Full text of DOI:10.1007/s003390000620

Appl. Phys. A 73, 97–101 (2001) / Digital Object Identifier (DOI) 10.1007/s003390000620
Applied Physics A
Materials
Science & Processing
Core-level and valence-band characteristics of carbon nitride films with
high nitrogen content
J.P. Zhao∗, Z.Y. Chen, T. Yano, T. Ooie, M. Yoneda, J. Sakakibara
Shikoku National Industrial Research Institute, Takamatsu 761-0395, Japan
Received: 26 June 2000/Accepted: 26 June 2000/Published online: 20 September 2000 –  Springer-Verlag 2000
Abstract. Carbon nitride films with high nitrogen content
were prepared by reactive pulsed-laser deposition at nitro-
gen partial pressures varying from 0.1 to 20.0 Torr. It was
found that the nitrogen content in the films first increases
with increase of the nitrogen pressure, reaches a maximum
of 46 at. % at 5.0 Torr, and then decreases to 37 at. % at
20.0 Torr. The almost pure carbon nitride films were sys-
tematically characterized by using X-ray photoelectron spec-
troscopy (XPS) concerning the core-level and valence-band
structures. Some fingerprint information, which shows the
role of nitrogen in controlling the electronic structure of car-
bon nitride films, was found based on the XPS studies. With
enhancing the nitrogen incorporation, both the binding energy
and the peak intensity of the core-level and the valence-band
spectra vary systematically as a function of nitrogen content
in the films.
absence of reliable fingerprint characteristics recorded from
one-phase or pure carbon nitride. In order to solve this prob-
lem, it is necessary to incorporate higher nitrogen content into
carbon nitride films. Although some claims on the achieve-
ment of crystalline carbon nitride have been made [2, 3, 9],
the crystalline phase still remains unclear. Besides the crys-
talline carbon nitride, there have been interesting results on
the properties of amorphous carbon nitride (CNx) films [7,
10]. Therefore, it is of great interest to synthesize and study
carbon nitride films with a nitrogen content closer to the de-
sired value in spite of the crystallinity. For this purpose, if
energetic nitrogen species were not introduced during deposi-
tion, then the sputtering effect could be much less important.
In fact, some successful depositions of the carbon nitride
films with a higher nitrogen content have been reported with
the introduction of only N2 or NH3 during deposition [11, 12].
In this work, we prepared the carbon nitride films by using
reactive pulsed-laser deposition (RPLD), in which the nitro-
gen content in the films was controlled by using different N2
partial pressures during the laser ablation of carbon. Com-
pared to other similar methods [11, 12], we used much higher
nitrogen partial pressure (0.1–20.0 Torr), which was not used
elsewhere to our knowledge. The aim in using such high pres-
sure is twofold: (i) to see whether the nitrogen content in
carbon nitride films can be increased closer to the desired
value, in which the C-C phase could be omitted; (ii) to inves-
tigate the bonding structure of the almost pure carbon nitride
films in order to find some fingerprint characteristics of the
C-N phase.
PACS: 68.55.a; 79.60.D; 81.15.F
Ever since the theoretical study of Liu and Cohen [1] in-
dicated the possible existence of super-hard β-phase carbon
nitride (β-C3N4), many attempts have been made to syn-
thesize and understand this hypothetical material by various
techniques [2–4]. Among these techniques, the properties
of energetic species are generally employed to enhance the
incorporation of nitrogen into the films and the formation
of metastable phases. However, due to the fact that nitro-
gen can be preferentially sputtered from the growing sur-
face by the energetic species present in the energetic-species-
assisted deposition [5, 6], the nitrogen content in most re-
ported works [5–8] is much lower than 57 at. % (N/C ratio
of 1.33) of the predicted β-C3N4 structure. Moreover, a large
fraction of C-C phase was found to exist in most carbon
nitride films synthesized by the energetic-species-assisted
deposition methods, with only a small amount being C-N
phase [5–8]. This situation has already induced many con-
tradictions and difficulties for investigating the real structures
and physical properties of carbon nitride films, due to the
1 Experimental
The films were prepared in a reactive pulsed-laser deposi-
tion chamber, in which an ion-beam assisting source is also
available. The fourth harmonic from a Q-switched Nd:YAG
laser with wavelength λ = 266 nm and pulse duration of 10 ns
was focused onto a high-purity (99.99%) highly oriented
pyrolytic-graphite (HOPG) target. The laser was pulsed at
a rate of 10 Hz. The laser fluence was kept around 12.7 J/cm2
during deposition. The base pressure of the deposition cham-
∗Corresponding author. (E-mail: zhao@sniri.go.jp)

98
ber is lower than 3 × 10−7 Torr. Nitrogen gas of 99.999%
purity was admitted to the chamber during deposition, with
pressure varying from 0.1 to 20.0 Torr. The target was ro-
tated by an external motor to provide each pulse with a fresh
surface. Silicon (100) wafers and CaF2 glass were used as
substrates for different measurements. The substrates were
not heated during deposition. The distance between the target
and the substrate was ∼ 3.5 cm. The properties of the films
were characterized using glancing-angle X-ray diffractome-
try (XRD), X-ray photoelectron spectroscopy (XPS) utilizing
a monochromatized Mg Kα (1253.6 eV) X-ray source with an
energy resolution of 0.8 eV, and UV–visible spectrophotome-
try. All the measurements were performed ex situ.
atomic ratio of ∼ 1 : 1 was close to the stoichiometric com-
position (57 at. %) of the C3N4 structure. The first increase of
the nitrogen content with the nitrogen pressure (< 5.0 Torr)
can be attributed to the increased collisions and reactions
between the laser-ablated carbon species and the nitrogen
molecules. Most of the carbon species reaching the substrate
will be bonded to the nitrogen, therefore resulting in the ni-
trogen incorporation increasing. With further raising of the
nitrogen pressure (5.0–20.0 Torr), the mean free path of the
particles in the high-pressure gas becomes much shorter than
the distance between the target and the substrate (3.5 cm).
Therefore, any energetic species generated by the pulsed laser
ablation and carbon–nitrogen collisions would be thermalized
and slowed down. It means that the increasing pressure hin-
ders the transport of ablated carbon species with nitrogen.
Consequently, only the species with fewer interactions with
N2 molecules, i.e., containing less nitrogen, could reach the
substrate surface, which resulted in reduced nitrogen incorpo-
ration in the pressure range of 5.0–20.0 Torr. Nevertheless,
there should be much less sputtering effect of nitrogen in all
the present cases than in the energetic-species-assisted depo-
sition. It has contributed to the global increase of the nitrogen
content in the RPLD-deposited films.
Beside the relative N/C atomic ratio, we also character-
ized the content of impurities in the deposited films because
the impurities, especially oxygen and fluorine, could dramat-
ically influence the XPS results of the films. In Fig. 2, the
typical core-level spectra of fluorine and oxygen of the de-
posited films are shown. We can see that no signal of fluorine
species was detected in the XPS spectra. In the case of oxy-
gen, the measured content was ∼ 2 at. % and no systematic
variation was observed for all the films. In addition, it was
found that the O 1s spectrum was symmetrically centered at
532 eV, which therefore suggested a surface contamination
due to exposure to the atmosphere during the transit of the
samples and the residual background gas in the XPS chamber.
In our experiment, the high-purity graphite target (99.99%)
and nitrogen gas (99.999%) were used and the base pressure
of the deposition chamber was lower than 3 ×10−7 Torr be-
fore admitting the nitrogen. Therefore, we could not expect
the incorporation of other elements including oxygen and flu-
orine during film deposition, even under the high nitrogen
pressure. The contamination resulting from the transit of sam-
ples and the background gas should be the same for all the
films in influencing the XPS results. Moreover, the measured
2 Results and discussion
The glancing-angle XRD analyses indicate that all the de-
posited films are amorphous in structure. A diffuse band
around 2θ = 25◦ appears in the XRD patterns of the car-
bon nitride films, which is not found for pure carbon films
deposited by the same method without nitrogen in the cham-
ber. The diffuse band should be carbon-nitride-related, that is,
caused by the incorporation of nitrogen and the presence of
C−N bonding in the films. Optical-absorption measurements
show that the films have an optical band gap of 1.5 ∼ 2.2 eV,
which is much larger than that of carbon nitride films pre-
pared by energetic-species-assisted deposition [8, 13].
The nitrogen content in the films was evaluated with
XPS as a function of the nitrogen partial pressure as shown
in Fig. 1. It was calculated using N/(N+C) = (AN/0.50)/
(AN/0.50+AC/0.31), where AN and AC are the areas under
the N 1s and C 1s core-level spectra, and the constants
0.50 and 0.31 are the atomic sensitivity factors of nitrogen
and carbon, respectively. The lowest nitrogen content was
found to be 37 at. % at the nitrogen pressure of 20.0 Torr,
which is larger than the upper limits of PECVD a-C:N:H
films (25 at. %) [14], IBAD a-C:N films (35 at. %) [15], and
MSIBD films (30 at. %) [16]. It is also seen from Fig. 1 that
the nitrogen content first increases with increase of the ni-
trogen pressure, reaches a maximum of 46 at. % at the nitro-
gen pressure of 5.0 Torr, and then decreases to 37 at. % at
20.0 Torr. The highest nitrogen content which gives a N/C
Fig. 1. Nitrogen content of the carbon nitride films formed by reactive
pulsed-laser deposition as a function of nitrogen partial pressure
Fig. 2. Typical core-level spectra of fluorine and oxygen of the carbon ni-
tride films

99
content of oxygen was much less than those reported by Lu
et al. (5 at. %) [17] and by Scharf et al. (3 at. %) [18] in their
studies of core-level and valence-band spectra of diamond-
like carbon and amorphous CN films. Therefore, based on the
above discussion, we could expect that the impurities of the
films should have a minor effect on the XPS analyses of the
films.
the cases of 0.1 and 20.0 Torr, the C-C phase should not be
neglected. The C 1s peak therefore has a marked contribu-
tion from the C-C bonding (∼ 285 eV) and shows relative
asymmetry as shown in Fig. 3. Although it is not difficult to
decompose the experimental C 1s peaks with several Gaus-
sian subpeaks, we will not perform a quantitative deconvo-
lution analysis because the bonding states of carbon atoms
are expected to be very complex [7]. Carbon atoms may
have zero, one, two, or three bonds with the nitrogen atoms,
and the deconvolution is possible with different intensities
of the respective subpeaks. Therefore, the results of decon-
volution could be quite uncertain. Nevertheless, the width
of the C 1s peaks of these almost pure carbon nitride films
strongly suggests that there are multiple bonding arrange-
ments in the films, possibly including C−N, > C=N, and
C ≡ N bonds.
The XPS C 1s core-level spectra of the RPLD-deposited
carbon nitride films as a function of nitrogen pressure are
shown in Fig. 3. In order to find some fingerprint informa-
tion for nitrogen incorporation, the corresponding spectrum
of a pulsed-laser-deposited pure carbon film is also plotted in
Fig. 3. Although the deconvolution of these spectra might be
useful and informative in certain cases in characterizing the
bonding structure of carbon and nitrogen atoms, the present
spectra already show very obvious features for characteriz-
ing the nitrogen incorporation. The C 1s peak of the pure
carbon film is symmetrically located at the binding energy
of 284.5 eV with a FWHM of ∼ 1.8 eV. It typically repre-
sents the C-C bonding related to the amorphous carbon (a-C)
containing both sp3 and sp2 bonds [8, 19]. However, as the ni-
trogen is incorporated into the films, the line shape and width
of the C 1s peak change markedly. The C 1s peak shifts to-
ward the higher binding energy and a broadening of the line
shape is observed. For all the nitrogen-incorporated films, the
FWHM of the C 1s peaks increases to ∼ 4 eV, and asymme-
try is found in the films deposited at the nitrogen pressures
of 0.1 and 20.0 Torr. The maximum chemical shift relative
to the pure carbon film is around 4.5 eV, which occurs at the
nitrogen pressure of 5.0 Torr for the film having the highest
nitrogen content. However, by either increasing or decreas-
ing the nitrogen pressure, i.e., decreasing the nitrogen content
in the films, the C 1s peaks shift to the lower binding en-
ergy approaching that of the pure carbon film. According to
the results shown in Fig. 1, the films prepared at 1.0, 5.0,
and 10.0 Torr contain more than 40 at. % nitrogen atoms, and
the N/C atomic ratio is close to 1 : 1. That is, most of the
carbon atoms in these films should be bonded with the ni-
trogen atoms in certain states; therefore, the C-N phase can
be omitted. Thus, the C 1s binding energy (287.5–288.8 eV)
of these films should indicate some reliable fingerprint in-
formation for the pure carbon nitride phase. When the ni-
trogen content reduces to less than 40 at. %, for example in
Figure 4 shows the XPS N 1s spectra of the carbon ni-
tride films deposited under the different nitrogen pressures.
A similar trend of N 1s binding-energy shifting with the ni-
trogen content as that of the C 1s peaks is clearly found. The
film with the highest nitrogen content (46 at. %) deposited at
the nitrogen pressure of 5.0 Torr gives the largest binding en-
ergy of 401.5 eV. When the nitrogen content decreases by
either increasing or decreasing the nitrogen pressure, the N
1s peak shifts to the lower binding energy of 399.2, 400.3,
401, and 400.7 eV for 0.1, 1.0, 10.0, and 20.0 Torr, respec-
tively. The binding energy of 400.3 eV has been suggested
to correspond to the tetrahedral C-N bonds [20]. By compar-
ison to Siegbahn’ s reference spectra and theoretical calcu-
lations [21], the higher binding energy at 401.5 eV is asso-
ciated with the nitrogen in a four-bond configuration. This
assignment is also consistent with the calculation based on
the electronegativity and partial ionic character of the bonds
by Holloway [22]. The lowest binding energy of 399.2 eV
can be assigned to nitrogen bonded to sp2 hybridized C [23].
Although the N 1s peaks become relatively narrower than
the C 1s peaks shown in Fig. 3, the FWHM of ∼ 3 eV still
strongly suggests that the multiple-bonding configurations
should present in every carbon nitride film with variable rela-
tive intensity.
Figures 3 and 4 indicate that both C 1s and N 1s core-
level peaks will shift toward the higher binding energy with
increasing nitrogen incorporation in the films. It is of inter-
Fig. 3. XPS C 1s spectra of the carbon nitride films deposited at different
nitrogen partial pressures
Fig. 4. XPS N 1s spectra of the carbon nitride films deposited at different
nitrogen partial pressures

100
est because Mansour and Ugolini [24] observed that the C 1s
peak shifts toward a higher binding energy, but the binding
energy of N 1s remains constant as the nitrogen concentration
is increased in their a-CNx:H films. The reason for this might
be due to the quite different nitrogen content presented in the
two works. The remaining C-C phase would influence the ob-
taining of reliable information on the C−N bonding structure
by using XPS.
structure is the regions II and III. The region I is hardly dis-
tinguished from the slope of the region II and the region IV
appears as a small shoulder of the region III. These features
are consistent with the reference spectra in [29, 30]. How-
ever, it can be clearly seen that quite different features appear
in the valence-band spectra when a large amount of nitrogen
was introduced into the films. The position and peak inten-
sity of these regions change with the increase of nitrogen
content, especially for regions I and IV. The peak position
changes in the same manner as that of the XPS core-level
spectra shown in Figs. 3 and 4. That is, for the film with
more nitrogen, the valence bands appear in higher binding
energy. A more apparent feature is the change of peak in-
tensity of the regions I and IV. With increase of nitrogen in
the films, the regions I and IV become more apparent and
the intensity increases. It implies a strong structural change
in these samples induced by the nitrogen incorporation. Due
to the existence of nitrogen and the formation of carbon–
nitrogen bonding, N 2s, N 2p and the corresponding s-p hy-
bridized bonding states appear in the valence-band spectra
with positions very close to those of carbon. We know that
the binding energies of the valence bands of nitrogen are
almost 2 eV (2p states) and 1.3 eV (2s states) higher than
those of carbon; therefore, it is not difficult to understand the
upper shift of the regions I and IV with increase of the ni-
trogen content. Moreover, because the photoemission cross
section of N 2s and N 2p (0.0841, 0.0025, and 0.0049 for
2s1/2, 2p1/2, and 2p3/2, respectively) is much higher than
The valence-band spectrum of carbon nitride material as
measured by XPS also can distinguish the effect of nitrogen
incorporation in the films. The valence-band spectrum is usu-
ally recorded using UV photoelectron spectroscopy (UPS).
So far, very few results on the valence-band structure of car-
bon nitride films have been reported [25], although the corres-
ponding studies on diamond, graphite, and amorphous carbon
have been extensively conducted [26]. The fingerprint cap-
acity for structural information of valence-band spectra due
to s and p characters in the bonds of carbon nitride materi-
als can be very valuable, since this information is sometimes
unobtainable from core-level photoelectron spectra [27]. Al-
though the valence-band density of states itself is a complex
and important research topic, especially for the carbon ni-
tride materials, we will discuss only its ability to predict the
structural information. It is of great interest to compare the
valence bands of the films with different nitrogen content.
Figure 5 shows the XPS valence-band spectra of the carbon
nitride films as a function of nitrogen content. The corres-
ponding spectrum of the pure carbon film is also shown for
comparison. Four distinct regions are found in the valence-
band spectra: region I at 2 ∼ 7 eV, region II at 7.5 ∼ 12 eV,
region III at 12.5 ∼ 20 eV, and region IV at 20 ∼ 30 eV. The
assignment of these regions to definite band structures is quite
complicated [13], because the intensity of valence-band spec-
tra not only depends on the density of states, but also on the
photoemission cross section, where the latter is strongly de-
pendent on the excitation energy [28], for example, UV or
soft X-ray. Here, based on the reference spectra of various
forms of carbon measured by McFreely et al. using XPS [29]
and by Wesner et al. using UPS [30], we could assert that
region I at 2 ∼ 7 eV is attributable to the 2p bands, region
II at 7.5 ∼ 12 eV is a mixture of 2s and 2p states, and re-
gions III and IV both arise from 2s-like bands. For the pure
carbon film shown in Fig. 5, the predominant valence-band
that of C 2s and C 2p (0.047, 0.0006, and 0.0012 for 2s1/2
,
2p1/2, and 2p3/2, respectively) when using Mg Kα excita-
tion, the intensity of the valence-band spectrum changes with
the nitrogen incorporation. Due to the fact that the pho-
toemission cross section of the s band is 13 times higher
than the p band for XPS valence-band spectra, the region
IV has the most obvious change compared to other regions.
To our knowledge, we have not found any similar reported
results indicating the obvious change in valence-band struc-
ture of carbon nitride induced by the presence of nitrogen.
The reason could be attributed to the very low nitrogen con-
tent in many reported films; therefore, the bonding struc-
tures are eventually controlled by C-C phase rather than C-N
structure.
It is known that the valence bands of oxygen and fluo-
rine are also positioned in the binding-energy region of the
valence bands of carbon and nitrogen. However, the fluorine
should not contribute the valence-band spectra of the films ac-
cording to the results shown in Fig. 2. As for the oxygen, no
spectra in Fig. 5 showed the band around 7.0 eV for O 2p.
The binding energy of O 2s is also known to be almost 3.6 eV
and 4.9 eV higher than that of N 2s and C 2s, respectively.
Therefore, considering the low content of oxygen on the sur-
face, the oxygen was not expected to significantly influence
the valence-band structure of the films.
In summary, in order to understand the role of nitrogen
in controlling the electronic structure of carbon nitride films,
some fingerprint information was found by systematically in-
vestigating the core-level and valence-band spectra of the
carbon nitride films with high nitrogen content prepared by
reactive pulsed-laser deposition. Due to the fact that this in-
formation was obtained from the almost pure carbon nitride
films, it will be useful and reliable for correctly characterizing
carbon nitride materials.
Fig. 5. XPS valence-band spectra of the carbon nitride films deposited at
different nitrogen partial pressures

101
Acknowledgements. J.P. Zhao and Z.Y. Chen are grateful for the financial
support provided by JST, Japan.
14. L.G. Jacobsohn, D.F. Franceschini, F.L. Freire, Jr.: Mater. Res. Soc.
Symp. Proc. 498, 283 (1998)
15. F. Rossi, B. Andre´, A. van Veen, P.E. Mijnorends, H. Schut, F. Labohm,
H. Dunlop, M.P. Delplancke, K. Hubbard: J. Mater. Res. 9, 2440
(1994)
16. V.S. Veerasamy, J. Yuan, G.A.J. Amaratunga, W.I. Milne, K.W.R. Gil-
kes, M. Weiler, L.M. Brown: Phys. Rev. B 48, 17954 (1993)
17. Y.F. Lu, Z.M. Ren, W.D. Song, D.S.H. Chan: J. Appl. Phys. 84, 2133
(1998)
18. T.W. Scharf, R.D. Ott, D. Yang, J.A. Barnard: J. Appl. Phys. 85, 3142
(1999)
References
1. A.Y. Liu, M.L. Cohen: Phys. Rev. B 41, 10727 (1990)
2. C. Niu, Y.Z. Lu, C.M. Lieber: Science 261, 334 (1993)
3. K.M. Yu, M.L. Cohen, E.E. Haller, W.L. Hansen, A.Y. Liu, I.C. Wu:
Phys. Rev. B 49, 5034 (1994)
4. A. Bousetta, M. Lu, A. Bensaoula, A. Schultz: Appl. Phys. Lett. 65,
696 (1994)
5. D. Marton, A.H. Al-Bayati, S.S. Todorov, K.J. Boyd, J.W. Rabalais:
Nucl. Instrum. Methods B 90, 277 (1994)
6. H. Sjöström, I. Ivanov, M. Johansson, L. Hultman, J. -E. Sundgren,
S.V. Hainsworth, T.F. Page, L.R. Wallenberg: Thin Solid Films 246,
103 (1994)
19. Z.M. Ren, Y.C. Du, Y. Qiu, J.D. Wu, Z.F. Ying, X.X. Xiong, F.M. Li:
Phys. Rev. B 51, 51 (1995)
20. Y. Taki, T. Kitagawa, O. Takai: Thin Solid Films 304, 183 (1997)
21. K. Siegbahn, C. Nordling, A. Fahlman, R. Nordberg, K. Hamrin,
J. Hedman, G. Johansson, T. Bergmark, S.-E. Karlsson, I. Lindgren,
B. Lindberg: ESCA: Atomic, Molecular and Solid State Structure
Studied by Means of Electron Spectroscopy (Almqvist & Wiksells,
Uppsala 1967)
7. B.C. Holloway, O. Kraft, D.K. Shuh, M.A. Kelly, W.D. Nix, P. Pianetta,
S. Hagström: Appl. Phys. Lett. 74, 3290 (1999)
8. Y.F. Lu, Z.M. Ren, T.C. Chong, B.A. Cheong, S.I. Pang, J.P. Wang,
K. Li: J. Appl. Phys. 86, 4954 (1999)
9. T. Yen, C. Chou: Appl. Phys. Lett. 67, 2081 (1995)
10. H. Sjöström, S. Stafstrom, M. Boman, J.-E. Sundgren: Phys. Rev. Lett.
75, 1336 (1995)
22. B.C. Holloway: Ph.D. Thesis, Leland Stanford Jr. University, 1997
23. R. Alexandrescu, F. Huisken, G. Pugna, A. Crunteanu, S. Petcu, S. Co-
jocaru, R. Cireasa, I. Morjan: Appl. Phys. A 65, 207 (1997)
24. A. Mansour, D. Ugolini: Phys. Rev. B 47, 10201 (1993)
25. A. K.M.S. Chowdhurg, D.C. Cameron, M.S.J. Hashmi: Thin Solid
Films 332, 62 (1998)
26. J. Robertson: Adv. Phys. 35, 317 (1986)
11. A.P. Caricato, G. Leggieri, A. Luches, A. Perrone, E. Gyorgy, I.N. Mi-
hailescu, M. Popescu, G. Barucca, P. Mengucci, J. Zemek, M. Trchova:
Thin Solid Films 307, 54 (1997)
12. I.N. Mihailescu, E. Gyorgy, R. Alexandrescu, A. Luches, A. Perrone,
C. Ghica. J. Werckmann, I. Cojocaru, V. Chumash: Thin Solid Films
323, 72 (1998)
27. D. Briggs, M.P. Seah: Practical Surface Analysis by Auger and X-ray
Photoelectron Spectroscopy (Wiley, New York 1983)
28. S.G. Painter, D.E. Ellis: Phys. Rev. 1, 4747 (1970)
29. F.R. McFreely, S.P. Kowalczyk, L. Ley, R.G. Cavell, R.A. Pollak,
D.A. Shirley: Phys. Rev. B 9, 5268 (1974)
30. D. Wesner, S. Krummacher, R. Car, T.K. Sham, M. Strongin, W. Eber-
hardt, S.L. Weng, G. Williams, M. Howells, F. Kampas, S. Heald,
F.W. Smith: Phys. Rev. B 28, 2152 (1983)
13. S. Bhattacharyya, C. Cardinand, G. Turban: J. Appl. Phys. 83, 4491
(1998)