- Email: [email protected]
Determination of interface recombination velocities and carrier lifetimes in SOI materials by a contactless optical modulation technique
Solid-Stare Elecfronics Vol. 38, No. 7, pp. 1359-1366. 1995 Copyright Q 1995 Elsevier Science Ltd 0038-1101(94)00262-2 Printed in Great Britain. All rights reserved 0038-l lot/95 169.50+ 0.00
Pergamon
DETERMINATION OF INTERFACE RECOMBINATION VELOCITIES AND CARRIER LIFETIMES IN SO1 MATERIALS BY A CONTACTLESS OPTICAL MODULATION TECHNIQUE YUN-SHAN
CHANG’, SHENG S. LI’ and PING-CHANG
YANG’
‘Department of Electrical Engineering, University of Florida, Gainesville, FL 32611, U.S.A. and IDepartment of Electrical Engineering, Feng Chia University, Taiwan, Republic of China (Received 23 August 1994; in revised form 26 October
1994)
Abstract-A novel contactless dual-beam optical modulation (DBOM) technique has been employed for determining the interface recombination velocities and substrate carrier lifetimes in a SIMOX (Separation by IMplantation of Oxygen) wafer. The DBOM method utilizes the optical modulation of the transmitted light intensity of an infrared (i.r.) probe beam (hv < Es) modulated by a CW visible laser pump beam (hv > Es) of different wavelengths (e.g., I, = 442 and 632.8 nm) via free-carrier absorption in the SIMOX wafer. The interface and bulk recombination velocities were determined by using pump beams of different wavelengths and incident angles. A theoretical model for the DBOM technique has been developed for extracting the interface recombination velocities and substrate lifetimes in the SIMOX wafers. The front-interface [Si film/buried oxide layer (BOX) interface] and back-interface (BOXjSi substrate interface) recombination velocities as well as the substrate carrier lifetimes were determined using this new technique. Mappings of the front- and back-interface recombination velocities and the substrate carrier lifetimes for several SIMOX wafers with different Si film thicknesses and oxygen implantation processes have been carried out.
1. INTRODUCITON
Recently, the development of fully-depleted (FD) SOI devices fabricated on ultra-thin SO1 films has drawn great interest in SIMOX and bonded SO1 wafers for high-speed ULSI applications. This is mainly due to the reduction of parasitic capacitances, body charging effects, threshold voltage,
latch-up effects, soft error rate, and the lower fabrication costs of device isolation. However, several device and material problems need to be overcome before mainstream IC applications of these SO1 materials can be fully realized. These include: (i) floating body effects; (ii) heat dissipation through the buried oxide layer; (iii) the effects of back interface on device reliability[l]; (iv) film thickness control in FD devices[2]; and (v) the necessity of low defect density, low cost ultra-thin film substrate (e.g., top Si film < 100 nm). As the SO1 technology enters the deep sub-micron CMOS regime, the supply voltage will be reduced below 2 V[3], the floating body effect, heat dissipation, and reliability problems become less significant. On the other hand, the fluctuation of SOI film thickness, which influences the threshold voltage, drive current, and latch-up voltage on the FD SOI devices, will have less important effect on the partially depleted (PD) devices with nonuniform channel doping and source/drain extension-halo instead[3]. One of the
bottlenecks in the widespread use of the SO1 technology is the availability of low defect density, low cost ultra-thin film SOI substrates. Although the optimization on ion-implantation and annealing conditions has significantly reduced the dislocation density and improved the interface property of SIMOX materials, it is highly desirable to develop a contactless and nondestructive diagnostic technique for routine screening of the SO1 wafers prior to IC fabrication. Although several methods such as capacitance[4,5], dynamic trans-conductance[6,7], thresholdvoltage[8], microwave lifetime measurement[9], surface photovoltage (SPV) [lo], photoluminescence scanning (PL) [ 111, atomic force microscopy (AFM) [ 121,and transmission electron microscopy (TEM) [131 are available for characterization of SO1 material quality, these techniques do not offer a direct means for determining the interface recombination velocities in SO1 materials. An optical modulation spectroscopy[l4] was reported earlier by Polla et al. for carrier lifetime measurement in HgCdTe. In this paper, we report a contactless dual-beam optical modulation (DBOM) technique[25,26] for determining the substrate carrier lifetimes and interface recombination velocities in SIMOX wafers. This DBOM technique can combine with the contactless dual-beam S-polarized reflectance (DBSPR) method [15] developed by us for quality control and defect study in SOI materials.
1359
1360
Yun-Shan
Incident Light
8 8 8 I
. . 00
.,,...,.,,..,,.,,.,.,...
,..,.
Chang
et al.
..
Air
_I R’ _.
_.
,..,..‘,
.,., .,.
Fig. 1. A schematic diagram of pump beams impinging on a SOI wafer under different angles of incidence at 0, and 0; and the corresponding total reflectances R and R’. transmittances T and T’; f, is the Si film thickness; f,, is the buried oxide thickness; noxand n,, are the refractive indices of SiO, layer and top Si film, respectively; S, , S,, q, and An,(x) are the recombination velocities, minority carrier lifetime, and minority excess carrier concentration in the top Si film, respectively; S,, rs, and An,(x) are the recombination velocities, minority carrier lifetime, and minority excess carrier concentration in the Si
substrate. respectively. 2. THEORY
-D,-
aAn
ax
In
this section, we describe the theory for determining the front-interface recombination velocity CS,), back-interface recombination velocity (S,), and the substrate carrier lifetime (r,) in a SIMOX wafer by using the DBOM technique. As shown in Fig. 1, a CW laser is impinging upon a p-type SOI substrate, the excess electron concentration An in the Si substrate can be obtained by solving the continuity eauation: D a*An An
DdL\n
nax
and the generation
=
QW,),
(3)
r=l,
=
S&(t, + t,),
(4)
.y=b.+I,
rate G(x) can be expressed
as:
in the top Si film
(5)
1
” with boundary
~-T+G(“)=O, ax*
in the Si substrate
conditions
ax
Pinhole
(6)
given by
dAn
D”--
R
G(x)=ct~~ocos82Te~“(“+‘~’
=
S, An(O),
(2)
r=O
IR Filler
\d
Meter
where cz, ‘I, &,, R, and T are the absorption coefficient, quantum efficiency, photon flux, total front surface reflectance, and back-interface transmittance at a given pump-beam wavelength, while, D,, tf, co,, 7, and S, are the diffusion coefficient, top Si film thickness, buried oxide (BOX) layer thickness, excess carrier lifetime, front-surface recombination velocity in the SO1 wafer, respectively. Note that both R and T can be determined by using the DBSPR method
u51. The excess electron concentration in the top Si film (An,) and the Si substrate (An*) can be obtained by solving eqn (1): An,(x) =
Fig. 2. Schematic diagram for the contactless optical modulation (DBOM) experimental
dual-beam setup.
c&,,( I -R - T)cos0,
Characterization
of SO1 materials
An,(x) =
x
e
-(.r-
(If+ In* N/L, _
e
-a
-
(If+ fo,))
(8)
9
where:
by optical
modulation
spectroscopy
1361
where f,, n, and p0 are the transmitted intensity, electron concentration, and hole concentration in the absence of pump-beam excitation, d is the sample thickness, urc = 6, + 0, is the total optical absorption and holes with cross-section of electrons 6, = 1 x lo-‘* A*cm* and o,, = 2.7 x IO-‘* 1* cm*[17], respectively, and i is the wavelength of the probe beam. The fractional change in the probe-beam transmit-
(9)
(10)
where O2is the refraction angle of the incident pum beam in the top Si film. Lr = fir and L, = J9D,,q are the diffusion lengths of excess minority carriers, and tr and rs are the minority carrier lifetimes in the top Si film and the Si substrate, respectively. When the pump beam is turned on, the excess carriers are generated in the top Si film (AN,) and Si substrate (AN,) which tend to modulate the i.r. transmitted intensity. Under low injection condition, the transmitted intensity of the probe beam, AN,, and AN? can be expressed as [16]:
ted intensity AI/L (with AI = I - 1,) can be expressed as:
In y+ (
1 =$= >
-u,(AN,+AN,)
x
L&,(1 -e-‘riLr) (
- L,C,(l - erriLr)
d AN,
@,n,+q+,)dx
crc +
s w+
b..
9
(11)
>
where
s w
AN, =
cl
An,(x) dx =
a~(1 - R - T)qb,cos 0,
L&,(1 - emrriLf)- L&,(1 - erriLr)
x
[
1,
1 + a (emZrr- 1)
(‘2)
and, d
AN2 =
An,(x) dx s c+ l0l (13)
Based on the facts that for ultra-thin Si film, with highly absorbed pump-beam (a > 4 x lo3 cm-‘), front low surface recombination velocity (S, x lo* cm/s[l8]), low film carrier lifetime (7rz 1 to 2 orders of magnitude smaller than bulk Si[20,21]), and higher interface trap density in SIMOX[6-81 (about one order of magnitude higher than that of the thermally oxidized silicon[ 19]), the following assumptions prevail in the ultra-thin film SIMOX wafers: (i) tf/LfG 1; (ii) aL,, aL, $ I; (iii) aD,, & S,; (iv) 0: $ S, S, Lf; (v) aD, B S,. Using these assumptions,
1362
Yun-Shan Chang et
al.
0.0
eqn (14) becomes:
0.7
AI - = -a,~
cos &do
I
(1 - R - T)z,
0.6 ^N '3
0.5
g
0.4
r_ r.
0.3 0.2 0.1
j
It should be noted that if the thickness of Si film is much smaller than the width of excess carrier distribution (e.g. tl < L,), the gradient of excess carrier concentration along the x direction (as shown in Fig. I) due to the diffusion process is very smaller, then, eqn (1) may no longer be suitable for describing the mechanism of excess carrier recombination. In Appendix A, we derived the excess carrier density (AN,) in the top Si film for ultra-thin film SO1 wafer. The result is identical to the part of Si film shown in eqn (15).
As shown in Fig. I, to determine the front-interface recombination velocity S, in a SOI wafer, a He-Cd CW laser (1 = 442 nm) is used as pump beam. Since the blue light is mainly absorbed in the Si film (see Fig. 3), and for an ultra-thin Si film with S, + S, > tr/7, (see Figs 4 and 5), then Sz can be deduced by eliminating the second term in eqn (I 5) under different incident angles 13,and 0; : -1 AI, AI, i
0
lwo0
t,(angstrom) Fig. 4. Ratio of (rr/Tr)/(S, + S,) in eqn (15) for different top Si film thicknesses and film lifetimes with S, + S, = 300 and 400 cm/s.
To determine the excess carrier lifetime z, in the SOI substrate, a He-He CW laser (2 = 632.8 nm) is used as the pump beam to illuminate on the back surface of the SO1 wafer. Since the reflectance R, of a not well-passivated silicon surface can be determined by the known r.m.s. values of surface slopes m and surface roughness a(221 and Si substrate of SO1 wafer, the fractional change of the transmitted probebeam intensity can be expected as AI -I = u,V&cos
(17)
e2(l - Rr)[5 (;;;;r;J]
and the substrate lifetime 7, is obtained from eqn (17) using the back surface recombination velocity of S, x 6 x lo4 cm/s[23]:
-
x [Ql -
e
-“r)]
1 - R, - T,
7, =
1 - R, - T,
X
T,
-
T,
(18)
(16)
>’
where subscripts 1 and 2 are the measured parameters corresponding to incident angles 0, and O;, respectively. S, is in the order of lO’cm/s for a well-passivated silicon surface[ 16,181.
where AI
I A=
32
\
T 0,?4, c0s e2(i
S&/E
- R,) aD,.
(19)
1.6 -
2624
0.0
2F
---63
1.4
-
_
-
s,+s~l5ocm/s
--
s,+s~26ocmfs
1.2
-1.0
t
3 '3
1.0
I=
- 0.6 & t - 0.6 6
-
0 102
0.0 103
rd
+bwtrom)
Fig. 3. Ratio of the absorption of pump beam in top Si film to Si substrate vs top Si film thickness under different incident angles.
0
2cm
_
_ t
Boo0
1WOO
t(angstrom)
Fig. 5. Ratio of (r,/r,)/(S, + S,) in eqn (I 5) for different top Si film thicknesses and film lifetimes with S, + Sz = 150 and 250 cm/s.
Characterization of SOI materials by optical modulation spectroscopy Similar to the determination of S,, the backinterface recombination velocity S, is obtained by measuring t, and using a He-Ne laser (1 = 632.8 nm) as pump beam. Since the He-Ne laser is mainly absorbed in the Si substrate (see Fig. 3). The S, can be determined from eqn (15) under different incident angles: s
w -UP,
=
3
(20)
1-L,K’
where --L
4
K=
arc~~o,cose,,(l-R,-T,)
’
(21)
where subscripts 1 and 2 are the measured parameters corresponding to incident angles 0, and 0;) respectively. Note that the above analysis can be applied to n-type SO1 wafers as well provided that the parameters for electrons are replaced by holes (i.e., D, by D,, and T” by 7p etc.).
impinging on the back surface of the SIMOX wafer. The r.m.s. values of the surface slope m and the surface roughness Q were measured by using Sloan Dektak II surface profiler to obtain the reflectance. The i.r. transmitted beam intensity I was first measured using the chopped probe beam and a lock-in amplifier. The change in the transmitted intensity AI was measured by using the chopped pump beam superimposed on the probe beam which was not chopped, and the resulting i.r. transmitted intensity was measured by using a lock-in amplifier. To determine the back-interface recombination velocity S,, the probe and pump beams were impinging on the front surface of the measured sample with the different oblique incident angles of the pumpbeam excitation. The measurements of I and AI are the same as in the determination of r,. Values of R were measured by using a laser power meter. For different angles of pump-beam excitation, the measurements of I, AI, and R are carried out in a similar procedure. The front interface recombination velocity S, was determined by using the He-Cd laser as pump beam and using the same procedures as described above. The S-polarized reflectances of pump beam were monitored by a laser power meter to determine the front surface reflectance R and the back-interface transmittance T of the SIMOX wafer. 4. RESULTS
3. EXPERIMENTAL
DETAILS
Figure 2 shows the schematic diagram of the DBOM experimental setup. A tungsten lamp, which is used as the probe beam, is passing through an i.r. filter (a low-doped Si wafer) with a cutoff wavelength of about 1.1 pm, and is focused to a beam size of about 4 mm dia. A 14 mW He-Cd CW laser or a 4mW He-Ne CW laser was used as the pump beam which is lined up with the probe beam in the experiment. Both laser beams are focused to a spot size of about 2 mm dia and polarized by the Dichroic linear polarizers (with extinction ratios of < 1.6 x 10m4for A = 442 nm and < 7.6 x lo-’ for I = 632.8 nm). Both probe beam and pump beam are chopped at 405 Hz for synchronous detection by a lock-in amplifier. The pump beam is reflected by half-silver coated mirrors and then focused into the same spot as the probe beam on the measured sample. In the experiment, the substrate carrier lifetime z, was measured by using an i.r. probe beam and a He-Ne laser pump beam Table
I.
Substrate
lifetimes,
front-interface
tr Sample
(A)
;I)
Milt SI2 M13t
2004 5300 1870
3479 3900 3744
tMultiple
implant
recombination method
4.1. Measurement velocity
recombination
Front-interface recombination velocity measurements were carried out in both n- and p-type SIMOX wafers with different top Si film thicknesses, annealing temperatures, and oxygen implant doses. From eqn (16) and the values of R and T obtained by the DBSPR method[ 151,we calculated the front-interface recombination velocity using the measured values of AI, I at the angles of incidence 0, = 23” and 0; = 63”, the average value of optical absorption coefficient CIz 3 x 104cm-i[19], ug z 9.5 x lo-i8cm2[17], q z 0.5[19], do,,z 7.48 x 10” cmm2 s-r at 8, = 23”, and & z 4.62 x 10” cm-* s-i at 0; = 63”. The results for several SIMOX wafers are summarized in Table 1. From the results, it is noted that the multiple implant sample has a larger defect density in the front interface than that of the single implant sample. This is consistent with previous work reported by Venables et al. [24].
velocities, and back-interface for several SIMOX samples
recombination
DOS
Anneal
Resistivity
(“C, h)
(type, Q-cm)
% (PG
1310.5 1285,6 1285,6
p, l&20 n, 6 p IO-20
23.26 1.39 10.79
wafer with doses of 0.5, 0.5, 0.8 x 10’scm~2.
AND DISCUSSION
of front-interface
(cm-*) 1.8 x 10’8 1.8 x IO” 1.8 x IO”
1363
velocities SI + s, @m.s-‘) 174.40 242.63 324.87
measured
by DROM s, (cm
se’)
44.70 95.99 59.79
Yun-Shan Chang et
1364
al.
Sample Ml3 Sl +S2 measurement
+ 25%
+5%
.‘::;:::. ;;;;;;:. average (324.37 cm/s) t.‘.‘.~‘.‘.‘.‘. -5%
-25%
Fig. 6. Mapping of the front interface recombination velocitties S, + S, for sample-M13.
For a thick-film (tf > 5000 A) SIMOX wafer with small film lifetime (TV (: 0.3 ps). eqn (16) may not give a good estimation of the front-interface recombination velocity, as shown in Figs 4 and 5. Under such conditions, a shorter wavelength pump beam (e.g., U.V. laser) can be employed to obtain the film lifetime (TV). The front-interface recombination velocity can be determined by substituting this measured zf into eqn
(15) and using the blue He-Cd laser as a pump beam and using different incident angles (e.g. t$ and 19;)[25]. Figure 6 shows the mapping profile of the interface recombination velocities (S, + S,) for sample-M13. The average value is 325 cm/s. For a well passivated silicon surface[l6,18] S, is about 100 cm/s, while S, was found to be 225 cm/s. We scanned 300 points on each SIMOX wafer and divided the 4” SIMOX wafer
Sample Ml3 ‘IS measurement
average (10.79ps)
Fig. 7. Mapping of the substrate lifetimes 5, for sample-MI3.
Characterization
of SOI materials
by optical
Table 2. Measured reflectance R, of the back surface for different
SIMOX samoles rs
Sample
m
G
RS
MI1 SI2 MI3
0.0456 0.0460 0.0495
0.3557 0.3311 0.3454
0.2371 0.2371 0.2371
tJ, = 6328 A is the wavelength of the incident pump beam. fR, = R, x R,, where R,, is the reflectance of a well passivated Si surface, and R,, is the relative reflectance[22] obtained from the measured m and 6.
60 squares in the DBOM measurements. Thus, the area of each square represents the average value of five measurements. From Fig. 6, it is shown that the uniformity of front-interface recombination velocities in sample-MI3 is lower near the center region than the upper edge region of the wafer. Sample-MI1 and SI2 have the similar results as sample-M13.
into
4.2. Measurement of substrate lifetimes The substrate lifetimes were determined from eqns (17) (18), and (19) using the measured values of m, 0, AI, 1, the average value of optical absorption coefficient c( z 4.1 x lo3 cm-i[l9], OrC% 9.5 x lo-‘* cm*[l7], q z 0.85[19], and c$,,c 4.02 x 10” cm-* SC’ at t$ = 23”. Values of R,in eqn (17) were calculated using eqns (27) and (39) given in Davies’ report[22] with the measured values of m and 0. The results of the calculated R,are listed in Table 2. The measured substrate lifetimes for several SIMOX wafers are summarized in Table 1. Sample-S1 has a lower t, than other SIMOX samples tested. This may be due to the heavy metal impurity introduced in this SIMOX wafer during the single oxygen implantation process. The heavy metal impurities are gettering in the Si
modulation
spectroscopy
substrate during the post implantation annealing [27,28]. The gettering impurities degrade the substrate lifetime. Figure 7 shows the mapping profile of the substrate lifetimes for sample-M13. The average value is 10.8 ps. We also scanned 300 points on each SIMOX wafer. From Fig. 7, a uniform distribution of substrate lifetime was observed and the lifetimes are higher near the center region than the edge region of the wafer. Sample-MI1 and S12 have similar uniformity profiles as sample-M13. 4.3. Measurement velocity
of back-interface
+ 25%
SSE 3817-F
of the back
interface
recombination
Similar to the front-interface recombination velocity measurements, the back-interface velocity can be determined from eqns (20) and (21) using the measured values of ‘ss, Al, I, the average value of optical absorption coefficient c( z 4.1 x lo3 err-‘[19], urCz 9.5 x IO-‘* cm*[l7], q x 0.85[19], &, = 4.02 x 10” cm-* SC’ at 0, = 23”, and c$,,o 9.96 x lOI cm-* SC’ at ~9;= 63”. Values of R and Tin eqn (21) were obtained from the DBSPR method[l5]. The results for several SIMOX wafers are summarized in Table 1. It is noted that sample-S11 has a higher back-interface recombination velocities than other SIMOX samples. This may be attributed to the post-implantation annealing induced by the copper diffusion from the Si surface into the buried oxide and Si substrate, with copper impurities precipitated in the back interface (e.g. intrinsic gettering)[27,28] of the SIMOX wafer. Figure 8 displays the mapping profile of the back interface recombination velocities for sample-M13.
Sample Ml3 S3 measurement
Fig. 8. Mapping
1365
recombination
velocities
S, for sample-M13.
Yun-Shan Chang et al.
1366
The average value is 59.8 cm/s. We also scanned 300 points on each SIMOX wafer. From Fig. 8, the back-interface recombination velocities are lower near the central region than in the edge region of the wafer. 5. CONCLUSION
In this work, a contactless dual beam optical modulation (DBOM) technique for determining the front- and back-interface recombination velocities and the substrate carrier lifetimes in SIMOX wafers has been demonstrated. This method is especially useful for quality control and defect studies of the SO1 wafer manufacturing. Using this technique, the interface properties and the quality of SOI wafers can be evaluated versus Processing and growth parameters. Thus, the contactless DBOM technique described in this paper may be used to obtain optimal manufacturing process for the SOI materials. Acknowledgements-The
authors would like to thank Dr Lisa Allen of Ibis Technology for providing SIMOX samples used in this study. The work performed at the University of Florida was supported in part by the Defense Nuclear Agency under a subcontract from Ibis Technology. REFERENCES
1. S. Cristoloveanu, S. M. Gulwadi, D. E. Ioannou, G. J. Campisi and H. L. Hughes, IEEE Electron Device Letr.
13, 603 (1992). 2. F. T. Brady and N. F. Haddad, IEEE SOI Conf. Proc., p. 130 (1993). 3. G. G. Shahidi, C. Blair, K. Beyer, T. Bucelot, T. Buti, P. N. Ghana. S. Chu. P. Coane, J. Comfort, B. Davari, R. Dennarz, S. Furkay, H. Hovel, J. Johnson, D. Klaus, K. Kiewtniack, R. Logan, T. Li, P. A. McFarland, N. Mazzeo, D. Moy, S. Neely, T. Ning, M. Rodriguez, D. Sadana, S. itiffler, J. Sin, F. &veil and J. Warnock. Svmo. on VLSI Tech.. D. 27 (1993). H. S. Chen ad i. S. Li, IEEE Trail. Eleciron bevices
12. T. R. Neal and P. C. Karulkar, IEEE SOI Conf. Proc., p. 174 (1993). 13. S. Seraphin and B. F. Cordts III, IEEE SOI Conf Proc., p. 86 (1991). 14. D. L. Polla, R. L. Aggarwal, D. A. Nelson, J. F. Shanley and M. B. Reine, Appl. Phys. Lerf. 43, 941 (1983). 15. Y. S. Chang and S. S. Li, 6th Inr. Symp. on SOI Tech. and Devices, paper no. 513, 185th ECS Meeting, San
Francisco (22-27 May 1994). 16. F. Sanii, F. P. Giles, R. J. Schwartz and J. L. Gray, Solid-St. Eleclron. 35, 3 I1 (1992). 17. D. K. Schroder, R. N. Thomas and J. C. Swartz, IEEE Trans. Electron Devices ED-25, 254 (1978). 18. A. S. Grove, Physics and Technology of Semiconductor Deuices. Wiley, New York (1967). 19. S. M. Sze, Physics of Semiconductor Devices, 2nd Edn. Wiley, New York (1981). 20. H. Hovel, J. Freeouf, K. Beyer, D. Sadana and S. Chu, IEEE SOI Conf. Proc., p. 40 (1993). 21. H. Baumgart, R. Egloff, E. Arnold, T. J. Letavic, s. Merchant, S. Mukherjee and H. Bhimnathwala, IEEE SOI Coflf: Proc., p. 44 (1993). 22. H. Davies, Proc. Insf. Elec. Engnr 101, 209 (1954). 23. Th. Flohr and R. Helbig, J. Appl. Phys. 66,306O (1989). 24. D. Venables, S. J. Krause, J. C. Park, J. D. Lee and P. Roitman, IEEE SOI Conf: Proc., p. 48 (1993). 25. P. C. Yang and S. S. Li, Appl. Phys. Letf. 61, 1408 (1992). 26. P. C. Yang and S. S. Li, Solid-St. Electron. 35, 927 (1992). 27. M. Delfino, M. Jaczvnski. A. E. Morgan, C. Vorst, M. E. Lunnon and P. Maillot, J. elect&hem. Sot. 134, 2027 (1987). 28. T. I. Kamnis and S. Y. Chiang, J. appl. Phys. 58,2559 (1985).
APPENDIX
For the ultra-thin Si film SO1 wafer, the photogenerated excess carrier concentration gradient is usually very small along the direction of incident beam. As a result, the diffusion process is negligible while the volume and surface recombination processes will dominate the excess carrier decay in the top Si film. Thus, eqn (1) becomes
G(x)-$0
39, 1740 (1992).
H. S. Chen and S. S. Li. IEEE Trans. Electron Devices P. C. Yang, H. S. Chen and S. S. Li, Solid-St. Electron.
‘=‘+‘+‘= 5 =i t,lS,
35. 1031 (1992).
(1993).
9. W. Rehwald, R. Morf and A. Vonlanthen, Semiconduc-
(Al)
where
39, 1747 (1992).
D.. I. Ioannou; X. Zhong, B. Mazhari, G. J. Campisi and H. L. Hughes, IEEE Electron Device Letr. 12,430 (1991). 8. P. C. Yang and S. S. Li, Solid-St. Electron 36, 801
A
(S, + S,) + ‘f 51 r,is,
‘I
(A2)
The total excess carrier concentration in the Si film can be obtained by solving eqns (5), (Al) and (A2) AN,=
4~,(X)dx=a~(l-R-T)~,cosB,r(l-e-J’~ s Cl
tar Sci. Technol. 6, 735 (1991).
10. L. Jastrzebski, G. Cullen and R. Soydan, J. elecrrochem. sot. 137, 303 (1990). 11. H. J. Hovel, IEEE SOI Conf. Proc., p. 26 (1993).
=q(l-R-T)+,cos0,
(A3)
Pergamon
DETERMINATION OF INTERFACE RECOMBINATION VELOCITIES AND CARRIER LIFETIMES IN SO1 MATERIALS BY A CONTACTLESS OPTICAL MODULATION TECHNIQUE YUN-SHAN
CHANG’, SHENG S. LI’ and PING-CHANG
YANG’
‘Department of Electrical Engineering, University of Florida, Gainesville, FL 32611, U.S.A. and IDepartment of Electrical Engineering, Feng Chia University, Taiwan, Republic of China (Received 23 August 1994; in revised form 26 October
1994)
Abstract-A novel contactless dual-beam optical modulation (DBOM) technique has been employed for determining the interface recombination velocities and substrate carrier lifetimes in a SIMOX (Separation by IMplantation of Oxygen) wafer. The DBOM method utilizes the optical modulation of the transmitted light intensity of an infrared (i.r.) probe beam (hv < Es) modulated by a CW visible laser pump beam (hv > Es) of different wavelengths (e.g., I, = 442 and 632.8 nm) via free-carrier absorption in the SIMOX wafer. The interface and bulk recombination velocities were determined by using pump beams of different wavelengths and incident angles. A theoretical model for the DBOM technique has been developed for extracting the interface recombination velocities and substrate lifetimes in the SIMOX wafers. The front-interface [Si film/buried oxide layer (BOX) interface] and back-interface (BOXjSi substrate interface) recombination velocities as well as the substrate carrier lifetimes were determined using this new technique. Mappings of the front- and back-interface recombination velocities and the substrate carrier lifetimes for several SIMOX wafers with different Si film thicknesses and oxygen implantation processes have been carried out.
1. INTRODUCITON
Recently, the development of fully-depleted (FD) SOI devices fabricated on ultra-thin SO1 films has drawn great interest in SIMOX and bonded SO1 wafers for high-speed ULSI applications. This is mainly due to the reduction of parasitic capacitances, body charging effects, threshold voltage,
latch-up effects, soft error rate, and the lower fabrication costs of device isolation. However, several device and material problems need to be overcome before mainstream IC applications of these SO1 materials can be fully realized. These include: (i) floating body effects; (ii) heat dissipation through the buried oxide layer; (iii) the effects of back interface on device reliability[l]; (iv) film thickness control in FD devices[2]; and (v) the necessity of low defect density, low cost ultra-thin film substrate (e.g., top Si film < 100 nm). As the SO1 technology enters the deep sub-micron CMOS regime, the supply voltage will be reduced below 2 V[3], the floating body effect, heat dissipation, and reliability problems become less significant. On the other hand, the fluctuation of SOI film thickness, which influences the threshold voltage, drive current, and latch-up voltage on the FD SOI devices, will have less important effect on the partially depleted (PD) devices with nonuniform channel doping and source/drain extension-halo instead[3]. One of the
bottlenecks in the widespread use of the SO1 technology is the availability of low defect density, low cost ultra-thin film SOI substrates. Although the optimization on ion-implantation and annealing conditions has significantly reduced the dislocation density and improved the interface property of SIMOX materials, it is highly desirable to develop a contactless and nondestructive diagnostic technique for routine screening of the SO1 wafers prior to IC fabrication. Although several methods such as capacitance[4,5], dynamic trans-conductance[6,7], thresholdvoltage[8], microwave lifetime measurement[9], surface photovoltage (SPV) [lo], photoluminescence scanning (PL) [ 111, atomic force microscopy (AFM) [ 121,and transmission electron microscopy (TEM) [131 are available for characterization of SO1 material quality, these techniques do not offer a direct means for determining the interface recombination velocities in SO1 materials. An optical modulation spectroscopy[l4] was reported earlier by Polla et al. for carrier lifetime measurement in HgCdTe. In this paper, we report a contactless dual-beam optical modulation (DBOM) technique[25,26] for determining the substrate carrier lifetimes and interface recombination velocities in SIMOX wafers. This DBOM technique can combine with the contactless dual-beam S-polarized reflectance (DBSPR) method [15] developed by us for quality control and defect study in SOI materials.
1359
1360
Yun-Shan
Incident Light
8 8 8 I
. . 00
.,,...,.,,..,,.,,.,.,...
,..,.
Chang
et al.
..
Air
_I R’ _.
_.
,..,..‘,
.,., .,.
Fig. 1. A schematic diagram of pump beams impinging on a SOI wafer under different angles of incidence at 0, and 0; and the corresponding total reflectances R and R’. transmittances T and T’; f, is the Si film thickness; f,, is the buried oxide thickness; noxand n,, are the refractive indices of SiO, layer and top Si film, respectively; S, , S,, q, and An,(x) are the recombination velocities, minority carrier lifetime, and minority excess carrier concentration in the top Si film, respectively; S,, rs, and An,(x) are the recombination velocities, minority carrier lifetime, and minority excess carrier concentration in the Si
substrate. respectively. 2. THEORY
-D,-
aAn
ax
In
this section, we describe the theory for determining the front-interface recombination velocity CS,), back-interface recombination velocity (S,), and the substrate carrier lifetime (r,) in a SIMOX wafer by using the DBOM technique. As shown in Fig. 1, a CW laser is impinging upon a p-type SOI substrate, the excess electron concentration An in the Si substrate can be obtained by solving the continuity eauation: D a*An An
DdL\n
nax
and the generation
=
QW,),
(3)
r=l,
=
S&(t, + t,),
(4)
.y=b.+I,
rate G(x) can be expressed
as:
in the top Si film
(5)
1
” with boundary
~-T+G(“)=O, ax*
in the Si substrate
conditions
ax
Pinhole
(6)
given by
dAn
D”--
R
G(x)=ct~~ocos82Te~“(“+‘~’
=
S, An(O),
(2)
r=O
IR Filler
\d
Meter
where cz, ‘I, &,, R, and T are the absorption coefficient, quantum efficiency, photon flux, total front surface reflectance, and back-interface transmittance at a given pump-beam wavelength, while, D,, tf, co,, 7, and S, are the diffusion coefficient, top Si film thickness, buried oxide (BOX) layer thickness, excess carrier lifetime, front-surface recombination velocity in the SO1 wafer, respectively. Note that both R and T can be determined by using the DBSPR method
u51. The excess electron concentration in the top Si film (An,) and the Si substrate (An*) can be obtained by solving eqn (1): An,(x) =
Fig. 2. Schematic diagram for the contactless optical modulation (DBOM) experimental
dual-beam setup.
c&,,( I -R - T)cos0,
Characterization
of SO1 materials
An,(x) =
x
e
-(.r-
(If+ In* N/L, _
e
-a
-
(If+ fo,))
(8)
9
where:
by optical
modulation
spectroscopy
1361
where f,, n, and p0 are the transmitted intensity, electron concentration, and hole concentration in the absence of pump-beam excitation, d is the sample thickness, urc = 6, + 0, is the total optical absorption and holes with cross-section of electrons 6, = 1 x lo-‘* A*cm* and o,, = 2.7 x IO-‘* 1* cm*[17], respectively, and i is the wavelength of the probe beam. The fractional change in the probe-beam transmit-
(9)
(10)
where O2is the refraction angle of the incident pum beam in the top Si film. Lr = fir and L, = J9D,,q are the diffusion lengths of excess minority carriers, and tr and rs are the minority carrier lifetimes in the top Si film and the Si substrate, respectively. When the pump beam is turned on, the excess carriers are generated in the top Si film (AN,) and Si substrate (AN,) which tend to modulate the i.r. transmitted intensity. Under low injection condition, the transmitted intensity of the probe beam, AN,, and AN? can be expressed as [16]:
ted intensity AI/L (with AI = I - 1,) can be expressed as:
In y+ (
1 =$= >
-u,(AN,+AN,)
x
L&,(1 -e-‘riLr) (
- L,C,(l - erriLr)
d AN,
@,n,+q+,)dx
crc +
s w+
b..
9
(11)
>
where
s w
AN, =
cl
An,(x) dx =
a~(1 - R - T)qb,cos 0,
L&,(1 - emrriLf)- L&,(1 - erriLr)
x
[
1,
1 + a (emZrr- 1)
(‘2)
and, d
AN2 =
An,(x) dx s c+ l0l (13)
Based on the facts that for ultra-thin Si film, with highly absorbed pump-beam (a > 4 x lo3 cm-‘), front low surface recombination velocity (S, x lo* cm/s[l8]), low film carrier lifetime (7rz 1 to 2 orders of magnitude smaller than bulk Si[20,21]), and higher interface trap density in SIMOX[6-81 (about one order of magnitude higher than that of the thermally oxidized silicon[ 19]), the following assumptions prevail in the ultra-thin film SIMOX wafers: (i) tf/LfG 1; (ii) aL,, aL, $ I; (iii) aD,, & S,; (iv) 0: $ S, S, Lf; (v) aD, B S,. Using these assumptions,
1362
Yun-Shan Chang et
al.
0.0
eqn (14) becomes:
0.7
AI - = -a,~
cos &do
I
(1 - R - T)z,
0.6 ^N '3
0.5
g
0.4
r_ r.
0.3 0.2 0.1
j
It should be noted that if the thickness of Si film is much smaller than the width of excess carrier distribution (e.g. tl < L,), the gradient of excess carrier concentration along the x direction (as shown in Fig. I) due to the diffusion process is very smaller, then, eqn (1) may no longer be suitable for describing the mechanism of excess carrier recombination. In Appendix A, we derived the excess carrier density (AN,) in the top Si film for ultra-thin film SO1 wafer. The result is identical to the part of Si film shown in eqn (15).
As shown in Fig. I, to determine the front-interface recombination velocity S, in a SOI wafer, a He-Cd CW laser (1 = 442 nm) is used as pump beam. Since the blue light is mainly absorbed in the Si film (see Fig. 3), and for an ultra-thin Si film with S, + S, > tr/7, (see Figs 4 and 5), then Sz can be deduced by eliminating the second term in eqn (I 5) under different incident angles 13,and 0; : -1 AI, AI, i
0
lwo0
t,(angstrom) Fig. 4. Ratio of (rr/Tr)/(S, + S,) in eqn (15) for different top Si film thicknesses and film lifetimes with S, + S, = 300 and 400 cm/s.
To determine the excess carrier lifetime z, in the SOI substrate, a He-He CW laser (2 = 632.8 nm) is used as the pump beam to illuminate on the back surface of the SO1 wafer. Since the reflectance R, of a not well-passivated silicon surface can be determined by the known r.m.s. values of surface slopes m and surface roughness a(221 and Si substrate of SO1 wafer, the fractional change of the transmitted probebeam intensity can be expected as AI -I = u,V&cos
(17)
e2(l - Rr)[5 (;;;;r;J]
and the substrate lifetime 7, is obtained from eqn (17) using the back surface recombination velocity of S, x 6 x lo4 cm/s[23]:
-
x [Ql -
e
-“r)]
1 - R, - T,
7, =
1 - R, - T,
X
T,
-
T,
(18)
(16)
>’
where subscripts 1 and 2 are the measured parameters corresponding to incident angles 0, and O;, respectively. S, is in the order of lO’cm/s for a well-passivated silicon surface[ 16,181.
where AI
I A=
32
\
T 0,?4, c0s e2(i
S&/E
- R,) aD,.
(19)
1.6 -
2624
0.0
2F
---63
1.4
-
_
-
s,+s~l5ocm/s
--
s,+s~26ocmfs
1.2
-1.0
t
3 '3
1.0
I=
- 0.6 & t - 0.6 6
-
0 102
0.0 103
rd
+bwtrom)
Fig. 3. Ratio of the absorption of pump beam in top Si film to Si substrate vs top Si film thickness under different incident angles.
0
2cm
_
_ t
Boo0
1WOO
t(angstrom)
Fig. 5. Ratio of (r,/r,)/(S, + S,) in eqn (I 5) for different top Si film thicknesses and film lifetimes with S, + Sz = 150 and 250 cm/s.
Characterization of SOI materials by optical modulation spectroscopy Similar to the determination of S,, the backinterface recombination velocity S, is obtained by measuring t, and using a He-Ne laser (1 = 632.8 nm) as pump beam. Since the He-Ne laser is mainly absorbed in the Si substrate (see Fig. 3). The S, can be determined from eqn (15) under different incident angles: s
w -UP,
=
3
(20)
1-L,K’
where --L
4
K=
arc~~o,cose,,(l-R,-T,)
’
(21)
where subscripts 1 and 2 are the measured parameters corresponding to incident angles 0, and 0;) respectively. Note that the above analysis can be applied to n-type SO1 wafers as well provided that the parameters for electrons are replaced by holes (i.e., D, by D,, and T” by 7p etc.).
impinging on the back surface of the SIMOX wafer. The r.m.s. values of the surface slope m and the surface roughness Q were measured by using Sloan Dektak II surface profiler to obtain the reflectance. The i.r. transmitted beam intensity I was first measured using the chopped probe beam and a lock-in amplifier. The change in the transmitted intensity AI was measured by using the chopped pump beam superimposed on the probe beam which was not chopped, and the resulting i.r. transmitted intensity was measured by using a lock-in amplifier. To determine the back-interface recombination velocity S,, the probe and pump beams were impinging on the front surface of the measured sample with the different oblique incident angles of the pumpbeam excitation. The measurements of I and AI are the same as in the determination of r,. Values of R were measured by using a laser power meter. For different angles of pump-beam excitation, the measurements of I, AI, and R are carried out in a similar procedure. The front interface recombination velocity S, was determined by using the He-Cd laser as pump beam and using the same procedures as described above. The S-polarized reflectances of pump beam were monitored by a laser power meter to determine the front surface reflectance R and the back-interface transmittance T of the SIMOX wafer. 4. RESULTS
3. EXPERIMENTAL
DETAILS
Figure 2 shows the schematic diagram of the DBOM experimental setup. A tungsten lamp, which is used as the probe beam, is passing through an i.r. filter (a low-doped Si wafer) with a cutoff wavelength of about 1.1 pm, and is focused to a beam size of about 4 mm dia. A 14 mW He-Cd CW laser or a 4mW He-Ne CW laser was used as the pump beam which is lined up with the probe beam in the experiment. Both laser beams are focused to a spot size of about 2 mm dia and polarized by the Dichroic linear polarizers (with extinction ratios of < 1.6 x 10m4for A = 442 nm and < 7.6 x lo-’ for I = 632.8 nm). Both probe beam and pump beam are chopped at 405 Hz for synchronous detection by a lock-in amplifier. The pump beam is reflected by half-silver coated mirrors and then focused into the same spot as the probe beam on the measured sample. In the experiment, the substrate carrier lifetime z, was measured by using an i.r. probe beam and a He-Ne laser pump beam Table
I.
Substrate
lifetimes,
front-interface
tr Sample
(A)
;I)
Milt SI2 M13t
2004 5300 1870
3479 3900 3744
tMultiple
implant
recombination method
4.1. Measurement velocity
recombination
Front-interface recombination velocity measurements were carried out in both n- and p-type SIMOX wafers with different top Si film thicknesses, annealing temperatures, and oxygen implant doses. From eqn (16) and the values of R and T obtained by the DBSPR method[ 151,we calculated the front-interface recombination velocity using the measured values of AI, I at the angles of incidence 0, = 23” and 0; = 63”, the average value of optical absorption coefficient CIz 3 x 104cm-i[19], ug z 9.5 x lo-i8cm2[17], q z 0.5[19], do,,z 7.48 x 10” cmm2 s-r at 8, = 23”, and & z 4.62 x 10” cm-* s-i at 0; = 63”. The results for several SIMOX wafers are summarized in Table 1. From the results, it is noted that the multiple implant sample has a larger defect density in the front interface than that of the single implant sample. This is consistent with previous work reported by Venables et al. [24].
velocities, and back-interface for several SIMOX samples
recombination
DOS
Anneal
Resistivity
(“C, h)
(type, Q-cm)
% (PG
1310.5 1285,6 1285,6
p, l&20 n, 6 p IO-20
23.26 1.39 10.79
wafer with doses of 0.5, 0.5, 0.8 x 10’scm~2.
AND DISCUSSION
of front-interface
(cm-*) 1.8 x 10’8 1.8 x IO” 1.8 x IO”
1363
velocities SI + s, @m.s-‘) 174.40 242.63 324.87
measured
by DROM s, (cm
se’)
44.70 95.99 59.79
Yun-Shan Chang et
1364
al.
Sample Ml3 Sl +S2 measurement
+ 25%
+5%
.‘::;:::. ;;;;;;:. average (324.37 cm/s) t.‘.‘.~‘.‘.‘.‘. -5%
-25%
Fig. 6. Mapping of the front interface recombination velocitties S, + S, for sample-M13.
For a thick-film (tf > 5000 A) SIMOX wafer with small film lifetime (TV (: 0.3 ps). eqn (16) may not give a good estimation of the front-interface recombination velocity, as shown in Figs 4 and 5. Under such conditions, a shorter wavelength pump beam (e.g., U.V. laser) can be employed to obtain the film lifetime (TV). The front-interface recombination velocity can be determined by substituting this measured zf into eqn
(15) and using the blue He-Cd laser as a pump beam and using different incident angles (e.g. t$ and 19;)[25]. Figure 6 shows the mapping profile of the interface recombination velocities (S, + S,) for sample-M13. The average value is 325 cm/s. For a well passivated silicon surface[l6,18] S, is about 100 cm/s, while S, was found to be 225 cm/s. We scanned 300 points on each SIMOX wafer and divided the 4” SIMOX wafer
Sample Ml3 ‘IS measurement
average (10.79ps)
Fig. 7. Mapping of the substrate lifetimes 5, for sample-MI3.
Characterization
of SOI materials
by optical
Table 2. Measured reflectance R, of the back surface for different
SIMOX samoles rs
Sample
m
G
RS
MI1 SI2 MI3
0.0456 0.0460 0.0495
0.3557 0.3311 0.3454
0.2371 0.2371 0.2371
tJ, = 6328 A is the wavelength of the incident pump beam. fR, = R, x R,, where R,, is the reflectance of a well passivated Si surface, and R,, is the relative reflectance[22] obtained from the measured m and 6.
60 squares in the DBOM measurements. Thus, the area of each square represents the average value of five measurements. From Fig. 6, it is shown that the uniformity of front-interface recombination velocities in sample-MI3 is lower near the center region than the upper edge region of the wafer. Sample-MI1 and SI2 have the similar results as sample-M13.
into
4.2. Measurement of substrate lifetimes The substrate lifetimes were determined from eqns (17) (18), and (19) using the measured values of m, 0, AI, 1, the average value of optical absorption coefficient c( z 4.1 x lo3 cm-i[l9], OrC% 9.5 x lo-‘* cm*[l7], q z 0.85[19], and c$,,c 4.02 x 10” cm-* SC’ at t$ = 23”. Values of R,in eqn (17) were calculated using eqns (27) and (39) given in Davies’ report[22] with the measured values of m and 0. The results of the calculated R,are listed in Table 2. The measured substrate lifetimes for several SIMOX wafers are summarized in Table 1. Sample-S1 has a lower t, than other SIMOX samples tested. This may be due to the heavy metal impurity introduced in this SIMOX wafer during the single oxygen implantation process. The heavy metal impurities are gettering in the Si
modulation
spectroscopy
substrate during the post implantation annealing [27,28]. The gettering impurities degrade the substrate lifetime. Figure 7 shows the mapping profile of the substrate lifetimes for sample-M13. The average value is 10.8 ps. We also scanned 300 points on each SIMOX wafer. From Fig. 7, a uniform distribution of substrate lifetime was observed and the lifetimes are higher near the center region than the edge region of the wafer. Sample-MI1 and S12 have similar uniformity profiles as sample-M13. 4.3. Measurement velocity
of back-interface
+ 25%
SSE 3817-F
of the back
interface
recombination
Similar to the front-interface recombination velocity measurements, the back-interface velocity can be determined from eqns (20) and (21) using the measured values of ‘ss, Al, I, the average value of optical absorption coefficient c( z 4.1 x lo3 err-‘[19], urCz 9.5 x IO-‘* cm*[l7], q x 0.85[19], &, = 4.02 x 10” cm-* SC’ at 0, = 23”, and c$,,o 9.96 x lOI cm-* SC’ at ~9;= 63”. Values of R and Tin eqn (21) were obtained from the DBSPR method[l5]. The results for several SIMOX wafers are summarized in Table 1. It is noted that sample-S11 has a higher back-interface recombination velocities than other SIMOX samples. This may be attributed to the post-implantation annealing induced by the copper diffusion from the Si surface into the buried oxide and Si substrate, with copper impurities precipitated in the back interface (e.g. intrinsic gettering)[27,28] of the SIMOX wafer. Figure 8 displays the mapping profile of the back interface recombination velocities for sample-M13.
Sample Ml3 S3 measurement
Fig. 8. Mapping
1365
recombination
velocities
S, for sample-M13.
Yun-Shan Chang et al.
1366
The average value is 59.8 cm/s. We also scanned 300 points on each SIMOX wafer. From Fig. 8, the back-interface recombination velocities are lower near the central region than in the edge region of the wafer. 5. CONCLUSION
In this work, a contactless dual beam optical modulation (DBOM) technique for determining the front- and back-interface recombination velocities and the substrate carrier lifetimes in SIMOX wafers has been demonstrated. This method is especially useful for quality control and defect studies of the SO1 wafer manufacturing. Using this technique, the interface properties and the quality of SOI wafers can be evaluated versus Processing and growth parameters. Thus, the contactless DBOM technique described in this paper may be used to obtain optimal manufacturing process for the SOI materials. Acknowledgements-The
authors would like to thank Dr Lisa Allen of Ibis Technology for providing SIMOX samples used in this study. The work performed at the University of Florida was supported in part by the Defense Nuclear Agency under a subcontract from Ibis Technology. REFERENCES
1. S. Cristoloveanu, S. M. Gulwadi, D. E. Ioannou, G. J. Campisi and H. L. Hughes, IEEE Electron Device Letr.
13, 603 (1992). 2. F. T. Brady and N. F. Haddad, IEEE SOI Conf. Proc., p. 130 (1993). 3. G. G. Shahidi, C. Blair, K. Beyer, T. Bucelot, T. Buti, P. N. Ghana. S. Chu. P. Coane, J. Comfort, B. Davari, R. Dennarz, S. Furkay, H. Hovel, J. Johnson, D. Klaus, K. Kiewtniack, R. Logan, T. Li, P. A. McFarland, N. Mazzeo, D. Moy, S. Neely, T. Ning, M. Rodriguez, D. Sadana, S. itiffler, J. Sin, F. &veil and J. Warnock. Svmo. on VLSI Tech.. D. 27 (1993). H. S. Chen ad i. S. Li, IEEE Trail. Eleciron bevices
12. T. R. Neal and P. C. Karulkar, IEEE SOI Conf. Proc., p. 174 (1993). 13. S. Seraphin and B. F. Cordts III, IEEE SOI Conf Proc., p. 86 (1991). 14. D. L. Polla, R. L. Aggarwal, D. A. Nelson, J. F. Shanley and M. B. Reine, Appl. Phys. Lerf. 43, 941 (1983). 15. Y. S. Chang and S. S. Li, 6th Inr. Symp. on SOI Tech. and Devices, paper no. 513, 185th ECS Meeting, San
Francisco (22-27 May 1994). 16. F. Sanii, F. P. Giles, R. J. Schwartz and J. L. Gray, Solid-St. Eleclron. 35, 3 I1 (1992). 17. D. K. Schroder, R. N. Thomas and J. C. Swartz, IEEE Trans. Electron Devices ED-25, 254 (1978). 18. A. S. Grove, Physics and Technology of Semiconductor Deuices. Wiley, New York (1967). 19. S. M. Sze, Physics of Semiconductor Devices, 2nd Edn. Wiley, New York (1981). 20. H. Hovel, J. Freeouf, K. Beyer, D. Sadana and S. Chu, IEEE SOI Conf. Proc., p. 40 (1993). 21. H. Baumgart, R. Egloff, E. Arnold, T. J. Letavic, s. Merchant, S. Mukherjee and H. Bhimnathwala, IEEE SOI Coflf: Proc., p. 44 (1993). 22. H. Davies, Proc. Insf. Elec. Engnr 101, 209 (1954). 23. Th. Flohr and R. Helbig, J. Appl. Phys. 66,306O (1989). 24. D. Venables, S. J. Krause, J. C. Park, J. D. Lee and P. Roitman, IEEE SOI Conf: Proc., p. 48 (1993). 25. P. C. Yang and S. S. Li, Appl. Phys. Letf. 61, 1408 (1992). 26. P. C. Yang and S. S. Li, Solid-St. Electron. 35, 927 (1992). 27. M. Delfino, M. Jaczvnski. A. E. Morgan, C. Vorst, M. E. Lunnon and P. Maillot, J. elect&hem. Sot. 134, 2027 (1987). 28. T. I. Kamnis and S. Y. Chiang, J. appl. Phys. 58,2559 (1985).
APPENDIX
For the ultra-thin Si film SO1 wafer, the photogenerated excess carrier concentration gradient is usually very small along the direction of incident beam. As a result, the diffusion process is negligible while the volume and surface recombination processes will dominate the excess carrier decay in the top Si film. Thus, eqn (1) becomes
G(x)-$0
39, 1740 (1992).
H. S. Chen and S. S. Li. IEEE Trans. Electron Devices P. C. Yang, H. S. Chen and S. S. Li, Solid-St. Electron.
‘=‘+‘+‘= 5 =i t,lS,
35. 1031 (1992).
(1993).
9. W. Rehwald, R. Morf and A. Vonlanthen, Semiconduc-
(Al)
where
39, 1747 (1992).
D.. I. Ioannou; X. Zhong, B. Mazhari, G. J. Campisi and H. L. Hughes, IEEE Electron Device Letr. 12,430 (1991). 8. P. C. Yang and S. S. Li, Solid-St. Electron 36, 801
A
(S, + S,) + ‘f 51 r,is,
‘I
(A2)
The total excess carrier concentration in the Si film can be obtained by solving eqns (5), (Al) and (A2) AN,=
4~,(X)dx=a~(l-R-T)~,cosB,r(l-e-J’~ s Cl
tar Sci. Technol. 6, 735 (1991).
10. L. Jastrzebski, G. Cullen and R. Soydan, J. elecrrochem. sot. 137, 303 (1990). 11. H. J. Hovel, IEEE SOI Conf. Proc., p. 26 (1993).
=q(l-R-T)+,cos0,
(A3)