1. Semiconductor Materials and Device Characterization
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

2. 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

4. 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

5. 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

6. Figure Scaling

7. Linear and Log Scaling

8. Four Point Probe: principle and equation

9. Resistivity and Conductivity
Non-uniform doped sample:
D. K. Schroder, p. 10

10. Doping Profile and depth: --How to determine Na-depth(x)?
D. K. Schroder, p. 29

11. How to determine Na-depth(x)?
Using eq. (1.38)
ρs = ρ/t ?
D. K. Schroder, p. 30

12. Identifying flats on silicon wafers:
D. K. Schroder, p. 42

13. Current flow through a metal-S.C junction
(1) Rectification contact:

16. n-type substrate:
Rectifying contact

17. Current flow through a metal-S.C junction
(2) Ohmic contact:

18. Ohmic contact with n-type S.C

19. Ohmic contact with p-type S.C

20. 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

21. Obtain doping density from resistivity
D. K. Schroder, p. 47

22. Thinking:
D. K. Schroder, p. 48

23. Homework 1:
(D. K. Schroder, ISBN: )
Review suggested: ~p. 44
Preview suggested:
a. gate capacitance
b. C-V curve

24. Hall effect (principle, measurement configuration)
Self-study and review
Review:
p. 43
Section 2.4.2, exercise 2.2
Preview:
p. 93~98
Hall effect (principle, measurement configuration)

25. 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