Temperature dependence of planar channeling in transmission experiments

NUCLEAR

INSTRUMENTS

AND

METHODS

I32

I69-I73;

(I976)

©

NORTH-HOLLAND

PUBLISHING

CO.

T E M P E R A T U R E D E P E N D E N C E OF PLANAR CHANNELING IN TRANSMISSION EXPERIMENTS S. U. C A M P I S A N O , G. F O T I , E. R I M I N I

Istituto di Struttura della Materia, Universith di Catania, Italy G. D E L L A M E A , A . V . D R I G O , S. LO R U S S O , P. M A Z Z O L D I

lstituto di Fisica, UniversitcJ di Padova, Italy and G.G. BENTINI L.A.M.E.L. Consiglio Nazionale delle Ricerche, Bologna, Italy Preliminary m e a s u r e m e n t s on t e m p e r a t u r e a n d energy dependence o f planar channeling in Si thin crystals are reported. Backscattering a n d transmission o f M e V H + have been used to obtain information on the half-thickness Xl/2 for escape on the critical angle a n d on the energy loss o f channeled particles. T h e Xl/2 values extracted from the backscattering data are smaller t h a n those obtained by transmission m e a s u r e m e n t s in crystals o f thicknesses comparable with Xl/2 values. A change o f a b o u t 15-20% has been m e a s u r e d in x~/2 on going from 80 K to 300 K for both backscattering a n d transmission techniques. A n increase at 80 K o f a b o u t 2 0 % has also been m e a s u r e d in the full-width at h a l f - m a x i m u m o f the transmitted angular distributions for particles i m p i n g i n g a r o u n d the { 110} plane. A c o m p a r i s o n o f these results with theoretical predictions suggest a value o f the screening distance lower t h a n the T h o m a s - F e r m i radius. A small but systematic decrease with temperature has been also f o u n d in the energy losses o f the well channeled particles.

1. Introduction Directional effects in the interaction of particles with crystalline solids, like critical angle, dechanneling, etc., depend strongly on the target temperature for incidence parallel to a low-index axis~). The dechanneling of planar channeled particles is less sensitive to the thermal vibrations of lattice atoms. This difference in behaviour can be related to the predominance of electronic reduced multiple scattering with respect to the nuclear one for planar channeled particles 2'3). The planar dechanneling data are usually interpreted in terms of a simple diffusion model 4) characterized by the half-thickness of escape, x~/2, which depends linearly on the beam energy. This energy dependence has been investigated both by backscattering s'6) and transmission s , 7) measurements. The transmission technique has been used to investigate the temperature dependence of planar dechanneling 7'8) in the temperature range 300-900 K; a detailed comparison between backscattering and transmission data has been given only at room temperature. To fit the energy spectra of planar transmitted protons a distance of closest approach of channeled particles to the atomic planes has been required which is a factor two lower than the common used estimates axv (Thomas-Fermi screening distance)9). It seems then interesting to extend the comparison between backscattering and transmission measurements to a

wider range of temperatures, with the aim to detail the temperature dependence of the escape length and its relationship to the closest distance of approach. In this work preliminary results are presented on planar channeling measurements performed at 80 K and at 300 K Si crystal temperatures. The half-thickness of escape extracted from backscattering and transmission data together with critical angle values are reported. The temperature dependence of the energy loss experienced by the well channeled particles has also been investigated.

2. Experimental Measurements have been performed by the transmission and backscattering technique on a 3 and 7/~m thick silicon crystals. Small and large acceptance angle detectors have been used to detect the transmitted particles with an overall resolution of 15 keV for 1.0 MeV H +. The experimental set-up has been previously described in ref. 10. Particles which were Rutherford scattered at 165 ° have been detected and the usual electronics have been used to handle the pulses. The goniometric stage, described in detail in ref. 1, allows to perform measurements at 80 K. The temperature reached by the thin silicon crystal supported by bulk silicon in thermal contact with the copper cooled finger has been checked using the temperature depenIV. C H A N N E L I N G

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dence of the axial aligned yield. The energy spectra of 1.0 MeV H ÷ scattered at 165 ° from a 7/~m thick Si crystal are shown in fig. I for a non-channeled incident direction and for the <111> axial direction. The decrease of the aligned yield with temperature indicates, by comparison with previous data on bulk samples, an effective temperature of about 80-100 K. 3. Results and discussion

3.1. DECHANNELINGANALYSIS The energy spectra obtained by a wide acceptanceangle (2 x 10 - 2 s t ) detector are reported in fig. 2 for 1.0 MeV H + transmitted through the {110} plane of a 7/zm thick silicon crystal. The measurements have been performed at 80 K and 300 K to investigate the temperature dependence of planar dechanneling. The energy spectrum for particles impinging in a nonchanneled direction is also shown. The arrows labelled ER and Ec indicate the energies of particles transmitted through a non-channeled direction and through the {ll0} plane, for their whole path. The obtained ratio between the average energy loss in the {110} channeled direction and a random one is 0.6. The distribution of particles transmitted with energies in the range Ec--ER shows exponential trends: one near ER due to particles dechanneled just after the surface and another near E o The whole spectrum should be described on the basis of a large number of Gaussian distributions for each group of particle trajectories. With increasing thickness the mixing produced by multiple scattering gives rise to a unique exponential decrease. In the normalized energy spectra the number

of still channeled particles is larger at 80 K than at 300 K. For a quantitative comparison the half-thickness, x~/2, for escape has been evaluated according to the procedure described in ref. 6. The obtained values are xl/2(80 K) = 3.8/~m and X l / 2 ( 3 0 0 K) = 3.2/~m. To obtain another independent evaluation of this quantity the backscattering technique has been applied. Backscattering energy spectra detected in the same experimental conditions are given in fig. 3. A smaller minimum yield Z, is measured at 80 K compared to that at room teperature. The decrease in the channeled fraction, [ 1 - z ( E ) ] / ( l - z 0 ) , is approximately an exponential function of energy till a value of about 20 %, for both target temperatures. The obtained values are: Z1/2(80 K) = 2.35/tm, and X1/2(300 K) = 2.1/~m. The room temperature value agrees very well with previous measurements 5. 6). The same relative difference in x,/2 with temperature is found with both techniques but larger absolute values are measured in transmission. For crystal thicknesses comparable with the half-thickness for escape, the contribution due to well channeled particles and to random ones are not well separated in the transmission energy spectra. The fit of the exponential rate of dechanneling for particles scattered in the crystal at energies between ER and Ec gives an ambiguous result because of the presence of a fiat component due to well channeled particles. The obtained '

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Fig. 1. Backscattering energy spectra o f 1.0 MeV H + impinging in a r a n d o m and in the aligned <111 > direction o f a 7/~m thick Si crystal maintained at 80 K ((~) and at 300 K ([]) respectively.

Fig. 2. Energy spectra o f 1.0 MeV H + transmitted through a 7 # m thick Si crystal and recorded by means o f a large-acceptance detector. The spectra refer to proton beam incident along the {110} plane o f the target at 80 K and at 300 K respectively, and along a non-channeled direction. The two arrows indicate the exit energies Ec and Er~ o f well channeled particles and o f particles incident along a non-channeled direction.

TEMPERATURE

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CHANNELING

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values, for these crystal thicknesses, are then larger than those measured by the backscattering method or by using thicker crystals. In the diffusive model proposed 4~6) to interpret the planar dechanneling, the temperature dependence of the half thickness for escape is determined by the temperature dependence of the square cut-off angle Of/2 (critical angle). A theoretical estimation l~) of the critical angle for planar channeling including thermal vibrations gives

good linear fit of the experimental values is obtained for a = 0.10 A. In the same figure are reported the fits obtained for a = aTE = 0.18 and a = 0.06 A, which do not cross the origin of coordinates. For an infinite value of the temperature Fps--, 0 and, for physical reasons, also the escape length must be zero. A screening radius of about ZaxF,1and comparable with the thermal vibration amplitude, is then required to fit dechanneling planar measurements, in agreement with previous measurements9).

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3.2. CRITICAL ANGLES

x (Ndp Z 1Z 2 a/E)* (degrees), where U~ = unidimensional thermal vibration amplitude in A, a = screening radius in ,~, dp = interplanar spacing, N = atomic density of the target, Za Z2 = atomic number of projectile and target, Fps = square root of adimensional planar potential using the Moli~re screening function. The temperature dependence of the half thickness for escape is then determined by the Fps function. The experimental xu2/E values obtained by backscattering or by transmission in thick crystals 7) and in the temperature range 80-900 K, are reported in fig. 4 vs Fps. To compare the different experiments the ordinate scale has been normalized as xt/2/E because of the linear dependence of x~/2 on proton energy. The temperature dependence of Fps has been evaluated for several values of the screening radius a and a

The critical angles 691/2 for Si {ll0} planar channeling have been measured at 80 K and 300 K crystal temperature. The angular distributions of transmitted protons have been determined by means of a small acceptance-angle (10-5 sr) detector and the results for 1.0 MeV H + are shown in fig. 5. The full widths at a level midway between the normal and the maximum value are 0.37 ° and 0.31 ° at 80 K and 300 K respectively. In these measurements all transmitted particles are counted for each emergence angle. A distribution of about 15 % narrower would be obtained considering only the fraction of the well channeled particles. The O1/2 values determined in this way represent then an upper limit to the critical angles. For this reason a comparison between backscattering and transmission angular data shows that the latter are systematically larger. In fig. 6 the experimental values obtained at 8"}0'

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Fig. 3. Backscattering energy spectra o f 1.0 M e V H + incident along a n o n - c h a n n e l e d direction a n d along the (110} plane o f a Si crystal m a i n t a i n e d at a t e m p e r a t u r e o f 80 K ((3) a n d 300 K ( x ) respectively.

Fig. 4. The ratio between the half-thickness for escape, xl/2, a n d the incident b e a m energy E as a function o f the adimensional planar potential Flus calculated using the Moli6re screened potential (see ref. 11). Several screening values have been a d o p t e d as fitting parameters: [] (ref. 7), • (present work). IV. C H A N N E L I N G

172

s . u . CAMPISANO et al.

80 K and 300 K are reported for proton energies ranging between 0.7 and 2.5 MeV. Analyses at 80 K have been performed using 7 #m thick crystal, those at 300 K have been performed with 3 and 7/~m thick crystals. The O1/2 values follow the usual square root energy dependence and the magnitude depends on target temperature. The experimental values have been comi

1.0MeVH~"on Si{110}

3.3. ENERGY LOSS Energy spectra recorded with a small acceptanceangle detector are shown in fig. 7 for 1.0 MeV H + impinging on a 7 #m thick Si {110} at 80 K and for several emergence angles. The zero level has been shifted for a better separation among the spectra. The low-energy-loss component decreases and shifts

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pared with theoretical calculations [see eq. (1)] and a value between 0.18 A and 0.1 A is required to get a good fit. For the thicker crystals the experimental values should be referred to energies lower than the incident ones because of the energy losses experienced by beam particles in traversing the crystal. The experimental points should be translated to the right hand side by about 5-10 % and lowered by about 15 % if one considers only the well channeled particles. A value of about 0.1 A seems then more reasonable to fit the data. A more detailed investigation is necessary to clarify the meaning of aTE in channeling measurements, and its implications in the atomic potential.

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ANGLEOFEMERGENCE (DEGREES) Fig. 5. A n g u l a r distribution o f 1.0 M e V p r o t o n b e a m incident along the {110} plane a n d e m e r g e n t from a 7 # m thick Si crystal. T h e m e a s u r e m e n t s refer to a 8 0 K (A) a n d to a 300 K ( A ) crystal t e m p e r a t u r e respectively; the full widths, 201/2, at a level m i d w a y between the n o r m a l (dashed line) a n d the m a x i m u m value are also represented.

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ENERGY(MeV) Fig. 7. Energy spectra o f 1.0 M e V H + incident along the {110} plane a n d emerging from a 7 # m thick Si crystal at 80 K. T h e spectra are recorded with a small acceptance-angle detector.

I?EMPERATURE D E P E N D E N C E OF P L A N A R C H A N N E L I N G

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the crystal temperature. This small temperature dependence (a few %) of the stopping power has been found systematically for different crystal thicknesses and in all the runs. A similar effect has also been observed for axial channeling. The measured temperature effect in the stopping power is larger than that expected by a simple evaluation of the change in the channel electronic density with thermal vibrations. A value of the screening radius comparable with the thermal amplitude ( ~ 0.08 A at room temperature) might enhance in the calculations the temperature dependence of the stopping power. In conclusion all the above experimental results point out that the T h o m a s - F e r m i Screening radius acts as a fitting parameter in the channeling description.

ANGLE OF EMERGENCE(DEGREES)

Fig. 8. Energy losses of well channeled particles as a function of the emergence angle for 1.0 MeV H+ incident along the (110} plane of a 7/~m thick Si crystal maintained at 80 K ([]) and at 300 K (11) respectively. toward lower energies, and the normal energy loss component increases with increasing emergence angles. The particle group at the right hand side of the energy spectrum has been analyzed by the usual procedure' 2) of fitting the high energy side of the spectrum with a Gaussian curve. The peak of the obtained Gaussian fit has been taken as the most probable energy loss of this particle group. The angular dependence of the so obtained most probable energy loss is shown in fig. 8 for the two crystal temperatures. The increase of the stopping power with the emergence angle indicates that the corresponding particles have been dechanneled at different depths. A smaller change in the stopping power for the best channeled particles has been measured by changing

References

1) G. Foti, F. Grasso, R. Quattrocchi and E. Rimini, Phys. Rev. B3 (1971) 2169. 2) D. S. Gemmel, Rev. Mod. Phys. 46 (1974) 129. z) F. Grasso, in Channeling theory; observation and applications (Ed. D. V. Morgan; J. Wiley, London, 1974). 4) j. Lindhard, Kgl. Danske, Vidensk. Selskab. Mat. Fys. Medd. 34, no. 14 (1965). 5) S. U. Campisano, G. Foti, F. Grasso, M. Lo Savio and E. Rimini, Rad. Effects 13 (1972) 157. 6) L.C. Feldman and B. R. Appleton, Phys. Rev. B 8 (1973) 935. 7) M . R . Altman, L.C. Feldman and W . M . Gibson, Rad. Effects 18 (1973) 171. 9) F. Fujimoto, K. Komaki, K. Ozawa, M. Mannami and T. Sakurai, Phys. Lett. 29A (1969) 332. 9) M . R . Altman, L.C. Feldman and W. M. Gibson, Phys. Rev. Lett. 24 (1970) 464. 10) G. Della Mea, A. V. Drigo, S. Lo Russo, P. Mazzoldi, S. U. Campisano, G. Foti, E. Rimini and G. G. Bentini, preceding article. 11) j. H. Barrett, Phys. Rev. B 3 (1971) 1527. 12) B. R. Appleton, C. Erginsoy and W. M. Gibson, Phys. Rev. 161 (1967) 330.

IV. C H A N N E L I N G