- Email: [email protected]
Si(111) interface
295
Applied Surface Science 40 (1990) 295-302 North-Holland
REGULAR
STEP ARRAYS AT THE SiO,/
0. JUSKO,
P. MARIENHOFF
Institut ftir Festkiirperphysik,
Si(ll1)
INTERFACE
and M. HENZLER
Universitiit Hannouer,
Received 13 June 1989; accepted for publication
Hannover,
Fed. Rep. of Germany
11 September 1989
A set of slightly misoriented Si(l1) wafers have been oxidized and annealed in different ways. After removal of the oxide the structure of the Si/SiO, interface has been studied by a high-resolution LEED system. The resulting LEED spots showed relatively sharp splitting for out-of-phase condition, indicating a nearly regular step array. The spot profiles are described precisely by a closed form terrace width distribution. The energy dependence of the spot profiles yields the vertical roughness of the samples. It can be shown that the selection of appropriate oxidation parameters decreases the deviations from the periodic structure.
1. Introduction The SiO,/Si interface is subject of vivid interest from both surface science and semiconductor technology. But in most cases only the structure of the precision oriented nearly plain surface is examined. Yet the vicinal surface is of special interest. Despite the fundamental question whether a regular step array is reproduced after oxidizing, the periodicity itself has consequences. A perfect regular step array can be regarded as a superlattice [ll]. The newly introduced lattice constant yield new gaps and zone boundaries (called minigaps and minizones) [l]. If the mean free path of the electrons is much longer than this period, the carriers will no longer move in the parabolic part of the conduction band. The closer they get to the minigaps, the heavier anomalies are expected [2]. This could be the guideline to a new high speed transistor concept - the “Bloch transistor”. But the interesting fact that two crystallographic directions can be distinguished from each other, leads to problems in the analysis of the diffraction pattern. Up to now, LEED theory was mostly restricted to a linear chain [lo]. For a lot of cases this is sufficient. Only in special cases twodimensional extensions were used. The analysis of the investigations reported here first will follow earlier evaluations of Si(ll1) wafers as closely as possible [7], so that for example the influence of the oxidation can be compared more 0169-4332/90/$03.50 (North-Holland)
0 Elsevier Science Publishers B.V.
easily. So here the “standard” one-dimensional analysis assuming a geometric distribution will be used for describing the vertical roughness of the terraces and to determine the kink density. Although the analysis of the geometric arrangement of a non-perfect step array is not completely separable in the two different directions (parallel and perpendicular to the step edges), this procedure provides the only available approach so far. The step array will be described by using a new terrace width distribution forming a monotonous sequence of steps.
2. Evaluation of spot profiles The evaluation of spot profiles is carried out using the kinematical approximation. An overview about surface defect analysis from spot profiles is found in refs. [3,4]. For the LEED investigations reported here, only a brief review is given with special emphasis on the nearly regular step array. A surface unit cell is found at r, = n + h(n)d, where n is a vector of a low-index lattice plane close to the surface orientation and d connects atoms of equivalent adjacent planes. Further analysis will be restricted to cases where all surface atoms belong to the same primitive sublattice and the first Brillouin zone (the OO-reflex and its
296
0. Jusko et al. / Regular step arra_wat the SiO,/St(ll
neighbourhood). So the parallel component of d has minor influence and will be neglected. The discrete function h(n) gives the height of the surface unit cell in the mesh n. A surface unit cell and the underlying bulk cells are combined to a scattering column with a given scattering amplitude f,. The diffracted intensity is: I(K) = c f,f, eldK,[Mn)-wm)l eiaq(n-w, (1) n,m
with K the scattering vector with parallel and normal component K,, and K, and d the normal component of d. If all scattering amplitudes are equal (homogeneous surface), I can be factorized I(K)=F(K).G(K),
F=
lf12.
(2a) Here F denotes the form factor, which contains information about one unit mesh. G denotes the lattice factor, which contains the geometrical arrangement of the unit meshes. In the kinematic approximation F(K) can be eliminated by normalization [13]:
I(K) I
=
+G(K)
total
= G(K).
(2b)
I) interface
+(m,h) denotes the pair correlation of a linear chain on the surface. This integration or averaging can be carried out at measure time. Using a slit aperture the intensity of one dimension is collected, what is equivalent to integrating a two-dimensional scan after measuring it. For a surface with random steps, we assume a constant probability p for finding a step at the nearest scatterer on the linear chain. So we obtain a geometrical terrace width distribution P(F) for finding a width of F atomic distances
P(r)
=p(l
The lattice
-p)? factor
def g = K,,a/2m,
G(g,s) =
def s =
[5]:
K,d/2r,
1 - p2
(5)
1 - 2p cos(277g) + p* .
For the two-layer p=
(5) for this case is known
[(l-p)‘4
case
p* + 2p(l
-p)
cos(27rs)
BZ
Since only the intensity but not the amplitude is the measurable quantity, the maximum achievable information is the pair correlation Q(r). G(r) and Q(r) are coupled by cc G(u,u,s) = @(m,n,h) e-2?r’(umtr’nish).
c
m,n,h
(3) The coordinates m and n now give lateral distances on the surface and h gives a vertical off-set in multiples of the lattice constants. Integrating G leads to special pair correlations with m, n or h = 0. Here an example for n = 0:
Jrdu
G( u,u,s)
0
=
g m,n,h= X
/
Q(~,o,~)
e-2ni(um+sh)
sin2(2ns)]“2.
The geometric distribution can be extended to two dimensions. But then further assumptions about the metrics have to be taken in account. Assuming isotropic metrics fits to LEED data of well oriented silicon surfaces [6,7]. But a geometric or in general a distribution with monotonically decreasing probability cannot describe a nearly regular step array. At first, we examine the case of a perfect staircase. The terrace distribution is very simple. But important is the maximum of P(F) at F = F,. A terrace width distribution describing a regular step array must have a distinct maximum near the mean terrace length, giving through the macroscopic misorientation: P(F=
r,)
= 1,
P(F)=O,
for TZF,.
-cc
The lattice factor for a perfect grating known from optical theory. So the perfect step array of terraces with length F. is:
oldu e-2Tio
= g
-p2
Q(~,o,~)
e-2ni(um+rh)
m,h=-m = m hg_m+(m,h)
G
e-2ni(um+sh).
=
sin2 ( K/2) sin’ ( k/2)
~24s n
+ k,,T, - 24.
is well regular
(6)
(4) From (6) we see that the reciprocal
lattice rods are
0. Jusko et al. / Regular step arrays at the SiO,/Si(Ill)
291
interface
inclined with slope kT, in comparison to the normal vector of the corresponding low-index plane. Hence a k,,-scan out-of-phase condition intersects two lattice rods and shows spot splitting. In reality, a perfect step array is not be expected. Possible deviations from the perfect staircase should be included into the model. For large surface distances the probability distribution should asymptotically approach the geometric distribution due to random correlation. For small distances the distribution should decay fast towards zero, because a terrace length of zero should not have finite probability. A terrace width distribution which fits in this scheme is the “gamma distribution”: =Pe-r’r.
P(r)
(7)
Fig. 1 visualizes eq. (7) for two different parameter choices. Since no analytical way is known to calculate the lattice factor G(K) for the gamma distribution, it can be done numerically using one of the published algorithms [8,5]. It allows G(K) to be calculated for any distribution and given scattering phase s. Let
-0.1 relative Fig. 2. Calculated
0.0
parallel
scattering
0.1 vectork,,a/Za
spot profiles for the terrace tions shown in fig. 1.
We assume parallel steps then the formula yields
only
width
in one direction,
-2nis
e 1 _ Fg
distribu-
1
__ e-21ris
l-F,,
)I.
(8)
9 tg=
means
the real part and gE stands
(1 -Fg)/[2i
for
sin(rg)].
In fig. 2 we can see two spot profiles calculated with (8) using the same parameters as in fig. 1.
3. Experimental
0
20
40 terrace
60 width
80
100
r
Fig. 1. Probability P(r) for finding a terrace of width r at the surface if a r-distribution is assumed. The distribution is plotted for two different parameter sets.
Six Si(lll)-wafer groups with a misorientation of 1.7” k 0.1” towards [ii21 direction have been polished with a commercial standard (Wacker Chemitronic), then oxidized with systematic variation of parameters, which are shown in table 1. The oxide of pre-oxidation (intended to improve smoothness) was removed before final oxidation. After removal of the final oxide by HF etching,
0. Jusko ei al. / Regular step arrays at the SO, / Si(lI1)
298 Table 1 Group
Treatment
I
II
III
IV
Preoxidation 100 nm dry 0,
X
X
X
X
Dry oxidation 950°C40nm
X
X
v
VI
X
1000°C90nm
the samples were transferred into the UHV chamber, where the LEED investigations took place. The system is equipped with a high-resolution LEED system with electrostatic deflection [9]. Spot profiles of the OO-reciprocal rod were recorded in the energy interval E = 65-90 eV. Three different kinds of scanning were used: (i) linear scan (two perpendicular directions of
X
X
interface
k,,)
Wet oxidation 950°C4min + dry oxidation 1000°C1l min at all 90 nm
X
(ii)
Z=Z(k,)
with k, = const.
Z=Z(k,)
with k, = const.;
or
area scan
X
Z=Z(k,,k,);
Annealing in N, atlOOO°Clh
X
X
X
X
(iii) linear integrated scan (an area scan with one-dimensional integration of data) I = jszdk,Z( k,, k,), where the integration is taken over the full width of a brillouin zone (I=). As mentioned above, integrated scans are necessary to simulate a slit detector, so that one-dimensional theory can be used for describing the data. Fig. 3 shows linear k,,-scans perpendicular to the step edges for four different electron energies taken with the same samples. A clear spot splitting can be observed except for in-phase condition of neighbouring terraces, which is proof for a nearly regular step array at the Si/SiO, interface.
-0.2 -0
0
-4
4
relative relative
parallel
scattering
0.2
0.0
8 vector
k,,a/2x
Fig. 3. Spot profiles of the m-beam for the four electron energies (from top): 71, 73, 75.5 and 77 eV. A clear spot splitting can be observed.
parallel
scattering
vector
Iclla/2~
Fig. 4. Spot profiles of the 00-beam at out-of-phase condition s = 5.5 for two samples (group I and VI). The difference in the FWHM of the peaks reflects the difference in regularity of the step arrays.
0. Jusko et al. / Regular step arrays at the SiO,/Si(Ill)
0.0
-0.00 relative
parallel
vector
299
0.06
k,
scattering
interface
klla/2a
Fig. 5. Two-dimensional spot profile of the 00-beam at s = 5.5
Fig. 4 compares two samples oxidized under different conditions. The difference in half-width of the spots show that the samples also differ in the regularities of the step array. Fig. 5 shows a side-view of an area scan at exact out-of-phase interference condition. The spot splitting is about 3.2% of the next normal spot distance. The spots have a half-width of 0.5%. Fig. 6 is a typical scan parallel to step edges. It is not distinguishable from arbitrary scans through the OO-reflex of a precision oriented Si(ll1) wafer [6], if oxidation parameters are identical.
relative parallel
scattering
4. Results Fig. 7 gives a idealized view of the examined surface. The terrace width r has statistical deviations. (The figure only shows nearly constant terrace width as measured from an edge atom to the corresponding edge atom of the next edge.) Kinks at the edges define a mean edge length of perfect ledge. Holes on the plain terrace and kinks yield a root mean square deviation of the surface atoms from an exactly periodic step array (vertical (rms) roughness). For getting quantitative results for
vector
+la/2?r
Fig. 6. Spot profile of the 00-beam. Scan direction is parallel to the steps. No splitting is observed
300
0. Jusko et al. / Regular step arrays at the SiO, / Si(l1 I) interface
Fig. 7. Regularly stepped surface (idealized).
these variables, the following calculations were made: At first the instrument function was recorded at in-phase condition. All defects except steps are therefore included into this “instrument function”. This function was deconvoluted from the scans prior to fitting. Then the split spots were fitted to calculated profiles, which were derived from a I’-distribution by the Pimbley-Lu method, for each energy respectively. A fitting set of parameters for the r-distribution is selected in such way that it fits for all other energies simultaneously at best. Fig. 8 shows a measured integrated k,,-scan together with a calculated one. The r-distribution describes the spot profile precisely even in the logarithmic plot.
-0.4
-0.2 relative
Fig. 8. Fit Of measured
parallel
The two parameters of the r-distribution provide the mean terrace width of about 10 nm and the mean deviation from the regular step array. Of course, the mean terrace width is also obtainable from the spot splitting distance or from an X-ray determination of the misorientation. All methods gave the same result of 1.7” + 0.1” for the misorientation. The profiles, which were measured perpendicular to the splitting, were fitted to lorentzians as in eq. (5). The assumption of an geometric distribution here was as suitable as in case of an unstepped surface (i.e. no misorientation). The corresponding fitting parameters gives the average length of the straight edge. The root mean square roughness of the terraces is derived from the rela-
0.0 scattering
0.2 vector
0.4 lc,,+*
integrated spot profile with a calculated one. Note the logarithmic intensity scale.
0. Jusko et al. / Regular step arrays at the SiO,/Si(I
II) interface
301
Table 2 Parameter
Group I
III
II
IV
v
VI
Std. dev. from reg. array (nm)
- *)
1.6
1.0
1.4
1.8
1.0
Rank of quality
6
4
1
3
5
1
12.4
17.9
20.9
16.7
19.7
32.7
6
4
2
5
3
1
The mean length of straight edge (nm) Rank of quality (rms) roughness (nm)
v
0.16 (all the same)
>
a) Scan type (iii) data of sample 1 is not sufficient for quantitative analysis. But the rank of quality can easily be estimated.
tive integral peak intensity as a function of energy. The roughness shows no significant differences for all samples. It is about half a double layer. Table 2 summarizes the results of the analysis:
5. Discussion For the first time nearly regular atomic scale step arrays could be observed at the Si/SiO, interface. Parallel to this investigations there were found pm-scale step arrays with ARLS (angular resolved light scattering) [6].
Fig. 10. Model of the surface after annealing.
The surface of the samples can be described in the following way: In the direction of the misorientation runs a step array with terrace lengths of 9.1-10.6 nm. Its regularity is coupled with the kink density at the terrace edges. Figs. 9 and 10 should make this coupling understandable. In fig. 9 we can see a less regular step array. The kink density is high and the roughening of the edges cuts deep into the terraces, so the standard deviation of the terrace width is high. Fig. 10 shows a surface after annealing. The terrace edges are quite straight, so that the standard deviation of the terrace width is low. This is considered as the dominant parameter for the oxidation quality, which is indicated in table 2. But as the step array
Fig. 9. Model of the surface before annealing.
302
0. Jusko et al. / Regulur step arrays at the SO, / Si(l I I) interface
can also have deviations from the perfect regular case, the mean edge length F, is not automatically related to the terrace width variation. We see also that the variations in the kink density are higher than in the deviation from the step array. From this fact it may be concluded that the step regularity is only slightly influenced by the oxidation. Improvements by appropriate processing are more drastic in the kink density. A surprising result is the extraordinary position of the wet-dry oxidation (group VI). The sample with this treatment shows best performance in all points. The pre-oxidation (group II-V) seems to have no effect on the LEED data. The regularity of the interface increases together with oxide thickness (group I-IV, II-III). Annealing in dry N, at 1000° C (group I-II, IV-III) leads to a clear improvement in all parameters. The homogeneity of the samples gives hope that future electrical measurements may show anisotropic conductivity. For vicinal Si(100) wafers already results exist [12]. It might be of interest to search for regular step arrays at the (100) interface, because steps on the (100) surface are between non-equivalent planes. The LEED data gives no information about the local view of the step edges. This question may be answered in the near future by STM pictures of the same samples.
Acknowledgments This project was in part supported by the European Research Organization of the US Army. The Si wafers were kindly provided by Wacker Chemitronic, Burghausen. We thank Professor J. Graul, Hannover for providing the oxidation of the wafers.
References [l] [2] [3] [4] [S] [6] [7] [8] [9] [lo] Ill] [12] [13]
L. Esaki and R. Tsu, IBM J. Res. Develop. 15 (1970) 1. H. Rromer, Phys. Rev. 109 (1958) 1856. M. HenrJer, Appl. Phys. A 34 (1984) 205. M. Henzler, Festkorperprobleme 27 (1987) 185. P. Marienhoff, PhD Thesis, Hannover (1988). G.J. Pietsch, M. Henzler and P.O. Hahn, in: INFOS ‘89 [Appl. Surface Sci. 39 (1989) 4571. J. Wollschhager, Diplomarbeit, Hannover (1986). J.M. Pimbley and T.M. Lu, J. Appl. Phys. 58 (1985) 2184. U. Scheithauer, G. Meyer and M. Henzler, Surface Sci. 117 (1982) 180. M. Presicci and T.M. Lu, Surface Sci. 141 (1984) 233. T. Cole, A. Lakhani and P. Stiles, Phys. Rev. Letters 38 (1977) 13. T. Cole, PhD Thesis, Providence (1978). M. Horn, U. Gotter and M. Henzler, J. Vacuum Sci. Technol. B 6 (1988) 727.
Applied Surface Science 40 (1990) 295-302 North-Holland
REGULAR
STEP ARRAYS AT THE SiO,/
0. JUSKO,
P. MARIENHOFF
Institut ftir Festkiirperphysik,
Si(ll1)
INTERFACE
and M. HENZLER
Universitiit Hannouer,
Received 13 June 1989; accepted for publication
Hannover,
Fed. Rep. of Germany
11 September 1989
A set of slightly misoriented Si(l1) wafers have been oxidized and annealed in different ways. After removal of the oxide the structure of the Si/SiO, interface has been studied by a high-resolution LEED system. The resulting LEED spots showed relatively sharp splitting for out-of-phase condition, indicating a nearly regular step array. The spot profiles are described precisely by a closed form terrace width distribution. The energy dependence of the spot profiles yields the vertical roughness of the samples. It can be shown that the selection of appropriate oxidation parameters decreases the deviations from the periodic structure.
1. Introduction The SiO,/Si interface is subject of vivid interest from both surface science and semiconductor technology. But in most cases only the structure of the precision oriented nearly plain surface is examined. Yet the vicinal surface is of special interest. Despite the fundamental question whether a regular step array is reproduced after oxidizing, the periodicity itself has consequences. A perfect regular step array can be regarded as a superlattice [ll]. The newly introduced lattice constant yield new gaps and zone boundaries (called minigaps and minizones) [l]. If the mean free path of the electrons is much longer than this period, the carriers will no longer move in the parabolic part of the conduction band. The closer they get to the minigaps, the heavier anomalies are expected [2]. This could be the guideline to a new high speed transistor concept - the “Bloch transistor”. But the interesting fact that two crystallographic directions can be distinguished from each other, leads to problems in the analysis of the diffraction pattern. Up to now, LEED theory was mostly restricted to a linear chain [lo]. For a lot of cases this is sufficient. Only in special cases twodimensional extensions were used. The analysis of the investigations reported here first will follow earlier evaluations of Si(ll1) wafers as closely as possible [7], so that for example the influence of the oxidation can be compared more 0169-4332/90/$03.50 (North-Holland)
0 Elsevier Science Publishers B.V.
easily. So here the “standard” one-dimensional analysis assuming a geometric distribution will be used for describing the vertical roughness of the terraces and to determine the kink density. Although the analysis of the geometric arrangement of a non-perfect step array is not completely separable in the two different directions (parallel and perpendicular to the step edges), this procedure provides the only available approach so far. The step array will be described by using a new terrace width distribution forming a monotonous sequence of steps.
2. Evaluation of spot profiles The evaluation of spot profiles is carried out using the kinematical approximation. An overview about surface defect analysis from spot profiles is found in refs. [3,4]. For the LEED investigations reported here, only a brief review is given with special emphasis on the nearly regular step array. A surface unit cell is found at r, = n + h(n)d, where n is a vector of a low-index lattice plane close to the surface orientation and d connects atoms of equivalent adjacent planes. Further analysis will be restricted to cases where all surface atoms belong to the same primitive sublattice and the first Brillouin zone (the OO-reflex and its
296
0. Jusko et al. / Regular step arra_wat the SiO,/St(ll
neighbourhood). So the parallel component of d has minor influence and will be neglected. The discrete function h(n) gives the height of the surface unit cell in the mesh n. A surface unit cell and the underlying bulk cells are combined to a scattering column with a given scattering amplitude f,. The diffracted intensity is: I(K) = c f,f, eldK,[Mn)-wm)l eiaq(n-w, (1) n,m
with K the scattering vector with parallel and normal component K,, and K, and d the normal component of d. If all scattering amplitudes are equal (homogeneous surface), I can be factorized I(K)=F(K).G(K),
F=
lf12.
(2a) Here F denotes the form factor, which contains information about one unit mesh. G denotes the lattice factor, which contains the geometrical arrangement of the unit meshes. In the kinematic approximation F(K) can be eliminated by normalization [13]:
I(K) I
=
+G(K)
total
= G(K).
(2b)
I) interface
+(m,h) denotes the pair correlation of a linear chain on the surface. This integration or averaging can be carried out at measure time. Using a slit aperture the intensity of one dimension is collected, what is equivalent to integrating a two-dimensional scan after measuring it. For a surface with random steps, we assume a constant probability p for finding a step at the nearest scatterer on the linear chain. So we obtain a geometrical terrace width distribution P(F) for finding a width of F atomic distances
P(r)
=p(l
The lattice
-p)? factor
def g = K,,a/2m,
G(g,s) =
def s =
[5]:
K,d/2r,
1 - p2
(5)
1 - 2p cos(277g) + p* .
For the two-layer p=
(5) for this case is known
[(l-p)‘4
case
p* + 2p(l
-p)
cos(27rs)
BZ
Since only the intensity but not the amplitude is the measurable quantity, the maximum achievable information is the pair correlation Q(r). G(r) and Q(r) are coupled by cc G(u,u,s) = @(m,n,h) e-2?r’(umtr’nish).
c
m,n,h
(3) The coordinates m and n now give lateral distances on the surface and h gives a vertical off-set in multiples of the lattice constants. Integrating G leads to special pair correlations with m, n or h = 0. Here an example for n = 0:
Jrdu
G( u,u,s)
0
=
g m,n,h= X
/
Q(~,o,~)
e-2ni(um+sh)
sin2(2ns)]“2.
The geometric distribution can be extended to two dimensions. But then further assumptions about the metrics have to be taken in account. Assuming isotropic metrics fits to LEED data of well oriented silicon surfaces [6,7]. But a geometric or in general a distribution with monotonically decreasing probability cannot describe a nearly regular step array. At first, we examine the case of a perfect staircase. The terrace distribution is very simple. But important is the maximum of P(F) at F = F,. A terrace width distribution describing a regular step array must have a distinct maximum near the mean terrace length, giving through the macroscopic misorientation: P(F=
r,)
= 1,
P(F)=O,
for TZF,.
-cc
The lattice factor for a perfect grating known from optical theory. So the perfect step array of terraces with length F. is:
oldu e-2Tio
= g
-p2
Q(~,o,~)
e-2ni(um+rh)
m,h=-m = m hg_m+(m,h)
G
e-2ni(um+sh).
=
sin2 ( K/2) sin’ ( k/2)
~24s n
+ k,,T, - 24.
is well regular
(6)
(4) From (6) we see that the reciprocal
lattice rods are
0. Jusko et al. / Regular step arrays at the SiO,/Si(Ill)
291
interface
inclined with slope kT, in comparison to the normal vector of the corresponding low-index plane. Hence a k,,-scan out-of-phase condition intersects two lattice rods and shows spot splitting. In reality, a perfect step array is not be expected. Possible deviations from the perfect staircase should be included into the model. For large surface distances the probability distribution should asymptotically approach the geometric distribution due to random correlation. For small distances the distribution should decay fast towards zero, because a terrace length of zero should not have finite probability. A terrace width distribution which fits in this scheme is the “gamma distribution”: =Pe-r’r.
P(r)
(7)
Fig. 1 visualizes eq. (7) for two different parameter choices. Since no analytical way is known to calculate the lattice factor G(K) for the gamma distribution, it can be done numerically using one of the published algorithms [8,5]. It allows G(K) to be calculated for any distribution and given scattering phase s. Let
-0.1 relative Fig. 2. Calculated
0.0
parallel
scattering
0.1 vectork,,a/Za
spot profiles for the terrace tions shown in fig. 1.
We assume parallel steps then the formula yields
only
width
in one direction,
-2nis
e 1 _ Fg
distribu-
1
__ e-21ris
l-F,,
)I.
(8)
9 tg=
means
the real part and gE stands
(1 -Fg)/[2i
for
sin(rg)].
In fig. 2 we can see two spot profiles calculated with (8) using the same parameters as in fig. 1.
3. Experimental
0
20
40 terrace
60 width
80
100
r
Fig. 1. Probability P(r) for finding a terrace of width r at the surface if a r-distribution is assumed. The distribution is plotted for two different parameter sets.
Six Si(lll)-wafer groups with a misorientation of 1.7” k 0.1” towards [ii21 direction have been polished with a commercial standard (Wacker Chemitronic), then oxidized with systematic variation of parameters, which are shown in table 1. The oxide of pre-oxidation (intended to improve smoothness) was removed before final oxidation. After removal of the final oxide by HF etching,
0. Jusko ei al. / Regular step arrays at the SO, / Si(lI1)
298 Table 1 Group
Treatment
I
II
III
IV
Preoxidation 100 nm dry 0,
X
X
X
X
Dry oxidation 950°C40nm
X
X
v
VI
X
1000°C90nm
the samples were transferred into the UHV chamber, where the LEED investigations took place. The system is equipped with a high-resolution LEED system with electrostatic deflection [9]. Spot profiles of the OO-reciprocal rod were recorded in the energy interval E = 65-90 eV. Three different kinds of scanning were used: (i) linear scan (two perpendicular directions of
X
X
interface
k,,)
Wet oxidation 950°C4min + dry oxidation 1000°C1l min at all 90 nm
X
(ii)
Z=Z(k,)
with k, = const.
Z=Z(k,)
with k, = const.;
or
area scan
X
Z=Z(k,,k,);
Annealing in N, atlOOO°Clh
X
X
X
X
(iii) linear integrated scan (an area scan with one-dimensional integration of data) I = jszdk,Z( k,, k,), where the integration is taken over the full width of a brillouin zone (I=). As mentioned above, integrated scans are necessary to simulate a slit detector, so that one-dimensional theory can be used for describing the data. Fig. 3 shows linear k,,-scans perpendicular to the step edges for four different electron energies taken with the same samples. A clear spot splitting can be observed except for in-phase condition of neighbouring terraces, which is proof for a nearly regular step array at the Si/SiO, interface.
-0.2 -0
0
-4
4
relative relative
parallel
scattering
0.2
0.0
8 vector
k,,a/2x
Fig. 3. Spot profiles of the m-beam for the four electron energies (from top): 71, 73, 75.5 and 77 eV. A clear spot splitting can be observed.
parallel
scattering
vector
Iclla/2~
Fig. 4. Spot profiles of the 00-beam at out-of-phase condition s = 5.5 for two samples (group I and VI). The difference in the FWHM of the peaks reflects the difference in regularity of the step arrays.
0. Jusko et al. / Regular step arrays at the SiO,/Si(Ill)
0.0
-0.00 relative
parallel
vector
299
0.06
k,
scattering
interface
klla/2a
Fig. 5. Two-dimensional spot profile of the 00-beam at s = 5.5
Fig. 4 compares two samples oxidized under different conditions. The difference in half-width of the spots show that the samples also differ in the regularities of the step array. Fig. 5 shows a side-view of an area scan at exact out-of-phase interference condition. The spot splitting is about 3.2% of the next normal spot distance. The spots have a half-width of 0.5%. Fig. 6 is a typical scan parallel to step edges. It is not distinguishable from arbitrary scans through the OO-reflex of a precision oriented Si(ll1) wafer [6], if oxidation parameters are identical.
relative parallel
scattering
4. Results Fig. 7 gives a idealized view of the examined surface. The terrace width r has statistical deviations. (The figure only shows nearly constant terrace width as measured from an edge atom to the corresponding edge atom of the next edge.) Kinks at the edges define a mean edge length of perfect ledge. Holes on the plain terrace and kinks yield a root mean square deviation of the surface atoms from an exactly periodic step array (vertical (rms) roughness). For getting quantitative results for
vector
+la/2?r
Fig. 6. Spot profile of the 00-beam. Scan direction is parallel to the steps. No splitting is observed
300
0. Jusko et al. / Regular step arrays at the SiO, / Si(l1 I) interface
Fig. 7. Regularly stepped surface (idealized).
these variables, the following calculations were made: At first the instrument function was recorded at in-phase condition. All defects except steps are therefore included into this “instrument function”. This function was deconvoluted from the scans prior to fitting. Then the split spots were fitted to calculated profiles, which were derived from a I’-distribution by the Pimbley-Lu method, for each energy respectively. A fitting set of parameters for the r-distribution is selected in such way that it fits for all other energies simultaneously at best. Fig. 8 shows a measured integrated k,,-scan together with a calculated one. The r-distribution describes the spot profile precisely even in the logarithmic plot.
-0.4
-0.2 relative
Fig. 8. Fit Of measured
parallel
The two parameters of the r-distribution provide the mean terrace width of about 10 nm and the mean deviation from the regular step array. Of course, the mean terrace width is also obtainable from the spot splitting distance or from an X-ray determination of the misorientation. All methods gave the same result of 1.7” + 0.1” for the misorientation. The profiles, which were measured perpendicular to the splitting, were fitted to lorentzians as in eq. (5). The assumption of an geometric distribution here was as suitable as in case of an unstepped surface (i.e. no misorientation). The corresponding fitting parameters gives the average length of the straight edge. The root mean square roughness of the terraces is derived from the rela-
0.0 scattering
0.2 vector
0.4 lc,,+*
integrated spot profile with a calculated one. Note the logarithmic intensity scale.
0. Jusko et al. / Regular step arrays at the SiO,/Si(I
II) interface
301
Table 2 Parameter
Group I
III
II
IV
v
VI
Std. dev. from reg. array (nm)
- *)
1.6
1.0
1.4
1.8
1.0
Rank of quality
6
4
1
3
5
1
12.4
17.9
20.9
16.7
19.7
32.7
6
4
2
5
3
1
The mean length of straight edge (nm) Rank of quality (rms) roughness (nm)
v
0.16 (all the same)
>
a) Scan type (iii) data of sample 1 is not sufficient for quantitative analysis. But the rank of quality can easily be estimated.
tive integral peak intensity as a function of energy. The roughness shows no significant differences for all samples. It is about half a double layer. Table 2 summarizes the results of the analysis:
5. Discussion For the first time nearly regular atomic scale step arrays could be observed at the Si/SiO, interface. Parallel to this investigations there were found pm-scale step arrays with ARLS (angular resolved light scattering) [6].
Fig. 10. Model of the surface after annealing.
The surface of the samples can be described in the following way: In the direction of the misorientation runs a step array with terrace lengths of 9.1-10.6 nm. Its regularity is coupled with the kink density at the terrace edges. Figs. 9 and 10 should make this coupling understandable. In fig. 9 we can see a less regular step array. The kink density is high and the roughening of the edges cuts deep into the terraces, so the standard deviation of the terrace width is high. Fig. 10 shows a surface after annealing. The terrace edges are quite straight, so that the standard deviation of the terrace width is low. This is considered as the dominant parameter for the oxidation quality, which is indicated in table 2. But as the step array
Fig. 9. Model of the surface before annealing.
302
0. Jusko et al. / Regulur step arrays at the SO, / Si(l I I) interface
can also have deviations from the perfect regular case, the mean edge length F, is not automatically related to the terrace width variation. We see also that the variations in the kink density are higher than in the deviation from the step array. From this fact it may be concluded that the step regularity is only slightly influenced by the oxidation. Improvements by appropriate processing are more drastic in the kink density. A surprising result is the extraordinary position of the wet-dry oxidation (group VI). The sample with this treatment shows best performance in all points. The pre-oxidation (group II-V) seems to have no effect on the LEED data. The regularity of the interface increases together with oxide thickness (group I-IV, II-III). Annealing in dry N, at 1000° C (group I-II, IV-III) leads to a clear improvement in all parameters. The homogeneity of the samples gives hope that future electrical measurements may show anisotropic conductivity. For vicinal Si(100) wafers already results exist [12]. It might be of interest to search for regular step arrays at the (100) interface, because steps on the (100) surface are between non-equivalent planes. The LEED data gives no information about the local view of the step edges. This question may be answered in the near future by STM pictures of the same samples.
Acknowledgments This project was in part supported by the European Research Organization of the US Army. The Si wafers were kindly provided by Wacker Chemitronic, Burghausen. We thank Professor J. Graul, Hannover for providing the oxidation of the wafers.
References [l] [2] [3] [4] [S] [6] [7] [8] [9] [lo] Ill] [12] [13]
L. Esaki and R. Tsu, IBM J. Res. Develop. 15 (1970) 1. H. Rromer, Phys. Rev. 109 (1958) 1856. M. HenrJer, Appl. Phys. A 34 (1984) 205. M. Henzler, Festkorperprobleme 27 (1987) 185. P. Marienhoff, PhD Thesis, Hannover (1988). G.J. Pietsch, M. Henzler and P.O. Hahn, in: INFOS ‘89 [Appl. Surface Sci. 39 (1989) 4571. J. Wollschhager, Diplomarbeit, Hannover (1986). J.M. Pimbley and T.M. Lu, J. Appl. Phys. 58 (1985) 2184. U. Scheithauer, G. Meyer and M. Henzler, Surface Sci. 117 (1982) 180. M. Presicci and T.M. Lu, Surface Sci. 141 (1984) 233. T. Cole, A. Lakhani and P. Stiles, Phys. Rev. Letters 38 (1977) 13. T. Cole, PhD Thesis, Providence (1978). M. Horn, U. Gotter and M. Henzler, J. Vacuum Sci. Technol. B 6 (1988) 727.