Optical Diagnostics and Imaging - Applied Optics Fundamentals and Device Applications - page 302

damaged regions, respectively. These values are calculated using values of
electron mobility from Blakemore [8] and corresponding anticipated free
carrier concentrations of between 10 16 and 10 18 cm −3 . Under the assumption
that the effective radius of the probe is 0.75 μm, the corresponding spreading
resistance values range between 4 and 186 Ω. The following table illustrates
these relations.

DegreeofDamage None Some Full

Electron concentration (cm −3 ) 10 18 10 17 10 16

Mobility (cm 2 /V/s) 3300 5300 7100

0.19 × 10 −2 1.2 × 10 −2 8.8 × 10 −2

Resistivity (Ω-cm)

4 25 186

Spreading resistance (Ω)

There are several approaches which can be used in applying spreading resis-
tance measurements to study damage in GaAs optical channel waveguides,
for example. The easiest and most straightforward is to expose a separate
unmasked sample of GaAs to the incident beam simultaneously with the
exposure of the main pattern sample. The separate sample can then be sac-
rificed and studied separately. Alternatively, the separate sample could be a
selected region on the main wafer, to be split off and studied separately. It is
also possible, though more tedious, to sacrifice and study the actual channels
with this method. The major difficulty is in achieving adequate alignment
between the channel, the lapping edges, and the electrodes.

6.7 MobilityMeasurement
Conwell and Weisskopf [9] determined a relationship between the carrier
concentration in a semiconductor and the carrier mobility:

−1

⎧

2

⎫

⎡ ⎤

3
2

⎛ ⎞

⎪ ⎪

⎢
⎢
⎢

⎥
⎥

2

64 π ε ( 2 kT ) 12 π ε kT

⎜
⎜

⎟
⎟

s s

μ = ln 1+ (6.12)

⎨ ⎬ 1

2

1
3 ⎪

⎪

⎥ ⎪

⎪

* )

Nq m

3

( q N

2

⎝ ⎠

⎣ ⎦

⎩ ⎭

A differential four-point van der Pauw measurement (Figure 6.9) can be per-
formed so that successive chemical etches of the wafer (each of known thick-
ness) will provide u ( d ). The N D ( d ) information obtained with a Post Office
profile provides