Chapter 1. RESISTIVITY. 1.1 INTRODUCTION 1.2 THE FOUR-POINT PROBE 1.3 WAFER MAPPING 1.4 RESISTIVITY PROFILING 1.5 CONTACTLESS METHODS 1.6 CONDUCRIVITY TYPE. 1.1 INTRODUCTION. The resistivity in the ingot is not uniform. The resistivity of epitaxial layers is uniform.
the contact resistance Rc , the spreading resistance Rsp ,
and the semiconductor resistance Rs
F1 corrects for sample thickness
F2 corrects for lateral sample dimensions
F3 corrects for the distance between
probe and sample edges
For conducting bottom
For F2 and F3 ≒ 1
Wafer thickness correction factors versus normalized wafer thickness;
t is the wafer thickness,
s the probe spacing.
For circular wafers D=wafer diameter;
for rectangular samples
Parallel to a non-conducting boundary
Perpendicular to a conducting boundary
Boundary proximity correction factors versus normalized distance d from
the boundary. F31 and F32 are for nonconducting boundaries, F33 and
F34 are for conducting boundaries.
Arbitrarily shaped sample
with four contacts.
A Greek cross sheet resistance test structure.
1. Sample size
2. Minority / majority carrier injection
3. Probe spacing
For small probe variations, the correction factor is
Recommended four-point probe current versus Si resistivity
6. High resistivity material
Temperature coefficient of resistivity versus sample resistivity for 18oC≦T≦28oC
for (a) Si, (b) Ge. For p-Si, the curve is valid only for boron-doped Si.
the doping uniformity, especially the ion
p(n) type impurity is implanted into n(p)
substrate with a dose Φ1 and energy E1.
The desire low dose impurity is implanted
with a dose Φ2 and energy E2,no
Φ2 ~10-2Φ1 and E2 ~ 80%-90% E1.
Measurement is performed right after the
Schematic diagram of the modulated photoreflectance apparatus
cause the volume, thermoelastic, and the optical
reflectivity to change.
The laser is modulated at a certain frequency thus
establish a periodic temperature variation in the wafer.
A probe laser is used to detect these changes, mainly
The thermal wave induced changes are proportional to
the implanted ions.
1011~1015 cm-2, contactless, non-destructive.
forming excess carrier distribution. The carrier density in the
substrate is constant.
UV shined on implant sensitive dye
Transparent substrate (glass)
No semiconductor wafer is used.
Compare the final to initial (before and after) optical transparency with calibrated results.
For uniformly doped sample.
the surface into the sample.
profiling, and secondary ion mass spectrometry.
Anodic oxidation method is adopted to grow a fixed thickness of oxide layer such that a certain portion of the silicon surface is consumed by etching the grown oxide.
This method has a good reproducibility.
Spreading resistance bevel block and the beveled sample with probes and
the probe path shown by the dashed line.
For a cylindrical contact
A cylindrical contact of diameter 2r to a semiconductor.
The arrows represent the current flow.
VT is the rms rf voltage.
n is the coil’s number of turns.
σ is the semiconductor conductivity.
t is the semiconductor thickness.
If VT is fixed, then
IT is proportional to ∫σ(x)dx or 1/ρs
For the above results to be valid, the sample thickness must be less than the skin depth, such that the current can be uniformly flow through the sample.
The skin depth is given by
Identifying flats on silicon wafers.
Usually, the primary flat is along the 〈110〉direction.
(C) Equivalent circuit for (b), and (d) experimental data adapted from ref.88.