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A new optical technique for characterization of technological semiconductor wafers
MATERIALS SCIENCE & ENGINEERING ELSEVIER
B
Materials Science and Engineering B34 (1995) 124 131
A new optical technique for characterization of technological semiconductor wafers O.V. Astafiev, V.P. Kalinushkin, V.A. Y u r y e v Laboratoo' ~ff' Laser D~J~ctoscopy of Semiconductors, General Physics Institute ~[ the Russian Academy of Science,~, 38 l~tt:ilol~ Street, V-333 GSP-I, Moscow 117942. Russia
Received 1 August 1994: in revised form 7 April 1995
Abstract A new non-destructive method for visualization of free carrier accumulations in standard semiconductor wafers is being proposed. This method has been developed on the basis of the conventional low-angle mid-IR-light-scattering technique and dark field microscopy. Being sensitive to low concentrations of free carriers in the accumulations, the method allows mapping and investigation of technological semiconductor wafers for determination of the distribution of free carrier accumulations. The method has been applied to visualization of large-scale electrically active defect accumulations in a number of semiconductor crystals. The method may be applied for both scientific research and wafer incoming and step inspection directly in a technological cycle. The perspectives for further development of the technique proposed are also discussed in the paper. Ke)'words: Semiconductors; Rayleigh scattering: Indium phosphide; Gallium arsenide; Silicon
I. Introduction In a number of papers [1 4], a method of low-angle mid-IR-light scattering (LALS) was described that allows investigation of the accumulations of electrically active defects (large-scale electrically active defect accumulations (LSDAs)) in the size range 1-50 gm which are usually present in semiconductor crystals [1 1 1]. (In fact, it allows investigation of all kinds of free carrier accumulations (FCAs), both natural and man made.) Being a laser heterodyne method, LALS exhibits very high sensitivity even to "weak" FCAs (or LSDAs) with free carrier concentrations down to 1014cm - 3 in them. Unfortunately it has the two following shortcomings. Firstly, it gives only average (integral) information about LSDAs through the probed volume of a crystal and, if there exist several classes of LSDAs with close parameters in the tested volume, the interpretation of the results becomes rather complicated. Secondly, it allows the estimation of only the concentration of accumulations C multiplied by the square of the maximum effective differential concentration of free carriers in the accumulation Anon. (and, of course, effective size
of defects ac~), whereas the latter An~,~...... is required, e.g. for evaluation of the activation energies of point centres constituting LSDAs. To overcome the above disadvantages, a new non-destructive method for investigation of FCAs in standard semiconductor wafer (SLALS) is being introduced in the current paper. Like LALS, SLALS is based on elastic low-angle scattering of a plane wave of laser radiation in the region of wavelengths where the light scattering by LSDAs predominates [2,4,11], i.e. in the mid-IR region.
2. Physical basis of SLALS The concentration of free carriers in an LSDA is different from that in a crystal bulk. This difference results in a corresponding change in the accumulation's dielectric constant at the cyclic frequency ~,J; the change is Ac=
47rAne 2
(1)
lyl eff(~O 2
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ElsevierScience S.A. All rights reserved S S D l 0921-5107(95)01226-5
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o.v. Astqfiev et al./ Materia& Science and Eng#leering B34 (1995) 124 131
where An is a difference in free carrier c o n c e n t r a t i o n between the crystal v o l u m e a n d the a c c u m u l a t i o n , e is the electron charge, a n d men- is the effective m a s s o f free carriers. It can be seen f r o m Eq. (1) t h a t ]Ae] increases with d e c r e a s i n g r a d i a t i o n frequency as oJ 2 It is k n o w n also t h a t the scattering intensity is p r o p o r t i o n a l to ClAe]22 4, so a p p l i c a t i o n o f l o n g - w a v e l e n g t h light m a k e s each m e t h o d b a s e d on light scattering ( a n d in p a r t i c u l a r S L A L S ) sensitive to crystal d o m a i n s with c h a n g e d free c a r r i e r c o n c e n t r a t i o n s (in p a r t i c u l a r to L S D A s ) , r a t h e r t h a n to o t h e r o p t i c a l i n h o m o g e n e i t i e s whose dielectric c o n s t a n t s are i n d e p e n d e n t o f the p r o b e b e a m wavelength (of course, if their c o n c e n t r a t i o n s are n o t t o o high). A s usual values o f An are small a n d IAel << ~, (e is the dielectric c o n s t a n t o f the s e m i c o n d u c t o r bulk) a n d C is n o t very high, L S D A s m a y be o b s e r v e d only in r a t h e r perfect crystals. T h e S L A L S t e c h n i q u e is s h o w n s c h e m a t i c a l l y in Fig. 1. T h e p l a n e wave from the laser source illuminates a thin s e m i c o n d i c t o r p a r a l l e l - s i d e d crystal with p o l i s h e d surfaces (usually a s t a n d a r d t e c h n o l o g i c a l wafer before structure p r o d u c t i o n ) . T h e wafer is l o c a t e d in the focal p l a n e o f a lens L I . Let a defect be in the crystal b u l k in the front focal p l a n e o f L1. It scatters the p r o b e wave, p r o d u c i n g an a d d i t i o n a l scattered wave which diverges in an angle o f the o r d e r o f 2 / a where ,i is a w a v e l e n g t h a n d a is the defect's c h a r a c t e r i s t i c size. A resultant wave after the defect is a sum o f the n o n - d i s t u r b e d p l a n e wave a n d that scattered by the defect. T h e lens L1 c o n d e n s e s the p l a n e wave in the b a c k focus to a spot with a size o f a b o u t 2J]/D 1 where D 1 is the d i a m e t e r o f the p r o b e p l a n e wave b e a m . A small m i r r o r t u r n e d at an angle o f 45 ° to the focal p l a n e o r a b s o r b i n g screen is p o s i t i o n e d in the b a c k focus for r e m o v i n g the p r o b e wave r a d i a t i o n . T h e scattered wave, being a l m o s t a plane wave with c h a r a c t e r i s t i c b e a m d i a m e t e r o f (2/a)f~ after L I , passes to the second lens L2 a l m o s t w i t h o u t losses - - if the screen size is smaller t h a n (2/a)f~. So the scattered wave w i t h o u t p r o b e r a d i a t i o n reaches the
2
L1
6 /
L2
--L'<
LI
T+4 5) D1
bo
T$
......
[
9
D2
Fig. l. The pictorial diagram of the SLALS technique: l, the probe wave; 2, the tested sample with polished surfaces; 3, a diaphragm with diameter of D1 in the plane of the lens L1; 4, the lens LI; 5, an opaque screen with a radius b, in the back focus plane of L1; 6, a diaphragm with a radius bo in the plane of the lens L2: 7, a diaphragm with a diameter D1 in the plane of the lens L2; 8, the lens L2; 9, the scattered wave; 10, a photoreceiver.
2
3
456
Fig. 2. The layout of the experimental set-up. 1, CO. laser; 2, an obturator; 3, the lens LI for probe wave focusing; 4, a sample; 5, an opaque screen; 6, the image-forming lens; 7, IR photoreceiver liquidnitrogen-cooled Cd Hg -Te); 8, an amplifier with a lock-in voltmeter; 9, analogue digital converter; 10, a step motor control system; 11, a computer for system control and data acquisition; 12, step motors for studied sample scanning. lens L2 a n d the i m a g e o f the defect is f o r m e d in the b a c k focus o f L2 in scattered rays. The scheme described a b o v e is the w e l l - k n o w n m e t h o d in m i c r o s c o p y o f the so called d a r k field [12] (which was f o r m e r l y referred to as the central d a r k g r o u n d T 6 p l e r F o u c a u l t m e t h o d [13]), b u t using a m i d - I R laser as a source o f a g o o d plane wave m a k e s it possible to visualize such w e a k optical i n h o m o g e n e i t i e s as a c c u m u l a t i o n s o f electrically active defects.
3. Experimental set-up T o realize the m e t h o d d e s c r i b e d a b o v e the experim e n t a l set-up was developed. T h e d i a g r a m o f the S L A L S set-up is shown in Fig. 2. It h a d some u n i m p o r t a n t differences f r o m the ideal set-up s h o w n in Fig. 1. A p r o b e wave f r o m the I R laser source passed t h r o u g h a l o n g - f o c a l - l e n g t h lens L1 0c= 100 mm), which slightly focused r a d i a t i o n on the sample. The s a m p l e was loc a t e d in front o f the focus o f the g e r m a n i u m short-focal-length lens L2 n e a r it; L2 f o r m e d an i m a g e o f the s a m p l e on the p h o t o r e c e i v e r . T h e p r o b e b e a m was r e m o v e d by m e a n s o f an a b s o r b i n g screen which was p l a c e d in front o f the p l a n e o f the lens L2. T h e d i a m e ter o f the p r o b e b e a m was m u c h smaller t h a n the d i a m e t e r o f L2 due to focusing with the lens L1, so the o p a q u e screen was m u c h bigger t h a n the p r o b e b e a m diameter. This m e a n s t h a t it a l m o s t does n o t m a t t e r where the o p a q u e screen is placed: in the b a c k focus o f L2 o r i m m e d i a t e l y in the p l a n e o f the lens L2. A COz laser was used as the source o f a p r o b e wave in the set-up; its wavelength was 10.6 g m a n d its p o w e r was a r o u n d 0.5 W. T h e s a m p l e was m o v e d in two c o o r d i n a t e s p e r p e n d i c ularly to the o p t i c a l axis a n d a signal p r o p o r t i o n a l to
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O.V. Astafiev et al./ Materials Science and Engineering B34 (1995) 124 131
the intensity of the scattered wave was registered by an IR photoreceiver ( C d - H g Te cooled with liquid nitrogen). The receiver detectivity was 3 x l012 Hz ~/2 W ~, the area of its receiving element was 150 x 150 jam2, and integration time for measurement in one point was about 10 2 s, i.e. the receiver detected approx. 5 x 10 J°W of the incident radiation power. The analogue signal was digitized and transferred into a computer to produce and save the image. This non-optimized set-up is sensitive to the free carrier concentration within a defect down to 1014 c m 3 (this value has been calculated for defects with sizes a of about 10 jam [14]).
4. Visualization of LSDAs in indium phosphide, gallium arsenide and silicon single crystals To illustrate the operation of the SLALS microscope, we present some results of investigations of indium phosphide, gallium arsenide and silicon single crystals obtained with the use of the instrument described in the present work and standard LALs. Crystals similar to those studied in this work were previously investigated in detail by LALS, e.g. in Refs. [7-10] (see also many references therein and references cited in [3,11]). The results obtained in the present work completely confirm the data given in these papers. First of all, let us introduce some designations for measured and estimated parameters of the scattered light and LSDAs, which are used in the paper: 0 is the light scattering angle in crystal, W is the probe beam power in the crystal per unit solid angle per unit tested volume, I is the scattered light intensity in the crystal per unit solid angle per unit tested volume, /0 = I(0 = 0), C is the concentration of scatterers, a is a scatterer radius, Art m is the m a x i m u m effective concentration of free carriers in the accumulations as in [9,10], Anm = m c n m / m a -- n~ where mc.a means respectively the effective masses of current carriers in the crystal bulk outside the scattering LSDAs (m*) and inside them (m*), nm means the m a x i m u m value of the free carrier concentration inside the LSDAs (it corresponds to a m a x i m u m magnitude Acre of the deviation of the dielectric constant I A e l - f ( f i ) where fi is the coordinates in the accumulation), and n~ is the free carrier concentration outside the LSDAs; LSDAs and the crystal bulk free of them may have different conductance types, e.g. for InP and G a A s the model of p-type LSDAs in an n-type crystal matrix is under consideration [9,10]; in such a case nm--Pm means the concentration of holes), p, means the amount of holes within the LSDAs per unit crystal volume, AEi = E i - E,, is the location of the levels of a point centre constituting LSDAs in the bandgap with respect to the valence band, and de,,, = Acm/C. The ratio I / W is
measured in inverse steradians per cubic centimetre (the instrument for LALS measurements was graduated against the diffraction of light on a calibrated hole in the aluminium foil).
4.1. I n P a n d G a A s
The pictures of undoped n-lnP and semi-insulating (SI) InP:Fe, both grown by the liquid-encapsulated Czochralski (LEC) process with B203 as an encapsulant, are shown in Fig. 3(a) and Fig. 3(b) respectively (2 x 2 m m 2 areas are presented); the corresponding LALS diagrams (the spatial frequency spectra) are presented in Fig. 3(c), curves 1 and 2. The free electron concentration in the samples of undoped InP was about 2 x 1 0 1 6 c m 3; the specific resistivity of InP:Fe was around 107 f] cm (all data hereafter are given for room temperature). The electron mobility in the materials was about 3 x 103 cm2V r s J; they had a dislocation density of about 5 × 104 c m 2. The thickness of the InP wafer was 600 ~tm; that of the InP:Fe one was 500 jam. The samples were polished mechanically up to the optical precision grade. The SLALS patterns of LEC S1 G a A s single crystals are depicted in Figs. 4(a) and 4(b); the former presents an as-grown industrial G a A s wafer 76 m m in diameter. Its specific resistivity was about 1.7 x 107f~cm, the mobility of electrons was about 6 x 103cm2V I s ~, and the etch pit density was about 7.5 x 104 c m 2. The wafer thickness was 580/am. The latter figure shows a 76 mm inductrial G a A s wafer, which was cut from the ingot annealed under vacuum in a sealed quartz ampoule at 900 °C. Its thickness was 625 ~tm, the specific resistivity was greater than 107 ~ cm, the carrier mobility was greater than 4 × 103cm 2V ~s ~, and the etch pit density was less than 105 cm 2. T h e GaAs wafers were produced at different establishments, but both were finished for use in processing equipment. Areas of 1.3 x 1.3 m m 2 are depicted in both figures. The LALS diagrams for the G a A s crystals are plotted in Fig. 4(c), curve 1 and curve 2 respectively. The defects - - white spots in the patterns the observation of which by LALS was previously reported in Refs. [9,10] are clearly seen in all the images. The shape of the defects is close to spherical (as far as the resolution of the real device for SLALS allows a judgement about it - a detailed analysis of SLALS is made in Ref. [14]), which was previously found in experiments on the influence of sample orientation on LALS [9]. The light scattering intensity from as-grown G a A s was about 100 times lower than that from an annealed wafer (which completely corresponds to the data from standard LALS measurements, but it should be noted that the signal-to-noise ratio in the SLALS images was rather close to unity in the case of as-grown GaAs).
O.V. Astafiev et al. / Materials Science and Engineering B34 (1995) 124-131
(a)
127
(b) -0.5
-1,0
~-1.5
•
o
!
•
o
o
•
o
o -2.o
-2.5 -
-3.0 50O
(c)
,0'00
15'00 20'00 zgoo k.sin
30'00 3goo
® , c m -~
Fig. 3. (a), (b) LSDAs in LEC indium phosphide (areas of 2 × 2 mm 2 are depicted): (a) undoped lnP; (b) InP:Fe. (c) LALS diagrams (spatial frequency spectra of light scattering) for undoped InP (curve 1) and InP:Fe (curve 2).
The parameters of LSDAs calculated from the LALS diagrams in the model of p-type accumulations [9,10] using the real concentration of LSDAs measured from the microphotographs are gathered in Table 1. It can be seen that both the estimates of the L S D A concentration and the estimates of the free carrier concentrations inside LSDAs are very close to the data presented in Refs. [9,10], and consequently the estimates of the thermal activation energies of the centres constituting LSDAs - - AEi = 15-50 meV for indium phosphide and AEi = 6 0 100meV for gallium arsenide made in [9,10] from the temperature dependences of LALS are valid.
For exhaustive explanation of the reasons that determined our choice of size intervals to which the observed defects belong (see Table 1), the reader should be referred to Refs. [10,11] and especially to Ref. [14]. We would like only to say here that the defects seem in the photographs to have equal dimensions mostly because of high spherical aberration of the optical system which blurs the images of LSDAs with small dimensions, and the size ranges were estimated from the values of the higher and lower cut-off spatial frequencies of the spatial frequency bandpass filter used for signal selection in the real instrument for SLALS [14]. To evaluate the concentration of LSDAs, the data obtained by laser t o m o g r a p h y at a wavelength of about
128
o.v. Astqfiev et al..' Materials Science and Engineering B34 (1995) 124 131
1 )am were used in [9,10] (see, for example, Ref. [15] for indium phosphide, and probably the analogous defects were observed in gallium arsenide in Refs. [16,17]). As was mentioned in [9], the method of laser t o m o g r a p h y is sensitive not to the FCAs but to the inclusions of
another material. The LSDAs were observed by laser tomography in indium phosphide and gallium arsenide most likely because they are composed not only of dissolved point defects but also of the microinclusions of Ga and those of In are likely to be present in the composition of LSDAs in gallium arsenide and indium phosphide respectively (see [9,10] and compare with [17]). The issue of L S D A composition in these materials is discussed in detail in Refs. [9,10]. It should be noted also that it is practically impossible to develop a technique for analysis of defect composition on the basis of the standard laser tomography [15] using light with a wavelength of about l g m , whereas the laser microscopy using the mid-IR light described in the present paper enables us to analyse the defect composition, e.g. measuring the LALS temperature dependences (see e.g. [2,7 11]) or photoexcitation spectra.
(a)
4.2. C : o c h r a l s k i - g r o w n S i : B
(b) -1.0
-1.5 -2.0 ~.~-2.5 ~-3.0 -8.5
-4.0 -4.5 500
1000
15f00 20~00 25~00 30~00 35100 k . sire 0 , c m -~
(c) Fig. 4. (a), (b) LSDAs in LEC SI gallium arsenide (for wafers produced at different establishments; areas of 1.3 × 1.3mm: are depicted): (a) as-grown: (b) annealed at 900 °C (amplification is 100 times lower). (c) LALS diagrams for as-grown (curve 1) and annealed (curve 2) GaAs.
The single crystals of standard industrial Si:B studied in this work were grown by the Czochralski (CZ) process and had a specific resistivity of 12 ~ cm. The thickness of the samples was 300 gm. Large-scale electrically active defects with dimensions ranging from 3 5 ~am to 40 50jam were observed previously in analogous crystals in Refs. [7,8]. Their concentrations were estimated as 105 10vcm 3; the values of &:m in them were evaluated as 10 a 10 3 Specimens markedly different in their concentrations of defects registered by selective etching were studied in the present work: their concentrations reached about 2 x 105cm 3 in sample 1 and about 2 × 104cm ~ in sample 2. Figs. 5(a) and 5(b) present the microphotographs of these samples obtained with the use of SLALS (areas of 2 x 2 m m 2 are depicted in the photographs). As in the photographs of indium phosphide and gallium arsenide, the white spots in the pictures are the images of LSDAs. The mean value of the light scattering intensity by the defects in Fig. 5(a) is around three times greater than that in Fig. 5(b)0 which is completely in agreement with the results obtained by LALS the ratio of the light scattering intensities by samples 1 and 2 in the LALS diagrams given in Fig. 5(c) is also nearly equal to 3. The concentration of defects registered in sample 1 reached about 106 cm 3 whereas that in sample 2 was about (4 5) x 10s c m 3. Note that the values of the concentrations of defects revealed in the analogous samples by the electronbeam-induced current (EBIC) with the special surface preparation described in [18] appeared to be nearly equal to the above values obtained by SLALS. The obtained results allow us to conclude the following: (1) using the SLALS microscope we visualized the
O.V. Astqfiev et al. Materials Science and Engineering B34 (1995) 124 131
129
Table 1 Parameters of LSDAs in indium phoshide and gallium arsenide " N
a (lain)
log(lo/W)
CAn~ (cm -9)
C (cm 3)
Pm (cm 3)
p, (cm-3)
1
11-14 6 7 14 19 6 7 9 12 ca. 12
-1.2 -0.8 - 1.5- -- 1.1 - 1.3- -- 1.0 2.0 --1.7 --2.5----2.4 ca. --0.9
(4-8.5) x 1037 (1.5-3) x 1039 (4-14) × 1036 (2--11)X 1038 (3--10) X 1036 ca. 103s
(1.5 2 ) × 105
(2.0 2 . 5 ) x 1017
( 3 - 6 ) × 10 TM
(2 3) x 105
(2 5) × 1016
(1 3) × 1014
(4.5 5 ) × 105 2 x 105
(1.5 3.5)× 1016 ca. 1.5 x 1017
(7 7.5) X 1013 ca. 2.5 × 1014
2 3 4
~' N, sample number; sample l, undoped InP: sample 2, lnP:Fe; sample 3, as-grown GaAs; sample 4, G a A s annealed at 900 °C; a, accumulation radius; Iog(lo/W), logarithm of the zero-angle scattering intensity per probe beam unit power (the units are log(st ~cm-3)); CAn~, a concentration parameter; C the concentration of LSDAs; Anm, effective m a x i m u m differential carrier concentration in LSDAs; Pro, m a x i m u m hole concentration inside accumulations; p,., total content of holes inside LSDAs per crystal unit volume.
defects which were previously investigated by LALS - so-called "weak impurity accumulations" [7,8]; (2) using EBIC with the special surface p r e p a r a t i o n - the data obtained by this method were used in [7,8] we also revealed "weak impurity accumulations", i.e. the estimations of LSDA parameters and thermal activation energies of the centres constituting LSDAs made in [7,8] are valid. The accumulations' radius calculated from the LALS diagrams given in Fig. 5(c) is a ~ 10 14 I~m. Measuring I o / W from LALS and determining C from SLALS one can easily estimate the values of c~em in LSDAs. They were (6.5 10) x 10 4 a n d (11 14) x 10 4 for sample 1 and sample 2 respectively. Remark also that the correlation between the concentrations of defects revealed by selective etching and SLALS is purely qualitative. This is also characteristic for most of the comparative experiments on etching and LALS. However, inquiring into the reasons for the discrepancies observed is beyond the scope of this paper.
5. Conclusion
In conclusion, let us summarize the main results given in the paper. A modification of the LALS technique has been made, which allows us to make mappings of technological seimconductor wafers, on the basis of dark field microscopy [12,13] used as a method of spatial signal filtering. The technique developed is sensitive, in the present realization, to crystal inhomogeneities with a deviation of dielectric constant with respect to the crystal dielectric constant down to 10 4, which corresponds in the case of LSDAs or different FCAs to a deviation in free carrier concentration of about 3 × 1014 cm 3. Defects with sizes from about 2/2 (5 ~tm for a probe beam wavelength of 10 p.m) to at least 50 ftm may be resolved with the system without information losses. Defects with sizes less than 2/2 are also registered but their sizes cannot be resolved.
We should note that there are many possiblities for improving strongly the characteristics of the method. In the case of refrective (dephasing) inhomogeneities, some limitations to achieving enhanced contrast might be removed if, for example, phase contrast microscopy is applied [19,20]. (Numerous practical layouts of phase contrast microscopes are given, e.g. in [21,22].) In any case, the methods of laser heterodyne microscopy must appear to be exclusively effective [23,24]. Application of these methods (especially in combination with acoustooptic beam modulating and deflecting devices and signal-processing systems [25]) will undoubtedly allow the optical-beam-induced LALS technique (OLALS) to be developed on the basis of SLALS and LALS with surface optical pumping [26,27], which will be in many respects analogous to such widely used methods of layer and electron microscopy as optical-beam-induced current and EBIC (the first OLALS images are presented in Ref. [11]). LALS tomography might be also devised from SLALS using heterodyne detection, although a large value of the microscope numerical aperture m is required for tomography, as the longitudinal selectivity of a heterodyne tomographic microscope may be estimated as Az = 2)o/m 2 [23]. The first results from LEC InP, LEC SI GaAs and CZ Si single crystals have been obtained by SLALS. In Si, GaAs and InP single crystals, LSDAs were formerly investigated in detail by conventional LALS [1-11]. Now new results of SLALS verify our previous view on this kind of defect by direct observations. The concentration of LSDAs has been shown to be in the range 105 10 6 c m 3 in these crystals, which fully corresponds to the estimates used in our previous work (see e.g. [7-101). It should be noted that the non-destructive SLALS technique is designed for application either in scientific research or directly in a technological cycle for substrate quality monitoring in incoming and step control systems. We should mention also that SLALS probably may be used not only for substrate characterization but also
130
O.V. Astqfiev et al./ Materials Science and Engineerin2; B34 (1995) 124 131
(a)
(b) -1.0
-
- L 5
-
!
~
-2.0
-
-2.5
-
-3.0
-
-3.5 500
(c)
/"
! 0~00
! 5'0 0
2 O0 0
/x
2 5~00
3 0~00
3 5~00
k. s i n ®, cm-'
Fig. 5. (a), (b) LSDAs in CZ Si (areas of 2 × 2 m m 2 are depicted): (a) sample 1: (b) sample 2. (c) LALS diagrams for sample 1 (curve I) and sample 2 (curve 2).
for non-destructive control and visualization o f elements of doped structures directly in the technological
cycle.
References [1] V.V. Voronkov, G.I. Voronkova, B.V. Zubov, V.P. Kalinushkin, B.B. Krynetsky, T.M. Murina and A.M. Prokhorov, So~. Phys. Solid State, 23 (1981) 65. [2] V.V. Voronkov, S.E. Zabolotskiy, V.P. Kalinushkin, D.I. Murin, M.G. Ploppa and V.A. Yuryev, J. Co'st. Growth, 103 (1990) 126. [3] V.P. Kalinushkin, Laser methods of defect investigations in semiconductors and dielectrics, Proe. Inst. Gen. Phys. Acad. Sci. USSR, Vol. 4, Nova, New York, 1988, p. 1. [4] V.P. Kalinushkin, V.1. Masychev, T.M. Murina, M.G. Ploppa
and A.M. Prokhorov, J. Teeh. Phys. Lett., 12 (3) (1986) 129. [5] V.V. Voronkov, G.I. Voronkova, V.N. Golovina, B.V. Zubov, V.P. Kalinushkin, T.M. Murina and A.M. Prokhorov, J. Cryst. Growth, 52 (1981) 939. [6] S.E. Zabolotskii, V.P. Kalinushkin, T.M. Murina, M.G. Ploppa and K. Tempelhoff, Phys. Status SolMi A, 88 (1985) 539. [7] A.N. Buzynin, S.E. Zabolotskiy, V.P. Kalinushkin, A.E. Luk'yanov, T.M. Murina, V.V. Osiko, M.G. Ploppa, V.M. Tatarintsev and A.M. Eidenson, Soy. Phys. Semieoml., 24 (2) (1990) 264. [8] O.V. Astafiev, A.N. Buzynin, A.I. Buvaltsev, D.I. Murin, V.P. Kalinushkin and M.G. Ploppa, Semieonduetors, 28 (3) (1994) 407. [9] V.P. Kalinushkin, V.A. Yuryev, D.I. Murin and M.G. Ploppa, Semieond. Sei. Teehnol. 7 (1992) A255. [10] V.A. Yuryev and V.P. Kalinushkin, Mater. Sei. Eng. B, 33 (1995) 103.
O.V. Astafiev et al./ Materials Seienee and Engineering B34 (1995) I24-131
[l 1] V.P. Kalinushkin, V.A. Yuryev and O.V. Astafiev, Proc. 1st Int. Conf. on Materials for Mieroelectronies, Barcelona, 17-19 October 1994, in Mater. Sei. Teehnol., submitted for publication. [12] L.I. Mandelstam, Complete Works, Vol. 3, Academy of Sciences of the USSR, Moscow, 1950, p. 337. [13] N.A. Smirnow, J. Russ. Phys.-Chem. Soc., 59 (1927) 359. [14] O.V. Astafiev, V.P. Kalinushkin and V.A. Yuryev, Microelectronics, in press. [15] T. Ogawa and N. Nango, Rev. Sci. lnstrum., 57 (1986) 1135. [16] T. Inada, Yo. Otoki, K. Ohata, S. Tabarasako and S. Kuma, J. Cryst. Growth, 96 (1989) 327. [17] J.P. Fillard, P. Gall, J.L. Weyher, M. Asgarinia and P.G. Montgomery, Proc. 5th Int. Conj'. on Semi-insulating I I I - V Materials, Malm6, 1-3 June 1988, Hilger, Bristol, 1988, p. 537. [18] A.N. Buzynin, N.A. Butylkina, V.P. Kalinushkin, A.E. Luk'yanov and V.M. Tatarintsev, USSR Patent 1,531,766, 1989. [19] F. Zernike, Mon. Not. R. Astron. Soc., 94 (1934) 377. [20] S.M. Rytov, Usp. Fiz. Nauk, 61 (1950) 425.
131
[21] M. Franqon, Le Microseope h Contraste de Phase et Microscope lnter[krentiel, Centre National de la Recherche Scientifique, Paris, 1954. [22] M. Franqon, Progress in Microscopy, International Series of Monographs on Pure and Applied Biology, Modern Trends in Physiological Sciences, Vol. 9, Pergamon, New York, 1961. [23] V.V. Protopopov and N.D. Ustinov, Laser Heterodyning, Nauka, Moscow, 1985. [24] T. Sawatari, Appl. Opt., 12 (1973) 2768. [25] A. Vanderlugt (ed.), Acousto-optic Signal Processing (special section), Proc. 1EEE, 69 (1) (1981) 48. [26] V.P. Kalinushkin, D.|. Murin, V.A. Yuryev, O.V. Astafiev and A.I. Buvaltsev, 2nd Int. Symp. on Advanced Laser Technologies, Prague, 8-13 November 1993, in Proc. Soc. Photo-Opt. Instrum. Eng., 2332 (1994) 146. [27] O.V. Astafiev, A.I. Buvaltsev, V.P. Kalinushkin, V.A. Yuryev and D.I. Murin, Phys. Chem. Mech. Surf, 4 (1995) 79.
B
Materials Science and Engineering B34 (1995) 124 131
A new optical technique for characterization of technological semiconductor wafers O.V. Astafiev, V.P. Kalinushkin, V.A. Y u r y e v Laboratoo' ~ff' Laser D~J~ctoscopy of Semiconductors, General Physics Institute ~[ the Russian Academy of Science,~, 38 l~tt:ilol~ Street, V-333 GSP-I, Moscow 117942. Russia
Received 1 August 1994: in revised form 7 April 1995
Abstract A new non-destructive method for visualization of free carrier accumulations in standard semiconductor wafers is being proposed. This method has been developed on the basis of the conventional low-angle mid-IR-light-scattering technique and dark field microscopy. Being sensitive to low concentrations of free carriers in the accumulations, the method allows mapping and investigation of technological semiconductor wafers for determination of the distribution of free carrier accumulations. The method has been applied to visualization of large-scale electrically active defect accumulations in a number of semiconductor crystals. The method may be applied for both scientific research and wafer incoming and step inspection directly in a technological cycle. The perspectives for further development of the technique proposed are also discussed in the paper. Ke)'words: Semiconductors; Rayleigh scattering: Indium phosphide; Gallium arsenide; Silicon
I. Introduction In a number of papers [1 4], a method of low-angle mid-IR-light scattering (LALS) was described that allows investigation of the accumulations of electrically active defects (large-scale electrically active defect accumulations (LSDAs)) in the size range 1-50 gm which are usually present in semiconductor crystals [1 1 1]. (In fact, it allows investigation of all kinds of free carrier accumulations (FCAs), both natural and man made.) Being a laser heterodyne method, LALS exhibits very high sensitivity even to "weak" FCAs (or LSDAs) with free carrier concentrations down to 1014cm - 3 in them. Unfortunately it has the two following shortcomings. Firstly, it gives only average (integral) information about LSDAs through the probed volume of a crystal and, if there exist several classes of LSDAs with close parameters in the tested volume, the interpretation of the results becomes rather complicated. Secondly, it allows the estimation of only the concentration of accumulations C multiplied by the square of the maximum effective differential concentration of free carriers in the accumulation Anon. (and, of course, effective size
of defects ac~), whereas the latter An~,~...... is required, e.g. for evaluation of the activation energies of point centres constituting LSDAs. To overcome the above disadvantages, a new non-destructive method for investigation of FCAs in standard semiconductor wafer (SLALS) is being introduced in the current paper. Like LALS, SLALS is based on elastic low-angle scattering of a plane wave of laser radiation in the region of wavelengths where the light scattering by LSDAs predominates [2,4,11], i.e. in the mid-IR region.
2. Physical basis of SLALS The concentration of free carriers in an LSDA is different from that in a crystal bulk. This difference results in a corresponding change in the accumulation's dielectric constant at the cyclic frequency ~,J; the change is Ac=
47rAne 2
(1)
lyl eff(~O 2
0921-5107/95/$09.50 ~;, 1995
ElsevierScience S.A. All rights reserved S S D l 0921-5107(95)01226-5
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o.v. Astqfiev et al./ Materia& Science and Eng#leering B34 (1995) 124 131
where An is a difference in free carrier c o n c e n t r a t i o n between the crystal v o l u m e a n d the a c c u m u l a t i o n , e is the electron charge, a n d men- is the effective m a s s o f free carriers. It can be seen f r o m Eq. (1) t h a t ]Ae] increases with d e c r e a s i n g r a d i a t i o n frequency as oJ 2 It is k n o w n also t h a t the scattering intensity is p r o p o r t i o n a l to ClAe]22 4, so a p p l i c a t i o n o f l o n g - w a v e l e n g t h light m a k e s each m e t h o d b a s e d on light scattering ( a n d in p a r t i c u l a r S L A L S ) sensitive to crystal d o m a i n s with c h a n g e d free c a r r i e r c o n c e n t r a t i o n s (in p a r t i c u l a r to L S D A s ) , r a t h e r t h a n to o t h e r o p t i c a l i n h o m o g e n e i t i e s whose dielectric c o n s t a n t s are i n d e p e n d e n t o f the p r o b e b e a m wavelength (of course, if their c o n c e n t r a t i o n s are n o t t o o high). A s usual values o f An are small a n d IAel << ~, (e is the dielectric c o n s t a n t o f the s e m i c o n d u c t o r bulk) a n d C is n o t very high, L S D A s m a y be o b s e r v e d only in r a t h e r perfect crystals. T h e S L A L S t e c h n i q u e is s h o w n s c h e m a t i c a l l y in Fig. 1. T h e p l a n e wave from the laser source illuminates a thin s e m i c o n d i c t o r p a r a l l e l - s i d e d crystal with p o l i s h e d surfaces (usually a s t a n d a r d t e c h n o l o g i c a l wafer before structure p r o d u c t i o n ) . T h e wafer is l o c a t e d in the focal p l a n e o f a lens L I . Let a defect be in the crystal b u l k in the front focal p l a n e o f L1. It scatters the p r o b e wave, p r o d u c i n g an a d d i t i o n a l scattered wave which diverges in an angle o f the o r d e r o f 2 / a where ,i is a w a v e l e n g t h a n d a is the defect's c h a r a c t e r i s t i c size. A resultant wave after the defect is a sum o f the n o n - d i s t u r b e d p l a n e wave a n d that scattered by the defect. T h e lens L1 c o n d e n s e s the p l a n e wave in the b a c k focus to a spot with a size o f a b o u t 2J]/D 1 where D 1 is the d i a m e t e r o f the p r o b e p l a n e wave b e a m . A small m i r r o r t u r n e d at an angle o f 45 ° to the focal p l a n e o r a b s o r b i n g screen is p o s i t i o n e d in the b a c k focus for r e m o v i n g the p r o b e wave r a d i a t i o n . T h e scattered wave, being a l m o s t a plane wave with c h a r a c t e r i s t i c b e a m d i a m e t e r o f (2/a)f~ after L I , passes to the second lens L2 a l m o s t w i t h o u t losses - - if the screen size is smaller t h a n (2/a)f~. So the scattered wave w i t h o u t p r o b e r a d i a t i o n reaches the
2
L1
6 /
L2
--L'<
LI
T+4 5) D1
bo
T$
......
[
9
D2
Fig. l. The pictorial diagram of the SLALS technique: l, the probe wave; 2, the tested sample with polished surfaces; 3, a diaphragm with diameter of D1 in the plane of the lens L1; 4, the lens LI; 5, an opaque screen with a radius b, in the back focus plane of L1; 6, a diaphragm with a radius bo in the plane of the lens L2: 7, a diaphragm with a diameter D1 in the plane of the lens L2; 8, the lens L2; 9, the scattered wave; 10, a photoreceiver.
2
3
456
Fig. 2. The layout of the experimental set-up. 1, CO. laser; 2, an obturator; 3, the lens LI for probe wave focusing; 4, a sample; 5, an opaque screen; 6, the image-forming lens; 7, IR photoreceiver liquidnitrogen-cooled Cd Hg -Te); 8, an amplifier with a lock-in voltmeter; 9, analogue digital converter; 10, a step motor control system; 11, a computer for system control and data acquisition; 12, step motors for studied sample scanning. lens L2 a n d the i m a g e o f the defect is f o r m e d in the b a c k focus o f L2 in scattered rays. The scheme described a b o v e is the w e l l - k n o w n m e t h o d in m i c r o s c o p y o f the so called d a r k field [12] (which was f o r m e r l y referred to as the central d a r k g r o u n d T 6 p l e r F o u c a u l t m e t h o d [13]), b u t using a m i d - I R laser as a source o f a g o o d plane wave m a k e s it possible to visualize such w e a k optical i n h o m o g e n e i t i e s as a c c u m u l a t i o n s o f electrically active defects.
3. Experimental set-up T o realize the m e t h o d d e s c r i b e d a b o v e the experim e n t a l set-up was developed. T h e d i a g r a m o f the S L A L S set-up is shown in Fig. 2. It h a d some u n i m p o r t a n t differences f r o m the ideal set-up s h o w n in Fig. 1. A p r o b e wave f r o m the I R laser source passed t h r o u g h a l o n g - f o c a l - l e n g t h lens L1 0c= 100 mm), which slightly focused r a d i a t i o n on the sample. The s a m p l e was loc a t e d in front o f the focus o f the g e r m a n i u m short-focal-length lens L2 n e a r it; L2 f o r m e d an i m a g e o f the s a m p l e on the p h o t o r e c e i v e r . T h e p r o b e b e a m was r e m o v e d by m e a n s o f an a b s o r b i n g screen which was p l a c e d in front o f the p l a n e o f the lens L2. T h e d i a m e ter o f the p r o b e b e a m was m u c h smaller t h a n the d i a m e t e r o f L2 due to focusing with the lens L1, so the o p a q u e screen was m u c h bigger t h a n the p r o b e b e a m diameter. This m e a n s t h a t it a l m o s t does n o t m a t t e r where the o p a q u e screen is placed: in the b a c k focus o f L2 o r i m m e d i a t e l y in the p l a n e o f the lens L2. A COz laser was used as the source o f a p r o b e wave in the set-up; its wavelength was 10.6 g m a n d its p o w e r was a r o u n d 0.5 W. T h e s a m p l e was m o v e d in two c o o r d i n a t e s p e r p e n d i c ularly to the o p t i c a l axis a n d a signal p r o p o r t i o n a l to
126
O.V. Astafiev et al./ Materials Science and Engineering B34 (1995) 124 131
the intensity of the scattered wave was registered by an IR photoreceiver ( C d - H g Te cooled with liquid nitrogen). The receiver detectivity was 3 x l012 Hz ~/2 W ~, the area of its receiving element was 150 x 150 jam2, and integration time for measurement in one point was about 10 2 s, i.e. the receiver detected approx. 5 x 10 J°W of the incident radiation power. The analogue signal was digitized and transferred into a computer to produce and save the image. This non-optimized set-up is sensitive to the free carrier concentration within a defect down to 1014 c m 3 (this value has been calculated for defects with sizes a of about 10 jam [14]).
4. Visualization of LSDAs in indium phosphide, gallium arsenide and silicon single crystals To illustrate the operation of the SLALS microscope, we present some results of investigations of indium phosphide, gallium arsenide and silicon single crystals obtained with the use of the instrument described in the present work and standard LALs. Crystals similar to those studied in this work were previously investigated in detail by LALS, e.g. in Refs. [7-10] (see also many references therein and references cited in [3,11]). The results obtained in the present work completely confirm the data given in these papers. First of all, let us introduce some designations for measured and estimated parameters of the scattered light and LSDAs, which are used in the paper: 0 is the light scattering angle in crystal, W is the probe beam power in the crystal per unit solid angle per unit tested volume, I is the scattered light intensity in the crystal per unit solid angle per unit tested volume, /0 = I(0 = 0), C is the concentration of scatterers, a is a scatterer radius, Art m is the m a x i m u m effective concentration of free carriers in the accumulations as in [9,10], Anm = m c n m / m a -- n~ where mc.a means respectively the effective masses of current carriers in the crystal bulk outside the scattering LSDAs (m*) and inside them (m*), nm means the m a x i m u m value of the free carrier concentration inside the LSDAs (it corresponds to a m a x i m u m magnitude Acre of the deviation of the dielectric constant I A e l - f ( f i ) where fi is the coordinates in the accumulation), and n~ is the free carrier concentration outside the LSDAs; LSDAs and the crystal bulk free of them may have different conductance types, e.g. for InP and G a A s the model of p-type LSDAs in an n-type crystal matrix is under consideration [9,10]; in such a case nm--Pm means the concentration of holes), p, means the amount of holes within the LSDAs per unit crystal volume, AEi = E i - E,, is the location of the levels of a point centre constituting LSDAs in the bandgap with respect to the valence band, and de,,, = Acm/C. The ratio I / W is
measured in inverse steradians per cubic centimetre (the instrument for LALS measurements was graduated against the diffraction of light on a calibrated hole in the aluminium foil).
4.1. I n P a n d G a A s
The pictures of undoped n-lnP and semi-insulating (SI) InP:Fe, both grown by the liquid-encapsulated Czochralski (LEC) process with B203 as an encapsulant, are shown in Fig. 3(a) and Fig. 3(b) respectively (2 x 2 m m 2 areas are presented); the corresponding LALS diagrams (the spatial frequency spectra) are presented in Fig. 3(c), curves 1 and 2. The free electron concentration in the samples of undoped InP was about 2 x 1 0 1 6 c m 3; the specific resistivity of InP:Fe was around 107 f] cm (all data hereafter are given for room temperature). The electron mobility in the materials was about 3 x 103 cm2V r s J; they had a dislocation density of about 5 × 104 c m 2. The thickness of the InP wafer was 600 ~tm; that of the InP:Fe one was 500 jam. The samples were polished mechanically up to the optical precision grade. The SLALS patterns of LEC S1 G a A s single crystals are depicted in Figs. 4(a) and 4(b); the former presents an as-grown industrial G a A s wafer 76 m m in diameter. Its specific resistivity was about 1.7 x 107f~cm, the mobility of electrons was about 6 x 103cm2V I s ~, and the etch pit density was about 7.5 x 104 c m 2. The wafer thickness was 580/am. The latter figure shows a 76 mm inductrial G a A s wafer, which was cut from the ingot annealed under vacuum in a sealed quartz ampoule at 900 °C. Its thickness was 625 ~tm, the specific resistivity was greater than 107 ~ cm, the carrier mobility was greater than 4 × 103cm 2V ~s ~, and the etch pit density was less than 105 cm 2. T h e GaAs wafers were produced at different establishments, but both were finished for use in processing equipment. Areas of 1.3 x 1.3 m m 2 are depicted in both figures. The LALS diagrams for the G a A s crystals are plotted in Fig. 4(c), curve 1 and curve 2 respectively. The defects - - white spots in the patterns the observation of which by LALS was previously reported in Refs. [9,10] are clearly seen in all the images. The shape of the defects is close to spherical (as far as the resolution of the real device for SLALS allows a judgement about it - a detailed analysis of SLALS is made in Ref. [14]), which was previously found in experiments on the influence of sample orientation on LALS [9]. The light scattering intensity from as-grown G a A s was about 100 times lower than that from an annealed wafer (which completely corresponds to the data from standard LALS measurements, but it should be noted that the signal-to-noise ratio in the SLALS images was rather close to unity in the case of as-grown GaAs).
O.V. Astafiev et al. / Materials Science and Engineering B34 (1995) 124-131
(a)
127
(b) -0.5
-1,0
~-1.5
•
o
!
•
o
o
•
o
o -2.o
-2.5 -
-3.0 50O
(c)
,0'00
15'00 20'00 zgoo k.sin
30'00 3goo
® , c m -~
Fig. 3. (a), (b) LSDAs in LEC indium phosphide (areas of 2 × 2 mm 2 are depicted): (a) undoped lnP; (b) InP:Fe. (c) LALS diagrams (spatial frequency spectra of light scattering) for undoped InP (curve 1) and InP:Fe (curve 2).
The parameters of LSDAs calculated from the LALS diagrams in the model of p-type accumulations [9,10] using the real concentration of LSDAs measured from the microphotographs are gathered in Table 1. It can be seen that both the estimates of the L S D A concentration and the estimates of the free carrier concentrations inside LSDAs are very close to the data presented in Refs. [9,10], and consequently the estimates of the thermal activation energies of the centres constituting LSDAs - - AEi = 15-50 meV for indium phosphide and AEi = 6 0 100meV for gallium arsenide made in [9,10] from the temperature dependences of LALS are valid.
For exhaustive explanation of the reasons that determined our choice of size intervals to which the observed defects belong (see Table 1), the reader should be referred to Refs. [10,11] and especially to Ref. [14]. We would like only to say here that the defects seem in the photographs to have equal dimensions mostly because of high spherical aberration of the optical system which blurs the images of LSDAs with small dimensions, and the size ranges were estimated from the values of the higher and lower cut-off spatial frequencies of the spatial frequency bandpass filter used for signal selection in the real instrument for SLALS [14]. To evaluate the concentration of LSDAs, the data obtained by laser t o m o g r a p h y at a wavelength of about
128
o.v. Astqfiev et al..' Materials Science and Engineering B34 (1995) 124 131
1 )am were used in [9,10] (see, for example, Ref. [15] for indium phosphide, and probably the analogous defects were observed in gallium arsenide in Refs. [16,17]). As was mentioned in [9], the method of laser t o m o g r a p h y is sensitive not to the FCAs but to the inclusions of
another material. The LSDAs were observed by laser tomography in indium phosphide and gallium arsenide most likely because they are composed not only of dissolved point defects but also of the microinclusions of Ga and those of In are likely to be present in the composition of LSDAs in gallium arsenide and indium phosphide respectively (see [9,10] and compare with [17]). The issue of L S D A composition in these materials is discussed in detail in Refs. [9,10]. It should be noted also that it is practically impossible to develop a technique for analysis of defect composition on the basis of the standard laser tomography [15] using light with a wavelength of about l g m , whereas the laser microscopy using the mid-IR light described in the present paper enables us to analyse the defect composition, e.g. measuring the LALS temperature dependences (see e.g. [2,7 11]) or photoexcitation spectra.
(a)
4.2. C : o c h r a l s k i - g r o w n S i : B
(b) -1.0
-1.5 -2.0 ~.~-2.5 ~-3.0 -8.5
-4.0 -4.5 500
1000
15f00 20~00 25~00 30~00 35100 k . sire 0 , c m -~
(c) Fig. 4. (a), (b) LSDAs in LEC SI gallium arsenide (for wafers produced at different establishments; areas of 1.3 × 1.3mm: are depicted): (a) as-grown: (b) annealed at 900 °C (amplification is 100 times lower). (c) LALS diagrams for as-grown (curve 1) and annealed (curve 2) GaAs.
The single crystals of standard industrial Si:B studied in this work were grown by the Czochralski (CZ) process and had a specific resistivity of 12 ~ cm. The thickness of the samples was 300 gm. Large-scale electrically active defects with dimensions ranging from 3 5 ~am to 40 50jam were observed previously in analogous crystals in Refs. [7,8]. Their concentrations were estimated as 105 10vcm 3; the values of &:m in them were evaluated as 10 a 10 3 Specimens markedly different in their concentrations of defects registered by selective etching were studied in the present work: their concentrations reached about 2 x 105cm 3 in sample 1 and about 2 × 104cm ~ in sample 2. Figs. 5(a) and 5(b) present the microphotographs of these samples obtained with the use of SLALS (areas of 2 x 2 m m 2 are depicted in the photographs). As in the photographs of indium phosphide and gallium arsenide, the white spots in the pictures are the images of LSDAs. The mean value of the light scattering intensity by the defects in Fig. 5(a) is around three times greater than that in Fig. 5(b)0 which is completely in agreement with the results obtained by LALS the ratio of the light scattering intensities by samples 1 and 2 in the LALS diagrams given in Fig. 5(c) is also nearly equal to 3. The concentration of defects registered in sample 1 reached about 106 cm 3 whereas that in sample 2 was about (4 5) x 10s c m 3. Note that the values of the concentrations of defects revealed in the analogous samples by the electronbeam-induced current (EBIC) with the special surface preparation described in [18] appeared to be nearly equal to the above values obtained by SLALS. The obtained results allow us to conclude the following: (1) using the SLALS microscope we visualized the
O.V. Astqfiev et al. Materials Science and Engineering B34 (1995) 124 131
129
Table 1 Parameters of LSDAs in indium phoshide and gallium arsenide " N
a (lain)
log(lo/W)
CAn~ (cm -9)
C (cm 3)
Pm (cm 3)
p, (cm-3)
1
11-14 6 7 14 19 6 7 9 12 ca. 12
-1.2 -0.8 - 1.5- -- 1.1 - 1.3- -- 1.0 2.0 --1.7 --2.5----2.4 ca. --0.9
(4-8.5) x 1037 (1.5-3) x 1039 (4-14) × 1036 (2--11)X 1038 (3--10) X 1036 ca. 103s
(1.5 2 ) × 105
(2.0 2 . 5 ) x 1017
( 3 - 6 ) × 10 TM
(2 3) x 105
(2 5) × 1016
(1 3) × 1014
(4.5 5 ) × 105 2 x 105
(1.5 3.5)× 1016 ca. 1.5 x 1017
(7 7.5) X 1013 ca. 2.5 × 1014
2 3 4
~' N, sample number; sample l, undoped InP: sample 2, lnP:Fe; sample 3, as-grown GaAs; sample 4, G a A s annealed at 900 °C; a, accumulation radius; Iog(lo/W), logarithm of the zero-angle scattering intensity per probe beam unit power (the units are log(st ~cm-3)); CAn~, a concentration parameter; C the concentration of LSDAs; Anm, effective m a x i m u m differential carrier concentration in LSDAs; Pro, m a x i m u m hole concentration inside accumulations; p,., total content of holes inside LSDAs per crystal unit volume.
defects which were previously investigated by LALS - so-called "weak impurity accumulations" [7,8]; (2) using EBIC with the special surface p r e p a r a t i o n - the data obtained by this method were used in [7,8] we also revealed "weak impurity accumulations", i.e. the estimations of LSDA parameters and thermal activation energies of the centres constituting LSDAs made in [7,8] are valid. The accumulations' radius calculated from the LALS diagrams given in Fig. 5(c) is a ~ 10 14 I~m. Measuring I o / W from LALS and determining C from SLALS one can easily estimate the values of c~em in LSDAs. They were (6.5 10) x 10 4 a n d (11 14) x 10 4 for sample 1 and sample 2 respectively. Remark also that the correlation between the concentrations of defects revealed by selective etching and SLALS is purely qualitative. This is also characteristic for most of the comparative experiments on etching and LALS. However, inquiring into the reasons for the discrepancies observed is beyond the scope of this paper.
5. Conclusion
In conclusion, let us summarize the main results given in the paper. A modification of the LALS technique has been made, which allows us to make mappings of technological seimconductor wafers, on the basis of dark field microscopy [12,13] used as a method of spatial signal filtering. The technique developed is sensitive, in the present realization, to crystal inhomogeneities with a deviation of dielectric constant with respect to the crystal dielectric constant down to 10 4, which corresponds in the case of LSDAs or different FCAs to a deviation in free carrier concentration of about 3 × 1014 cm 3. Defects with sizes from about 2/2 (5 ~tm for a probe beam wavelength of 10 p.m) to at least 50 ftm may be resolved with the system without information losses. Defects with sizes less than 2/2 are also registered but their sizes cannot be resolved.
We should note that there are many possiblities for improving strongly the characteristics of the method. In the case of refrective (dephasing) inhomogeneities, some limitations to achieving enhanced contrast might be removed if, for example, phase contrast microscopy is applied [19,20]. (Numerous practical layouts of phase contrast microscopes are given, e.g. in [21,22].) In any case, the methods of laser heterodyne microscopy must appear to be exclusively effective [23,24]. Application of these methods (especially in combination with acoustooptic beam modulating and deflecting devices and signal-processing systems [25]) will undoubtedly allow the optical-beam-induced LALS technique (OLALS) to be developed on the basis of SLALS and LALS with surface optical pumping [26,27], which will be in many respects analogous to such widely used methods of layer and electron microscopy as optical-beam-induced current and EBIC (the first OLALS images are presented in Ref. [11]). LALS tomography might be also devised from SLALS using heterodyne detection, although a large value of the microscope numerical aperture m is required for tomography, as the longitudinal selectivity of a heterodyne tomographic microscope may be estimated as Az = 2)o/m 2 [23]. The first results from LEC InP, LEC SI GaAs and CZ Si single crystals have been obtained by SLALS. In Si, GaAs and InP single crystals, LSDAs were formerly investigated in detail by conventional LALS [1-11]. Now new results of SLALS verify our previous view on this kind of defect by direct observations. The concentration of LSDAs has been shown to be in the range 105 10 6 c m 3 in these crystals, which fully corresponds to the estimates used in our previous work (see e.g. [7-101). It should be noted that the non-destructive SLALS technique is designed for application either in scientific research or directly in a technological cycle for substrate quality monitoring in incoming and step control systems. We should mention also that SLALS probably may be used not only for substrate characterization but also
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O.V. Astqfiev et al./ Materials Science and Engineerin2; B34 (1995) 124 131
(a)
(b) -1.0
-
- L 5
-
!
~
-2.0
-
-2.5
-
-3.0
-
-3.5 500
(c)
/"
! 0~00
! 5'0 0
2 O0 0
/x
2 5~00
3 0~00
3 5~00
k. s i n ®, cm-'
Fig. 5. (a), (b) LSDAs in CZ Si (areas of 2 × 2 m m 2 are depicted): (a) sample 1: (b) sample 2. (c) LALS diagrams for sample 1 (curve I) and sample 2 (curve 2).
for non-destructive control and visualization o f elements of doped structures directly in the technological
cycle.
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