Elevated temperature measurement of the minority carrier lifetime in the depletion layer of a semiconductor wafer
First Claim
1. A method for determining a depletion layer minority carrier lifetime τ
-
o in a depletion layer within a semiconductor wafer comprising;
a) measuring a first surface photovoltage Δ
Vo1 at a selected point of the wafer, at a temperature T1 in a range between 303°
K-373°
K and at a low light modulation frequency;
b) measuring a second surface photovoltage Δ
V1 at the selected point, at a temperature T2 and at a frequency ω
within the frequency range where the surface photovoltage is inversely proportional to frequency;
c) determining a surface photovoltage response time τ
max1 of the selected point by;
space="preserve" listing-type="equation">τ
.sub.max1 =ω
.sup.-1 {(Δ
V.sub.o1 /Δ
V.sub.1).sup.2 -1}.sup.1/2;
andd) determining the depletion layer lifetime τ
o by;
space="preserve" listing-type="equation">τ
.sub.o =τ
.sub.max1 ·
exp [(T.sub.2 -T.sub.0)E.sub.A /kT.sub.o ·
T.sub.2 ] whereTo is room temperature,k=8.6×
10-5 eVK-1,EA =k(ln τ
1 /τ
2)·
(T1 ·
T2)/(T2 -T1),where τ
1 and τ
2 are the values of τ
max1 at temperatures T1 and T2.
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Abstract
A method for determining the depletion layer minority carrier lifetime τo 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 T1. A surface photovoltage is induced on the surface of the wafer with modulated light. A surface photovoltage ΔVo1 is measured at a selected point of the wafer, at T1 and at a low light modulation frequency where the surface photovoltage is substantially independent of frequency. A surface photovoltage ΔV1 is measured at the selected point, at T1 and at a higher light modulation frequency ω which is within a frequency range where the surface photovoltage is inversely proportional to frequency. A surface photovoltage response time τmax1 is determined by the relationship: τmax1 =ω1-1 [(ΔVo1 /ΔV1)2 -1]1/2. The wafer is heated to a temperature T2, greater than the temperature T1. A surface photovoltage ΔVo2 is measured at the selected point, at T2 and at the low light modulation frequency. A surface photovoltage ΔV2 is measured at the selected point, at T2 and at a frequency ω2 in a range where the photovoltage is inversely proportional to frequency. A surface photovoltage response time τmax2 is determined by the relationship τmax2 =ω2- 1[(ΔVo2 /ΔV2)2 -1]1/2. The room temperature depletion layer lifetime τo is determined by the relationship:
τ.sub.o =τ.sub.max2 ·exp [(T.sub.2 -T.sub.0)E.sub.A
/kTo ·T2 ],
where To is room temperature.
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Citations
14 Claims
-
1. A method for determining a depletion layer minority carrier lifetime τ
-
o in a depletion layer within a semiconductor wafer comprising;
a) measuring a first surface photovoltage Δ
Vo1 at a selected point of the wafer, at a temperature T1 in a range between 303°
K-373°
K and at a low light modulation frequency;b) measuring a second surface photovoltage Δ
V1 at the selected point, at a temperature T2 and at a frequency ω
within the frequency range where the surface photovoltage is inversely proportional to frequency;c) determining a surface photovoltage response time τ
max1 of the selected point by;
space="preserve" listing-type="equation">τ
.sub.max1 =ω
.sup.-1 {(Δ
V.sub.o1 /Δ
V.sub.1).sup.2 -1}.sup.1/2;and d) determining the depletion layer lifetime τ
o by;
space="preserve" listing-type="equation">τ
.sub.o =τ
.sub.max1 ·
exp [(T.sub.2 -T.sub.0)E.sub.A /kT.sub.o ·
T.sub.2 ]where To is room temperature, k=8.6×
10-5 eVK-1,EA =k(ln τ
1 /τ
2)·
(T1 ·
T2)/(T2 -T1),where τ
1 and τ
2 are the values of τ
max1 at temperatures T1 and T2.
-
o in a depletion layer within a semiconductor wafer comprising;
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2. A method for determining a depletion layer minority carrier lifetime τ
-
o in a depletion layer within a semiconductor wafer comprising;
a) inducing a depletion or inversion layer on a surface of the semiconductor wafer; b) heating the semiconductor wafer to a first temperature T1 in a range between 303°
K-373°
K;c) inducing a surface photovoltage on the surface of the semiconductor wafer with modulated light; d) measuring a first surface photovoltage Δ
Vo1 at a selected point of the wafer, at T1 and at a low light modulation frequency where the surface photovoltage is independent of frequency;e) measuring a second surface photovoltage Δ
V1 at the selected point, at T1, at a higher light modulation frequency ω
which is within a frequency range where the surface photovoltage is inversely proportional to frequency;f) determining a first surface photovoltage response time τ
max1 of the selected point by;
space="preserve" listing-type="equation">τ
.sub.max1 =ω
.sub.1.sup.-1 {(Δ
V.sub.o1 /Δ
V.sub.1).sup.2 -1}.sup.1/2;g) heating the semiconductor wafer to a second temperature T2 in the range between 303°
K-373°
K, the second temperature T2 greater than the first temperature T1 ;h) measuring a third surface photovoltage Δ
Vo2 at the selected point, at T2 and at the low light modulation frequency;i) measuring a fourth surface photovoltage Δ
V2 at the selected point, at T2 and at a frequency ω
2 within the frequency range where the surface photovoltage is inversely proportional to frequency;j) determining a second surface photovoltage response time τ
max2 of the selected point by;
space="preserve" listing-type="equation">τ
.sub.max2 =ω
.sub.2.sup.-1 {(Δ
V.sub.o2 /Δ
V.sub.2).sup.2 -1}.sup.1/2 ; andk) determining the depletion layer lifetime τ
o by;
space="preserve" listing-type="equation">τ
.sub.0 =τ
.sub.max2 ·
exp {(T.sub.2 -T.sub.0)E.sub.A /kT.sub.o ·
T.sub.2}where To is room temperature. - View Dependent Claims (3, 4, 5, 6, 7, 8, 9, 10)
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o in a depletion layer within a semiconductor wafer comprising;
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11. A system for determining a depletion layer minority carrier lifetime τ
-
o in a depletion layer within a semiconductor wafer, the system comprising a measurement device configured to measure a series of surface photovoltages including;
a first surface photovoltage Δ
Vo1 at a first temperature T1 and at a low light modulation frequency where the surface photovoltage is independent of frequency;a second surface photovoltage Δ
V1 at T1 and at a frequency ω
which is higher than the low light modulation frequency and where the surface photovoltage is inversely proportional to frequency;a third surface photovoltage Δ
Vo2 at a second temperature T2 and at the low light modulation frequency;a fourth surface photovoltage Δ
V2 at T2 and at the frequency; anda controller which receives electrical signals representative of the first, second, third and fourth photovoltages and determines; a first surface photovoltage response time τ
max1 by;
space="preserve" listing-type="equation">τ
.sub.max1 =ω
.sub.1.sup.-1 [(Δ
V.sub.o1 /Δ
V.sub.1).sup.2 -1].sup.1/2;a second surface photovoltage response time τ
max2 by;
space="preserve" listing-type="equation">τ
.sub.max2 =ω
.sub.2.sup.-1 [(Δ
V.sub.o2 /Δ
V.sub.2).sup.2 -1].sup.1/2 ; anda depletion layer lifetime τ
o by;
space="preserve" listing-type="equation">τ
.sub.0 =τ
.sub.max2 ·
exp [(T.sub.2 -T.sub.0)E.sub.A /kT.sub.o ·
T.sub.2 ]where To is room temperature. - View Dependent Claims (12, 13, 14)
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o in a depletion layer within a semiconductor wafer, the system comprising a measurement device configured to measure a series of surface photovoltages including;
Specification