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Energy and angular distributions of ions backscattered from the sidewalls during the implantation into deep trenches
Vacuum/volume 42/numbers Printed in Great Britain
i/2/pages
17 to 19/l
0042-207x/91 $3.00+.00 (‘~ 1990 Pergamon Press plc
991
Energy and angular distributions of ions backscattered from the sidewalls during the implantation into deep trenches MPosselt and G Otto, Academy of Sciences of the GDR, Central Institute for Nuclear Research, Rossendorf, PF 19, DDR-8051,
Dresden,
GDR
A characteristic feature of implantation into deep trenches is the grazing incidence bombardment of the trench sidewalls. This leads to a considerable backscattering of the incoming ions. Most of the backscattered particles are reimplanted into the opposite sidewalls of the trench. For grazing incidence implantation of As’ ions into Si we determine the backscattering yield and energy and angular distributions of the reflected ions using TRIM Monte Carlo simulations. Our investigations may be considered a first step in a semi-analytical calculation of the dopant profiles in the trench. Therefore, we fit the histograms obtained for the energy and directional distributions of the backscattered ions to analytical expressions.
I. Introduction Deep trench capacitor technology is often favoured to increase the packing density of VLSI DRAM cells. Ion implantation is one way of doping the sidewalls of these trenches. Since the ions are implanted at a shallow angle to the sidewall surface some specific phenomena appear’ ‘. After some collisions in the substrate a considerable part of the incident particles is backscattered and may be reimplanted into the opposite sidewall of the trench. The enhanced sputtering yield can lead to important modifications of the sidewall surface if the implantation doses are sufficiently high. In the present work, we investigate the backscattering yield and energy and angular distributions of the backscattered particles for the grazing incidence implantation using TRIM Monte Carlo simulations”. Characteristic examples of The histograms trench implantation of As+ are considered. obtained for the energy and directional distributions of the reflected ions are fitted to analytical expressions using a leastsquares fit method. 2. Results and discussion If the direction of the incident ions is not identical with the surface perpendicular of the target the energy and angular distribution of the backscattered particles can be determined for two different cases : (i) for a point source and (ii) for a line source of incident ions at the target surface. We consider the second case illustrated in Figure 1. In our case the trench wall corresponds to the J~-Z
/xy
lncldmt Ion beam
Figure 1. Two-dimensional
geometry
used in the calculations
plane and the line source is in the :-direction. Then, for a given incidence angle 0, (0 < O,, < 7r/2) and implantation energy E,, the energy and directional distribution of the reflected ions depends on two variables : (i) the energy E of the particles and (ii) the direction of motion characterized by the angle $ (0 ,< $ < n). The given intervals for 0, and i/j and Figure I clearly show that there is no symmetry in the problem about the .u-axis. It should be noted that II, is not a polar angle in spherical coordinates but the polar angle in the _y-_rplane. In our TRIM simulations the direction of motion of the particles is characterized by three direction cosines. The projection of this direction on the S-J plane gives the value of the polar angle +. For particles moving towards the negative or the positive .u-axis we obtain 0 d ti < n or 7~< $ < 2n, respectively. During the Monte Carlo simulation we count the number d Y, of backscattered ions per incident particle.
d YB = _yB(E, Ic/) dE d$
(1)
v,JE,$) is the energy and angular distribution of the reflected ions or the differential backscattering yield. The total backscattering yield Y, is obtained from (1) by integration. We studied grazing incidence implantation of As+ into Si for implantation energies of 80, 1I5 and 150 keV and incidence angles of 4’, 6 , 8’, and IO” to the target surface. About 5000 particle histories were simulated. The values obtained for the backscattering yield are given in Table I. In the case of grazing incidence implantation YB strongly depends on the incidence angle. For 0, = 8’- about 35% of the incoming ions are reflected. The backscattering yields of Table 1 are nearly independent of the implantation energy. Figures 2a and 3a show the energy and angular distributions y,(E, $) of the reflected particles for 80 and I50 keV As+ implantation and 0, = 8 The figures demonstrate that forward scattering dominates. In the region 3n/8 < $ < 7-1 only a few particles with E < 0.15 E, were found by the TRIM simulations. Therefore, this part of the histograms for _rH(E, $) is not shown in the figures. The minimum value _rHmlnof l’X(Y,,,” # 0) which could still be calculated by our Monte Carlo 17
M Posse/t
and G Otto:
Energy
and angular
distributions
of Ions
IEo
AS’---SS
Table I. Retlection coeliicicnts
150
Kr!‘,8g
flO)
@,,(deg) E,, (kcV)
1
6
8
IO
x0 I IS I so
0.503 0.509 0.496
0.43 1 0.422 0.415
0.363 0.349 0.367
0.304 0.284 0.200
energy and dlrectlonal
h\\
\
energy
and dlrectlonai
dlstrlbot!on (lOml IN'
rad~‘)
/
dlstrlbutlon
0
10 ENERGY
ENERGY Figure 2a. Energy
and angular
AS’--
III
distribution
SI
(L)
(TRIM
(Egz80
histo~rnm)
KU,eo:801
3lT/ 8
energy and dlrectlonal dlstrlbutlon
0
,”
1n
Figure 3b. Energy
c
wits about
simulations that
there
:und anfuklr
exists
.I’,,,,,,,, = 5
a maximum i
d
18
and angular
distrihulion
(parameter
lit)
angle
.I’ H 3 .vNllrIi,
for
.1’/, < .~‘HIWli
for $ > lb,,,(E).
In the region
E 2 0.
I ,I
(p;lramrtcr
. IO ’ $,,,(E)
kcV
lit).
’ ~-ad ‘.
We
I‘ounJ
with
lb,,,(E)
(3)
I EC,.(I?~,( E)
I),,,(E) = 1 u,(E;‘E,,)’ ’ Figure 2b. Energy
distribution
can
be dcscribcd
(I/?,)!in t-ad).
by
(3)
/1/1Posse/t and G Otto: Energy and angular
distributions
Table 2. As+ -+ Si (E, = 80 keV, 0, Coefficients
= 8”)
a, -0.151E+01
(i = 0.3) Coefficients i=O i=
of ions
0.273E+Ol .~
-0.260EfOl
0.140E+01
b,, (j = 0.3) (.j = 0.3) (.j = 0.3) (j = 0.3)
1
i=2 i=3
0.695E+02 -0.928E+02 O.l98E+02 0.237E+Ol
-0.389E+03 0513E+03 -0.106Ef03 -0.120Ef02
0.6256+ 03 -0.814B+03 O.l69B+03 O.l32E+02
-0.233E+03 0.300E+03 -0.714E+02 0.464B+Ol
Table 3. As + + Si (E, = 150 keV, 0, = 8”) Coefficients
a, ~0.190E+ol
(i = 0.3) Coefficients
0.362B+Ol
O.l56E+Ol
b,,
i=O i= 1 i=2 i=3
(.j = 0.3) (j = 0.3) (,j = 0.3) (j = 0.3)
0.434Ef 02 -0.587E+02 0.147Ef02 0.6596+00
-0.239B+03 0.319I.?+03 -0.7666+02 -0.342E+Ol
The four coefficients a, obtained from a least-squares fit procedure are given in Tables 2 and 3. For 0 < E < E. and 0 < IJ < $,(E) we fitted the histograms of Figures 2a and 3a to analytical expressions characterized by 16 parameters b,, (see Tables 2 and 3)
YEd-6$) = 1 hi,(E/E”)3 ‘qj3 ’ 2.,-O
($inradandy,inlO
-0.328EfOl
‘keV
0.374/z+o3 -0.488E+03 O.lllE+03 0.371E+ol
-O.l27E+03 o.l58B+03 -0.3366+02 O.l86E+Ol
3. Conclusions We have developed a method to calculate the backscattering yield and energy and directional distributions of the backscattered particles in the case of a grazing incidence implantation. The obtained histograms for the energy and angular distributions have been fitted to analytical expressions which may be useful for a semi-analytical calculation of the dopant profiles in the trench.
‘radd’) References
The results are shown in Figures 2b and 3b. The agreement with the histograms is satisfactory. However, the maximum in the histograms at specular reflection and high energies is reproduced poorly. Our fit procedure may be improved by the choice of a more appropriate fit function, e.g. an expansion with respect to (t/-O,). The application of the fit procedures leads to an important reduction of information without the loss of relevant features of the differential backscattering yield yH(E, $I) : 800 data of the histograms are described by 20 parameters u, and h,,.
’ G Fuse, H Unimoto, S Odanaka, M Wakabayashi, M Fukumoto and T Ohrone, J Ekctrochem Sot, 133, 996 ( 1986). ‘R Kakoschke, H Binder, S Rohl, M MaReli. I W Rangelow, S Saler and R Kassing, Nuci Instrum Meth, B21, 142 (1987). ‘K Oura, H Ugawa and T Hanawa, J Appl Phys, 64, 1795 (1988). ‘K Kato, IEEE Tram Electron Decic~s, ED-35, 1820 (1988). ‘G Fuse, H Ogawa, K Tamura, Y Naito and H Iwasaki, Appl Phys Lrtt, 54, 1534 (1989). ‘J F Ziegler, J P Biersack and U Littmark, The Stoppin,q and Range of Ions in Solids. Pergamon Press, Oxford (1985).
19
i/2/pages
17 to 19/l
0042-207x/91 $3.00+.00 (‘~ 1990 Pergamon Press plc
991
Energy and angular distributions of ions backscattered from the sidewalls during the implantation into deep trenches MPosselt and G Otto, Academy of Sciences of the GDR, Central Institute for Nuclear Research, Rossendorf, PF 19, DDR-8051,
Dresden,
GDR
A characteristic feature of implantation into deep trenches is the grazing incidence bombardment of the trench sidewalls. This leads to a considerable backscattering of the incoming ions. Most of the backscattered particles are reimplanted into the opposite sidewalls of the trench. For grazing incidence implantation of As’ ions into Si we determine the backscattering yield and energy and angular distributions of the reflected ions using TRIM Monte Carlo simulations. Our investigations may be considered a first step in a semi-analytical calculation of the dopant profiles in the trench. Therefore, we fit the histograms obtained for the energy and directional distributions of the backscattered ions to analytical expressions.
I. Introduction Deep trench capacitor technology is often favoured to increase the packing density of VLSI DRAM cells. Ion implantation is one way of doping the sidewalls of these trenches. Since the ions are implanted at a shallow angle to the sidewall surface some specific phenomena appear’ ‘. After some collisions in the substrate a considerable part of the incident particles is backscattered and may be reimplanted into the opposite sidewall of the trench. The enhanced sputtering yield can lead to important modifications of the sidewall surface if the implantation doses are sufficiently high. In the present work, we investigate the backscattering yield and energy and angular distributions of the backscattered particles for the grazing incidence implantation using TRIM Monte Carlo simulations”. Characteristic examples of The histograms trench implantation of As+ are considered. obtained for the energy and directional distributions of the reflected ions are fitted to analytical expressions using a leastsquares fit method. 2. Results and discussion If the direction of the incident ions is not identical with the surface perpendicular of the target the energy and angular distribution of the backscattered particles can be determined for two different cases : (i) for a point source and (ii) for a line source of incident ions at the target surface. We consider the second case illustrated in Figure 1. In our case the trench wall corresponds to the J~-Z
/xy
lncldmt Ion beam
Figure 1. Two-dimensional
geometry
used in the calculations
plane and the line source is in the :-direction. Then, for a given incidence angle 0, (0 < O,, < 7r/2) and implantation energy E,, the energy and directional distribution of the reflected ions depends on two variables : (i) the energy E of the particles and (ii) the direction of motion characterized by the angle $ (0 ,< $ < n). The given intervals for 0, and i/j and Figure I clearly show that there is no symmetry in the problem about the .u-axis. It should be noted that II, is not a polar angle in spherical coordinates but the polar angle in the _y-_rplane. In our TRIM simulations the direction of motion of the particles is characterized by three direction cosines. The projection of this direction on the S-J plane gives the value of the polar angle +. For particles moving towards the negative or the positive .u-axis we obtain 0 d ti < n or 7~< $ < 2n, respectively. During the Monte Carlo simulation we count the number d Y, of backscattered ions per incident particle.
d YB = _yB(E, Ic/) dE d$
(1)
v,JE,$) is the energy and angular distribution of the reflected ions or the differential backscattering yield. The total backscattering yield Y, is obtained from (1) by integration. We studied grazing incidence implantation of As+ into Si for implantation energies of 80, 1I5 and 150 keV and incidence angles of 4’, 6 , 8’, and IO” to the target surface. About 5000 particle histories were simulated. The values obtained for the backscattering yield are given in Table I. In the case of grazing incidence implantation YB strongly depends on the incidence angle. For 0, = 8’- about 35% of the incoming ions are reflected. The backscattering yields of Table 1 are nearly independent of the implantation energy. Figures 2a and 3a show the energy and angular distributions y,(E, $) of the reflected particles for 80 and I50 keV As+ implantation and 0, = 8 The figures demonstrate that forward scattering dominates. In the region 3n/8 < $ < 7-1 only a few particles with E < 0.15 E, were found by the TRIM simulations. Therefore, this part of the histograms for _rH(E, $) is not shown in the figures. The minimum value _rHmlnof l’X(Y,,,” # 0) which could still be calculated by our Monte Carlo 17
M Posse/t
and G Otto:
Energy
and angular
distributions
of Ions
IEo
AS’---SS
Table I. Retlection coeliicicnts
150
Kr!‘,8g
flO)
@,,(deg) E,, (kcV)
1
6
8
IO
x0 I IS I so
0.503 0.509 0.496
0.43 1 0.422 0.415
0.363 0.349 0.367
0.304 0.284 0.200
energy and dlrectlonal
h\\
\
energy
and dlrectlonai
dlstrlbot!on (lOml IN'
rad~‘)
/
dlstrlbutlon
0
10 ENERGY
ENERGY Figure 2a. Energy
and angular
AS’--
III
distribution
SI
(L)
(TRIM
(Egz80
histo~rnm)
KU,eo:801
3lT/ 8
energy and dlrectlonal dlstrlbutlon
0
,”
1n
Figure 3b. Energy
c
wits about
simulations that
there
:und anfuklr
exists
.I’,,,,,,,, = 5
a maximum i
d
18
and angular
distrihulion
(parameter
lit)
angle
.I’ H 3 .vNllrIi,
for
.1’/, < .~‘HIWli
for $ > lb,,,(E).
In the region
E 2 0.
I ,I
(p;lramrtcr
. IO ’ $,,,(E)
kcV
lit).
’ ~-ad ‘.
We
I‘ounJ
with
lb,,,(E)
(3)
I EC,.(I?~,( E)
I),,,(E) = 1 u,(E;‘E,,)’ ’ Figure 2b. Energy
distribution
can
be dcscribcd
(I/?,)!in t-ad).
by
(3)
/1/1Posse/t and G Otto: Energy and angular
distributions
Table 2. As+ -+ Si (E, = 80 keV, 0, Coefficients
= 8”)
a, -0.151E+01
(i = 0.3) Coefficients i=O i=
of ions
0.273E+Ol .~
-0.260EfOl
0.140E+01
b,, (j = 0.3) (.j = 0.3) (.j = 0.3) (j = 0.3)
1
i=2 i=3
0.695E+02 -0.928E+02 O.l98E+02 0.237E+Ol
-0.389E+03 0513E+03 -0.106Ef03 -0.120Ef02
0.6256+ 03 -0.814B+03 O.l69B+03 O.l32E+02
-0.233E+03 0.300E+03 -0.714E+02 0.464B+Ol
Table 3. As + + Si (E, = 150 keV, 0, = 8”) Coefficients
a, ~0.190E+ol
(i = 0.3) Coefficients
0.362B+Ol
O.l56E+Ol
b,,
i=O i= 1 i=2 i=3
(.j = 0.3) (j = 0.3) (,j = 0.3) (j = 0.3)
0.434Ef 02 -0.587E+02 0.147Ef02 0.6596+00
-0.239B+03 0.319I.?+03 -0.7666+02 -0.342E+Ol
The four coefficients a, obtained from a least-squares fit procedure are given in Tables 2 and 3. For 0 < E < E. and 0 < IJ < $,(E) we fitted the histograms of Figures 2a and 3a to analytical expressions characterized by 16 parameters b,, (see Tables 2 and 3)
YEd-6$) = 1 hi,(E/E”)3 ‘qj3 ’ 2.,-O
($inradandy,inlO
-0.328EfOl
‘keV
0.374/z+o3 -0.488E+03 O.lllE+03 0.371E+ol
-O.l27E+03 o.l58B+03 -0.3366+02 O.l86E+Ol
3. Conclusions We have developed a method to calculate the backscattering yield and energy and directional distributions of the backscattered particles in the case of a grazing incidence implantation. The obtained histograms for the energy and angular distributions have been fitted to analytical expressions which may be useful for a semi-analytical calculation of the dopant profiles in the trench.
‘radd’) References
The results are shown in Figures 2b and 3b. The agreement with the histograms is satisfactory. However, the maximum in the histograms at specular reflection and high energies is reproduced poorly. Our fit procedure may be improved by the choice of a more appropriate fit function, e.g. an expansion with respect to (t/-O,). The application of the fit procedures leads to an important reduction of information without the loss of relevant features of the differential backscattering yield yH(E, $I) : 800 data of the histograms are described by 20 parameters u, and h,,.
’ G Fuse, H Unimoto, S Odanaka, M Wakabayashi, M Fukumoto and T Ohrone, J Ekctrochem Sot, 133, 996 ( 1986). ‘R Kakoschke, H Binder, S Rohl, M MaReli. I W Rangelow, S Saler and R Kassing, Nuci Instrum Meth, B21, 142 (1987). ‘K Oura, H Ugawa and T Hanawa, J Appl Phys, 64, 1795 (1988). ‘K Kato, IEEE Tram Electron Decic~s, ED-35, 1820 (1988). ‘G Fuse, H Ogawa, K Tamura, Y Naito and H Iwasaki, Appl Phys Lrtt, 54, 1534 (1989). ‘J F Ziegler, J P Biersack and U Littmark, The Stoppin,q and Range of Ions in Solids. Pergamon Press, Oxford (1985).
19