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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 = 12. 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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Non-uniform doped sample:

Resistivity and Conductivity

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

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)

Current meter

Rectification method

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. 93~98Hall 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