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Band structure of black phosphorus studied by angle-resolved ultraviolet photoemission spectroscopy
~
Solid State Communications, Printed in Great Britain.
Vol.45,No.]|,
BAND STRUCTURE
OF BLACK PHOSPHORUS ULTRAVIOLET
T. Takahashi, Department
pp.945-948,
0038-]098/83/]10945-04503.00/0 Pergamon Press Ltd.
STUDIED BY ANGLE-RESOLVED
PHOTOEMISSION
K. Shirotani~
of Physics,
|983.
SPECTROSCOPY
S. Suzuki and T. Sagawa
Tohoku University,
Sendal 980, Japan
*The Institute for Solid State Physics, The University of Tokyo, Roppongi, Minato-ku, Tokyo 106, Japan ( Received 8 January 1983 by H. Kawamura
)
Band structure of black phosphorus has been first experimentally determined by the angle-resolved ultraviolet photoemission spectroscopy. The experimental results have been compared with the recently presented band calculations by Asahina et al. The overall features of the valence bands show a good correspondence between them although the observed band width is fairly narrower than the calculated one.
Orthorhombic black phosphorus (black P) is the most stable form of phosphorus under normal condition I and has a layered structure consisting of socalled packered layers with four atoms per unit cell~ Early experiments S'~ on polycrystalllne black P revealed that it is a p-type semiconductor with a narrow gap of about 0.3 eV. It has been also found that the orthorhombic form undergoes a reversible structural transformation under high pressure to successively denser rhombohedral and cubic forms~ '6 being accompanied by the semlconductor-semimetal-metal transition~ On the other hand, the electrical and optical properties has not yet been well elucidated. This is mainly due to the difficulty in preparing an enough size of a large single crystal of black P to ensure precise electrical and optical measurementSo In fact, most of the experimental studies on black P reported so far have been carried out with polycrystalS-1°or tiny fragment of single crystal~ 1'12 Recently, however, attempts for growing a large black P single crystal have been intensively made~S'1~being provoked by the current interest in layered materials~ s A preliminary neutron scatterin~ study on a single crystal has been reported~ ~ Very recently we have succeeded in growing a relatively large(3mm~×Smm length) black P single crystal under high pressureISwith which we can perform a photoemission measurement. We have already reported17an XPS(xray photoemission spectroscopy) spectrum of the single crystal and discussed the valence electronic states of black P. In this letter, we present the results of the first angle-resolved ultraviolet photoemission spectroscopy(ARUPS) study on the black P single crystal. ARUPS is a powerful means which gives us a direct information on the electronic band structure of solids~ s Especially for layered materials like as black P, ARUPS enables us to experimentally plot the band structure with no prior knowledge of the electonic structure of the materials only leaving an ambiguity in a small energy dispersion along the interlayer direction! 8 In this letter, the experimentally derived band structure of black P is compared with the recently presented theoretical calculations! 9'20
Black P crystal(about 3mm~×5mmlength) used in this study was prepared from red phosphorus under high pressure using a wedge-type cubic anvil apparatus~ S Red phosphorus was melted in a carbon furnace at about II00°C under a pressure of 23 Kbar, and then slowly cooled. The black P sample thus obtained was nearly a single crystal IS and could be easily cleaved along the layered (ac) plane. A small piece of single crystal(l.5×2.5×0.5 mm 3) cut out from the black P crystal prepared as mentioned above was pasted onto a copper substrate of the sample manipulater of the photoelectron spectrometer. The orientation of the sample was checked by the Laue x-ray diffraction pattern. Under ultrahigh vacuum(less than 3×10-9 Torr), the black P single crystal was cleaved to obtain a fresh and clean surface for the photoemission measurements. The surface was observed to remain clean for a several days21under the ultrahigh vacuum probably because of the inactive layered structure and/or the relatively high vapor pressure of phosphorus itself° The ARUPS spectra were measured using an angle-resolved photoelectron spectrometer constructed at our laboratory~2with a He I resonance Iine(21.22 eV) as an exciting source. The energy resolution was about O.1 eV and the angular resolution was estimated to be less than 2°: the illuminated spot on the sample was about 0.5 mm~ or less. The photon incidence angle was about 45 ° to the surface normal. The relative position between the sample and the electron energy analyser of the ARUPS spectrometer was determined roughly in advance by the Laue pattern and precisely in situ by the azimuthal and polar angle dependence of ARUPS spectra. ARUPS spectra were measured as a function of the polar angle 8 at an interval of 2 ° in the F-T-T~-Z plane and the FX-L-Z plane indicated by shaded areas in Pig.l. The ARUPS spectra were observed to be very sensitive to the polar angle @ because of the fairly high angular resolution in the present study and the complicated band structure of black P as shown in Fig.2. Before proceeding to the experimental results, it is instructive to briefly summarize the 945
946
BAND STRUCTURE OF BLACK PHOSPHORUS
Iiz
~kx Fig.l
The Brillourin
zone of black phosphorus
z~ 2"
j
zf Z~-
z~ z
T"
Fig.2
T
r
A
X
R
L
U
Z
l
I!
point has been attributed to the packered layer structure of black P and the interlayer interaction of the 3p z orbitals~e'2°which gives rise to a relatively large energy dispersion for the 3pz originated bands along the interlayer (F-Z) direction. This is the case for the highest valence and the lowest conduction band. Fig.3 shows some representative ARUPS spectra measured as a function of the polar angle e in the F-T-T'-Z plane. Polar angle 8 is taken with respect to the surface normal. The binding energy of the abscissa is measured from the peak position of the first band of the spectrum of e=0 = in order to directly compare with the SCP calculation result in Fig.2. In Fig.3 are not shown the higher-binding energy part of the spectra originating mainly from the 3s states. From the observed peaks we can derive an experimental band structure referred to the wavevector component parallel to the surface! 8 The experimental results for the F-T-T'-Z plane are compiled in Fig.4 together with the composite calculated bands of the F-T and Z-T" directions. In Fig.5 are also shown the results for the F-X-L-Z plane. In the course of mapping the experimental bands, some ambiguous structures appearing in the ARUPS
~'r."
z:
Vol. 45, No.
black P He I (21.22
1 eV) /
I--T-T'- Z plane
F
The energy bands of black phosphorus calculated by Asahina et al~°using the self-consistent pseudopotential method. The binding energy of the ordinate is taken from the Z~ point, the top of the valence bands.
.D L=. v
uI 3
band structure of black P. Figs.l and 2 show the Brillourin zone and the energy bands of black P calculated by Asahina et al. using a self-consistent pseudopotential(SCP) method. A little different results have been given by Takao et allgwith a tight binding(TB) approach. The latest XPS study of black P single crysta117prefers the SCP calculation to the TB one because the observed three bands in the 3p-derived density of states are well reproduced in the SCP calculation. As is shown in Fig.2, we find sixteen bands and the lower ten bands are occupied since the primitive cell of black P has four atoms with five valence electrons each. The shaded area separates the valence and conduction bands. As for the origin of the valence bands, the higher located bands in the energy range of 0-7 eV are mainly due to the 3p orbitals except for the two bands starting from F~ and Z~ points, which have largely the 3s character! 9 In Fig.2, we find that the minimum direct gap appears at Z point, the Brillourin zone edge in the interlayer direction while a relatively large energy gap is observed at F point. This narrowing of the energy gap at Z
o c~
e| = 2 o °
5 0 Binding energy (eV) Fig.3
Angle-resolved He I photoemission spectra measured as a function of the polar angle @ in the r-T-T -Z plane. Polar angle is taken with respect to the surface normal. For details see text.
/
O
Vol. 45, No. (a) z
SCP T'
(b) z
• T
0 " ........ " " ' " ' ' ' " ' ,
947
BAND STRUCTURE OF BLACK PHOSPHORUS
1]
T'
r"
-
(a)
expt. T
"1
L x
z F
L x
O-- .
.........."'"'0":-,:.
0
(b) expt.
SCP
z r
-
::e". . . .
--o-e--i-e.-e..i "e, --o.~.~.
c
-o.- -o.o.~.= "% ' e '"~ ,_o~Iile{ -o~o..~'~'~-l,.e_M-~ "o.
"-°"
~x
.o. ~
e~*"* °"o, o • .-*-~
5
g >
5- ~4~*
O1 ¢-
:~ 10
"
t5
15-
Fig.4
Experimentally derived band structure in the F-T-T'-Z plane;(b). Filled circles indicate prominate peaks and open circles are for shoulders or small peaks. Circles are tentatively connected by dashed lines . The composite calcilated bands of the r-T(solid lines) and Z-T'(broken lines) directions are also shown for comparison;(a).
spectra were neglected at the moment for simplicity. As is found in Figs.4 and 5, the agreement of the overall features between the experiment and the calculation is quite excellent° The slowly declining feature of the highest valence band from zt along T' axis is clearly observed in the experimental results(Fig.4(b)). We also find that the experimental result in Figo5(b) shows the characteristic feature that the calculated highest two valence bands cross each other at about middle point of Z and L. In Fig.4(b) is apparently detected the steep band running from r or Z point of about 4 eV to the zone edge of about 9 eV binding energy , which should correspond to the steep two bands from F~ to Z~ and from Z~ to F~. These bands are of the 3s origin as just mentioned above. In spite of these excellent agreements in the overall feature, however~ it seems that the calculated valence band width is fairly wide: the observed band around 6.5 eV at r(Z) point may correspond to zt or Ft which is located
C
Fig.5
oe I
,.e..e _ _ ~ _ o - ~ o - o ~ o
~3 10" .. . . .
"~o ~'o,
o
"o
== .o...o.o..o
coo
.
/ /
L.
0~
• ~o -e
~
10-
Experimentally determined band structure in the F-X-L-Z plane;(b). Filled circles indicate prominate peaks and open circles represent shoulders or small peaks. They are tentatively connected by dashed lines The composite calculated bands of the F-X(solid lines) and Z-L (broken lines) directions are also shown for comparision; (a).
at 7-8 eV. The wider feature of the valence bands of the SCP calculation2°has been also confirmed by the latest XPS study~ ? This overestimate of the valence band width in the SCP calculation may be improved by the correction of the potential along the interlayer direct$on because the highest valence bands, Z~.and r2, and the 3p-derived lowest bands, Ft and zT, have a lot of the 3pz character~ 9 As for the 3s-derived portion, we observe two bands around 9.5 and 12.3 eV at F or Z point(see Fig.4(b) and Fig.5~b)). These two bands may correspond to Ft or Z2(around 10.4 eV) and F~ or Z~ (14-15 eV), respectively. The observed bands locate at the lower binding energy compared with the calculations although the position of the observed deepest band at about 12.3 eV has some ambiguity because of a large background due to the inelastically scattered electrons. Finally we must add some comments on the experimentally derived band structure. As is shown in Fig.4(b), we found a small shoulder just above
948
BAND STRUCTURE OF BLACK PHOSPHORUS
the prominent first band in some ARUPS spectra: the shoulder is indicated by three open circle just above the highest valence band in the r-TT'-Z plane. The origin of this shoulder is unknown at the present stage: it may be due to a misalignment of the sample or might come from some surface states. The second comment is on the relatively large energy dispersion along the F-Z (interlayer) direction, which may modify the observed ARUPS spectra, especially the highest two valence bands. At the present stage, however, it is unknown to what extent the observed ARUPS spectra were affected by the interlayer dispersion whereas the characteristic features of the highest two bands show a good correspondence between the experiment and the calculation. This
Vol. 45, No. 11
problem can be removed by the combination of the photoemission experiments with different photon energies. In order to study the band structure of black P in detail, especially the higher part of the valence bands, we are now undertaking the photoemission experiment with various(Ne I and Ar I) exciting sources. Ackowledgement-The authors are grateful to Dr. H. Asahina and Prof. A.Morita, Tohoku University, and Prof. Y.Harada, The University of Tokyo, for their helpful discussion. They also thank H. Tokairin and T. Yokotsuka for their technical help in the photoemission measurements. This work was supported by the Grant-in-Aid for Scientific Research from the Ministry of Education.
REFERENCES i. A.F.WelIs, Structural Inorganic Chemistry 4th ed.(Clarendon, Oxford, 1975)p.674. 2. A.Brown & S.Rundqvist, Acta. Cryst. 19, 684 (1965). 3. R.W.Keyes, Phys.Rev. 92, 580(1953). 4. D.Warschauer, J.Appl.Phys. 34, 1853(1963). 5. J.C.Jamieson, Science 139, 129(1963). 6. M.L.Duggin, J.Phys. Chem. Solids 33, 1267(1972). 7. J.Witting & B.T.Matthias, Science 160, 994 (1968). 8. G.Wiech, Z.f~r Phys. 216, 472(1968). 9. L.Cartz, S.R.Srinivasa, R.J.Riedner, J.D.Jorgensen & T.G.Worlton, J.Che~.Phys. 71, 1718(1979). i0. J.S.Lannin & B.V.Shanabrook, Inst.Phys. Conf. Ser. 43, 643(1979). Ii. Y.Maruyama, S.Suzuki, K.Kobayashi & S.Tanuma, Physica 105B, 99(1981). 12. S.Sugai, T.Ueda & K.Murase, J.Phys.Soc.Jpn. 50,3356(1981) . 13. l. Sbirotani, R.Maniwa, H.Sato, A.Fukizawa, N.Sato, Y.Maruyama, T.Kajiwara, H.Inokuehl & S.Akimoto, Nippon Kagaku Kaishi i0, 1604 (1981) ( in Japanese) ; I. Shirotani, Mol. Cryst. Liq. Cryst. 86(Proc. Int.Conf. Low-Dimensional Conductors, Boulder, Colorado, 1981), 1943 (1982).
14. S.Endo, Y.Akahama, S.Terada & S.Narita, Jpn. J.Appl.Phys. 21, L482(1982). 15. For example, see Physica B 105(Proc. Yamada Conf. Physics and Ch~istry of Layered Materials, Sendai 1980), (1981). 16. Y.Fujii, Y.Akahama, S.Endo, S.Narita, Y.Yamada & G. Shirane, Solid State Commun. 44, 579 (1982). 17. Y.Harada, K.Murano, l.Shirotani, T.Takahashi & Y.Maruyama, Solid State Commun. 44, 877 (1982). 18. N.V.Smith, Angular Dependent Photoemission in Photoemission in Solid Ied. by M.Cardona & L.Ley(Springer-Verlag, Berlin 1978)p.237. 19. Y.Takao & A.Morita, Physica 105B, 93(1981); Y.Takao, H.Asahina & A.Morlta, J.Phys.Soc.Jpn. 50, 3362(1981). 20. H.Asahlna, A.Morita & K.Shindo, J.Phys.Soc. Jpn. 49 Suppl. A(Proc. 15th Int. Conf.Phys. Semicond. Kyoto, 1980), 85(1980);H.Asahina, K.Shindo & A.Morita, J.Phys.Soc.Jpn. 51, 1193 (1982). 21. No photoemission spectral change was observed after a week. 22. S.Suzuki, K.Furusawa, M.Terasawa, M.Yoshida & T.Sagawa, Sci. Rep. Tohoku Univ. 8th Ser. i , 16(1980).
Solid State Communications, Printed in Great Britain.
Vol.45,No.]|,
BAND STRUCTURE
OF BLACK PHOSPHORUS ULTRAVIOLET
T. Takahashi, Department
pp.945-948,
0038-]098/83/]10945-04503.00/0 Pergamon Press Ltd.
STUDIED BY ANGLE-RESOLVED
PHOTOEMISSION
K. Shirotani~
of Physics,
|983.
SPECTROSCOPY
S. Suzuki and T. Sagawa
Tohoku University,
Sendal 980, Japan
*The Institute for Solid State Physics, The University of Tokyo, Roppongi, Minato-ku, Tokyo 106, Japan ( Received 8 January 1983 by H. Kawamura
)
Band structure of black phosphorus has been first experimentally determined by the angle-resolved ultraviolet photoemission spectroscopy. The experimental results have been compared with the recently presented band calculations by Asahina et al. The overall features of the valence bands show a good correspondence between them although the observed band width is fairly narrower than the calculated one.
Orthorhombic black phosphorus (black P) is the most stable form of phosphorus under normal condition I and has a layered structure consisting of socalled packered layers with four atoms per unit cell~ Early experiments S'~ on polycrystalllne black P revealed that it is a p-type semiconductor with a narrow gap of about 0.3 eV. It has been also found that the orthorhombic form undergoes a reversible structural transformation under high pressure to successively denser rhombohedral and cubic forms~ '6 being accompanied by the semlconductor-semimetal-metal transition~ On the other hand, the electrical and optical properties has not yet been well elucidated. This is mainly due to the difficulty in preparing an enough size of a large single crystal of black P to ensure precise electrical and optical measurementSo In fact, most of the experimental studies on black P reported so far have been carried out with polycrystalS-1°or tiny fragment of single crystal~ 1'12 Recently, however, attempts for growing a large black P single crystal have been intensively made~S'1~being provoked by the current interest in layered materials~ s A preliminary neutron scatterin~ study on a single crystal has been reported~ ~ Very recently we have succeeded in growing a relatively large(3mm~×Smm length) black P single crystal under high pressureISwith which we can perform a photoemission measurement. We have already reported17an XPS(xray photoemission spectroscopy) spectrum of the single crystal and discussed the valence electronic states of black P. In this letter, we present the results of the first angle-resolved ultraviolet photoemission spectroscopy(ARUPS) study on the black P single crystal. ARUPS is a powerful means which gives us a direct information on the electronic band structure of solids~ s Especially for layered materials like as black P, ARUPS enables us to experimentally plot the band structure with no prior knowledge of the electonic structure of the materials only leaving an ambiguity in a small energy dispersion along the interlayer direction! 8 In this letter, the experimentally derived band structure of black P is compared with the recently presented theoretical calculations! 9'20
Black P crystal(about 3mm~×5mmlength) used in this study was prepared from red phosphorus under high pressure using a wedge-type cubic anvil apparatus~ S Red phosphorus was melted in a carbon furnace at about II00°C under a pressure of 23 Kbar, and then slowly cooled. The black P sample thus obtained was nearly a single crystal IS and could be easily cleaved along the layered (ac) plane. A small piece of single crystal(l.5×2.5×0.5 mm 3) cut out from the black P crystal prepared as mentioned above was pasted onto a copper substrate of the sample manipulater of the photoelectron spectrometer. The orientation of the sample was checked by the Laue x-ray diffraction pattern. Under ultrahigh vacuum(less than 3×10-9 Torr), the black P single crystal was cleaved to obtain a fresh and clean surface for the photoemission measurements. The surface was observed to remain clean for a several days21under the ultrahigh vacuum probably because of the inactive layered structure and/or the relatively high vapor pressure of phosphorus itself° The ARUPS spectra were measured using an angle-resolved photoelectron spectrometer constructed at our laboratory~2with a He I resonance Iine(21.22 eV) as an exciting source. The energy resolution was about O.1 eV and the angular resolution was estimated to be less than 2°: the illuminated spot on the sample was about 0.5 mm~ or less. The photon incidence angle was about 45 ° to the surface normal. The relative position between the sample and the electron energy analyser of the ARUPS spectrometer was determined roughly in advance by the Laue pattern and precisely in situ by the azimuthal and polar angle dependence of ARUPS spectra. ARUPS spectra were measured as a function of the polar angle 8 at an interval of 2 ° in the F-T-T~-Z plane and the FX-L-Z plane indicated by shaded areas in Pig.l. The ARUPS spectra were observed to be very sensitive to the polar angle @ because of the fairly high angular resolution in the present study and the complicated band structure of black P as shown in Fig.2. Before proceeding to the experimental results, it is instructive to briefly summarize the 945
946
BAND STRUCTURE OF BLACK PHOSPHORUS
Iiz
~kx Fig.l
The Brillourin
zone of black phosphorus
z~ 2"
j
zf Z~-
z~ z
T"
Fig.2
T
r
A
X
R
L
U
Z
l
I!
point has been attributed to the packered layer structure of black P and the interlayer interaction of the 3p z orbitals~e'2°which gives rise to a relatively large energy dispersion for the 3pz originated bands along the interlayer (F-Z) direction. This is the case for the highest valence and the lowest conduction band. Fig.3 shows some representative ARUPS spectra measured as a function of the polar angle e in the F-T-T'-Z plane. Polar angle 8 is taken with respect to the surface normal. The binding energy of the abscissa is measured from the peak position of the first band of the spectrum of e=0 = in order to directly compare with the SCP calculation result in Fig.2. In Fig.3 are not shown the higher-binding energy part of the spectra originating mainly from the 3s states. From the observed peaks we can derive an experimental band structure referred to the wavevector component parallel to the surface! 8 The experimental results for the F-T-T'-Z plane are compiled in Fig.4 together with the composite calculated bands of the F-T and Z-T" directions. In Fig.5 are also shown the results for the F-X-L-Z plane. In the course of mapping the experimental bands, some ambiguous structures appearing in the ARUPS
~'r."
z:
Vol. 45, No.
black P He I (21.22
1 eV) /
I--T-T'- Z plane
F
The energy bands of black phosphorus calculated by Asahina et al~°using the self-consistent pseudopotential method. The binding energy of the ordinate is taken from the Z~ point, the top of the valence bands.
.D L=. v
uI 3
band structure of black P. Figs.l and 2 show the Brillourin zone and the energy bands of black P calculated by Asahina et al. using a self-consistent pseudopotential(SCP) method. A little different results have been given by Takao et allgwith a tight binding(TB) approach. The latest XPS study of black P single crysta117prefers the SCP calculation to the TB one because the observed three bands in the 3p-derived density of states are well reproduced in the SCP calculation. As is shown in Fig.2, we find sixteen bands and the lower ten bands are occupied since the primitive cell of black P has four atoms with five valence electrons each. The shaded area separates the valence and conduction bands. As for the origin of the valence bands, the higher located bands in the energy range of 0-7 eV are mainly due to the 3p orbitals except for the two bands starting from F~ and Z~ points, which have largely the 3s character! 9 In Fig.2, we find that the minimum direct gap appears at Z point, the Brillourin zone edge in the interlayer direction while a relatively large energy gap is observed at F point. This narrowing of the energy gap at Z
o c~
e| = 2 o °
5 0 Binding energy (eV) Fig.3
Angle-resolved He I photoemission spectra measured as a function of the polar angle @ in the r-T-T -Z plane. Polar angle is taken with respect to the surface normal. For details see text.
/
O
Vol. 45, No. (a) z
SCP T'
(b) z
• T
0 " ........ " " ' " ' ' ' " ' ,
947
BAND STRUCTURE OF BLACK PHOSPHORUS
1]
T'
r"
-
(a)
expt. T
"1
L x
z F
L x
O-- .
.........."'"'0":-,:.
0
(b) expt.
SCP
z r
-
::e". . . .
--o-e--i-e.-e..i "e, --o.~.~.
c
-o.- -o.o.~.= "% ' e '"~ ,_o~Iile{ -o~o..~'~'~-l,.e_M-~ "o.
"-°"
~x
.o. ~
e~*"* °"o, o • .-*-~
5
g >
5- ~4~*
O1 ¢-
:~ 10
"
t5
15-
Fig.4
Experimentally derived band structure in the F-T-T'-Z plane;(b). Filled circles indicate prominate peaks and open circles are for shoulders or small peaks. Circles are tentatively connected by dashed lines . The composite calcilated bands of the r-T(solid lines) and Z-T'(broken lines) directions are also shown for comparison;(a).
spectra were neglected at the moment for simplicity. As is found in Figs.4 and 5, the agreement of the overall features between the experiment and the calculation is quite excellent° The slowly declining feature of the highest valence band from zt along T' axis is clearly observed in the experimental results(Fig.4(b)). We also find that the experimental result in Figo5(b) shows the characteristic feature that the calculated highest two valence bands cross each other at about middle point of Z and L. In Fig.4(b) is apparently detected the steep band running from r or Z point of about 4 eV to the zone edge of about 9 eV binding energy , which should correspond to the steep two bands from F~ to Z~ and from Z~ to F~. These bands are of the 3s origin as just mentioned above. In spite of these excellent agreements in the overall feature, however~ it seems that the calculated valence band width is fairly wide: the observed band around 6.5 eV at r(Z) point may correspond to zt or Ft which is located
C
Fig.5
oe I
,.e..e _ _ ~ _ o - ~ o - o ~ o
~3 10" .. . . .
"~o ~'o,
o
"o
== .o...o.o..o
coo
.
/ /
L.
0~
• ~o -e
~
10-
Experimentally determined band structure in the F-X-L-Z plane;(b). Filled circles indicate prominate peaks and open circles represent shoulders or small peaks. They are tentatively connected by dashed lines The composite calculated bands of the F-X(solid lines) and Z-L (broken lines) directions are also shown for comparision; (a).
at 7-8 eV. The wider feature of the valence bands of the SCP calculation2°has been also confirmed by the latest XPS study~ ? This overestimate of the valence band width in the SCP calculation may be improved by the correction of the potential along the interlayer direct$on because the highest valence bands, Z~.and r2, and the 3p-derived lowest bands, Ft and zT, have a lot of the 3pz character~ 9 As for the 3s-derived portion, we observe two bands around 9.5 and 12.3 eV at F or Z point(see Fig.4(b) and Fig.5~b)). These two bands may correspond to Ft or Z2(around 10.4 eV) and F~ or Z~ (14-15 eV), respectively. The observed bands locate at the lower binding energy compared with the calculations although the position of the observed deepest band at about 12.3 eV has some ambiguity because of a large background due to the inelastically scattered electrons. Finally we must add some comments on the experimentally derived band structure. As is shown in Fig.4(b), we found a small shoulder just above
948
BAND STRUCTURE OF BLACK PHOSPHORUS
the prominent first band in some ARUPS spectra: the shoulder is indicated by three open circle just above the highest valence band in the r-TT'-Z plane. The origin of this shoulder is unknown at the present stage: it may be due to a misalignment of the sample or might come from some surface states. The second comment is on the relatively large energy dispersion along the F-Z (interlayer) direction, which may modify the observed ARUPS spectra, especially the highest two valence bands. At the present stage, however, it is unknown to what extent the observed ARUPS spectra were affected by the interlayer dispersion whereas the characteristic features of the highest two bands show a good correspondence between the experiment and the calculation. This
Vol. 45, No. 11
problem can be removed by the combination of the photoemission experiments with different photon energies. In order to study the band structure of black P in detail, especially the higher part of the valence bands, we are now undertaking the photoemission experiment with various(Ne I and Ar I) exciting sources. Ackowledgement-The authors are grateful to Dr. H. Asahina and Prof. A.Morita, Tohoku University, and Prof. Y.Harada, The University of Tokyo, for their helpful discussion. They also thank H. Tokairin and T. Yokotsuka for their technical help in the photoemission measurements. This work was supported by the Grant-in-Aid for Scientific Research from the Ministry of Education.
REFERENCES i. A.F.WelIs, Structural Inorganic Chemistry 4th ed.(Clarendon, Oxford, 1975)p.674. 2. A.Brown & S.Rundqvist, Acta. Cryst. 19, 684 (1965). 3. R.W.Keyes, Phys.Rev. 92, 580(1953). 4. D.Warschauer, J.Appl.Phys. 34, 1853(1963). 5. J.C.Jamieson, Science 139, 129(1963). 6. M.L.Duggin, J.Phys. Chem. Solids 33, 1267(1972). 7. J.Witting & B.T.Matthias, Science 160, 994 (1968). 8. G.Wiech, Z.f~r Phys. 216, 472(1968). 9. L.Cartz, S.R.Srinivasa, R.J.Riedner, J.D.Jorgensen & T.G.Worlton, J.Che~.Phys. 71, 1718(1979). i0. J.S.Lannin & B.V.Shanabrook, Inst.Phys. Conf. Ser. 43, 643(1979). Ii. Y.Maruyama, S.Suzuki, K.Kobayashi & S.Tanuma, Physica 105B, 99(1981). 12. S.Sugai, T.Ueda & K.Murase, J.Phys.Soc.Jpn. 50,3356(1981) . 13. l. Sbirotani, R.Maniwa, H.Sato, A.Fukizawa, N.Sato, Y.Maruyama, T.Kajiwara, H.Inokuehl & S.Akimoto, Nippon Kagaku Kaishi i0, 1604 (1981) ( in Japanese) ; I. Shirotani, Mol. Cryst. Liq. Cryst. 86(Proc. Int.Conf. Low-Dimensional Conductors, Boulder, Colorado, 1981), 1943 (1982).
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