Elevated temperature measurement of the minority carrier lifetime in the depletion layer of a semiconductor wafer

A method for determining the depletion layer minority carrier lifetime .tau..sub.o in a depletion layer of a semiconductor wafer includes the following. A depletion layer is induced on a surface of the wafer. The wafer is heated to a temperature T.sub.1. A surface photovoltage is induced on the surface of the wafer with modulated light. A surface photovoltage .DELTA.V.sub.o1 is measured at a selected point of the wafer, at T.sub.1 and at a low light modulation frequency where the surface photovoltage is substantially independent of frequency. A surface photovoltage .DELTA.V.sub.1 is measured at the selected point, at T.sub.1 and at a higher light modulation frequency .omega. which is within a frequency range where the surface photovoltage is inversely proportional to frequency. A surface photovoltage response time .tau..sub.max1 is determined by the relationship: .tau..sub.max1 =.omega..sub.1.sup.-1 [(.DELTA.V.sub.o1 /.DELTA.V.sub.1).sup.2 -1].sup.1/2. The wafer is heated to a temperature T.sub.2, greater than the temperature T.sub.1. A surface photovoltage .DELTA.V.sub.o2 is measured at the selected point, at T.sub.2 and at the low light modulation frequency. A surface photovoltage .DELTA.V.sub.2 is measured at the selected point, at T.sub.2 and at a frequency .omega..sub.2 in a range where the photovoltage is inversely proportional to frequency. A surface photovoltage response time .tau..sub.max2 is determined by the relationship .tau..sub.max2 =.omega..sub.2.sup.- 1[(.DELTA.V.sub.o2 /.DELTA.V.sub.2).sup.2 -1].sup.1/2. The room temperature depletion layer lifetime .tau..sub.o is determined by the relationship: EQU .tau..sub.o =.tau..sub.max2 .multidot.exp [(T.sub.2 -T.sub.0)E.sub.A /kT.sub.o .multidot.T.sub.2 ], PA1 where T.sub.o is room temperature.

BACKGROUND OF THE INVENTION 
The invention relates to determining the minority carrier lifetime in the 
depletion layer of a semiconductor wafer. 
The performance and reliability of semiconductor electronic and 
optoelectronic devices, and the integrated circuits into which they are 
incorporated, depends in part upon the purity of the semiconductor from 
which the devices are made, and, in particular, on the level of 
contaminants or impurities which may be introduced during manufacture and 
processing. One measure of the level of impurities used in quality control 
is the determination of the minority carrier lifetime. When a minority 
carrier is introduced into a region where carriers of opposite polarity 
(i.e, majority carriers) are present, there is a tendency for 
recombination and a consequent annihilation of the minority carrier. The 
lifetime of a carrier depends on how many impurities or defects which form 
sites where the recombination occurs are present. The distance that the 
carrier travels during their lifetime is called the diffusion length. Both 
the lifetime and the diffusion length provide a measure of the impurity or 
defect concentration. 
There are two types of minority carrier lifetime, the recombination 
lifetime .tau..sub.R (discussed above) and the generation lifetime 
.tau..sub.G. These lifetimes are distinguished based on their relationship 
to electron-hole recombination and electron-hole generation, respectively. 
In silicon, both of these processes are governed by impurity or defect 
levels E.sub.T. In a p-type semiconductor, the recombination lifetime is 
related to an annihilation of electrons (excess minority carriers). The 
recombination is very efficient in the bulk region where free holes 
(majority carriers) are present. The generation lifetime relates to an 
opposite process. That is the creation of the minority carriers due to 
thermal generation. Again, the impurities and defects serve as sites for 
the generation. The generation lifetime is important in the depletion 
layer where virtually no majority carriers are present and thus the 
recombination is very inefficient. 
The depletion layer generation lifetime is ideally suited for monitoring 
impurities or defects in these semiconductor layers such as epitaxial 
layers and denuded zones which are extensively utilized in semiconductor 
microelectronic devices and circuits. 
Determining lifetime using surface photovoltage (i.e., the change of the 
surface potential caused by illumination) techniques has been limited to 
measuring the recombination lifetime, including the bulk recombination 
lifetime .tau..sub.R, the effective recombination lifetime .tau..sub.eff 
which contains contributions from recombination in the bulk and at the 
surface; and the surface recombination lifetime .tau..sub.s. SPV surface 
recombination lifetime measuring tools are being produced by Semitest, 
Inc., Billerica, Mass. and QC Solutions, Woburn, Mass. Both of these tools 
perform single frequency, room temperature SPV measurements. 
Measurement of the depletion layer generation lifetime in thin epitaxial 
layers, on the other hand, has been limited to those techniques which 
utilize test junctions or test MOS capacitors. Another method uses a 
corona charge pulse applied to a small site on the surface and determines 
the generation lifetime from the contact potential transient following the 
pulse. These approaches use capacitance transient measurements in response 
to a bias pulse applied to the junction or to the gate of the MOS device 
(see Kang et al., The Pulsed MIS Capacitor, Phys. Stnt. Sol. 89:13, 1985). 
SUMMARY OF THE INVENTION 
This invention provides a method for measuring the surface photovoltage 
(SPV) under experimental conditions which highlight minority carrier 
generation lifetime .tau..sub.G associated with the depletion layer in a 
thin epitaxial layer of a semiconductor wafer. This generation lifetime 
characteristic refers selectively to the creation of minority carriers due 
to thermal generation via impurity or defect levels within the depletion 
layer. In particular, the magnitude of SPV is measured at elevated 
temperatures within an optimum range as a function of a modulation 
frequency of illuminating light. Measuring the magnitude of SPV as a 
function of frequency in the optimum elevated temperature range ensures 
that the measurement is representative of the depletion layer generation 
lifetime and not from other minority carrier supply mechanisms. 
In one aspect of the invention, the method for determining the depletion 
layer minority carrier lifetime .tau..sub.G in a depletion layer of a 
semiconductor wafer includes the following steps. A first surface 
photovoltage .DELTA.V.sub.o1 is measured at a selected point of the wafer, 
at a temperature T.sub.1 in a range between 30-100.degree. C. and at a low 
light modulation frequency. A second surface photovoltage .DELTA.V.sub.1 
is measured at the selected point, at a temperature T.sub.2 and at a 
frequency .omega..sub.2 within the frequency range where the surface 
photovoltage is inversely proportional to frequency. A surface 
photovoltage response time .tau..sub.max1 of the selected point is 
determined by: 
EQU .tau..sub.max1 =.omega..sub.2.sup.-1 [(.DELTA.V.sub.o1 
/.DELTA.V.sub.1)-1].sup.1/2 ; and 
the depletion layer lifetime .tau..sub.o is determined by: 
EQU .tau..sub.o =.tau..sub.max1 .multidot.exp [(T.sub.2 -T.sub.0)E.sub.A 
/kT.sub.o .multidot.T.sub.2 ] 
where T.sub.o is room temperature. 
In another aspect of the invention, the method for determining the 
depletion layer minority carrier lifetime .tau..sub.G in a depletion layer 
of a semiconductor wafer includes the following steps. A depletion or 
inversion layer is induced on a surface of the semiconductor wafer. The 
wafer is then heated to a first temperature T.sub.1 in a range between 
30-100.degree. C. A surface photovoltage is induced on the surface of the 
semiconductor wafer with modulated light. A first surface photovoltage 
.DELTA.V.sub.o1 is measured at a selected point of the wafer, at T.sub.1 
and at a low light modulation frequency where the surface photovoltage is 
substantially independent of frequency. A second surface photovoltage 
.DELTA.V.sub.1 is measured at the selected point, at T.sub.1 and at a 
higher light modulation frequency .omega. (.omega.=2.pi.f is the angular 
frequency, where f is the standard modulation frequency) which is within a 
frequency range where the surface photovoltage is inversely proportional 
to frequency. A first surface photovoltage response time .tau..sub.max1 is 
determined by the relationship: .tau..sub.max1 =.omega..sub.1.sup.-1 
[(.DELTA.V.sub.o1 /.DELTA.V.sub.1).sup.2 -1].sup.1/2. The semiconductor 
wafer is heated to a second temperature .tau..sub.2, greater than the 
first temperature T.sub.1 and in the range between 30-90.degree. C. A 
third surface photovoltage .DELTA.V.sub.o2 is measured at the selected 
point, at T.sub.2 and at the low light modulation frequency. A fourth 
surface photovoltage .DELTA.V.sub.2 is measured at the selected point, at 
T.sub.2 and at a frequency .omega..sub.2 in a range where the photovoltage 
is inversely proportional to frequency. A second surface photovoltage 
response time .tau..sub.max2 is determined by the relationship 
.tau..sub.max2 =.omega..sub.2.sup.-1 [(.DELTA.V.sub.o2 
/.DELTA.V.sub.2).sup.2 -1].sup.1/2. The room temperature depletion layer 
lifetime .tau..sub.G is determined by the relationship: 
EQU .tau..sub.G =.tau..sub.max2 .multidot.exp [(T.sub.2 -T.sub.0)E.sub.A 
/kT.sub.o .multidot.T.sub.2 ], 
where T.sub.o is room temperature. 
Preferred embodiments of this aspect include one or more of the following 
features. Before determining the depletion layer lifetime T.sub.o, a 
response time activation energy E.sub.A based on the following 
relationship is calculated: E.sub.A =k(ln .tau..sub.max1 
/.tau..sub.max2)(T.sub.1 .multidot.T.sub.2)/(T.sub.2 -T.sub.1). The value 
of E.sub.A provides an indication of the validity of the depletion layer 
minority carrier lifetime measurement. For example, for silicon, the value 
of E.sub.A should be in a range between 0.4 to 0.7 eV and preferably close 
to 0.55 eV. If the value of E.sub.A is outside this range, would indicate 
that a minority carrier supply mechanism other than that associated with 
the generation lifetime is dominating the measurement. 
For silicon, the optimum elevated temperature range is between 40 and 
80.degree. C. For example, temperature T.sub.1 is preferably in a range 
between about 40 and 60.degree. C., while temperature T.sub.2 is in a 
range between about 60 and 80.degree. C. The low light modulation 
frequency is preferably in a range between 0.1 to 100 Hz and frequency 
.omega. (where the surface photovoltage is inversely proportional to 
frequency) is in a range between 100 to 5 KHz. 
In order to ensure that the depletion layer has a weak surface inversion 
layer, in one embodiment, the method includes a step performed prior to 
heating the semiconductor wafer to temperature T.sub.1. This step includes 
adjusting the surface barrier to ensure that it is within an optimal range 
defined by: 
##EQU1## 
Depending on the value of V.sub.s, either positive or negative corona is 
applied to the wafer surface until V.sub.s is in the desired range. 
In another aspect of the invention, a system for determining the depletion 
layer minority carrier lifetime .tau..sub.G comprises a measurement device 
configured to measure a series of surface photovoltages including a first 
surface photovoltage .DELTA.V.sub.o1 at a first temperature T.sub.1 and at 
a low light modulation frequency where the surface photovoltage is 
independent of frequency; a second surface photovoltage .DELTA.V.sub.1 at 
T.sub.1 and at a frequency .omega. which is higher than the low light 
modulation frequency and where the surface photovoltage is inversely 
proportional to frequency; a third surface photovoltage .DELTA.V.sub.o2 at 
a second temperature T.sub.2 and at the low light modulation frequency; a 
fourth surface photovoltage .DELTA.V.sub.2 at T.sub.2 and at the 
frequency. The system also includes a controller which receives electrical 
signals representative of the first, second, third and fourth 
photovoltages and determines a first surface photovoltage response time 
.tau..sub.max1 by: 
EQU .tau..sub.max1 =.omega..sub.1.sup.-1 [(.DELTA.V.sub.o1 
/.DELTA.V.sub.1).sup.2 -1].sup.1/2 ; 
a second surface photovoltage response time .tau..sub.max2 by: 
EQU .tau..sub.max2 =.omega..sub.2.sup.-1 [(.DELTA.V.sub.o2 
/.DELTA.V.sub.2).sup.2 -1].sup.1/2); and 
a depletion layer lifetime .tau..sub.o by: 
EQU .tau..sub.0 =.tau..sub.max2 .multidot.exp [(T.sub.2 -T.sub.0)E.sub.A 
/kT.sub.0 .multidot.T.sub.2 ] 
where T.sub.0 is room temperature. 
In embodiments of this aspect, the system may include one or more of the 
following additional features. The system includes a first 
variable-temperature wafer stage configured to support and heat the 
semiconductor wafer at temperature T.sub.1 and a second 
variable-temperature wafer stage configured to support and heat the 
semiconductor wafer at temperature T.sub.2. The system may also include a 
charge deposition device configured to induce a depletion or inversion 
layer on the surface of the semiconductor wafer. 
Among other advantages, the invention provides a non-contact approach for 
measuring the generation lifetime without requiring the fabrication of 
separate test junctions or test MOS capacitors. Elevating the temperature 
at which the SPV measurements are performed accelerates the minority 
carrier generation and permits to perform measurement many timer faster 
than standard measurements at room temperature. This enables mapping the 
entire wafer in a practical amount of time (e.g., below 30 min, whereas 
room temperature measurements would take days). 
Embodiments of the invention may include one or more of the following 
features. 
The invention is particularly well suited for characterizing oxidized 
epitaxial silicon wafers having epitaxial layers on highly doped 
substrates of the same conductivity type as the epitaxial layer (e.g., 
n/n.sup.+ and p/p.sup.+) or oxidized wafers with denuded zones (i.e., 
thermally treated to remove contaminants during wafer manufacturing). 
Other features and advantages will become apparent from the following 
description and from the claims.

DESCRIPTION 
Referring to FIG. 1, a computer controlled test system 10 for measuring the 
generation lifetime of thin epitaxial layers deposited over a 
semiconductor wafer 2 (FIG. 2A) formed of semiconductor silicon is shown. 
Test system 10 includes a corona charging and surface barrier (CCSB) 
measurement station 20, an elevated surface photovoltage (AC-SPV) 
measurement station 30, a prealigner station 16, and a robotic wafer 
handler 12 for moving wafer 2 about the stations of the system. A computer 
18 controls robotic wafer handler 12 and transmits control signals to and 
receives data signals from cassette holder 14, CCSB measurement station 
20, elevated AC-SPV measurement station 30 and positioners associated with 
the measurement stations. 
CCSB station 20 and the AC-SPV measuring station 30 in are placed in dark 
boxes which prevent stray light interference in during measurements. 
Referring to FIG. 2A and 2B, the CCSB measurement station 20 includes a 
Monroe-type sensor 22, positioned over a stage 23, for measuring the 
contact potential in dark and illuminated light conditions with respect to 
a reference electrode of a probe 25. Probe 25 is used to provide 
electrical signals representative of the semiconductor surface potential 
to computer 18 through an amplifier circuit 21. In use, probe 25 is spaced 
from wafer 2 by an air gap of about a millimeter or less. Wafer 2 is held 
in place on stage 23 with a vacuum system such as that which is described 
in U.S. Pat. No. 5,773,989. 
Sensor 22 includes a light source (not shown) which illuminates the portion 
of the wafer under examination. In one embodiment, a fiber optic bundle is 
positioned to the side of probe 25 to convey the light from the light 
source at an angle as shown in FIG. 2A. Where greater intensity of the 
illumination is required, a second fiber optic bundle may be provided on 
the opposite side of probe 25. 
Referring to FIG. 2B, in an alternative embodiment, a Kelvin-type probe 27 
is used in which the light is directed through the probe itself. Kelvin 
and Monroe type sensors are described, respectively, in G. W. Reedyk and 
M. M. Perlman: Journal of the Electrochemical Society, Vol. 115, p. 49 
(1968); and in R. E. Vosteen: Conference Records, 1974 IEEE-IAS 9th Annual 
Meeting, p. 799, the entire contents of which are incorporated herein by 
reference. An example of a commercially available Monroe-type device is 
the Isoprobe model 162 by Monroe Electronics, Lyndonville, N.Y. 14098. 
As will be described in greater detail below, CCSB measurement station 20 
is used to ensure that the semiconductor surface potential barrier V.sub.s 
is within an optimum range prior to continuing with measuring the 
modulated light AC-surface photovoltage .DELTA.V.sub.spv required for 
determining the generation lifetime of the thin epitaxial layer on the 
wafer. 
Elevated AC-SPV measurement station 30 includes a pair of 
temperature-controlled wafer chucks 32, 34 each of which includes electric 
heating and air-cooling elements (not shown) for controlling the 
temperature of the chucks to a pre-selected temperature from e.g., 
30-100.degree. C. Both chucks 32, 34 hold the wafer by means of a vacuum 
suction which assures good thermal contact. Wafer chucks 32, 34 are 
individually controlled by computer 18 to maintain the temperature across 
the surface of respective chucks within about 1.degree. C. As will be 
discussed in greater detail below, because the process for determining the 
generation lifetime requires performing measurements at least two 
different elevated temperatures, separate wafer chucks 32, 34 are used to 
eliminate waiting periods associated with increasing/decreasing the 
temperature of a single chuck. 
Elevated AC-SPV measurement station 30 includes a measurement probe 36 for 
measuring the AC small signal surface photovoltage (e.g., 1 .mu.V-10 mV) 
as a function of the frequency (e.g., 0.1 Hz to 10.sup.5 Hz) of chopped 
illumination light. Light should be of the wavelength shorter than 0.8 
.mu.m to be absorbed within less than 10 .mu.m beneath the surface of the 
silicon wafer 2. The illumination light is provided by a light source (not 
shown), for example, a red, yellow or green LED having a light output 
pulsed from an LED power supply or a variable frequency light-chopping 
circuit. An exemplary measurement probe suitable for this application is 
described in Lagowski U.S. Pat. No. 5,177,351, in Lagowski, "Determining 
Long Minority Carrier Diffusion Length", U.S. Ser. No. 08/312119, filed 
Aug. 26, 1994, and in Lagowski, "Measurement of the Mobile Ion 
Concentration in the Oxide Layer of a Semiconductor Wafer", U.S. Ser. No. 
08/502660, filed Jul. 14, 1995, the entire contents of which are 
incorporated herein by reference. A suitable device is also described in: 
P. Edelman, J. Lagowski, L. Jastrzebski, "Surface Charge Imaging in 
Semiconductor Wafers by Surface Photovoltage (SPV)" MRS Symposium 
Proceedings, 261, pp. 223 (1992), the entire contents of which are 
incorporated by reference. 
Measurement probe 36 is mounted to a Y-axis positioner 38 which moves probe 
36 over wafer chucks 32, 34 in a Y direction. Wafer chucks 32, 34 are both 
mounted to an X-axis positioner 40 which moves chucks 32, 34 beneath 
measurement probe 36 in an X direction. Y-axis positioner 38 and X-axis 
positioner 40 move in response to control signals from computer 18. 
Test system 10 further includes a wafer cassette holder 14 for storing the 
semiconductor wafers to be tested and a prealigning stage 16 for accurate 
positioning of the wafer as it is moved from device to device, thereby 
minimizing positioning errors from measurement to measurement. The 
prealigner station 16 is used for pre-orientation of wafer prior to 
measurement by using a notch or flat formed by wafer manufacturers near 
the edge of the circular wafer for registration purposes. 
Measurement Procedure 
The measurement procedure provides a non-contact approach for measuring the 
generation lifetime within depletion layers, the value being 
representative of the amount of impurity contaminants within the depletion 
layer, a region just below the wafer surface having a thickness of about 
1.mu. or less, where virtually no free carriers (electrons and holes) are 
present. The procedure enables probing thin epitaxial layers so long as 
the thickness of the depletion layer is less than the thickness of the 
epitaxial layers. 
With reference to FIG. 3, a silicon semiconductor wafer 2 includes a 
SiO.sub.2 layer 3 formed over a relatively thin epitaxial layer 5 which in 
turn is formed over the bulk region 6 of the semiconductor wafer. 
Epitaxial layer 5 includes a diffusion layer 7 having a relatively weak 
surface inversion layer 8 just below the interface with SiO.sub.2 layer 3. 
In response to illumination directed onto the surface of semiconductor 
wafer 2, excess electron-hole pairs 50 are generated within depletion 
layer 7 which alter inversion layer 8 having minority carriers 52. Supply 
of these minority carriers 52 from the depletion layer 7 (where they are 
generated by process 50 but do not stay due to electric field) is desired 
to be the dominant source of minority carriers in the generation lifetime 
characteristic being measured. However, other sources of minority carriers 
can exist which interfere with the detection of minority carrier 
generation in an illuminated probe region 53 of wafer 2. For example, 
minority carriers 54 outside the illuminated probe region 53 and within 
surface inversion layer 8 may be present. Minority carriers 56 generated 
within epitaxial layer bulk region 6 and in the substrate may also be 
present. Interface traps within SiO.sub.2 layer 3 may also be a source of 
minority carriers 58. 
As will be described in greater detail below, the measurement procedure of 
the invention is performed in a manner that the generation lifetime within 
the depletion layer is the dominant mechanism for generating minority 
carriers and the influence of minority carriers 54 (from outside the 
illuminated probe region 23) due to lateral transport phenomena in surface 
inversion layer 8, minority carriers 56 supplied from bulk region 6 and 
minority carriers 58 from SiO.sub.2 are all minimized. 
With reference to FIG. 4, a flow chart illustrates the approach for 
determining the generation lifetime within a depletion layer of a 
semiconductor substrate. 
The presence of a weak inversion layer 8 above depletion layer 7 is 
required for detecting the behavior of the minority carriers and for 
performing surface photovoltage measurements used to measure the minority 
carrier generation lifetime within depletion layer 7. If the inversion 
layer is too strong, the supply of minority carriers from inversion layer 
8 around illuminated probe region 53 will dominate, thereby interfering 
with the measurement of minority carriers generated thermally from 
impurities within the depletion layer 7. 
To ensure that the surface barrier potential is within a range consistent 
with providing a weak inversion layer 8, the wafer is moved to stage 23 of 
CCSB measurement station 20 where photovoltage transducer probe 24 is used 
to determine the surface barrier potential V.sub.s (step 100). To do so, 
the contact potential difference V.sub.CPD of the wafer is measured under 
dark light conditions to obtain V.sub.CPD.sup.dark. The V.sub.CPD is also 
measured with the wafer subjected to constant, strong illumination to 
obtain V.sub.CPD.sup.ill. The value of the surface barrier potential 
V.sub.s is then determined as follows: 
EQU V.sub.s =V.sub.CPD.sup.dark -V.sub.CPD.sup.ill 
The value of V.sub.s is compared with an optimal range corresponding to a 
weak inversion layer. For p-type silicon, the optimal range is: 
##EQU2## 
where: n.sub.i =1.4 e 10 cm.sup.-3 is the intrinsic carrier concentration 
in silicon at room temperature; 
kT=0.026 eV (the thermal energy); 
q is the elemental charge; and 
N.sub.a is the acceptor concentration in silicon. 
For silicon with a dopant concentration between 10.sup.14 and 10.sup.16 
cm.sup.-3, an optimum range for the surface barrier potential V.sub.s is 
from about 0.25 V to 0.50 V. 
If V.sub.s is too small, for example V.sub.s =-0.01 V, shown as point 60 in 
the FIG. 5, then a positive corona is deposited on SiO.sub.2 layer 3 in 
small doses of about 2.times.10.sup.10 charge/cm.sup.2 per dose with 
photovoltage transducer probe by passing wafer 2 under a corona charging 
wire 24 connected to a DC voltage supply (not shown). V.sub.s is measured 
with probe 25 after each dose. The charging is continued until V.sub.s 
reaches a value within an optimum range (shown as point 62). 
If V.sub.s is too large, for example 0.67 V, shown as point 64, than a 
negative corona charge is deposited in small doses until V.sub.s is 
reduced to a value within the optimum range. 
Upon determining that the surface barrier potential V.sub.s is within the 
appropriate range, wafer 2 is transferred to temperature-controlled wafer 
chuck 32 of elevated AC-SPV measurement station 30 which has been 
preheated to a temperature T.sub.1 in a range between 40-60.degree. C. 
Before measuring the small signal AC .DELTA.V.sub.spv as a function of 
light-chopping frequency, it is important that the intensity of the 
illuminating light be sufficiently low to ensure linearity between the 
.DELTA.V.sub.spv and light intensity (step 102). To verify that this 
condition is met, the magnitude of the surface photovoltage 
.DELTA.V.sub.spv of wafer 2 is measured with probe 36 under low-light 
illumination at two light intensities I.sub.1 and I.sub.2 and illumination 
modulated at a chopping frequency in a range between 1-10 Hz. It is 
desired that the linearity be within 2.5%, as expressed by the following 
relationship: 
##EQU3## 
where: 0.975.ltoreq.a.ltoreq.1.00 and .DELTA.V.sub.SPV1 and 
.DELTA.V.sub.SPV2 correspond to I.sub.1 and I.sub.2, respectively. 
This condition is typically satisfied when .DELTA.V.sub.spv is smaller than 
5 mV. Adjusting the light intensity (I) to provide a linear relationship 
between the surface photovoltage and the light intensity can be 
accomplished by changing the supply current to the light source (e.g., 
light emitting diode). Alternatively, a pre-calibrated neutral density 
filter can be inserted into the light path of the light source. 
After adjusting light intensity I to ensure measurement within a linear 
.DELTA.V.sub.spv range, small signal AC surface photovoltage (SPV) 
measurements with probe 36 as a function of light-chopping frequency can 
be performed. 
Referring to FIG. 6, with wafer chuck 32 heated to 57.degree. C., 
.DELTA.V.sub.spv is measured while the light-chopping frequency is varied 
or swept over a frequency range extending from about 2 Hz to about 5 KHz, 
thereby producing a curve 70 (corresponding to 57.degree. C. or 
330.degree. K) (step 104). The frequency range must extend from a low 
frequency plateau region 72 (.DELTA.V.sub.spv .tbd..DELTA.V.sub.o) 
including the frequency (point 74) where .DELTA.V.sub.o is measured, to a 
high frequency linear (i.e., .DELTA.V.sub.SPV 
.tbd..DELTA.V.about..function..sup.-1) region 76. 
The SPV response time .tau..sub.max1 at T.sub.1 is calculated using the 
following relationship: 
EQU .tau..sub.max1 =.omega..sup.-1 [(.DELTA.V.sub.o /.DELTA.V).sup.2 
-1].sup.1/2 where .omega.=2.pi..function. (step 106). 
.omega. corresponds to the .function. value at which .DELTA.V value is 
taken, for example point 82. 
At T.sub.1 of 57.degree. C., .DELTA.V.sub.o is measured at a frequency 
.function..ltoreq.5 Hz while .DELTA.V is measured at a frequency 
.gtoreq.100 Hz. At these frequencies, the calculated value of 
.tau..sub.max1 is 5.9 ms. 
Wafer 2 is then transferred to the measuring stage associated with wafer 
chuck 34 which is pre-heated to an elevated temperature T.sub.2 (e.g., 
77.degree. C. or 350.degree. K) and the magnitude of the SPV signal is 
measured again as a function of frequency, thereby producing curve 80 
(step 108). 
The response time at T.sub.2 is calculated using the following relationship 
: 
EQU .tau..sub.max2 =.omega..sup.-1 [(.DELTA.V.sub.o /.DELTA.V).sup.2 
-1].sup.1/2 where .omega.=2.pi..function. (step 110). 
The values of frequencies used to select the plateau value .DELTA.V.sub.o 
and the linear .DELTA.V for T.sub.2 are typically higher than those for 
T.sub.1 because of the shift of the plateau to a higher frequency range. 
The value corresponding to the curve 80 in FIG. 6 is .tau..sub.max2 =1.8 
ms. 
In order to verify the validity of the measurements used to calculate 
.tau..sub.max1 and .tau..sub.max2, the response time activation energy, 
E.sub.A, is determined using the following expression: 
EQU E.sub.A =k(ln .tau..sub.1 /.tau..sub.2) (T.sub.1 T.sub.2)/(T.sub.2 -T.sub.1 
) 
where .tau..sub.1 and .tau..sub.2 are the values of .tau..sub.max at 
absolute temperature T.sub.1 and T.sub.2 respectively, and k is the 
Boltzman constant (k=8.6.times.10.sup.-5 eVK.sup.-1). 
Using the values for .tau..sub.max1 =5.9 ms and .tau..sub.max2 =1.8 ms 
obtained above, E.sub.A =0.59 eV. This value is verified to ensure that it 
falls within a theoretically expected E.sub.A range (step 112) for energy 
levels near the middle of the energy gap contributing to the generation of 
minority carriers within a depletion layer. For silicon, the energy gap is 
1.1 eV, and ideally E.sub.a =0.55 eV. The total expected energy level 
range is 0.4 to 0.7 eV. Lower or higher values of E.sub.A generally 
indicate that other minority carrier supply mechanisms, such as the 
lateral transport mechanism are contributing significantly. In this case, 
the energy level value of E.sub.A =0.59 eV is within the expected range 
and, thus the measurement result is valid. 
The response time value at room temperature T.sub.o =295.degree. K 
(22.degree. C.) is extrapolated from the response time at either T.sub.1 
or T.sub.2 using the value of activation energy. Extrapolation from 
T.sub.2 gives: 
EQU .tau..sub.G =.tau..sub.2 .multidot.exp [(T.sub.2 -T.sub.o)E.sub.A /kT.sub.o 
.multidot.T.sub.2 ] (step 114). 
For the values used in the example above, the minority carrier depletion 
layer lifetime .tau..sub.G =70 ms. 
Temperatures T.sub.1 and T.sub.2 of wafer chucks 32, 34, respectively, are 
required to be within an optimum range to assure that the depletion layer 
lifetime .tau..sub.G measurement is indicative of the minority carrier 
generation in the depletion layer and not of other interfering mechanisms. 
For temperatures outside this range, other minority carrier supply 
processes dominate. Thus for lower temperatures the lateral transport and 
supply from the interface states may dominate. At higher temperatures, the 
generation of minority carrier via the energy gap, rather than from the 
impurity levels become dominant. 
For single point measurements, the center of the wafer is typically 
selected for performing the measurements described above. Carrier charging 
to adjust the surface barrier height is done once for the whole wafer 
using the whole water charging station 24. Thus measurements can be 
performed as well at other preselected of sites on the wafer. Moreover, 
because higher frequencies can be used to determine the response time at 
elevated temperatures, the measurements can be performed more quickly. 
Thus, mapping of the entire wafer can also be performed more quickly 
(e.g., 10 to 20 minutes per wafer) than if performed at room temperature 
(i.e., 22.degree. C.). 
In a high accuracy mapping procedure, the AC-SPV measuring steps described 
above are performed at every desired point of the wafer. This procedure is 
accurate because an activation energy E.sub.A is calculated for every 
point. 
On the other hand, a still relatively accurate mapping approach can be used 
to increase the speed of the mapping procedure. In this procedure, the 
measuring steps are performed at a single point (preferably the center) as 
described above. After completion of this process, two sets of 
measurements are performed with wafer 2 positioned on wafer chuck 34. The 
position of wafer 2 is changed using X and Y positioners 38, 40 to map the 
entire surface. First, the .DELTA.V.sub.spv at the low frequency (e.g., 20 
Hz) is mapped at points across the surface and stored within computer 18. 
Then .DELTA.V.sub.spv is measured at a high frequency (e.g., 500 Hz). The 
SPV response time .tau..sub.max2 is determined for each point and 
corresponding values of .tau..sub.G at every point are extrapolated to 
room temperature. 
Other embodiments are within the scope of the claims.