半導體量測技術
Semiconductor Materials and Device Characterization
Topic 1: resistivity and Four point Probe
Instructor: Dr. Yi-Mu Lee
Department of Electronic Engineering
National 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:
ρ= 2Πs (V/I)
1. S = 1.588mm, 2Πs = 1
2. Smaller probe spacings allow measurements closer to wafer edges
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Four point probe
Special Features:
ρ= 2Πs (V/I)
1. S = 1.588mm, 2Πs = 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)
ρs = ρ/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. 93~98
Hall effect (principle, measurement configuration)
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Homework:
1. 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
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