Proceedings of 7th Thin Film Materials & Devices Meeting
November 5-6, 2010, Nara, Japan
http://www.tfmd.jp/

Minority Carrier Lifetime Measurement by Photo-Induced Carrier
Microwave Absorption Method
T. Nagao1, S. Yoshidomi1, M. Hasumi1, T. Sameshima1 and T. Mizuno2
1

Tokyo University of Agriculture and Technology, 2-24-16, Nakacho, Koganei,
Tokyo 184-8588, Japan
2
Kanagawa University, 2946, Tsuchiya, Hiratsuka, Kanagawa 259-1293, Japan

Keywords: effective lifetime, free carrier absorption, photo-induced carrier, recombination,
surface passivation

Abstract. We propose a measurement system of photo-induced minority carrier absorption of 9.35
GHz-microwave using periodically pulsed light illumination at 620 nm. The ratio of average carrier
density during light illumination ON to light illumination OFF, P, was theoretically analyzed for
different light pulse widths. Analysis of P resulted in a formula giving minority carrier lifetime, eff, ofsilicon under continuous light illumination. eff for hole was experimentally determined by the formulaand its recombination sites were obtained for n-type silicon substrates coated with thermally grown SiO2
layers. We also demonstrated increase in eff with high pressure H2O vapor heat treatment.
Introduction
Semiconductor solar cells have been attractive as a device producing electrical power from sun light[1]. High quality of semiconductor and its surfaces are demanded for achieving high conversion
efficiency. Analysis of photo induced carrier properties of semiconductor is therefore important.
Nondestructive and noncontact measurement system is attractive. Measurements of microwave
photo-conductive decay and quasi-steady-state photo conductance have been widely used for themeasurement of the photo induced minority carrier lifetime. We have developed a microwave free
carrier absorption measurement system with continuous wave (CW) light illumination [2]. Free carriers
in semiconductors respond to the incident electrical field of microwave on the order of GHz andcomplex refractive indexes can be changed so that the transmissivity changes with the density of free
carriers. When CW light is illuminated to a semiconductor sample, the density of minority carrier per
unit area N is effectively given by the carrier generation rate G per unit area, and the effective minoritycw
carrier lifetime  eff
as,cw
N   effG .

(1)

N was precisely measured by change in microwave intensity under illumination of CW light. However,cw
it is not easy to experimentally determine  eff because G strongly depends on light reflection loss, which
is sometimes unknown. Transient measurement system is therefore important to obtain the minority
carrier lifetime.
In this paper, we propose a free carrier microwave absorption measurement system withperiodically pulsed light illumination which precisely gives the effective minority carrier lifetime eff
under a low light intensity. A ratio of the average carrier density during dark and light illumination P ismeasured by time integration during illumination with many light pulses. Analysis of P gives a formulacw
determining eff which is close to 
eff . We discuss carrier annihilation properties using P and eff. We
demonstrate measurement of eff using the present method without information of G for n-type

110107067-1

crystalline silicon. We also demonstrate increase in eff with high pressure H2O vapor heat treatment.
TheoryWe supposed that photo-induced carriers were annihilated at recombination sites which
concentrated at the surfaces and uniformly distributed in the bulk substrate. The recombination sites atthe surfaces gave the surface recombination velocities, Stop and Srear. Stop was defined as the surface
recombination velocity at the top surface illuminated with light. Srear was one at the other surface. The
recombination sites uniformly distributed in the bulk substrate gave the bulk lifetime b. When light wasabsorbed at the top surface region of semiconductor with a sufficiently high absorption coefficient,
generation of photo-induced carriers was limited just at the top surface region. The photo induced
carriers diffused with time. The carrier volume density n(x,t) at a depth of x and at the time of t wascalculated using a time-evolution type finite element differentially diffusion model when light was
periodically illuminated for duration of T, and light was subsequently off for T. The minority carrier
density per unit area N(t) was also calculated by integration of n(x,t) with x from 0 to the thickness of
substrate. N(t) increases during light illumination and decreases in dark. It is essential that N(t) must
periodically changes according to periodic light illumination after sufficient times from initiation of effcw, as
illumination. N(t) consists of the zero frequency (CW) component, which includes information of 
well as components of integral multiples of the fundamental frequency of 0.5T -1. After sufficient time
passed, time zero (t = 0) was defined in order to calculate periodic N(t) during light ON and OFF. The
average carrier density during light illumination, Non, was calculated by time integration from 0 to T.
The average density of residual carriers in dark (light OFF), Noff, was also obtained by time integrationfrom T to 2T. We defined P(T) as the ratio of Noff/Non as,

1 2TT
T0 N (t )dt
N
P(T )  off  T T2T
1
N on
N (t )dt .

T
0
T

(2)

We calculated P(T) as a function of T with different b, Stop, and Srear in cases of minority carriers of hole.
When Stop = Srear = 0, N(t) was simply expressed by a model with a single time constant b. Therefore,
P(T) was given as,

b 

T
 

 1  e b TN
P(T )  off 
T
T

 
N on


1  e b  b 1  e b  .

T 


(3)

P(T) monotonously decreased from 1 to 0 as T increased. When T = b, P(T) was as,e 1(4)~ 0.859
2.
When light pulses with a width as b was periodically illuminated, the most of minority carriers
remained in semiconductor in dark duration in the case of Stop = Srear = 0. When T = 2b, P(T) was as,
P( b ) 1  e2(5)~ 0.615 .
1  3e2
P(T) decreased from 0.859 to 0.615 as T increased from b to 2b. We named the pulse width for P(T) at
0.859 as pulse in general cases, as,P(2 b )  pulse  T  P  0.859 .

(6)110107067-2

Moreover, we defined R as,R

T  P  0.615  T  P  0.859 T  P  0.859 .

(7)

pulse and R were b and 1 in the limited case of Stop = Srear = 0. pulse and R were used to characterize
minority carrier annihilation properties and to obtain the effective minority carrier lifetime for thepresent method.
According to the free carrier absorption model in semiconductors, the absorption coefficient  wasapproximately proportional to n(x,t) and the carrier mobility . Integration of n(x,t) with depth gave arelation between microwave transmittance Tr and N(t) as,,(8)

where Tr0 was the microwave transmittance in the dark field and C was a constant including . P(T)defined by eq. (2) is therefore experimentally obtained by logarithm of the microwave transmittance as,  ln T  ln T  dt
P(T )   ln T  ln T  dt .
2T

T
T
0

ro

r

ro

r

(9)

Experimental Procedure
N-type silicon substrates with a resistivity of 15 cm and a thickness of 520 m were prepared. The
both surfaces were coated with 100 nm thick thermally grown SiO2 layers (sample I). The SiO2 layer at
the top surface was thinned to about 2 nm by 5% diluted hydro florid acid to make a defective surface
with a high surface recombination velocity at the top surface (sample II). We also prepared n-typesilicon substrates with a 4-inch diameter and a 150-μm thickness coated with 10-nm thick thermallygrown SiO2 layers (sample III). We then annealed them with 1x106 Pa H2O vapor at 300oC in for 30min(sample IV). Moreover we prepared silicon substrates coated with 100 nm thermally grown SiO2 layers
and different minority carrier lifetimes to evaluate the theory described above.
The 9.35 GHz microwave transmittancemeasurement system was constructed bywaveguide tubes, as shown in Fig. 1. It had anarrow gap for placing a sample wafer. A small
hole was opened at a wall of the waveguide tube toplace an optical fiber for introducing light of 620
nm light emitting diode (LED). The light was
switched with pulse widths ranging from 5x10-5 to
1x10-2 s. A Teflon plate was aslant placed in the
waveguide tube to reflect and diffuse LED light.
Consequently, the sample was uniformly
illuminated at 0.8 mW/cm2 with periodic light Fig. 1 Schematic experimental apparatus
pulses. Microwave was coincidentally switchedwith light pulse ON or OFF, respectively, using a coincident switching circuit to obtain changes in
microwave transmittance during light ON or OFF. The microwave, which transmitted the sample, wasrectified by a high speed diode and integrated with time with a time constant of 5 s. Change intransmittance of microwave was also measured in the case of CW light illumination for comparison.

Results and discussion

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Figure 2 shows calculated P(T) as a function of T for the hole minority carrier for 520 m- thicksilicon substrate in cases of b [s], Stop [cm/s], Srear [cm/s] as; A: 1x10-5, 0, 0, B:1, 0, 5200, C: 1, 5200, 0,
D: 1, 2600, 2600 (a) and as, E: 4x10-4, 0, 0, F: 1, 0, 130, G: 1, 130, 0, and H: 1, 65, 65 (b), respectively.
In order to discuss minority carrier annihilation properties, an effective lifetime classical, which has been
widely used [3], is also introduced as,

.

(10)

classical was 1x10-5 s for the four cases shown in Fig.

2(a), and 4x10-4 s for the four cases shown in Fig.
2(b). P(T) was high almost 1 when T was shorter
than 1x10-5 s for the every case, as shown in Fig.
2(a). This means that the average carrier density wasalmost same between light ON and OFF states
because light switching was sufficiently rapid
compared with carrier annihilation rate. P(T)monotonously decreased as T increased. The average
carrier density during light OFF was lower than that
=10μs
during light ON when T was long because minority
carriers annihilated during a long dark duration.
Change in P(T) with T was simply described by asingle time constant of 1x10-5 s in the case A, as
given in eq. (3). On the other hand, P(T) kept 1 until
T of 7x10-5 s in the case B because minority carriers
were alive until time of diffusion from the top
surface to the rear surface. P(T) then rapidly=400μsdecreased as T increased from 7x10-5 s. On the other
hand, P(T) gradually decreased as T increased in thecase of defective top surface C. Photo-induced
carriers effectively annihilated at the surface for any Fig. 2 Calculated P(T) for the hole minority
pulse widths. But some carriers diffused into thecarrier for 520μm-thick. τclassical was 1x10-5
substrate and were alive for a long time until back tos (a), and it was 4x10-4 s (b).
the top surface because there was almost no defect inbulk and at the rear surface. P(T) value was therefore
rather high for a long pulse width case. Photo-induced carriers annihilate at the top surface as well as therear surface in the case D. It was similar to case C for a half of the substrate thickness. P(T) was
therefore lower than that in the case C. Those results of the cases from A to D shown in Fig. 2(a)indicate that the present method can characterize the defect localization. On the other hand, P(T)characteristics were similar among cases from E to H, as shown in Fig. 2(b). Those results come fromthat low carrier annihilation rate gave similar density of photo-induced carriers and its in-depth
distribution for any defect localization types. In low carrier annihilation cases, classical goes effect anddefect localization cannot be distinguished.
The effective carrier lifetime were obtained by analysis of P(T) values. Through many numericalinvestigations, we propose the effective carrier lifetime eff as, eff  pulse1  log  R (11).

eff was equivalent to classical in a limited condition of Stop = Srear = 0. In this case, P(T) was governedby b as given by eq. (3). pulse was b equivalent to classical as given by eqs. (3) and (10). R was 1 in thiscondition as given by eq. (7). In other cases, especially highly defective surfaces, eff was not equivalent

110107067-4

to classical, as discuss above. The advantage of the present method of microwave transmission
measurement under periodically pulsed light illumination is that no information of the carrier generation
rate G is necessary. Therefore, the present method can be applied to measurement of the minority carrier
lifetime for sample with complicated surface structure with no information of surface reflectivity.
Figure 3 shows experimental P(T) as a function of
T for sample I and II in the cases of pulsed lightillumination to the top and rear surfaces. The R of
sample I was almost 1 and eff obtained by eq. (11) was
1.05x10-3 s. P(T) were shifted to short pulse width
regions for sample II. In the case of illumination to the
top surface, P(T) gradually decreased as T increased. R
was 1.5 and eff was 7.0x10-5 s. On the other hand, P(T)
was almost 1 until 8x10-5 s in the case of illumination
to the rear surface. R was 0.8 and eff was 1.7x10-4 s.
Two different eff clearly indicate that carrier
annihilation property depends on light illumination
way for a defective sample. Analysis of P(T) curves
resulted in most possible b, Stop, and Srear to be Fig.3 P(T) for sample I and sample II in the
5.2x10-3 s, 680 cm/s, and 20 cm/s, respectively, for cases of pulsed light illumination to the top
sample II. Etching of SiO2 layer increased the surface with a 2 nm thick SiO2 layer and to
the rear surface with a 100 nm thick SiO2
recombination velocity at the top surface.
Figure 4 shows logarithmic change in layer.
experimental transmissivity caused by CW lightillumination, lnTr0 - lnTr, as a function of eff
obtained by periodical pulsed light illumination forthe different silicon samples coated with 100 nm
thick thermally grown SiO2. lnTr0 - lnTr was clearly
proportional to eff. From the present theory andexperimental demonstration of Figs. 2 and 3, we
cw
believe eff was equivalent to  effand classical wheneff was high enough. This results in a carrier
generation rate of 1.5×1015 s-1cm-2 in the present
condition from Fig. 4 and by eqs. (1) and (8). The
carrier generation rate allows accurate measurementcw
cw
of  eff even if  eff was very low. Moreover, wemeasured a transient decay signal of microwave
transmittance when light turned off after light ON Fig.4 Logarithmic change in transmissivity
for 1x10-2 s for a silicon sample, which had a long caused by CW light illumination as a functioneff of 1.03x10-3 s, using digital oscilloscope [4]. This of eff
is a sort of photoconductive decay method. A time
constant, which was defined as a time at which lnTr
decreased to lnTr/e since light pulse off, was 1.06x10-3 s, which was almost equivalent to eff obtained by
the present method.
Figure 5 shows the spatial distribution of eff for sample III analyzed from P(T) curves. R was 1.0 inevery measurement point andeff ranged from 4.6x10-4 to 5.9x10-4 s. eff was increased by 1x106 Pa H2Ovapor heat treatment at 300oC for 30 min (sample IV). It ranged from 7.8x10-4 to 1.06x10-3 s. Figure 6
shows surface recombination velocity S for different measurement points of samples III and IV. S was
obtained by eq. (10) for Stop = Srear and long b. The recombination velocity in every measurement point
was markedly decreased by 1x106 Pa H2O vapor heat treatment. Moreover, the recombination velocity
had a lower limit of 7.1 cm/s at the present condition, as shown by the dashed line in Fig.6. This may
suggest a possibility of uniform and long eff over the silicon wafer by an optimized condition of highpressure H2O vapor heat treatment.

110107067-5

Fig. 5 Spatial distribution of τeff for Sample III

Fig. 6 Surface recombination velocity for
different measurement point for Samples III
and IV

Summary
We reported the measurement system of photo-induced minority carrier absorption of 9.35 GHz
microwave using periodically pulsed light illumination at 620 nm at 0.8 mW/cm2. We also developed
numerical analysis of photo-induced carrier generation, diffusion, and annihilation at surfaces with Stop,
Srear and in bulk substrate with b. The ratio of average carrier density during light illumination ON tolight illumination OFF, P(T), was introduced to investigate carrier annihilation properties. We defined
the effective minority carrier lifetime eff using P(T) curves. We demonstrated that eff well agreed withthe minority carrier lifetime for CW light illumination. It is possible to determine the minority carrier
lifetime without information of carrier generation rate including surface reflection loss using our method.
eff for hole minority carrier was experimentally demonstrated for n-type silicon samples coated with 100
nm thick SiO2 layers. When the SiO2 layer at the top surface was etched to 2 nm, we measured two
different eff of 7x10-5 and 1.7x10-4 s in the cases of light illumination to the top and rear surface,respectively. This indicated that carrier annihilation property depended on light illumination way fordefective samples. We also demonstrated spatial distribution of eff in 4 inch n-type silicon samples. effranged from 4.6x10-4 to 5.9x10-4 s for initial sample. it was increased from 7.8x10-4 to 1.06x10-3 s by
1x106 Pa H2O vapor heat treatment at 300oC for 30 min.

Acknowledgments
This work was partially supported by a Grant-in-Aid for Science Research C, No. 22560292 from the
Ministry of Education, Science, and Technology in Japan.

References[1] M. A. Green, Prog. Photovolt. Res. Appl. 17 (2009) 183.
[2] T. Sameshima, H. Hayasaka and T. Haba, Jpn. J. Appl. Phys. 48 (2009) 021204-1.
[3] J. W. Orton and P. Blood, The Electrical Characterization of Semiconductors: Measurement of
Minority Carrier Properties Chap. 4. (Academic Press, London, 1990)[4] T. Sameshima, T. Nagao, S. Yoshidomi, K. Kogure, and M. Hasumi, to be published in Jpn. J. Appl.
Phys. (2011).

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