac voltage at probe 2 is
Then voltage drop V42 is small (because
metal-S.C. is forward biased) --When ac voltage
at probe 2 is - Then voltage drop V42 is
large (because metal-S.C. is reversed biased)
Fig. from D. K. Schroder, p. 43
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Obtain doping density from resistivity
D. K. Schroder, p. 47
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Thinking
D. K. Schroder, p. 48
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Homework 1 1.14 1.16 1.19 (D. K. Schroder,
ISBN 0-471-24139-3) Review suggested p.
44 Preview suggested a. gate capacitance b.
C-V curve
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Self-study and review

• Review
• p. 43
• Section 2.4.2, exercise 2.2
• Preview
• p. 9398
• Hall effect (principle, measurement
  configuration)

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Homework

• To measure the sheet resistance of a resistor
  layer, taking into account the parastic series
  contact resistance, a test structure consisting
  of resistors with the same width and different
  length is provided. Measuring the resistances of
  the resistors with lengths L1 10 µm and L2 30
  µm, the following values are obtained R1 365
  ohm and R2 1085 ohm, respectively. If the width
  of the resistors is 5 µm, determine the sheet
  resistance and the contact resistance values.
• Chapter 2
• 2.1
• 2.8