Noncontact measurement of transport properties
of long-bulk-carrier-lifetime Si wafers using
photothermal radiometry
Alex Salnick, Andreas Mandelis, and Claude Jean
a)
Department of Mechanical and Industrial Engineering, Photothermal and Optoelectronic Diagnostics
Laboratory, University of Toronto, 5 King’s College Road, Toronto, Ontario M5S 3G8, Canada
Received 12 June 1996; accepted for publication 22 August 1996
A theoretical model for the photothermal radiometric signal from semiconductors of finite thickness
has been used to measure simultaneously the carrier diffusion coefficient, carrier lifetime, and
surface recombination velocity of FZ Si wafers with very long bulk carrier lifetimes industrial
microelectronic grade. The results showed the importance of accounting for the finite thickness of
the substrate in obtaining accurate measurements of these parameters using the entirely
noncontacting radiometric approach. © 1996 American Institute of Physics.
S0003-69519602143-2
Photothermal infrared radiometric PTR measurements
of photoexcited excess carrier lifetime in a semiconductor
using both frequency domain
1–3
and rate-window
4,5
detec-
tion configurations have been reported. A semi-infinite semi-
conductor sample approach assuming the carrier diffusion
length much shorter than the sample thickness has been used.
However, for long lifetime 100 s and/or thin 500
m semiconductor wafers the foregoing approximation is
not valid and the effects introduced by a finite thickness
should be taken into account.
In this letter we report a feasibility study of the PTR
technique to measure carrier transport parameters in indus-
trially relevant long bulk lifetime FZ–Si wafers.
It has been shown earlier that the photoinjected excess
carrier concentration Nx m
-3
as a solution of the one-
dimensional carrier continuity equation for a finite semicon-
ductor of thickness L m with optical absorption coefficient
m
-1
, minority carrier lifetime s, carrier diffusivity
D
n
m
2
/s and the front and back surface recombination ve-
locities s
1
and s
2
m/s , respectively, are
N x =
I
0
h v D
2
-
n
2
1
2
-
2
1
e
-L
+
n
2
-
1
e
-2
n
L
e
-
n
x
+
1
-
2
e
-L
-
n
2
-
1
e
-2
n
L
e
x -2 L
-e
-ax
, 1
where
1
=
D
n
n
-s
1
D
n
n
+s
1
,
2
=
D
n
n
+s
2
D
n
n
-s
2
,
2
1
=
D
n
+s
1
D
n
n
+s
1
,
2
=
D
n
-s
2
D
n
n
-s
2
,
and I
0
W cm
-2
is the light flux, hv is the photon energy
J, and the complex plasma-wave vector
n
is defined as
n
=
1 +i / D
n
. 3
The PTR signal from a plasma-dominated semiconductor has
been shown to be proportional to
6
S
PTR
0
L
N x dx . 4
Upon calculating the foregoing integral for Nx from Eq.
1 we obtain
S
PTR
=
const
D
n
n
2
-
n
2
1
2
-x
2
1
e
-L
+
n
+
1
e
-
n
L
-
2
e
-L
1 -e
n
L
2
-
1
e
-2
n
L
-
n
1 -e
-L
. 5
Assuming a strong optical absorption at the front surface
L1 and, in addition, |
n
| , Eq. 5 reduces to
S
PTR
= const
1 -e
-
n
L
n
D
n
n
+s
1
2
+e
-
n
L
2
-
1
e
-2
n
L
6
and for rough unpolished back surface ( s
2
D
n
|
n
| )
2
-1 in Eq. 2 and the PTR signal can be written as
S
PTR
=
const
D
n
n
D
n
n
+s
1
1 -e
-
n
L
2
1 +
1
e
-2
n
L
7
or
S
PTR
=S
PTR
1 -e
-
n
L
2
1 +
1
e
-2
n
L
, 8
a
MITEL S.C.C. Bromont, Que ´bec J0E 1L0, Canada.
2522 Appl. Phys. Lett. 69 (17), 21 October 1996 0003-6951/96/69(17)/2522/3/$10.00 © 1996 American Institute of Physics
Downloaded¬20¬Jul¬2008¬to¬128.100.49.17.¬Redistribution¬subject¬to¬AIP¬license¬or¬copyright;¬see¬http://apl.aip.org/apl/copyright.jsp