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SiO2 interface
Applied Surface North-Holland
Science 41/42
HRTEM
OBSERVATION
Hiroyuki
AKATSU
(1989) 357-364
8 November
OF THE Si/SiO,
INTERFACE
and Iwao OHDOMARI
School of Science and Engineering, Received
357
Waseda University,
1988; accepted
for publication
Tokyo, Japan 5 April 1989
Interfaces with crystalline Si (c-Si) and dry oxide grown over the c-Si have been observed using high resolution transmission electron microscopy (HRTEM). The lattice image of c-Si near the interface varies depending on the specimen thickness. For a very thin region of the specimen, the interface was observed to be very much roughened, and seemed to be abrupt (the so called interfacial layer was not observed between the c-Si and the amorphous SiO, (a-SiO,)). On the contrary, the interface seemed to be flat and to consist of some steps of one or two monolayers high for the thick region. Furthermore, a lattice image with Si(220) periodicity has been observed at the interface. A possible structure for the Si/SiO, interface derived from the observed interface image is that the roughened surface of the c-Si protrusions is directly connected to the SiO, network with no interface layer between them. The observed flat interface of the thick region is a superposed image of the randomly distributed Si protrusions over the direction of the transmitted electron beam. In order to examine the postulated interface structure, a simulation of the lattice image has been performed. The results of the simulation indicate that the half-space image observed at the interface of the thick region can be attributed to the interface roughness, and the abrupt interface image observed for the thin region can be obtained by the same interface structure. Since a completely flat interface cannot provide such a specimen thickness dependence of the image, the (lOO)Si/SiO, interface must be rough, and in our sample, the height of the roughness was about 4 monolayers.
1. Introduction As the integration of Si semiconductor devices progresses, the size of each transistor or capacitor in dynamic random access memory (DRAM) cells has been reduced not only laterally but also vertically. The capacitor oxide which is the most important and the thinnest film in very large scale integrated circuits becomes about 10 nm in 1 mega-bit DRAMS. Because of the reduction of the oxide thickness, the dielectric breakdown and leakage current become critical for the reliability of the devices. The morphology of the Si/SiO, interface has a great influence on the dielectric properties of the oxide. It is reported that the interface roughness is related to the dielectric breakdown voltage of the oxide films [l] and the carrier mobility in the inversion layer [2]. Therefore, control of the interface morphology is important for the device reliability and performance. Although a variety of stacked capacitor films such as oxide-nitride (ON) or oxide-nitride-oxide (ONO) have been pro0169-4332/89/$03.50 (North-Holland)
0 Elsevier Science Publishers
B.V.
posed recently as an alternative to the extremely thin oxide, a development of the technology to form a good quality and highly reliable oxide film uniformly over a broad area of the Si surface is still of great interest because it does not require a big change in the process technology. Hence a better understanding of the interface structure remain of primary importance. From a physical point of view, it is interesting to investigate the effects of impurities, substrate orientation, and temperature on the oxidation kinetics and resulting interface morphology because this will give us a clue to understanding why amorphous oxide is grown by the thermal oxidation of c-Si. In spite of the importance of and the great deal of effort devoted to this subject, both the morphology and atomic configuration at the Si/SiOz interface have not been clarified. The main reason for the slow progress of the investigation on the interface morphology and the atomic arrangement is that there are very few experimental methods that can be used.
H. Akarsu, I. Oh&man
35x
/ HRTEM
Cross sectional observation of the Si/SiO, interface using HRTEM provides information on the interface morphology and the periodicity of the crystalline phase [1,335]. It was observed that the (lOO)Si/SiO, interface is roughened when it is formed by low temperature dry oxidation and a subsequent high temperature heat treatment makes the interface roughness small [l]. Furthermore, the interface morphology has a c-Si orientation dependence, i.e., the (lll)Si/SiO, interface is observed to be always extremely flat [5]. More recently, a periodic image which is different from the one of c-Si was observed for the (100)Si/Si02 interface formed by the dry oxidation of an atomically flat Si surface and it was attributed to the existence of tridymite between c-Si and a-SiO, [6]. In the analysis using the lattice image, however, one has to be very careful because observed images do not necessarily reflect the actual atomic arrangement, but give only the difference in the amplitude of the electron wave functions due to the interference of the transmitted and of several diffracted beams. Therefore the distorted atoms do not contribute to the lattice image formation and the optical condition in the microscope would also effect this. In this paper, the interface between the (lOO)Si and thermally grown Si oxide has been observed using HRTEM. From the specimen thickness dependence of the observed interface morphology and the through-focus observation of the lattice image of the c-Si at the interface, the interface morphology has been assumed to have pyramidlike undulations. Then a simulation of the lattice image has been carried out using a simple model with a completely flat interface on one side and an undulated interface on the other side. Finally, the actual interface morphology of our sample will be discussed by comparing the HRTEM images and the results of the simulation.
2. HRTEM
observation
of the Si/SiO,
interface
2.1. Specimen preparation The Si/SiO, interface was formed by thermal oxidation of a (lOO)Si wafer in dry oxygen at 950°C. The wafers used in this experiment were
ohserwtrot~ oj rhr SI / S/O, rnierfrre
commercially available and had undergone no special treatment to obtain an atomically flat Si surface. After the 30 nm oxide growth. poly-Si was deposited over the oxide in order to protect the Si/SiO, interface region from damage caused by the subsequent specimen preparation process for the HRTEM observation. The specimen for HRTEM observation was prepared by mechanical lapping followed by Ar ion thinning. A wafer was scribed into rectangular strips then two strips were glued together to meet the poly-Si surface side each other. The glued strips were cut parallel to the (110) direction of c-Si into pieces so that the cross section structure of the wafer appears. A piece of the specimen was lapped mechanically until it became some several tens of microns thick. Further thinning was done by using the dual Ar ion beams and this was continued until the edge of the perforation reached to the interface region of the specimen. The lattice image can be observed only around the edge of the perforation. The cross sections were examined in a JEM2000EX electron microscope at a primary voltage of 200 keV and with a point-topoint resolution of 0.21 nm. 2.2. HRTEM
observation
Typical HRTEM images of the Si/SiOz interface region are shown in fig. 1 for different specimen thickness and defocus conditions. The thickness of the specimen was judged from the thickness fringes observed in the lattice image of c-si as the half-space images. Because the specimen thickness increases gradually from the edge of the perforation, regions exhibiting half-space images are almost parallel to the edge. Hereafter, we will designate the region in the vicinity of the edge of the perforation “thin”, and the region between the first thickness fringe and the second one “thick”. The difference in the defocus value between the two photographs is about 65 nm and the smaller defocus value is just below (about - 10 nm) the good focus point judged from the Fresnel fringe at the specimen edge. Both of these conditions are far from the Scherzer defocus value (about - 50 nm), but they are not chosen with any special intent.
H. Akatsu,
I. Ohdomari
/ HRTEM
observation of the S/SO_,
interface
359
360
H. Akatsu,
I. Ohdomuri
/ HRTEM
A typical feature of the image for the “thin” region is a rough interface. Through-focus observation of the same area suggested that the interface roughness is not continuous along the direction of the specimen thickness but randomly distributed Si protrusions, because the positions of the Si protrusions in the HRTEM image are different for the different defocus conditions. Very large protrusions of nearly 2 mm high can be observed in the very thin region, while the average height of the protrusion is about 1 nm. Another feature is interface sharpness. The lattice image of the c-Si continues to the interface and no interfacial layer can be observed. The images of the “thick” region exhibit different features from the one in the “thin” region. The interface is observed to be a terrace-like structure, which consists of steps of one or two atomic layers high but is almost flat. Furthermore, the most noticeable feature of the “thick” region is the lattice image at the interface, which exhibits the half periodicity of Si(ll0). The thickness of the interface layer corresponds to two or four monolayers of c-Si, and can be observed for both defocus conditions. This kind of image was observed by Ourmazd et al. [6] and is attributed to the c-SiO, phase of tridymite grown epitaxially over an atomically flat surface of c-Si during the oxidation. However, Ourmazd’s model is not appropriate in our case because the interface is roughened and the half-space image can be observed along with the rough interface. Sometimes a lattice image of Si can be observed beyond the interface layer (inside the SiO, region) although the image is vague. By HRTEM image simulation, the vague image was attributed to Si protrusions in a-SiO, where the a-SiO, and c-Si are superimposed along the direction of incident electron beam. The simulation has also shown that the c-Si lattice image is visible even when the thickness of the c-Si region is 50% of the entire specimen thickness [7]. Since the “ thin” and “thick” regions discussed above are adjacent to each other in a single specimen, it is hard to suppose that the interface structures of two regions are different. In other words a single interface structure appears differently in HRTEM images depending on the specimen
ohsrrr:utim
of rhe Si/ SiO, Inrerfuce
thickness. Therefore it is reasonable to assume that the flat interface observed for the “thick” region is a result of superposing randomly distributed Si protrusions over the entire thickness of the specimen. Thus the roughness of the actual interface must be greater than that observed by HRTEM and the protrusions higher than the average that can be observed as a vague image above the clearly defined flat interface plane. However. it is critical to decide whether the very large protrusions of c-Si observed for the very thin region is intrinsic to dry oxidation because the effect of the Ar ion thinning process, which has not been clarified, should be considered for such a thin specimen. In the next section, a simulation of the HRTEM image has been done in order to examine the relationship between the interface roughness and the half-space image observed at the interface of the “thick” region.
3. Simulation of HRTEM
images
3.1. Simulution conditions The cluster used for the simulation is illustrated in fig. 2. Because the problem is a lattice image of c-Si, the cluster consists of a diamond structure of c-Si only and a random network model of a-SiO, has not been taken into account. The effect of a-SiO, on the lattice image can be neglected because it contributes only to an increase in the background of the contrast in simulation images and not to the lattice image itself. In addition, it is assumed that the phase changes abruptly from c-Si to a-SiO, at the interface. The possibility of a quasi-periodic atomic arrangement of SiOL in the vicinity of the interface [7] and the deviation of atomic positions from lattice sites due to the formation of the interface are not taken into account. The interface roughness is simplified to be modeled as Si protrusions with the same height which continue in a direction perpendicular to the incident electron beam. It is assumed that each protrusion is delineated by {lll}Si facets because the distortion energy of the Si/SiO, interface hecomes a minimum for the { 1 11 } plane of the c-Si when the interface is abrupt [g]. The height of the
H. Akatsu,
I. Ohdomari
/ HRTEM
obseroation of the Si/St02
interface
361
roughened View
surface (100)
incident
dlrection 4 m0n0 T layers ....._ * ._..._........................
beam
flat Fig. 2. Illustative
surface drawing
of the cluster used in the lattice image simulation.
roughness is four monolayers in our simulation. On the other side of the cluster, an atomically flat interface is formed to examine the difference in image due to the interface roughness. The simulation of the lattice image has been performed by the multi-slice method. The parameters used for the simulation were decided according to the standard values of the JEM2000EX and are summarized in table 1. 64 X 64 sampling points in the back focal plane (BFP) are used for most of the calculation. Since the simulated images obtained using 128 X 128 points have a thickness dependence which is very similar to the images obtained using 64 X 64 points, the calculation using the 64 X 64 points is good enough for giving the proper simulated images for our cluster size. The aperture size is large enough to contain the (111) (200) and (220) reflection beams. The speci-
used for the simulation
Accelerate voltage Cell size Slice thickness Cluster thickness Number of sampling points in the BFP Aperture size Spherical aberation Chromatic aberation Incident beam angle Output resolution defocus
observed
. . . .. . . ..I.. ... .
electron
Table 1 Parameters
of
200 keV 1.54 nm X 4.34 nm 0.192 nm 5-30 nm 64x64 0.17 nm 0.7 mm 13 mm 1 mrad 89 x 127 lo-80 nm
men thickness and defocus value are varied to specify the experimental photographing condition for HRTEM. Because of the use of a fast Fourier transformation in the multi-slice method, a periodic boundary condition is applied to the calculated cell. We have maintained the condition only for the horizontal direction of the interface to minimize the effect of the cluster size, and for the direction perpendicular to the interface the cell size was taken to be larger than the size of model in order to suppress the effect of the neighboring virtual clusters. 3.2. Results The resulting images are shown in figs. 3 and 4 with corresponding experimental images for several specimen thickness. Fig. 3 is for a small defocus and fig. 4 for large defocus. For both figures, parts (a) to (e) are HRTEM images at the Si/SiO, interface and (f) gives images obtained by the simulation. The specimen thickness increases from (a) to (e). In fig. 3 parts (d) and (e) are not shown. Parts (a) in both figures are the images of the “ thin” region and correspond to the simulated images in parts (f) for the thickness of 50 nm. Parts (b) are the regions of the first thickness fringe, so the images of c-Si exhibit the half-space image. The corresponding simulated image is shown in (f)-15 nm. Parts (c), (d), and (e) are obtained from the “thick” region and the corresponding simulated images are obtained for thickness between 20 and 30 nm. It is noteworthy that
H. Akatsu,
362
I. Oh&mm-i
/ HRTEM
ohserrmon
SPECIMEN THIN
(a)
cc>
Ib)
of the SI /SO,
rnterJuc.e
THICKNESS THICK
SiO2
Si TEM
IMAGE 50
siMuLA~i0~ Fig. 3. Specimen
150
(DEFOCUS
thickness
dependence
200
220
: iooii) of the HRTEM
250
300
350
(0 and simulated
part (e) of fig. 4 and the simulated image for the model of 30 nm thick are in good agreement. Around this thickness, the effect of the (200) reflections is dominant and the images are elongated laterally rather than being discrete spots. By comparing the thickness dependence of the c-Si lattice images of the simulation for several defocus conditions with that observed experimentally, the smaller defocus value has been specified as - 10 nm and the larger one as - 80 nm. It is apparent from the figures that the thickness dependence of the simulated lattice image for
images of the Si/SiO,
interface
for the smaller defocus
value.
a rough interface is in good agreement with the ones obtained experimentally for both defocus values. For the “thin” region no interface layer is observed and the image of the topmost layer of the c-Si is vague (parts (f)-5 nm). The simulated images of the “thick” region exhibit the half-space lattice images (parts (f)-20 nm and (f)-25 nm), which are very similar to the experimentally observed ones at the interface of the “thick” region. On the contrary the simulated image of the flat side does not exhibit such a thickness dependence, and the lattice images seen in the middle of the
H. Akatsu,
I. Ohdomari
/ HRTEM
SPECIMEN
observation of the Si/Si02
mterface
363
THICKNESS
Si
TEM IMAGE 50
SIMULATION Fig. 4. Specimen
150
( DEFOCUS thickness
dependence
200
: 8OOi) of the HRTEM
220
250
300
350
ci,
(0 and simulated
images of the Si/SiO,
interface
for the larger defocus
value.
models reach the surface of the flat side. Thus no interfacial images are obtained even for the “thick” region.
half-space image observed at the interface. A possible reason for the half-space image at the inter-
3.3. Discussion
the interface layer satisfies the condition to exhibit the half-space image of c-Si when the specimen
The good agreement between the HRTEM observation and image simulation indicates that the half-space image observed at the interface of the “thick” region can be attributed to the interface roughness. This means that there is no necessity to suppose that there exists a different crystalline phase between c-Si and a-SiO, to provide the
face is the reduction of the effective thickness of the c-Si due to the interface roughness. Therefore
thickness
is thicker
thickness
fringe.
than
However,
the region
of the first
the simulation
shows
that the interface layer exhibits the half-space image even when the total c-Si thickness is thicker than the condition of the half-space image, and the intensity of the half-space image at the interface is stronger than the one observed at the
364
H. Akutsu, I. Ohdomari
/ HRTEM
thickness fringe in the c-Si. It may be due to the effect of the termination of the c-Si at the interface and this should be investigated further. As has been discussed above, the interface roughness observed by HRTEM is caused by Si protrusions, which are not distributed over the entire thickness of the specimen but are randomly located on the c-Si surface. Therefore a rough interface structure probably tends to be formed at the (lOO)Si/SiO, interface. This suggests that the rough structure has a lower free energy than a flat one and this result is qualitatively consistent with the results of a calculation of the atomic distortion energy on the Si/SiO, interfaces reported previously [8]. The simulation performed in this work is based on some assumptions. In order to investigate the Si/SiO, interface in more detail, the conditions ignored may have to be taken into account. For example, the atomic rearrangement in the SiO, region just above the c-Si surface needs to be considered because it tends to be quasi-periodic due to the necessity of joining the periodic structure of the c-Si substrate [7].
4. Conclusion The interface between (lOO)Si and Si dioxide grown thermally on Si has been observed with HRTEM. Thickness and defocus dependence of the HRTEM image at the interface have been discussed. The Si/SiO, interface consists of protrusions of c-Si which are randomly located on the c-Si surface and form a interdigitated structure in the interface. When a TEM specimen has a thickness of about 20 nm, the contribution of many protrusions to the HRTEM image along the incident electron beam is averaged over the entire thickness of the specimen and the amplitude of roughness seems to be smaller than it actually is. In a thinner TEM specimen, the interface roughness appears as it is. The observed amplitude of roughness was about 4 monolayers. Simulated HRTEM images of a Si/SiO, interface based on the c-Si model with surface roughness of 4 monolayers high coincided nicely with the experimental observation for both the “thin” and “thick” re-
observation
of the Si/SiO?
interJucr
gions. Half period lattice images observed at the interface of “thick” specimens were also reproduced by the image simulation. This conclusion deduced from the HRTEM observation is verified by the simulation. Therefore the Si/SiO, interface is roughened more than the observed interface morphology. In our sample, which is prepared by dry oxidation at 950° C, the average height of roughness is about four monolayers and sometimes very large protrusions, 2 nm high, can be observed. Although the simulation involves a lot of assumptions, it is plausible that the degree of interface roughness can be predicted qualitatively by using the combination of the simulation and the HRTEM observation for the “thick” specimen.
Acknowledgment The authors are very grateful for the close collaboration of Mr. K. Kai of OK1 Electric Inc., for his fruitful comments and suggestions during this work. The authors would like to express their sincere thanks to Dr. Ozawa, Mr. Matsunaga, and Mr. Kakumu of Toshiba Corporation for their supply of oxidized Si wafers. A part of this work has been supported by a Grant-in-Aid for Scientific Research (B) (1988) from the Ministry of Education, Science and Culture.
References [I] A.H. Carim and A. Bhattacharyya. Appl. Phys. Letters 46 (1985) 872. [2] T. Ando. Surface Sci. 98 (1980) 327. [3] O.L. Krivanek, D.C. Tsui, T.T. Sheng and A. Kamgar, in: Proc. Intern. Topical Conf. on The Physxs of SiO and Its Interfaces, Ed. ST. Pantelides (Pergamon, New York, 1978) p. 356. [4] S.M. Goodnick, D.K. Ferry, C.W. Wilmsen, Z. Liliental, D. Fathy and O.L. Krivanek. Phys. Rev. B 32 (1985) 8171. [5] J.H. Mazur, R. Gronsky and J. Washburn, Inst. Phys. Conf. Ser. 67 (1983) 77. [6] A. Ourmazd, D.W. Taylor. J.A. Rentschler and J. Bevk. Phys. Rev. Letters 59 (1987) 213. [7] I. Ohdomari, T. Mihara and K. Kai, J. Appl. Phys. 59 (I 986) 2798. [8] I. Ohdomari, H. Akatsu, Y. Yamakoshi and K. Kishimoto. J. Non-Cryst. Solids 89 (1987) 239.
Science 41/42
HRTEM
OBSERVATION
Hiroyuki
AKATSU
(1989) 357-364
8 November
OF THE Si/SiO,
INTERFACE
and Iwao OHDOMARI
School of Science and Engineering, Received
357
Waseda University,
1988; accepted
for publication
Tokyo, Japan 5 April 1989
Interfaces with crystalline Si (c-Si) and dry oxide grown over the c-Si have been observed using high resolution transmission electron microscopy (HRTEM). The lattice image of c-Si near the interface varies depending on the specimen thickness. For a very thin region of the specimen, the interface was observed to be very much roughened, and seemed to be abrupt (the so called interfacial layer was not observed between the c-Si and the amorphous SiO, (a-SiO,)). On the contrary, the interface seemed to be flat and to consist of some steps of one or two monolayers high for the thick region. Furthermore, a lattice image with Si(220) periodicity has been observed at the interface. A possible structure for the Si/SiO, interface derived from the observed interface image is that the roughened surface of the c-Si protrusions is directly connected to the SiO, network with no interface layer between them. The observed flat interface of the thick region is a superposed image of the randomly distributed Si protrusions over the direction of the transmitted electron beam. In order to examine the postulated interface structure, a simulation of the lattice image has been performed. The results of the simulation indicate that the half-space image observed at the interface of the thick region can be attributed to the interface roughness, and the abrupt interface image observed for the thin region can be obtained by the same interface structure. Since a completely flat interface cannot provide such a specimen thickness dependence of the image, the (lOO)Si/SiO, interface must be rough, and in our sample, the height of the roughness was about 4 monolayers.
1. Introduction As the integration of Si semiconductor devices progresses, the size of each transistor or capacitor in dynamic random access memory (DRAM) cells has been reduced not only laterally but also vertically. The capacitor oxide which is the most important and the thinnest film in very large scale integrated circuits becomes about 10 nm in 1 mega-bit DRAMS. Because of the reduction of the oxide thickness, the dielectric breakdown and leakage current become critical for the reliability of the devices. The morphology of the Si/SiO, interface has a great influence on the dielectric properties of the oxide. It is reported that the interface roughness is related to the dielectric breakdown voltage of the oxide films [l] and the carrier mobility in the inversion layer [2]. Therefore, control of the interface morphology is important for the device reliability and performance. Although a variety of stacked capacitor films such as oxide-nitride (ON) or oxide-nitride-oxide (ONO) have been pro0169-4332/89/$03.50 (North-Holland)
0 Elsevier Science Publishers
B.V.
posed recently as an alternative to the extremely thin oxide, a development of the technology to form a good quality and highly reliable oxide film uniformly over a broad area of the Si surface is still of great interest because it does not require a big change in the process technology. Hence a better understanding of the interface structure remain of primary importance. From a physical point of view, it is interesting to investigate the effects of impurities, substrate orientation, and temperature on the oxidation kinetics and resulting interface morphology because this will give us a clue to understanding why amorphous oxide is grown by the thermal oxidation of c-Si. In spite of the importance of and the great deal of effort devoted to this subject, both the morphology and atomic configuration at the Si/SiOz interface have not been clarified. The main reason for the slow progress of the investigation on the interface morphology and the atomic arrangement is that there are very few experimental methods that can be used.
H. Akarsu, I. Oh&man
35x
/ HRTEM
Cross sectional observation of the Si/SiO, interface using HRTEM provides information on the interface morphology and the periodicity of the crystalline phase [1,335]. It was observed that the (lOO)Si/SiO, interface is roughened when it is formed by low temperature dry oxidation and a subsequent high temperature heat treatment makes the interface roughness small [l]. Furthermore, the interface morphology has a c-Si orientation dependence, i.e., the (lll)Si/SiO, interface is observed to be always extremely flat [5]. More recently, a periodic image which is different from the one of c-Si was observed for the (100)Si/Si02 interface formed by the dry oxidation of an atomically flat Si surface and it was attributed to the existence of tridymite between c-Si and a-SiO, [6]. In the analysis using the lattice image, however, one has to be very careful because observed images do not necessarily reflect the actual atomic arrangement, but give only the difference in the amplitude of the electron wave functions due to the interference of the transmitted and of several diffracted beams. Therefore the distorted atoms do not contribute to the lattice image formation and the optical condition in the microscope would also effect this. In this paper, the interface between the (lOO)Si and thermally grown Si oxide has been observed using HRTEM. From the specimen thickness dependence of the observed interface morphology and the through-focus observation of the lattice image of the c-Si at the interface, the interface morphology has been assumed to have pyramidlike undulations. Then a simulation of the lattice image has been carried out using a simple model with a completely flat interface on one side and an undulated interface on the other side. Finally, the actual interface morphology of our sample will be discussed by comparing the HRTEM images and the results of the simulation.
2. HRTEM
observation
of the Si/SiO,
interface
2.1. Specimen preparation The Si/SiO, interface was formed by thermal oxidation of a (lOO)Si wafer in dry oxygen at 950°C. The wafers used in this experiment were
ohserwtrot~ oj rhr SI / S/O, rnierfrre
commercially available and had undergone no special treatment to obtain an atomically flat Si surface. After the 30 nm oxide growth. poly-Si was deposited over the oxide in order to protect the Si/SiO, interface region from damage caused by the subsequent specimen preparation process for the HRTEM observation. The specimen for HRTEM observation was prepared by mechanical lapping followed by Ar ion thinning. A wafer was scribed into rectangular strips then two strips were glued together to meet the poly-Si surface side each other. The glued strips were cut parallel to the (110) direction of c-Si into pieces so that the cross section structure of the wafer appears. A piece of the specimen was lapped mechanically until it became some several tens of microns thick. Further thinning was done by using the dual Ar ion beams and this was continued until the edge of the perforation reached to the interface region of the specimen. The lattice image can be observed only around the edge of the perforation. The cross sections were examined in a JEM2000EX electron microscope at a primary voltage of 200 keV and with a point-topoint resolution of 0.21 nm. 2.2. HRTEM
observation
Typical HRTEM images of the Si/SiOz interface region are shown in fig. 1 for different specimen thickness and defocus conditions. The thickness of the specimen was judged from the thickness fringes observed in the lattice image of c-si as the half-space images. Because the specimen thickness increases gradually from the edge of the perforation, regions exhibiting half-space images are almost parallel to the edge. Hereafter, we will designate the region in the vicinity of the edge of the perforation “thin”, and the region between the first thickness fringe and the second one “thick”. The difference in the defocus value between the two photographs is about 65 nm and the smaller defocus value is just below (about - 10 nm) the good focus point judged from the Fresnel fringe at the specimen edge. Both of these conditions are far from the Scherzer defocus value (about - 50 nm), but they are not chosen with any special intent.
H. Akatsu,
I. Ohdomari
/ HRTEM
observation of the S/SO_,
interface
359
360
H. Akatsu,
I. Ohdomuri
/ HRTEM
A typical feature of the image for the “thin” region is a rough interface. Through-focus observation of the same area suggested that the interface roughness is not continuous along the direction of the specimen thickness but randomly distributed Si protrusions, because the positions of the Si protrusions in the HRTEM image are different for the different defocus conditions. Very large protrusions of nearly 2 mm high can be observed in the very thin region, while the average height of the protrusion is about 1 nm. Another feature is interface sharpness. The lattice image of the c-Si continues to the interface and no interfacial layer can be observed. The images of the “thick” region exhibit different features from the one in the “thin” region. The interface is observed to be a terrace-like structure, which consists of steps of one or two atomic layers high but is almost flat. Furthermore, the most noticeable feature of the “thick” region is the lattice image at the interface, which exhibits the half periodicity of Si(ll0). The thickness of the interface layer corresponds to two or four monolayers of c-Si, and can be observed for both defocus conditions. This kind of image was observed by Ourmazd et al. [6] and is attributed to the c-SiO, phase of tridymite grown epitaxially over an atomically flat surface of c-Si during the oxidation. However, Ourmazd’s model is not appropriate in our case because the interface is roughened and the half-space image can be observed along with the rough interface. Sometimes a lattice image of Si can be observed beyond the interface layer (inside the SiO, region) although the image is vague. By HRTEM image simulation, the vague image was attributed to Si protrusions in a-SiO, where the a-SiO, and c-Si are superimposed along the direction of incident electron beam. The simulation has also shown that the c-Si lattice image is visible even when the thickness of the c-Si region is 50% of the entire specimen thickness [7]. Since the “ thin” and “thick” regions discussed above are adjacent to each other in a single specimen, it is hard to suppose that the interface structures of two regions are different. In other words a single interface structure appears differently in HRTEM images depending on the specimen
ohsrrr:utim
of rhe Si/ SiO, Inrerfuce
thickness. Therefore it is reasonable to assume that the flat interface observed for the “thick” region is a result of superposing randomly distributed Si protrusions over the entire thickness of the specimen. Thus the roughness of the actual interface must be greater than that observed by HRTEM and the protrusions higher than the average that can be observed as a vague image above the clearly defined flat interface plane. However. it is critical to decide whether the very large protrusions of c-Si observed for the very thin region is intrinsic to dry oxidation because the effect of the Ar ion thinning process, which has not been clarified, should be considered for such a thin specimen. In the next section, a simulation of the HRTEM image has been done in order to examine the relationship between the interface roughness and the half-space image observed at the interface of the “thick” region.
3. Simulation of HRTEM
images
3.1. Simulution conditions The cluster used for the simulation is illustrated in fig. 2. Because the problem is a lattice image of c-Si, the cluster consists of a diamond structure of c-Si only and a random network model of a-SiO, has not been taken into account. The effect of a-SiO, on the lattice image can be neglected because it contributes only to an increase in the background of the contrast in simulation images and not to the lattice image itself. In addition, it is assumed that the phase changes abruptly from c-Si to a-SiO, at the interface. The possibility of a quasi-periodic atomic arrangement of SiOL in the vicinity of the interface [7] and the deviation of atomic positions from lattice sites due to the formation of the interface are not taken into account. The interface roughness is simplified to be modeled as Si protrusions with the same height which continue in a direction perpendicular to the incident electron beam. It is assumed that each protrusion is delineated by {lll}Si facets because the distortion energy of the Si/SiO, interface hecomes a minimum for the { 1 11 } plane of the c-Si when the interface is abrupt [g]. The height of the
H. Akatsu,
I. Ohdomari
/ HRTEM
obseroation of the Si/St02
interface
361
roughened View
surface (100)
incident
dlrection 4 m0n0 T layers ....._ * ._..._........................
beam
flat Fig. 2. Illustative
surface drawing
of the cluster used in the lattice image simulation.
roughness is four monolayers in our simulation. On the other side of the cluster, an atomically flat interface is formed to examine the difference in image due to the interface roughness. The simulation of the lattice image has been performed by the multi-slice method. The parameters used for the simulation were decided according to the standard values of the JEM2000EX and are summarized in table 1. 64 X 64 sampling points in the back focal plane (BFP) are used for most of the calculation. Since the simulated images obtained using 128 X 128 points have a thickness dependence which is very similar to the images obtained using 64 X 64 points, the calculation using the 64 X 64 points is good enough for giving the proper simulated images for our cluster size. The aperture size is large enough to contain the (111) (200) and (220) reflection beams. The speci-
used for the simulation
Accelerate voltage Cell size Slice thickness Cluster thickness Number of sampling points in the BFP Aperture size Spherical aberation Chromatic aberation Incident beam angle Output resolution defocus
observed
. . . .. . . ..I.. ... .
electron
Table 1 Parameters
of
200 keV 1.54 nm X 4.34 nm 0.192 nm 5-30 nm 64x64 0.17 nm 0.7 mm 13 mm 1 mrad 89 x 127 lo-80 nm
men thickness and defocus value are varied to specify the experimental photographing condition for HRTEM. Because of the use of a fast Fourier transformation in the multi-slice method, a periodic boundary condition is applied to the calculated cell. We have maintained the condition only for the horizontal direction of the interface to minimize the effect of the cluster size, and for the direction perpendicular to the interface the cell size was taken to be larger than the size of model in order to suppress the effect of the neighboring virtual clusters. 3.2. Results The resulting images are shown in figs. 3 and 4 with corresponding experimental images for several specimen thickness. Fig. 3 is for a small defocus and fig. 4 for large defocus. For both figures, parts (a) to (e) are HRTEM images at the Si/SiO, interface and (f) gives images obtained by the simulation. The specimen thickness increases from (a) to (e). In fig. 3 parts (d) and (e) are not shown. Parts (a) in both figures are the images of the “ thin” region and correspond to the simulated images in parts (f) for the thickness of 50 nm. Parts (b) are the regions of the first thickness fringe, so the images of c-Si exhibit the half-space image. The corresponding simulated image is shown in (f)-15 nm. Parts (c), (d), and (e) are obtained from the “thick” region and the corresponding simulated images are obtained for thickness between 20 and 30 nm. It is noteworthy that
H. Akatsu,
362
I. Oh&mm-i
/ HRTEM
ohserrmon
SPECIMEN THIN
(a)
cc>
Ib)
of the SI /SO,
rnterJuc.e
THICKNESS THICK
SiO2
Si TEM
IMAGE 50
siMuLA~i0~ Fig. 3. Specimen
150
(DEFOCUS
thickness
dependence
200
220
: iooii) of the HRTEM
250
300
350
(0 and simulated
part (e) of fig. 4 and the simulated image for the model of 30 nm thick are in good agreement. Around this thickness, the effect of the (200) reflections is dominant and the images are elongated laterally rather than being discrete spots. By comparing the thickness dependence of the c-Si lattice images of the simulation for several defocus conditions with that observed experimentally, the smaller defocus value has been specified as - 10 nm and the larger one as - 80 nm. It is apparent from the figures that the thickness dependence of the simulated lattice image for
images of the Si/SiO,
interface
for the smaller defocus
value.
a rough interface is in good agreement with the ones obtained experimentally for both defocus values. For the “thin” region no interface layer is observed and the image of the topmost layer of the c-Si is vague (parts (f)-5 nm). The simulated images of the “thick” region exhibit the half-space lattice images (parts (f)-20 nm and (f)-25 nm), which are very similar to the experimentally observed ones at the interface of the “thick” region. On the contrary the simulated image of the flat side does not exhibit such a thickness dependence, and the lattice images seen in the middle of the
H. Akatsu,
I. Ohdomari
/ HRTEM
SPECIMEN
observation of the Si/Si02
mterface
363
THICKNESS
Si
TEM IMAGE 50
SIMULATION Fig. 4. Specimen
150
( DEFOCUS thickness
dependence
200
: 8OOi) of the HRTEM
220
250
300
350
ci,
(0 and simulated
images of the Si/SiO,
interface
for the larger defocus
value.
models reach the surface of the flat side. Thus no interfacial images are obtained even for the “thick” region.
half-space image observed at the interface. A possible reason for the half-space image at the inter-
3.3. Discussion
the interface layer satisfies the condition to exhibit the half-space image of c-Si when the specimen
The good agreement between the HRTEM observation and image simulation indicates that the half-space image observed at the interface of the “thick” region can be attributed to the interface roughness. This means that there is no necessity to suppose that there exists a different crystalline phase between c-Si and a-SiO, to provide the
face is the reduction of the effective thickness of the c-Si due to the interface roughness. Therefore
thickness
is thicker
thickness
fringe.
than
However,
the region
of the first
the simulation
shows
that the interface layer exhibits the half-space image even when the total c-Si thickness is thicker than the condition of the half-space image, and the intensity of the half-space image at the interface is stronger than the one observed at the
364
H. Akutsu, I. Ohdomari
/ HRTEM
thickness fringe in the c-Si. It may be due to the effect of the termination of the c-Si at the interface and this should be investigated further. As has been discussed above, the interface roughness observed by HRTEM is caused by Si protrusions, which are not distributed over the entire thickness of the specimen but are randomly located on the c-Si surface. Therefore a rough interface structure probably tends to be formed at the (lOO)Si/SiO, interface. This suggests that the rough structure has a lower free energy than a flat one and this result is qualitatively consistent with the results of a calculation of the atomic distortion energy on the Si/SiO, interfaces reported previously [8]. The simulation performed in this work is based on some assumptions. In order to investigate the Si/SiO, interface in more detail, the conditions ignored may have to be taken into account. For example, the atomic rearrangement in the SiO, region just above the c-Si surface needs to be considered because it tends to be quasi-periodic due to the necessity of joining the periodic structure of the c-Si substrate [7].
4. Conclusion The interface between (lOO)Si and Si dioxide grown thermally on Si has been observed with HRTEM. Thickness and defocus dependence of the HRTEM image at the interface have been discussed. The Si/SiO, interface consists of protrusions of c-Si which are randomly located on the c-Si surface and form a interdigitated structure in the interface. When a TEM specimen has a thickness of about 20 nm, the contribution of many protrusions to the HRTEM image along the incident electron beam is averaged over the entire thickness of the specimen and the amplitude of roughness seems to be smaller than it actually is. In a thinner TEM specimen, the interface roughness appears as it is. The observed amplitude of roughness was about 4 monolayers. Simulated HRTEM images of a Si/SiO, interface based on the c-Si model with surface roughness of 4 monolayers high coincided nicely with the experimental observation for both the “thin” and “thick” re-
observation
of the Si/SiO?
interJucr
gions. Half period lattice images observed at the interface of “thick” specimens were also reproduced by the image simulation. This conclusion deduced from the HRTEM observation is verified by the simulation. Therefore the Si/SiO, interface is roughened more than the observed interface morphology. In our sample, which is prepared by dry oxidation at 950° C, the average height of roughness is about four monolayers and sometimes very large protrusions, 2 nm high, can be observed. Although the simulation involves a lot of assumptions, it is plausible that the degree of interface roughness can be predicted qualitatively by using the combination of the simulation and the HRTEM observation for the “thick” specimen.
Acknowledgment The authors are very grateful for the close collaboration of Mr. K. Kai of OK1 Electric Inc., for his fruitful comments and suggestions during this work. The authors would like to express their sincere thanks to Dr. Ozawa, Mr. Matsunaga, and Mr. Kakumu of Toshiba Corporation for their supply of oxidized Si wafers. A part of this work has been supported by a Grant-in-Aid for Scientific Research (B) (1988) from the Ministry of Education, Science and Culture.
References [I] A.H. Carim and A. Bhattacharyya. Appl. Phys. Letters 46 (1985) 872. [2] T. Ando. Surface Sci. 98 (1980) 327. [3] O.L. Krivanek, D.C. Tsui, T.T. Sheng and A. Kamgar, in: Proc. Intern. Topical Conf. on The Physxs of SiO and Its Interfaces, Ed. ST. Pantelides (Pergamon, New York, 1978) p. 356. [4] S.M. Goodnick, D.K. Ferry, C.W. Wilmsen, Z. Liliental, D. Fathy and O.L. Krivanek. Phys. Rev. B 32 (1985) 8171. [5] J.H. Mazur, R. Gronsky and J. Washburn, Inst. Phys. Conf. Ser. 67 (1983) 77. [6] A. Ourmazd, D.W. Taylor. J.A. Rentschler and J. Bevk. Phys. Rev. Letters 59 (1987) 213. [7] I. Ohdomari, T. Mihara and K. Kai, J. Appl. Phys. 59 (I 986) 2798. [8] I. Ohdomari, H. Akatsu, Y. Yamakoshi and K. Kishimoto. J. Non-Cryst. Solids 89 (1987) 239.