- Email: [email protected]
Computer simulation programs for nuclear reaction analysis
502
Nuclear
COMPUTER
SIMULATION
J.C.B. SIMPSON Radiation
PROGRAMS
Instruments
FOR NUCLEAR
and Methods
in Physics
REACTION
Research B15 (1986) 502-507 North-Holland, Amsterdam
ANALYSIS
and L.G. EARWAKER
Centre, Depurtrnent af Physics. Unioersity of Birmingham,
Birmingham
BIS 2TT, UK
Two FORTRAN computer programs have been written to simulate the experimental data obtained in prompt radiation techniques. The first of these programs calculates the emitted particle energy spectrum from the ion beam bombardment of any given target. This program is able to deal with both nuclear reactions and Rutherford scattering and with any experimental geometry. Particular examples cited relate to the use of the “C(d, p)13C and ‘eO(d, a)14N nuclear reactions and also to alpha particle backscattering. The second program deals with the case of proton induced resonant gamma emission, producing a graph of gamma yield versus incident proton energy. and may be applied to any reaction involving a Breit-Wigner resonance. Examples given are of profiling using the ‘7Al(p, y)% resonance at 992 keV and the wider 19F(p. t~y)‘~O resonance at 872 keV.
1. Introduction Prompt radiation analysis has become quite familiar as a technique for surface characterisation [lL3]. Of the various commonly used techniques, Rutherford backscattering, nuclear reactions and (p, y) resonance analysis can yield information with regard to the depth distribution of surface constituents. In order to reduce data analysis times and to maximize the amount of information that may be obtained, a suite of computer programs has been written to simulate the experimental spectra and yield curves obtained using these techniques. An early version of the nuclear reaction simulation program is described in ref. [4]. This has now been modified and extended to allow analysis of Rutherford backscattering spectra. The (p. -r) resonance simulation program has not been reported previously. Both programs follow an iterative approach, allowing the user to define an initial elemental distribution from which the computer constructs a simulation. which may be compared to the experimental data and the proposed target structure altered accordingly. The first of these programs calculates the emitted particle energy spectrum from any given nuclear interaction induced by the ion beam bombardmeilt of a given target. Nuclear reactions require the input of the relevant cross-section data in the energy range of interest for the element being profiled whereas RBS simulations use cross sections internally generated from the Rutherford scattering formula. The code is able to deal with all geometries, including transmission, and has facilities for including the effects of a detector dead layer or of any absorber foil that may have been placed in front of the detector. The second program evaluates the form of the yield 0168-583X/86/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
curves from nuclear resonance reactions where gamma rays are detected. The resonance cross section may be specified to be of the Breit-Wigner form or alternatively approximated. to reduce computing time. by a Gaussian. The program can accept any incident beam direction and it is also possible to include background contributions, for example, from lower energy resonances.
2. Description
of the programs
The first stage of the RBS/NRA simulation program requires the user to define the detector geometry, along with the various other parameters that are not related to the target structure. The detector geometry, as shown in fig. 1, is specified in terms of the solid angle it subtends at the target and its angle to the incident beam. The parameters of any detector foil that might have been used, for example to prevent pulse pileup due to backscattered deuterons in the case of (d, p) reactions, may be specified in terms of thickness, density and composition. A target structure of up to twenty layers may be defined, each of which may be assigned any given thickness and a composition of up to four elements as initially suggested by prior knowledge of the material under investigation and the user’s experience in analysing spectra. Calculation proceeds using Bragg’s rule combined with the simple analytical expression S(E) for stopping powers as suggested by Eskildsen [5]. AEO.5
S(E)= 1+
BE’).5+
CE
’
CIUENT
Ii TERAC A: GLE
ION
____----_--DETECTOK
OF TARGET (NOT TO SC?LE)
SOLID
detector angles but proves to be a problem if simulations are required for glancing angle geometries. In many respects the gamma ray resonance program is similar to the first program. Factors such as resonance energy and shape, beam energy step and detector geometry are again defined initially, with the target structure being the only variable for subsequent simulations. The target structure is defined in a similar fashion and the same stopping power formulation is used. The straggling formulation, being of primary importance. is a more complicated expression based on the Lindhard-Scharff model [ll] taken in combination with the Eskildsen stopping powers. This yields the following expression for straggling [12]: .n;_s,a2a = { IL(x). 1.
DETECTOR
L(x) Fsg. 1. Schematic of the detector geometry CCnventions used by both programs.
for x 6 3, forxa3.
and target structure
wnere E is the particle energy and A. B and C are free p.trameters chosen to fit the published data for each element. The usual kinematic calculations [6] are applied to obtain the interaction particle energy. The number of detected particles (Y) corresponding to a sublayer (fig. 1) of thickness dx is given by:
where I is the total number of incident ions, N is the number density of the target nuclei, do/dD is the dtfferential cross section for the interaction, d0 is the solid angle subtended by the detector at the target and 6’ is the angle of the incident beam to the target normal. The number of particles recorded in a given energy channel is calculated by weighting the value Y in inverse proportion to the detected energy spread corresponding to dx. Cross sections are incorporated in the above using either the standard Rutherford cross section [6] for RBS or by using tabulated data [7-91 in the c,lse of nuclear reaction simulations. Having obtained the basic spectrum of counts in e,tch energy channel, the various energy broadening terms such as straggling and detector resolution are included using a convolution technique. Straggling is cdculated using Bohr’s formulation [lo], and where compounds are being considered the total straggling is calculated using Bragg’s rule. At present other energy broadening effects have been ignored. These include kmematic spreading due to non-zero detector solid angle (in most cases this effect is small) and multiple scattering effects. This is a reasonable omission for samples analysed with near normal incident beam and
= 1.36x”‘-
0.016x”*,
where 9, is the straggling determined using the Bohr model, and x is a reduced energy variable = 4.0321 X 10m5 E[in eV]/Z,M,[in amu], where E and M, are the energy and mass of the incident particle and Z, is the atomic number of the target atoms. For x < 3 it can be shown that
dD:, = C,v%(l -
C,E)
S(E) 1
-IdE [
,
where C, and C, are constants. The gamma yield for any particular incident proton energy is then obtained by convoluting the straggled beam energy profile with the resonance shape and the target element distribution. Finally, the yield curve has the user specified background included and is multiplied by a detection efficiency scaling factor which is determined from measurements on a sample of known composition.
3. Data used in the programs Both programs use the analytical expression of Eskildsen [5] for calculations of the target stopping powers. The parameters in this formula have been determined by a least-squares fit to the semiempirical data of Ziegler [13.14] and are considered to be within the experimental uncertainty of the stopping powers. Whenever possible, cross-section data used in the nuclear reaction simulation program are taken from the literature [7-91. Clearly data are not always available, in which case either the most suitable data are used (e.g. these quoted for a slightly different angle but in the same energy range) or values are estimated from spectra obtained from targets of uniform known composition [41.
The values of Breit-Wigner resonance widths are usually well documented [6,9]. Because the total gamma yield in any measurement is dependent on many variaX. NUCLEAR
REACTION
ANALYSIS
504
J. C. B. Smpm,
L. G. Earwaker / Computer srnzulrr/on propuns
for NRA
20000 TANTALUM i z
15000
ALW’I IN IUM
2 a w L $ 10000 3 8 5000
0
0
128
256 CHANNEL
Fig. 2. Spectra of backscattered alpha particles measured The smooth curves show the calculated spectra.
384
at 120” from the 2.0 MeV bombardment
bles, such as detector efficiency, simulated yield curves are normalised to those obtained experimentally from standard samples and absolute cross sections are not therefore required.
4. Simulations
of data from well-known
materials
Spectra and yield curves have been obtained number of well-known targets and comparisons
51
NUPlBER
from a made
of pure samples
of Ta. In and Al.
with simulations in order to check the operation of the programs. Both aspects of the Rutherford-backscattering/ nuclear-reaction program have been checked. Firstly alpha particle backscattering spectra from samples of Ta, In and Al have been simulated (fig. 2). These spectra were obtained using 2 MeV normally incident alpha particles with a 120” detection angle. The simulations, obtained assuming an 800 A detector gold layer, coincide well with the leading edges of the experimental
*\ . ij 3000
SPECTKUM
: .
E 4 u E 2000
. .
*
2 t3 5 8 1000
-
0
256
128 CHANNEL
384
512
NUElBER
Fig. 3. Spectra of protons measured at 135” from the 1.5 MeV and 2.0 MeV deuteron smooth curves show the calculated spectra.
bombardment
of a sample of pure carbon.
The
505
8 000 2810
x
2000
0
J
I
6200
6100
ENERGY
6400
6300
( AR213ITRAKY
UN ITS)
F g. 4. Gamma ray yield curYe and simulation from a 2800 A layer of Al on Ta, as shown in the inset. using the “Al(p. resonance at 992 keV. The energy scale is nonlinear. 1 keV corresponds to 7.0 units over the range indicated. spectra. Those corresponding to In and Al are in good agreement with the experimental data across the entire energy range. However. there is some discrepancy in the case of the Ta target which is most likely due to some inaccuracy in the stopping power formulatioI1. The second test involved the nuclear reaction simulation mode of operation. A thick piece of pure carbon was analysed using the “Cfd. p)“C reaction. Two spectra were taken. at 1.5 MeV and 2.0 MeV. both using a 135” detection angle and a 25 pm aluminium absorber
y)“Si
foil. These spectra and simulations are shown in fig. 3. There are probably two main reasons for the discrepancies in these fits. First is the presence of background in the low energy region which is especially noticeable on the 2 MeV spectrum and second, because the low energy part of the spectra correspond to depths of the order of 10 pm. the effects of multiple scattering may be important and contribute to the loss of resolution. A sample of tantalum with a 2800 A vacuum de-
2000
i 1500 k I L f 1000 z 5 C L:
500
0 0
CHANNEL
512
384
256
128
NUMBER
Fig. 5. Spectrum of backscattered alpha particles from the 2.5 MeV bombardment using a 150” detection angle. The smooth curves show the simulated spectrum elements.
of a layered silicon structure, together with the contributions
X. NUCLEAR
as shown in the inset. from the individual
REACTION
ANALYSIS
506
J. C. B. Simpson,
L. G. Eanwker
/ Cornpurer simulation
posited layer of aluminium on its surface, was taken as a standard for (p, y) resonance analysis. The gamma yield curve, obtained using the 27Al(p, y )‘sSi resonance at 992 keV is shown in fig. 4 together with the computer generated curve. The slight discrepancy between the fit and the experimental data on the leading edge is most likely due to contamination on the surface of the sample.
5. Applications
In the field of semiconductor technology silicon oxide and nitride are used for insulation and for masking devices during manufacture [15]. The thicknesses and compositions are of crucial importance with regard to the operation of the completed devices. Two examples of characterisation of these films are given, the first relating to a RBS study of a nitride on oxide on silicon sample [16] and the second to the use of the lhO(d, ao)14N nuclear reaction to investigate a buried oxide layer in silicon. Fig. 5 shows the energy spectrum of backscattered alpha particles from the 2 MeV bombardment of a silicon device with a structure determined by simulation to consist of 1000 A of SijN4 on 10600 A of SiO, on bulk silicon, as shown in the inset. Disagreement between the simulation and the experimental data is almost certainly due to low energy X-ray emission resulting from charge buildup in the insulating surface layer
progrcrms for NRA
giving rise to a low energy background in the experimental spectrum. The use of the lhO(d, CQ)‘~N reaction has been shown to be a powerful method for extracting high resolution (as good as 200 A) depth distributions of oxygen in various substrates [17]. Using this technique a sample of oxygen implanted silicon was investigated [18] and compared to a sample with a stoichiometric surface oxide. The energy spectra of emitted particles, together with a simulation, obtained using 900 keV normally incident deuterons and a 160’ reaction angle, are shown in fig. 6. The inset shows the structure of the buried oxide layer assumed in the simulation. In order to fit the 160(d, p)“O peaks it was necessary to reduce the simulated yield with respect to the ‘“O(d, a,,)14N distribution. This indicates that there is some discrepancy in the cross-section data, most probably in the (d, p) values, which are more rapidly changing at these energies. This simulation provides evidence for a region of nonstoichiometry at the front of the buried SiO,. This is most likely to be due to diffusion into and trapping of oxygen in the highly damaged region at a depth somewhat less than the range of the implanted ions [19]. The use of the (p, y) resonance program is illustrated by the 19F(p, a~)‘~0 resonance at 872 keV used for profiling a layer of LiF on the surface of silicon. This is a wide resonance having a full width half-maximum of 4.5 keV, and the alternative analysis method of deconvolution of the yield curves is conse-
800
256
512
384 CHANNEL
640
768
NUMBER
Fig. 6. Energy spectra of particles emitted from the 900 keV deuteron bombardment of samples of (a) SiO, on silicon and (b) oxygen implanted silicon. The smooth curve shows a simulation of the spectrum from the implanted sample assuming the structure shown in the inset.
J.C. B. Smpson. L.C. Euiwoker / Computer
srn~ularronpropwm
forNRA
2240 Q12000
507
ri
-
;: ;1 a
8000
-
4000
-
5 2
0 5100
5300 ENERGY
5500 (ARBITRARY
5700
UNITS)
F g. 7. Gamma ray yield curve obtained from a sample of LiF on silicon using the 19F(p, ocy)lhO resonance at 872 keV. The smooth c,‘rve is a calculation based on the structure shown in the inset. The energy scale is nonlinear. 1 keV corresponds to 6.7 units over the r;ange indicated.
quently difficult. The results of the computer simulation (fig. 7) show that the LiF is uniform throughout its e.
6. Conclusion Simulated spectra produced using both the computer codes are found to be in good agreement with the data from standard samples. An alpha particle backscattering simulation has been used to rapidly reveal the layer structure of a surface of Si,N, on SiO, on bulk Si. The ” O(d, a,)14N reaction has also been used in relation to semiconductors, this time to characterize a buried oxide layer produced by the oxygen implantation of a silicon wafer. Finally, the (p, y) resonance simulation code has been used to verify the stoichiometry of a LiF film again on silicon, using the 19F(p, cwy)lhN resonance at 872 keV. The authors wish to Saint, K.S. Forcey and some of the experimental grateful to the SERC and financial support through
express their gratitude to A. I.M. Sturland for providing results. One of us (J.C.B.S.) is AERE Harwell for providing the CASE scheme.
References [I] Proc. eds., Instr. [2] Proc.
6th Int. Conf. Ion Beam Analysis. Tempe AZ, USA. W.A. Lanford, I.S.T. Tsong and P. Williams, Nucl. and Meth. 218 (1983) 1. 5th Int. Conf. Ion Beam Analysis, Sydney, Australia.
eds., J.R. Bird and G.J. Clarke, Nucl. Instr. and Meth. 191 (1981) 1. [3] Proc. 4th Int. Conf. Ion Beam Analysis. Aarhus, Denmark, eds.. H.H. Andersen. J. Berttiger and H. Knudsen, Nucl. Instr. and Meth. 168 (1980) 1. Vacuum 34 (1984) [41 J.C.B. Simpson and L.C. Earwaker. 899. [51 S.S. Eskildsen. internal report, Institute of Physics, University of Aarhus, Denmark (1984). for [61 J.W. Mayer and E. Rimini (eds.). Ion Beam Handbook Material Analysis (Academic Press, New York. 1977). Report, University of Manchester [71 R.A. Jarjis, Internal (1979). and F. Ajzenberg-Selove, Nucl. Phys. All PI T. Lauritsen (1959) 1. Nucl. Phys. A360 (1981) 1. [91 F. Ajzenberg-Selove, Medd. 18 [lOI N. Bohr, K. Dan. Vidensk. Selsk. Mat.-Fys. (1948) no. 8. and M. Scharff, K. Dan. Vidensk. Selsk. 1111 J. Lindhard Mat.-Fys. Medd. 27 (1953) no. 15. (1984). [121 S.S. Eskildsen. private communication Andersen and J.F. Ziegler, Hydrogen Stopping 1131 H.H. Powers and Ranges in all Elements (Pergamon, New York, 1977). Powers and Ranges in all P41 J.F. Ziegler, Helium Stopping Elemental Matter (Pergamon, New York, 1977). to Semicon[I51 D.V. Morgan and K. Board. An Introduction ductor Technology (Wiley Interscience, New York, 1983). M.Sc. Thesis. University of Birmingham. 1161 I.M. Chambers, England (1984). [I71 J.C.B. Simpson, J.M.C. Groves and L.C. Earwaker, Nucl. Instr. and Meth. B9 (1985) 321. (1984). [I81 A. Saint, private communication No. 4 [I91 S.T. Picraux and P.S. Peercy, Scientific American (1985) 84. X. NUCLEAR
REACTION
ANALYSIS
Nuclear
COMPUTER
SIMULATION
J.C.B. SIMPSON Radiation
PROGRAMS
Instruments
FOR NUCLEAR
and Methods
in Physics
REACTION
Research B15 (1986) 502-507 North-Holland, Amsterdam
ANALYSIS
and L.G. EARWAKER
Centre, Depurtrnent af Physics. Unioersity of Birmingham,
Birmingham
BIS 2TT, UK
Two FORTRAN computer programs have been written to simulate the experimental data obtained in prompt radiation techniques. The first of these programs calculates the emitted particle energy spectrum from the ion beam bombardment of any given target. This program is able to deal with both nuclear reactions and Rutherford scattering and with any experimental geometry. Particular examples cited relate to the use of the “C(d, p)13C and ‘eO(d, a)14N nuclear reactions and also to alpha particle backscattering. The second program deals with the case of proton induced resonant gamma emission, producing a graph of gamma yield versus incident proton energy. and may be applied to any reaction involving a Breit-Wigner resonance. Examples given are of profiling using the ‘7Al(p, y)% resonance at 992 keV and the wider 19F(p. t~y)‘~O resonance at 872 keV.
1. Introduction Prompt radiation analysis has become quite familiar as a technique for surface characterisation [lL3]. Of the various commonly used techniques, Rutherford backscattering, nuclear reactions and (p, y) resonance analysis can yield information with regard to the depth distribution of surface constituents. In order to reduce data analysis times and to maximize the amount of information that may be obtained, a suite of computer programs has been written to simulate the experimental spectra and yield curves obtained using these techniques. An early version of the nuclear reaction simulation program is described in ref. [4]. This has now been modified and extended to allow analysis of Rutherford backscattering spectra. The (p. -r) resonance simulation program has not been reported previously. Both programs follow an iterative approach, allowing the user to define an initial elemental distribution from which the computer constructs a simulation. which may be compared to the experimental data and the proposed target structure altered accordingly. The first of these programs calculates the emitted particle energy spectrum from any given nuclear interaction induced by the ion beam bombardmeilt of a given target. Nuclear reactions require the input of the relevant cross-section data in the energy range of interest for the element being profiled whereas RBS simulations use cross sections internally generated from the Rutherford scattering formula. The code is able to deal with all geometries, including transmission, and has facilities for including the effects of a detector dead layer or of any absorber foil that may have been placed in front of the detector. The second program evaluates the form of the yield 0168-583X/86/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
curves from nuclear resonance reactions where gamma rays are detected. The resonance cross section may be specified to be of the Breit-Wigner form or alternatively approximated. to reduce computing time. by a Gaussian. The program can accept any incident beam direction and it is also possible to include background contributions, for example, from lower energy resonances.
2. Description
of the programs
The first stage of the RBS/NRA simulation program requires the user to define the detector geometry, along with the various other parameters that are not related to the target structure. The detector geometry, as shown in fig. 1, is specified in terms of the solid angle it subtends at the target and its angle to the incident beam. The parameters of any detector foil that might have been used, for example to prevent pulse pileup due to backscattered deuterons in the case of (d, p) reactions, may be specified in terms of thickness, density and composition. A target structure of up to twenty layers may be defined, each of which may be assigned any given thickness and a composition of up to four elements as initially suggested by prior knowledge of the material under investigation and the user’s experience in analysing spectra. Calculation proceeds using Bragg’s rule combined with the simple analytical expression S(E) for stopping powers as suggested by Eskildsen [5]. AEO.5
S(E)= 1+
BE’).5+
CE
’
CIUENT
Ii TERAC A: GLE
ION
____----_--DETECTOK
OF TARGET (NOT TO SC?LE)
SOLID
detector angles but proves to be a problem if simulations are required for glancing angle geometries. In many respects the gamma ray resonance program is similar to the first program. Factors such as resonance energy and shape, beam energy step and detector geometry are again defined initially, with the target structure being the only variable for subsequent simulations. The target structure is defined in a similar fashion and the same stopping power formulation is used. The straggling formulation, being of primary importance. is a more complicated expression based on the Lindhard-Scharff model [ll] taken in combination with the Eskildsen stopping powers. This yields the following expression for straggling [12]: .n;_s,a2a = { IL(x). 1.
DETECTOR
L(x) Fsg. 1. Schematic of the detector geometry CCnventions used by both programs.
for x 6 3, forxa3.
and target structure
wnere E is the particle energy and A. B and C are free p.trameters chosen to fit the published data for each element. The usual kinematic calculations [6] are applied to obtain the interaction particle energy. The number of detected particles (Y) corresponding to a sublayer (fig. 1) of thickness dx is given by:
where I is the total number of incident ions, N is the number density of the target nuclei, do/dD is the dtfferential cross section for the interaction, d0 is the solid angle subtended by the detector at the target and 6’ is the angle of the incident beam to the target normal. The number of particles recorded in a given energy channel is calculated by weighting the value Y in inverse proportion to the detected energy spread corresponding to dx. Cross sections are incorporated in the above using either the standard Rutherford cross section [6] for RBS or by using tabulated data [7-91 in the c,lse of nuclear reaction simulations. Having obtained the basic spectrum of counts in e,tch energy channel, the various energy broadening terms such as straggling and detector resolution are included using a convolution technique. Straggling is cdculated using Bohr’s formulation [lo], and where compounds are being considered the total straggling is calculated using Bragg’s rule. At present other energy broadening effects have been ignored. These include kmematic spreading due to non-zero detector solid angle (in most cases this effect is small) and multiple scattering effects. This is a reasonable omission for samples analysed with near normal incident beam and
= 1.36x”‘-
0.016x”*,
where 9, is the straggling determined using the Bohr model, and x is a reduced energy variable = 4.0321 X 10m5 E[in eV]/Z,M,[in amu], where E and M, are the energy and mass of the incident particle and Z, is the atomic number of the target atoms. For x < 3 it can be shown that
dD:, = C,v%(l -
C,E)
S(E) 1
-IdE [
,
where C, and C, are constants. The gamma yield for any particular incident proton energy is then obtained by convoluting the straggled beam energy profile with the resonance shape and the target element distribution. Finally, the yield curve has the user specified background included and is multiplied by a detection efficiency scaling factor which is determined from measurements on a sample of known composition.
3. Data used in the programs Both programs use the analytical expression of Eskildsen [5] for calculations of the target stopping powers. The parameters in this formula have been determined by a least-squares fit to the semiempirical data of Ziegler [13.14] and are considered to be within the experimental uncertainty of the stopping powers. Whenever possible, cross-section data used in the nuclear reaction simulation program are taken from the literature [7-91. Clearly data are not always available, in which case either the most suitable data are used (e.g. these quoted for a slightly different angle but in the same energy range) or values are estimated from spectra obtained from targets of uniform known composition [41.
The values of Breit-Wigner resonance widths are usually well documented [6,9]. Because the total gamma yield in any measurement is dependent on many variaX. NUCLEAR
REACTION
ANALYSIS
504
J. C. B. Smpm,
L. G. Earwaker / Computer srnzulrr/on propuns
for NRA
20000 TANTALUM i z
15000
ALW’I IN IUM
2 a w L $ 10000 3 8 5000
0
0
128
256 CHANNEL
Fig. 2. Spectra of backscattered alpha particles measured The smooth curves show the calculated spectra.
384
at 120” from the 2.0 MeV bombardment
bles, such as detector efficiency, simulated yield curves are normalised to those obtained experimentally from standard samples and absolute cross sections are not therefore required.
4. Simulations
of data from well-known
materials
Spectra and yield curves have been obtained number of well-known targets and comparisons
51
NUPlBER
from a made
of pure samples
of Ta. In and Al.
with simulations in order to check the operation of the programs. Both aspects of the Rutherford-backscattering/ nuclear-reaction program have been checked. Firstly alpha particle backscattering spectra from samples of Ta, In and Al have been simulated (fig. 2). These spectra were obtained using 2 MeV normally incident alpha particles with a 120” detection angle. The simulations, obtained assuming an 800 A detector gold layer, coincide well with the leading edges of the experimental
*\ . ij 3000
SPECTKUM
: .
E 4 u E 2000
. .
*
2 t3 5 8 1000
-
0
256
128 CHANNEL
384
512
NUElBER
Fig. 3. Spectra of protons measured at 135” from the 1.5 MeV and 2.0 MeV deuteron smooth curves show the calculated spectra.
bombardment
of a sample of pure carbon.
The
505
8 000 2810
x
2000
0
J
I
6200
6100
ENERGY
6400
6300
( AR213ITRAKY
UN ITS)
F g. 4. Gamma ray yield curYe and simulation from a 2800 A layer of Al on Ta, as shown in the inset. using the “Al(p. resonance at 992 keV. The energy scale is nonlinear. 1 keV corresponds to 7.0 units over the range indicated. spectra. Those corresponding to In and Al are in good agreement with the experimental data across the entire energy range. However. there is some discrepancy in the case of the Ta target which is most likely due to some inaccuracy in the stopping power formulatioI1. The second test involved the nuclear reaction simulation mode of operation. A thick piece of pure carbon was analysed using the “Cfd. p)“C reaction. Two spectra were taken. at 1.5 MeV and 2.0 MeV. both using a 135” detection angle and a 25 pm aluminium absorber
y)“Si
foil. These spectra and simulations are shown in fig. 3. There are probably two main reasons for the discrepancies in these fits. First is the presence of background in the low energy region which is especially noticeable on the 2 MeV spectrum and second, because the low energy part of the spectra correspond to depths of the order of 10 pm. the effects of multiple scattering may be important and contribute to the loss of resolution. A sample of tantalum with a 2800 A vacuum de-
2000
i 1500 k I L f 1000 z 5 C L:
500
0 0
CHANNEL
512
384
256
128
NUMBER
Fig. 5. Spectrum of backscattered alpha particles from the 2.5 MeV bombardment using a 150” detection angle. The smooth curves show the simulated spectrum elements.
of a layered silicon structure, together with the contributions
X. NUCLEAR
as shown in the inset. from the individual
REACTION
ANALYSIS
506
J. C. B. Simpson,
L. G. Eanwker
/ Cornpurer simulation
posited layer of aluminium on its surface, was taken as a standard for (p, y) resonance analysis. The gamma yield curve, obtained using the 27Al(p, y )‘sSi resonance at 992 keV is shown in fig. 4 together with the computer generated curve. The slight discrepancy between the fit and the experimental data on the leading edge is most likely due to contamination on the surface of the sample.
5. Applications
In the field of semiconductor technology silicon oxide and nitride are used for insulation and for masking devices during manufacture [15]. The thicknesses and compositions are of crucial importance with regard to the operation of the completed devices. Two examples of characterisation of these films are given, the first relating to a RBS study of a nitride on oxide on silicon sample [16] and the second to the use of the lhO(d, ao)14N nuclear reaction to investigate a buried oxide layer in silicon. Fig. 5 shows the energy spectrum of backscattered alpha particles from the 2 MeV bombardment of a silicon device with a structure determined by simulation to consist of 1000 A of SijN4 on 10600 A of SiO, on bulk silicon, as shown in the inset. Disagreement between the simulation and the experimental data is almost certainly due to low energy X-ray emission resulting from charge buildup in the insulating surface layer
progrcrms for NRA
giving rise to a low energy background in the experimental spectrum. The use of the lhO(d, CQ)‘~N reaction has been shown to be a powerful method for extracting high resolution (as good as 200 A) depth distributions of oxygen in various substrates [17]. Using this technique a sample of oxygen implanted silicon was investigated [18] and compared to a sample with a stoichiometric surface oxide. The energy spectra of emitted particles, together with a simulation, obtained using 900 keV normally incident deuterons and a 160’ reaction angle, are shown in fig. 6. The inset shows the structure of the buried oxide layer assumed in the simulation. In order to fit the 160(d, p)“O peaks it was necessary to reduce the simulated yield with respect to the ‘“O(d, a,,)14N distribution. This indicates that there is some discrepancy in the cross-section data, most probably in the (d, p) values, which are more rapidly changing at these energies. This simulation provides evidence for a region of nonstoichiometry at the front of the buried SiO,. This is most likely to be due to diffusion into and trapping of oxygen in the highly damaged region at a depth somewhat less than the range of the implanted ions [19]. The use of the (p, y) resonance program is illustrated by the 19F(p, a~)‘~0 resonance at 872 keV used for profiling a layer of LiF on the surface of silicon. This is a wide resonance having a full width half-maximum of 4.5 keV, and the alternative analysis method of deconvolution of the yield curves is conse-
800
256
512
384 CHANNEL
640
768
NUMBER
Fig. 6. Energy spectra of particles emitted from the 900 keV deuteron bombardment of samples of (a) SiO, on silicon and (b) oxygen implanted silicon. The smooth curve shows a simulation of the spectrum from the implanted sample assuming the structure shown in the inset.
J.C. B. Smpson. L.C. Euiwoker / Computer
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F g. 7. Gamma ray yield curve obtained from a sample of LiF on silicon using the 19F(p, ocy)lhO resonance at 872 keV. The smooth c,‘rve is a calculation based on the structure shown in the inset. The energy scale is nonlinear. 1 keV corresponds to 6.7 units over the r;ange indicated.
quently difficult. The results of the computer simulation (fig. 7) show that the LiF is uniform throughout its e.
6. Conclusion Simulated spectra produced using both the computer codes are found to be in good agreement with the data from standard samples. An alpha particle backscattering simulation has been used to rapidly reveal the layer structure of a surface of Si,N, on SiO, on bulk Si. The ” O(d, a,)14N reaction has also been used in relation to semiconductors, this time to characterize a buried oxide layer produced by the oxygen implantation of a silicon wafer. Finally, the (p, y) resonance simulation code has been used to verify the stoichiometry of a LiF film again on silicon, using the 19F(p, cwy)lhN resonance at 872 keV. The authors wish to Saint, K.S. Forcey and some of the experimental grateful to the SERC and financial support through
express their gratitude to A. I.M. Sturland for providing results. One of us (J.C.B.S.) is AERE Harwell for providing the CASE scheme.
References [I] Proc. eds., Instr. [2] Proc.
6th Int. Conf. Ion Beam Analysis. Tempe AZ, USA. W.A. Lanford, I.S.T. Tsong and P. Williams, Nucl. and Meth. 218 (1983) 1. 5th Int. Conf. Ion Beam Analysis, Sydney, Australia.
eds., J.R. Bird and G.J. Clarke, Nucl. Instr. and Meth. 191 (1981) 1. [3] Proc. 4th Int. Conf. Ion Beam Analysis. Aarhus, Denmark, eds.. H.H. Andersen. J. Berttiger and H. Knudsen, Nucl. Instr. and Meth. 168 (1980) 1. Vacuum 34 (1984) [41 J.C.B. Simpson and L.C. Earwaker. 899. [51 S.S. Eskildsen. internal report, Institute of Physics, University of Aarhus, Denmark (1984). for [61 J.W. Mayer and E. Rimini (eds.). Ion Beam Handbook Material Analysis (Academic Press, New York. 1977). Report, University of Manchester [71 R.A. Jarjis, Internal (1979). and F. Ajzenberg-Selove, Nucl. Phys. All PI T. Lauritsen (1959) 1. Nucl. Phys. A360 (1981) 1. [91 F. Ajzenberg-Selove, Medd. 18 [lOI N. Bohr, K. Dan. Vidensk. Selsk. Mat.-Fys. (1948) no. 8. and M. Scharff, K. Dan. Vidensk. Selsk. 1111 J. Lindhard Mat.-Fys. Medd. 27 (1953) no. 15. (1984). [121 S.S. Eskildsen. private communication Andersen and J.F. Ziegler, Hydrogen Stopping 1131 H.H. Powers and Ranges in all Elements (Pergamon, New York, 1977). Powers and Ranges in all P41 J.F. Ziegler, Helium Stopping Elemental Matter (Pergamon, New York, 1977). to Semicon[I51 D.V. Morgan and K. Board. An Introduction ductor Technology (Wiley Interscience, New York, 1983). M.Sc. Thesis. University of Birmingham. 1161 I.M. Chambers, England (1984). [I71 J.C.B. Simpson, J.M.C. Groves and L.C. Earwaker, Nucl. Instr. and Meth. B9 (1985) 321. (1984). [I81 A. Saint, private communication No. 4 [I91 S.T. Picraux and P.S. Peercy, Scientific American (1985) 84. X. NUCLEAR
REACTION
ANALYSIS