- Email: [email protected]
amu hydrogen ions in solid N2
Nuclear Instruments and Methods 194 (1982) 71-74 North-Holland Publishing Company
STOPPING
OF 1-2 keV/amu
Peter BI3RGESEN, CHEN
HYDROGEN
Hao-Ming*
71
IONS IN SOLID N 2
and Hans SORENSEN
Association Euratom-Ris~ National l~boratory, DK-4000 Roskilde, Denmark
Thin films of N 2 on a substrate of solid Xe were bombarded with 1-2 keV/amu Hi+ , H~-, and H 3+ ions, and the energy spectra for those positive ions backscattered through 135 ° were measured. The minimum energy loss of particles scattered from the Xe-surface was found to vary linearly with film thickness up to typically-- 150 ,~, where multiple collision effects become important. It is argued that stopping powers for solid N 2 may be extracted from these measurements. Existing stopping powers for gaseous N 2 are about twice as large as our results.
1. Introduction
2. Technique
In order to understand experiments on the erosion of condensed gases by light ions, of keV energies, we expect to need stopping powers for such targets. Generally, the measurement of stopping powers in solids at the present low energies is very rarely attempted, and for a target like solid N 2 no data are available. Only two sets of values [1,2] are found even for gaseous N 2 below 10 keV. These show quite different energy dependences, and although they agree to within ~ 20% at 5 keV, the analytical fits suggest a difference of over 50% at 1 keV. Only one set of measurements [2] actually extends to energies below 5 keV, however. Whether or not gas values are directly applicable to solid N 2 appears to be an open question, but we expect any g a s / s o l i d effect to be smaller than the uncertainty in the existing data. The most significant difference between molecules in various phases is the difference in outer-shell excitation levels [3,4] generally suggesting a smaller stopping power in solids [5]. Differences of 10-20% have been found in some targets near the stopping power maximum, but it is difficult to extrapolate such results to our case: For one thing it is important to distinguish between several classes of condensed phases according to electronic structure, and furthermore we are concerned with much lower energies. Low energy stopping powers in condensed gases may be measured by two rather independent methods [6] involving quite different assumptions. The simplest of these (a kind of backscattering method) was used for the case of solid N 2.
The experimental technique is described in more detail elsewhere [6-8]: As substrate we use a very thick Xe-film ( ~ 1.5/~m) deposited on a gold plate suspended below a liquidhelium cryostat and cooled to ~ 4.2 K. By renewing the Xe-film frequently we maintain a very clean substrate surface. Films of solid N 2 are deposited on this substrate by admitting a jet of cooled gas, and removed again by heating the substrate to ~ 50 K by means of an electrical heater [8]. At this temperature Xe has a vapour pressure of less than 1 0 - s Torr and thus remains essentially undisturbed. The gas-inlet system is calibrated with a quartz-crystal film-thickness monitor placed at the position of the target plate [6]. Beams of 1-2 k e V / a m u H~+ , H ~ , and H ~ ions are extracted from a duoplasmatron ion source and selected by a 45 ° magnet. The beam current may be determined by deflecting the beam into a Faraday cup placed below the target. Positive ions backscattered through 135 ° are energy analysed in a 90 ° electrostatic analyser and detected in a channel electron multiplier. To minimize scattering inside the analyser the two curved deflector plates are formed by a series of razor blades [9]. Raising the whole analyser to a retarding voltage, which reduces the analysed energy by a factor of 5, we obtain an energy window of ~ 3% of the initial energy [6].
* Present address: Eng. Phys. Dept., Tsinghua University, Peking, China. 0029-554X/82/0000-0000/$02.75
© 1982 North-Holland
3. Principle of the method The energy spectra of light particles reflected from a heavy substrate might be expected to have well-defined "front edges" corresponding to scattering from the surface. For hydrogen incident onto Xe these front I. ENERGY L O S S / MULTIPLE SCATTERING
P. BtYrgesenet aL / Stopping oj hydrogen ions
72
I
edges approach the incident energies: A single scattering of 135 ° gives an elastic energy loss of less than 3% and plural scattering may given even less. A N 2-film of thickness A X (fig. 1) on the substrate will cause the spectrum to be shifted to lower energies. A beam of primary energy Ei. will reach the substrate with reduced energy E~ due to stopping in the film: E I = Ein -- AEin.
(I)
Corresponding, the maximum energy E~_ -~- E~ of the reflected beam is reduced to Ef,o,t(A X) traversing the film again: Efront(A X) -- E 2 - AEout,
t
I
I
I
(
3keY H3+ ~N2/Xe
>105
A.A,
Z IJ.I I.--
(2)
and, of course, energies corresponding to scattering deeper in the Xe are also reduced. Fig. 2 shows two examples of "front edges" of energy spectra: The maximum reflected energies are estimated as Efront(54 A) ~ (992 --+6) eV and Err<,nt(105 A) ~ (945 + 5) eV. Signals of higher energy simply constitute the noise level. Error bars indicate counting statistics (see below). Consider now particles penetrating the N2-film along straight paths and reflected through 135 ° at the Xesurface, i.e. with E 2 = KE~ and K ~ 1, to be finally detected with energy Efront( A S). Such particles are very rare, except for sufficiently thin films (small A X). For such films the stopping power S ( E ) -- d E / d X does not vary much along the path, and we may let AEin = S( Ein ) A X,
,
_t70 900
1000 ENERGY (eV)
Fig. 2. I keY/atom H3~ ions inc'idcnt on 54A N2/Xe and 105 A N2/Xe. Experimental energy distributions (high energy part) of positive particles emitted at/3-45 °. Efront is energy of intersection between signal and noise level for each film thickness. Error bars indicate counting statistics.
For an appropriate energy cg between Ein and Efron t we then have
Ef ..... ( A X ) = E~...... (0) - S( E ) A X ( S<+ 1~cos IX). (2a)
(3)
and
AEou , = S(Efro.t) AX/cos ~.
-*-- A X
(4)
,.
Beam
1100
Simple estimates including the variation of S ( E ) show Er,,nt(AX) to vary essentially linearly with A X for reasonably thin films. As E approaches E~,, for A X ~ 0 we may then obtain an estimate of S(E~,) from the slope of the linear part of the Efro,t(A X)-curve. This is a well known [10] principle for MeV-energies, but at the present low energies one may expect problems. The principle was applied to H 2 and D 2 targets with apparent success [6].
_
"!, "~
/
x,\/
/ /
E'~J ~s° // 2x
/
4. Discussion of the method
[\ ~ .~+j
( ( , ¢
f Analyser Fig. 1. Principle of backscattering measurement. Beam~ N2/Xe. Primary energy Ei,. Inward energy EI(AX) at Xesurface. Max. reflected energy E z = - E r Max. exit energy Effort( A X). Detection angle/7=45 °.
Particles may undergo scattering in the N2-film before or after reflection from the Xe, but this will generally result in longer paths, additional energy loss and thus energies below Er,,,t(AX). The same is obviously the case for particles reflected from behind the Xesurface. However, particles undergoing plural or multiple scattering in the N2-film may be reflected a total of 135 ° without ever reaching the Xe, and thus possibly lose less energy along the path. This might result in a detected energy larger than the Erront(A X) of eq. (2a). Such an effect is easily recognized, since the correspond-
73
P. Bttrgesen et aL / Stopping of hydrogen ions
ing energy does not vary with increasing A X. Straggling effects are likely to influence the detected energies, giving smaller minimum energy losses A Ein and A Eo, ' than given by the stopping power S(E). This would tend to give a thickness dependence of Ef~ont of the form ( A X - - c A X I / 2 ) , i.e. a clear deviation from linearity. In order to minimize erosion of the Nz-film we are forced to work with rather short beam pulses, particularly with the thinnest films. This again reduces the detected scattering yields, so each point of an energy spectrum was determined as the sum of the yields from several independent films. Thus, a spectrum like those in fig. 2 is the result of irradiating at least 30 films. Finally, we expect Ef~ont(AX) to be non-linear for thicknesses so small that the beam does not reach charge equilibrium, for the sake of estimate we take the charge-exchange cross sections as o~0 ~ 6 × 10 ~6 cm 2 [11] and o 0 j ~ 1 0 -16 cm2 [12]. From this we expect charge equilibrium after penetration of ~ 25 ,~.
5. R e s u l t s
and discussion
As the reflected intensities decrease rapidly with increasing energy, prohibitively long beam pulses are required a b o v e ~ 2 keV/atom in order to exceed the noise. The stability of the beam during a longer period of time (namely, while collecting an entire spectrum) proved to" be one of the most critical requirements at these low energies. We, therefore, preferred to work with H3+ -beams, assuming these would dissociate immediately upon impact. It was checked that the intensity of reflected, undissociated molecules near the primary energy was negligible. For primary energies between 1 and 2 keV/amu the maximum reflected energy was indeed observed to vary linearly with A X for sufficiently thin films. An example is shown in fig. 3. For larger AX ( > 200,~ in fig. 3) the energy approached a constant ("bulk") level. For primary energies below 1 keV/amu the "linear range" became very small. For incidence of H3+ = beams the Erront(AX) values were all larger than would be expected from ane equal sharing of the primary energy by dissociation. This may be explained by a so-called "Coulomb explosion" due to electron loss during dissociation [I 3]. Such a mechanism would easily account for the observed "extra"~ 100 eV in the laboratory system. In order to investigate this, measurements were also made with Hj+ and H f beams at a few energies. The resulting Erront(A X) curves for a given energy were all essentially parallel, but with no "extra" energy for Hi+ ! Fig. 4 shows the resulting stopping power values, extracted by means of eq. (2a). The rather large error
I ----Y
I
I
- I
I
--
+
/,,keV H 3 -,"-
N2/Xe 1300
-
1200 X
LLI
X
\ 'x.
1100 L
t
0
I
100
\
I
J
200 ZXx (/~)
I ~
300
Fig. 3. Maximum reflected energy at fl=45 °, for 1.33 keV/atom H3+ ~A X N2/Xe. Also best straight line through Err,,.t( A X) values for AX< 150 A.
bars are estimated from statistical uncertainties and reproducibility, and indicate the quality of the H3+" values. Due to the much larger difficulties involved in maintaining good Hi+ and H• beams, the corresponding uncertainties for these are even larger. Apparently the stopping power is approximately proportional to the energy, but the energy range is much too small to determine the energy dependence. For comparison are also shown the experimental values for N z-gas of Dose and Sele [2], and the serniempirical fit Se of Andersen and Ziegler [14]. Our results are 40-60% lower than these, which is not unsatisfactory considering the energy region. An extrapolation of Ormrod's data [1] from above 5 keV would be 37-51%
E 6.0
E
5.0
F
I
2
0
H;]
0
H[J
-
>
I
I Se (A~*Z.)sj -
-.>. N2
I~E3
4.0 -
b
/ / O /
w
f
3.0 /
2.0 / z 1,0 ft. o.. o 0.0 0.0
/
/
/
/
Sn I
I
I
1.0
I 2.0
E (keV/amu)
Fig. 4. Stopping power vs. energy for hydrogen in N 2. Our results for Hi+ (<~), H~ (V) and H~ (©) beams in solid N 2. Exp. values (7q) for Nz-gas [2], and semiempirical electronic stopping power (broken curve) [14]. Also theoretical [ 15] nuclear stopping power (full curve). I. ENERGY LOSS / MULTIPLE SCATTERING
74
P. BtIrgeven et al. / Stopping of l~vdrogen lon.s
higher than those of Dose and Sele in this region. Still, the difference between our results and those of Dose and Sele is larger than the combined uncertainties of both measurements. This may not be explained by different contributions from the nuclear stopping power [15] S., which is typically 10-20% of S~ (fig. 4) at these energies, Ranges calculated on the basis of our stopping power are in good agreement with experimental ranges [16] measured in solid N~. This consistency is very encouraging.
6. Conclusion The stopping powe r for I - 2 k e V / a m u hydrogen ions in solid N 2 was measured. Results for Hi + , H + , and H 3+ ions were in reasonable mutual agreement, and are supported by independent [16] range measurements. The rather large uncertainties (+20%) may apparently not account for the deviation from existing values for gaseous N 2. However, more data for both gaseous and solid targets are needed before statements shoud be made regarding possible phase effects. It is our pleasure to thank Dr. P. Sigmund and Dr. P. Hvelplund for valuable discussions and advice. We also
thank Dr. W. Eckstein for computer simulations of the reflection from Xe.
References [I] [2] [3] [4] [51 [6] [7] [8] [91 [10] [I 1] [12] [13] [14]
[15] [16]
J.H. Ormrod, Can. J. Phys. 46 (1968) 497. V. Dose and (i. Sele, Z Physik A 272 (1975) 237. M. Inokuti, Rev. Modl. Phys. 43 ([97[) 297. M. Inokuti, Proc. 6th Syrup. on Microdosimetr)', Brussels (1978). W.K. Chu, V.L. Moruzzi and J.F. Ziegler, J. Appl. Phys. 46 (1975) 2817. P. B~rgesen and H. SeCrensen, to be published. H. S~rensen, Appl. Phys. 9 (1976) 321. H. SeCrensen and J. Schou, J. Appl. Phys. 49 (1978) 531 [. H. Verbeek, W. Eekstein and F.E.P. Matschke, J. Phys. El0 (1977) 944. e.g.W.K. Chu and D. Powers, Phys. Rev. 187 (1969) 478. P.M. Stier and C.F. Barnett, Phys. Rev. 103 (1956) 896. N. Noda, J. Phys. Soc. Jap. 41 (1976) 625. D.S. Gemmell, Chem. Rev. g0 (1980) 301. H.H. Andersen and J.F. Ziegler, Hydrogen stopping powers and ranges in all elements (Pergamon, New York, 1977). J. Lindhard, V. Nielsen and M. Scharff, Dan. Vid. Selsk. Matt. Fys. Medd. 36 (1968) no. 10. Chen Hao-Ming, H. Secrensen, and P. Becrgesen, to be published.
STOPPING
OF 1-2 keV/amu
Peter BI3RGESEN, CHEN
HYDROGEN
Hao-Ming*
71
IONS IN SOLID N 2
and Hans SORENSEN
Association Euratom-Ris~ National l~boratory, DK-4000 Roskilde, Denmark
Thin films of N 2 on a substrate of solid Xe were bombarded with 1-2 keV/amu Hi+ , H~-, and H 3+ ions, and the energy spectra for those positive ions backscattered through 135 ° were measured. The minimum energy loss of particles scattered from the Xe-surface was found to vary linearly with film thickness up to typically-- 150 ,~, where multiple collision effects become important. It is argued that stopping powers for solid N 2 may be extracted from these measurements. Existing stopping powers for gaseous N 2 are about twice as large as our results.
1. Introduction
2. Technique
In order to understand experiments on the erosion of condensed gases by light ions, of keV energies, we expect to need stopping powers for such targets. Generally, the measurement of stopping powers in solids at the present low energies is very rarely attempted, and for a target like solid N 2 no data are available. Only two sets of values [1,2] are found even for gaseous N 2 below 10 keV. These show quite different energy dependences, and although they agree to within ~ 20% at 5 keV, the analytical fits suggest a difference of over 50% at 1 keV. Only one set of measurements [2] actually extends to energies below 5 keV, however. Whether or not gas values are directly applicable to solid N 2 appears to be an open question, but we expect any g a s / s o l i d effect to be smaller than the uncertainty in the existing data. The most significant difference between molecules in various phases is the difference in outer-shell excitation levels [3,4] generally suggesting a smaller stopping power in solids [5]. Differences of 10-20% have been found in some targets near the stopping power maximum, but it is difficult to extrapolate such results to our case: For one thing it is important to distinguish between several classes of condensed phases according to electronic structure, and furthermore we are concerned with much lower energies. Low energy stopping powers in condensed gases may be measured by two rather independent methods [6] involving quite different assumptions. The simplest of these (a kind of backscattering method) was used for the case of solid N 2.
The experimental technique is described in more detail elsewhere [6-8]: As substrate we use a very thick Xe-film ( ~ 1.5/~m) deposited on a gold plate suspended below a liquidhelium cryostat and cooled to ~ 4.2 K. By renewing the Xe-film frequently we maintain a very clean substrate surface. Films of solid N 2 are deposited on this substrate by admitting a jet of cooled gas, and removed again by heating the substrate to ~ 50 K by means of an electrical heater [8]. At this temperature Xe has a vapour pressure of less than 1 0 - s Torr and thus remains essentially undisturbed. The gas-inlet system is calibrated with a quartz-crystal film-thickness monitor placed at the position of the target plate [6]. Beams of 1-2 k e V / a m u H~+ , H ~ , and H ~ ions are extracted from a duoplasmatron ion source and selected by a 45 ° magnet. The beam current may be determined by deflecting the beam into a Faraday cup placed below the target. Positive ions backscattered through 135 ° are energy analysed in a 90 ° electrostatic analyser and detected in a channel electron multiplier. To minimize scattering inside the analyser the two curved deflector plates are formed by a series of razor blades [9]. Raising the whole analyser to a retarding voltage, which reduces the analysed energy by a factor of 5, we obtain an energy window of ~ 3% of the initial energy [6].
* Present address: Eng. Phys. Dept., Tsinghua University, Peking, China. 0029-554X/82/0000-0000/$02.75
© 1982 North-Holland
3. Principle of the method The energy spectra of light particles reflected from a heavy substrate might be expected to have well-defined "front edges" corresponding to scattering from the surface. For hydrogen incident onto Xe these front I. ENERGY L O S S / MULTIPLE SCATTERING
P. BtYrgesenet aL / Stopping oj hydrogen ions
72
I
edges approach the incident energies: A single scattering of 135 ° gives an elastic energy loss of less than 3% and plural scattering may given even less. A N 2-film of thickness A X (fig. 1) on the substrate will cause the spectrum to be shifted to lower energies. A beam of primary energy Ei. will reach the substrate with reduced energy E~ due to stopping in the film: E I = Ein -- AEin.
(I)
Corresponding, the maximum energy E~_ -~- E~ of the reflected beam is reduced to Ef,o,t(A X) traversing the film again: Efront(A X) -- E 2 - AEout,
t
I
I
I
(
3keY H3+ ~N2/Xe
>105
A.A,
Z IJ.I I.--
(2)
and, of course, energies corresponding to scattering deeper in the Xe are also reduced. Fig. 2 shows two examples of "front edges" of energy spectra: The maximum reflected energies are estimated as Efront(54 A) ~ (992 --+6) eV and Err<,nt(105 A) ~ (945 + 5) eV. Signals of higher energy simply constitute the noise level. Error bars indicate counting statistics (see below). Consider now particles penetrating the N2-film along straight paths and reflected through 135 ° at the Xesurface, i.e. with E 2 = KE~ and K ~ 1, to be finally detected with energy Efront( A S). Such particles are very rare, except for sufficiently thin films (small A X). For such films the stopping power S ( E ) -- d E / d X does not vary much along the path, and we may let AEin = S( Ein ) A X,
,
_t70 900
1000 ENERGY (eV)
Fig. 2. I keY/atom H3~ ions inc'idcnt on 54A N2/Xe and 105 A N2/Xe. Experimental energy distributions (high energy part) of positive particles emitted at/3-45 °. Efront is energy of intersection between signal and noise level for each film thickness. Error bars indicate counting statistics.
For an appropriate energy cg between Ein and Efron t we then have
Ef ..... ( A X ) = E~...... (0) - S( E ) A X ( S<+ 1~cos IX). (2a)
(3)
and
AEou , = S(Efro.t) AX/cos ~.
-*-- A X
(4)
,.
Beam
1100
Simple estimates including the variation of S ( E ) show Er,,nt(AX) to vary essentially linearly with A X for reasonably thin films. As E approaches E~,, for A X ~ 0 we may then obtain an estimate of S(E~,) from the slope of the linear part of the Efro,t(A X)-curve. This is a well known [10] principle for MeV-energies, but at the present low energies one may expect problems. The principle was applied to H 2 and D 2 targets with apparent success [6].
_
"!, "~
/
x,\/
/ /
E'~J ~s° // 2x
/
4. Discussion of the method
[\ ~ .~+j
( ( , ¢
f Analyser Fig. 1. Principle of backscattering measurement. Beam~ N2/Xe. Primary energy Ei,. Inward energy EI(AX) at Xesurface. Max. reflected energy E z = - E r Max. exit energy Effort( A X). Detection angle/7=45 °.
Particles may undergo scattering in the N2-film before or after reflection from the Xe, but this will generally result in longer paths, additional energy loss and thus energies below Er,,,t(AX). The same is obviously the case for particles reflected from behind the Xesurface. However, particles undergoing plural or multiple scattering in the N2-film may be reflected a total of 135 ° without ever reaching the Xe, and thus possibly lose less energy along the path. This might result in a detected energy larger than the Erront(A X) of eq. (2a). Such an effect is easily recognized, since the correspond-
73
P. Bttrgesen et aL / Stopping of hydrogen ions
ing energy does not vary with increasing A X. Straggling effects are likely to influence the detected energies, giving smaller minimum energy losses A Ein and A Eo, ' than given by the stopping power S(E). This would tend to give a thickness dependence of Ef~ont of the form ( A X - - c A X I / 2 ) , i.e. a clear deviation from linearity. In order to minimize erosion of the Nz-film we are forced to work with rather short beam pulses, particularly with the thinnest films. This again reduces the detected scattering yields, so each point of an energy spectrum was determined as the sum of the yields from several independent films. Thus, a spectrum like those in fig. 2 is the result of irradiating at least 30 films. Finally, we expect Ef~ont(AX) to be non-linear for thicknesses so small that the beam does not reach charge equilibrium, for the sake of estimate we take the charge-exchange cross sections as o~0 ~ 6 × 10 ~6 cm 2 [11] and o 0 j ~ 1 0 -16 cm2 [12]. From this we expect charge equilibrium after penetration of ~ 25 ,~.
5. R e s u l t s
and discussion
As the reflected intensities decrease rapidly with increasing energy, prohibitively long beam pulses are required a b o v e ~ 2 keV/atom in order to exceed the noise. The stability of the beam during a longer period of time (namely, while collecting an entire spectrum) proved to" be one of the most critical requirements at these low energies. We, therefore, preferred to work with H3+ -beams, assuming these would dissociate immediately upon impact. It was checked that the intensity of reflected, undissociated molecules near the primary energy was negligible. For primary energies between 1 and 2 keV/amu the maximum reflected energy was indeed observed to vary linearly with A X for sufficiently thin films. An example is shown in fig. 3. For larger AX ( > 200,~ in fig. 3) the energy approached a constant ("bulk") level. For primary energies below 1 keV/amu the "linear range" became very small. For incidence of H3+ = beams the Erront(AX) values were all larger than would be expected from ane equal sharing of the primary energy by dissociation. This may be explained by a so-called "Coulomb explosion" due to electron loss during dissociation [I 3]. Such a mechanism would easily account for the observed "extra"~ 100 eV in the laboratory system. In order to investigate this, measurements were also made with Hj+ and H f beams at a few energies. The resulting Erront(A X) curves for a given energy were all essentially parallel, but with no "extra" energy for Hi+ ! Fig. 4 shows the resulting stopping power values, extracted by means of eq. (2a). The rather large error
I ----Y
I
I
- I
I
--
+
/,,keV H 3 -,"-
N2/Xe 1300
-
1200 X
LLI
X
\ 'x.
1100 L
t
0
I
100
\
I
J
200 ZXx (/~)
I ~
300
Fig. 3. Maximum reflected energy at fl=45 °, for 1.33 keV/atom H3+ ~A X N2/Xe. Also best straight line through Err,,.t( A X) values for AX< 150 A.
bars are estimated from statistical uncertainties and reproducibility, and indicate the quality of the H3+" values. Due to the much larger difficulties involved in maintaining good Hi+ and H• beams, the corresponding uncertainties for these are even larger. Apparently the stopping power is approximately proportional to the energy, but the energy range is much too small to determine the energy dependence. For comparison are also shown the experimental values for N z-gas of Dose and Sele [2], and the serniempirical fit Se of Andersen and Ziegler [14]. Our results are 40-60% lower than these, which is not unsatisfactory considering the energy region. An extrapolation of Ormrod's data [1] from above 5 keV would be 37-51%
E 6.0
E
5.0
F
I
2
0
H;]
0
H[J
-
>
I
I Se (A~*Z.)sj -
-.>. N2
I~E3
4.0 -
b
/ / O /
w
f
3.0 /
2.0 / z 1,0 ft. o.. o 0.0 0.0
/
/
/
/
Sn I
I
I
1.0
I 2.0
E (keV/amu)
Fig. 4. Stopping power vs. energy for hydrogen in N 2. Our results for Hi+ (<~), H~ (V) and H~ (©) beams in solid N 2. Exp. values (7q) for Nz-gas [2], and semiempirical electronic stopping power (broken curve) [14]. Also theoretical [ 15] nuclear stopping power (full curve). I. ENERGY LOSS / MULTIPLE SCATTERING
74
P. BtIrgeven et al. / Stopping of l~vdrogen lon.s
higher than those of Dose and Sele in this region. Still, the difference between our results and those of Dose and Sele is larger than the combined uncertainties of both measurements. This may not be explained by different contributions from the nuclear stopping power [15] S., which is typically 10-20% of S~ (fig. 4) at these energies, Ranges calculated on the basis of our stopping power are in good agreement with experimental ranges [16] measured in solid N~. This consistency is very encouraging.
6. Conclusion The stopping powe r for I - 2 k e V / a m u hydrogen ions in solid N 2 was measured. Results for Hi + , H + , and H 3+ ions were in reasonable mutual agreement, and are supported by independent [16] range measurements. The rather large uncertainties (+20%) may apparently not account for the deviation from existing values for gaseous N 2. However, more data for both gaseous and solid targets are needed before statements shoud be made regarding possible phase effects. It is our pleasure to thank Dr. P. Sigmund and Dr. P. Hvelplund for valuable discussions and advice. We also
thank Dr. W. Eckstein for computer simulations of the reflection from Xe.
References [I] [2] [3] [4] [51 [6] [7] [8] [91 [10] [I 1] [12] [13] [14]
[15] [16]
J.H. Ormrod, Can. J. Phys. 46 (1968) 497. V. Dose and (i. Sele, Z Physik A 272 (1975) 237. M. Inokuti, Rev. Modl. Phys. 43 ([97[) 297. M. Inokuti, Proc. 6th Syrup. on Microdosimetr)', Brussels (1978). W.K. Chu, V.L. Moruzzi and J.F. Ziegler, J. Appl. Phys. 46 (1975) 2817. P. B~rgesen and H. SeCrensen, to be published. H. S~rensen, Appl. Phys. 9 (1976) 321. H. SeCrensen and J. Schou, J. Appl. Phys. 49 (1978) 531 [. H. Verbeek, W. Eekstein and F.E.P. Matschke, J. Phys. El0 (1977) 944. e.g.W.K. Chu and D. Powers, Phys. Rev. 187 (1969) 478. P.M. Stier and C.F. Barnett, Phys. Rev. 103 (1956) 896. N. Noda, J. Phys. Soc. Jap. 41 (1976) 625. D.S. Gemmell, Chem. Rev. g0 (1980) 301. H.H. Andersen and J.F. Ziegler, Hydrogen stopping powers and ranges in all elements (Pergamon, New York, 1977). J. Lindhard, V. Nielsen and M. Scharff, Dan. Vid. Selsk. Matt. Fys. Medd. 36 (1968) no. 10. Chen Hao-Ming, H. Secrensen, and P. Becrgesen, to be published.