- Email: [email protected]
APS and XPS spectra of vanadium carbide: correlation with an APW band structure calculation
Volume 41, number 2
CHEMICAL PHYSICS LETTERS
APS AND XPS SPECIIU CORRBIATION
OF VANADIUM
CARBIDE:
WITH AN APW BAND STRUCTURE
K. SCHWARZ, A. NECKEL Technische Elektrochemie. A-2060 Vienna. Austri2 Institut f~
IS JuIy 1976
CALCULATION
Te
and AM. BEUDSHAW* Institut fti Physikalische Chemie und Tbeoretische Chemie, Technische UniversitOt Miinchen. D-8046
Garching, Federal Republic of Germany
Received 31 March 1976
Appearance potential spectra and X-ray photoelectron spectra for vanadium carbide are calculated using new APW band structure data. The good agreement with experimental spectra reinforces evidence from soft X-ray emission that the APW calculation provides a reasonable description of the electronic band structure.
The electronic band structure of several refractory metal compounds has recentiy been calculated using the augmented plane wave (APW) method [I]. In this method the unit cell is divided into two regions: the atomic spheres centred around each atomic site and the region around the spheres. Within the approximation afforded by this spatial separation, the total density of states (DOS) g(E) can be decomposed into local partial densities of states, termed character densities of states, as described in ref. [l] :
emission from the valence band, where a core level is not involved, the total DOS is however the appropriate quantity to compare with experiment. In the present letter we calculate APS and XPS spectra for stoichiometric vanadium carbide using in each case the appropriate APW-DOS function and compare the results with experimental data. SXS spectra for VC have already been interpreted using APW calculations [2]. According to this model the C-K spectrum, without broadening, is given by
d..)
&g(E)
= xou’(a
+ g x:w (1) , where Xf(E) is the number of states (electrons) per Rydberg and unit cell at energy E which reside in sphere t and are characterised by spherical harmonics with azimuthal quantum nmmber 2. x”“‘(E) corresponds to the fraction of the electrons outside the spheres [I]. These character densities of states play an important role for the interpretation of experiments involving the excitation of a core hole, such as soft X-ray appearance potential spectroscopy (APS), or the relaxation of a core hole, such as soft X-ray emission spectroscopy (SXS). For &toelcctric _.
* Present address: Fritz-Haber-Institut schaft, 1000 Berlin 33, Germany.
der Enax-PlanckCesell-
Of [MC&
and the V--LIB &
&)
Is*E)]2
x;(E),
(2)
spectrum by
QI C CM, (s, 2~9
E)l 2 x y GE)
+$ C&,4d,2p,E)12 x:(-W,
(3)
where [Mr(Z, 62’. E)] 2 is the radial transition probability for a core state lt’l’ within the atomic sphere F to be filled by an electron in an I-like valence state with energy E. The factor y3, where v is the frequency of the transition, has been assumed to be constant over the width of the spectrum. Convolution of I0 (E) according to (2) or (3) with a lorentzian to account for life-time broadening yields theoretical spectra in good agreement with experiment [2]. 311
Volume 41, number 2
CHEMICAL
PHYSICS
In the APS experiment [3] ’ electrons of well-defied energy EP hit the surface of a sample, which leads_to emission of characteristic X-radiation on a Bremsstrahlung background. When the energy of the incident electrons is scanned, t.hJesholds appear ti the total photon yield corresponding to the appearance of additional characteristic radiation as successive core levels are ionised. The usual electronic differentiation technique leads to a spectrum of peak=like features. Park and Houston [6] first showed that valuable density of states information could be obtained with the method. More recently Webb and Wiliiams !7] have investigated the band structure of certain layer compounds by deconvoluting experimental threshold structures [7] _A schematic energy level diagram within the one-electrcn approximation is shown in fg_ 1. The Fermi level, EF, is taken as the origin of the energy scale. If the energy Ep of the incident electron is greater than the binding energy Eb of a core electron, then this core electron may be excited inf,o an empty conduction band state e1 where it shares the excess energy Ep f E,, with the primary electron, which will be scattered to the empty state ~2. The care hole excitation rate can be written as [S]
15 July 1976
LETTERS
P(Ep) = ~CZ(E”-Ep)dE” -00
J” @(Et-Eb)dE’
_E”
(4)
E”+p
X s
u(E’, el) d(E”, E2) 6 (E”+E’-e1-e2)deI,
0 where u(E’,el) describes the probability corresponding to the up-transition from the core level E’ (centred
around J!$.,)to the empty conduction band state IQ, and d(E”, Ed) the down-transition from E” (centred around EJ to ~2. The &function takes energy conservation into account. S2(E”-E,) accounts for the thermal spread of the incident electron and the instrument function_ @(E’- E,.,) is the core hole line-shape function. In the following a model for calculating APS spectra is used, in which constant matrix elements are assumed and for both the up- and dowrz-transitions just the local DOS (inside that sphere where the transition occurs) is taken [8] :
d(E” e2)= xf(e2).
(6)
So far both the up- and down-transitions are given in histogram form. The life-time broadening of the valence states, assuming a lorentzian line shape (with an energy-dependent halfwidth r(E)), can be taken into account analytically using the procedure of Goodings and Harris [9] as described in ref. [2]. The broa’dened up-transition is then given by
’ For recent :eviews see refs. [4,5].
U(E) = ~-l Cr” (Ei) i ’
’
E-Ei+q
E-Ei-q
arctg r(Ei)/2
- arctg r&i)/2
C
(7)
where 2s is the width of the histogram blocks. The sum over i is carried out over all histogram blocks (centred around Ei), which he above E, _The broadened down-transition a is obtained similarly. Eq. (4) can thus be rewritten as 0
EsOrEf
+=Eb)
P(Ep)=rSL(E”-Ep)dE” -w
Eb
Fig. 1. Schematic one-electron energy Ievei iliag~m
s +(E’-Eb)dE’ -E”
E’+E” for A?%
x ,f ii (E;) l7(e’+ E”0
312.
1’
El) dq.
Volume 3 1,
~Umbei
CHEMICAL PHYSICS LETFJZRS
2
15 July 1976
ments cFnf?umed that this pretieatment
1,. 0 energy
, , , lo
above
20 threshold.
.c
eV
Fii. 2. Experimental (solid lint) and calculated carbon-K APS spectrum for vanadium carbide. lated spectrum the following halfwidths for the functions were used: core = 0.25 eV, thermal + 0.4 eV and valence, r(E) = Z y2 eV.
(broken line) For the calcubroadening instrument =
The theoretical APS spectrum is given by the energy derivative of P(Ep). The experimental APS spectra were taken in a compact spectrometer with a KC1 photocathode described previously [lo]. The (lOO)-oriented surface of the
vanadium carbide crystal (nominal composition VCo 85) was bombarded for several hours with argon ions-to remove the oxide layer. A light annealing at 400 K produced an APS spectrum, which is judged characteristic of a carbide [ 111. Later XPS measure-
produced a clean vanadium carbide surface [lo]. Fig. ~-&LOWSthe experimental C-K APS spectrum toiether with the calculated spectrum and fig- 3 the corresponding V-I.,,, spectra. The details of the spectra depend to a certain extent on the particular choice ofbroadening functions, the main features remain however and agree well with experiment. If tke up-transition is not approximated with the local DOS but is treated analogously to SXS using optical selection rules according to (2) or (3), tie computed spectra are very similar to those shown in figs. 2 and 3. However for the V-K spectrum, which could not be measured experimentally, there would be ii significant difference.
The experimental valence band XFS spectrum of vanadium carbide was measured with an AEI 20OA photoeIectron spectrometer using a Mg Kcr source. The same cleaning procedures were used as in the APS experiment described above. The spectrum is shown in fig. 4 together with the calculated spectrum, for which the total DOS from the APW calcu?ation was convoluted with an asymmetric broadening function. (It is assumed that in the XPS experiment all fdled k states in the Brillouin zone contribute with the same weight.) The broadening function used was the C-K core level profde from pyrolytic graphite (without loss structure) which, with a halfwidth of z 1.0 eV, was considered to be a good approximation to the instrument function. ‘The separation between the carbon s-band (at i= - 12 eV) and the carbon p-band (at = -5 eV) [l] is about 1.5 eV smaller in the theoretical than in the experimental spectrum. The relative intensities of the different bands are well reproduced, which implies that differences in the
t
0
10
energy above
20‘ threshold,
30 eV
Fig. 3. Experimental (solid line) and calculated (broken line) vanadium-L1lI1ll APS spectrum (in arbitrary units) for vanadium carblde. For the calculated spectrum the following halfwidths for the broadening functions were used: core = 0.7 eV, thermal + instrument = 0.4 eV and valence, JT(.!?) = E ‘I* eV. The separation of the superimposed L~II and LIE spectra was taken from the experiment to be 7.5 eV and the intensity ratio 0.9.
Fig. 4. Experimental (solid line) and calculated (broken tine) v&??~ band XPS spectrum of vanadium carbide.
313
Vcttumel 1, number 2
CHEMICAL PHYSICS LETTERS
ion&&ion cross secti+s are not very pronounced at this @n-titular excitation energy (1254 eV)_ T&e present results indicate that the APW calcnlation predicts a realistic band structure for vandium carbide, ex&pt for the separation of the carbon sand p-bands_ S&e the samk discrepancy is found in SXS 1223the deviation is most likely to be due to the band structure rather than the one-electron, ground state wavefunction models used foi describing the experiments_.The fact &at the experiments were performed on non-stqichiometric VC, f-umay even have been below 0.85 in the surface region after cl,“aning) is not considered to alter this conclusion. As Neckel et al. [I21 have &own, different VC, phases exhbit a fairly “rigid band structure”. The authors are grateful to E. Wimmer for extending the AF’Wcalculation to higher energies necessary for the calculation of the APS spectrum and to U. Krause for assistance with experimental work.
314
15 July 1976
References [l] A. Neckel, P. Rastl, R. Eibler, P. Weinberger and K. Schwan, J. Phys C 9 (1976) 579; A. Neckel. K. Schwae, P. W&nberBer, R. Erbler and P. Rest& Ber. Bunsenges Physik- Chem. 79 (1975) 1053. 121 K. Schwarz and A. Neckel, Ber. Bunsenger Physik, Chem. 79 (197.5) 1071. _ [3; R-I,. F%uk,J.E. Houston and D.G. Schreiner, Rev. Sci. Instr.-441 (1970) 1810. f41 A.M. Bradshaw, Snrfam and Defect Properties of Solids 3 (1974) 153. [S) R-L. Park,Surface Sci 48 (1975) 80. [6] R-L. Park and J-E. Houston, Phys. Rev. B6 (1972) 1073. [7] C. Webb and P.M. Williams, Phys. Rev. BI 1 (1975) 2082. [S] J.C. Tracy, J. Appt Phys 43 (1972) 4164. [9] D.A. Coodings and R Harris, J. Phys. C.2 (1969) 1808. [ 101 A.M. Bradshaw and U. Krause, Ber. Bunsenges. Physik. Chem. 79 (1975) 1095. [ll] J-E. Houston and R-E. Park. J_ Vacuum Sci. Technol. 8 (1971) 91. [ 121 A. Neckel, P. Rasti, K. Schwaa and R. Eibler-Mechffer, Z. Naturforsch. 29a (1974) 107.
CHEMICAL PHYSICS LETTERS
APS AND XPS SPECIIU CORRBIATION
OF VANADIUM
CARBIDE:
WITH AN APW BAND STRUCTURE
K. SCHWARZ, A. NECKEL Technische Elektrochemie. A-2060 Vienna. Austri2 Institut f~
IS JuIy 1976
CALCULATION
Te
and AM. BEUDSHAW* Institut fti Physikalische Chemie und Tbeoretische Chemie, Technische UniversitOt Miinchen. D-8046
Garching, Federal Republic of Germany
Received 31 March 1976
Appearance potential spectra and X-ray photoelectron spectra for vanadium carbide are calculated using new APW band structure data. The good agreement with experimental spectra reinforces evidence from soft X-ray emission that the APW calculation provides a reasonable description of the electronic band structure.
The electronic band structure of several refractory metal compounds has recentiy been calculated using the augmented plane wave (APW) method [I]. In this method the unit cell is divided into two regions: the atomic spheres centred around each atomic site and the region around the spheres. Within the approximation afforded by this spatial separation, the total density of states (DOS) g(E) can be decomposed into local partial densities of states, termed character densities of states, as described in ref. [l] :
emission from the valence band, where a core level is not involved, the total DOS is however the appropriate quantity to compare with experiment. In the present letter we calculate APS and XPS spectra for stoichiometric vanadium carbide using in each case the appropriate APW-DOS function and compare the results with experimental data. SXS spectra for VC have already been interpreted using APW calculations [2]. According to this model the C-K spectrum, without broadening, is given by
d..)
&g(E)
= xou’(a
+ g x:w (1) , where Xf(E) is the number of states (electrons) per Rydberg and unit cell at energy E which reside in sphere t and are characterised by spherical harmonics with azimuthal quantum nmmber 2. x”“‘(E) corresponds to the fraction of the electrons outside the spheres [I]. These character densities of states play an important role for the interpretation of experiments involving the excitation of a core hole, such as soft X-ray appearance potential spectroscopy (APS), or the relaxation of a core hole, such as soft X-ray emission spectroscopy (SXS). For &toelcctric _.
* Present address: Fritz-Haber-Institut schaft, 1000 Berlin 33, Germany.
der Enax-PlanckCesell-
Of [MC&
and the V--LIB &
&)
Is*E)]2
x;(E),
(2)
spectrum by
QI C CM, (s, 2~9
E)l 2 x y GE)
+$ C&,4d,2p,E)12 x:(-W,
(3)
where [Mr(Z, 62’. E)] 2 is the radial transition probability for a core state lt’l’ within the atomic sphere F to be filled by an electron in an I-like valence state with energy E. The factor y3, where v is the frequency of the transition, has been assumed to be constant over the width of the spectrum. Convolution of I0 (E) according to (2) or (3) with a lorentzian to account for life-time broadening yields theoretical spectra in good agreement with experiment [2]. 311
Volume 41, number 2
CHEMICAL
PHYSICS
In the APS experiment [3] ’ electrons of well-defied energy EP hit the surface of a sample, which leads_to emission of characteristic X-radiation on a Bremsstrahlung background. When the energy of the incident electrons is scanned, t.hJesholds appear ti the total photon yield corresponding to the appearance of additional characteristic radiation as successive core levels are ionised. The usual electronic differentiation technique leads to a spectrum of peak=like features. Park and Houston [6] first showed that valuable density of states information could be obtained with the method. More recently Webb and Wiliiams !7] have investigated the band structure of certain layer compounds by deconvoluting experimental threshold structures [7] _A schematic energy level diagram within the one-electrcn approximation is shown in fg_ 1. The Fermi level, EF, is taken as the origin of the energy scale. If the energy Ep of the incident electron is greater than the binding energy Eb of a core electron, then this core electron may be excited inf,o an empty conduction band state e1 where it shares the excess energy Ep f E,, with the primary electron, which will be scattered to the empty state ~2. The care hole excitation rate can be written as [S]
15 July 1976
LETTERS
P(Ep) = ~CZ(E”-Ep)dE” -00
J” @(Et-Eb)dE’
_E”
(4)
E”+p
X s
u(E’, el) d(E”, E2) 6 (E”+E’-e1-e2)deI,
0 where u(E’,el) describes the probability corresponding to the up-transition from the core level E’ (centred
around J!$.,)to the empty conduction band state IQ, and d(E”, Ed) the down-transition from E” (centred around EJ to ~2. The &function takes energy conservation into account. S2(E”-E,) accounts for the thermal spread of the incident electron and the instrument function_ @(E’- E,.,) is the core hole line-shape function. In the following a model for calculating APS spectra is used, in which constant matrix elements are assumed and for both the up- and dowrz-transitions just the local DOS (inside that sphere where the transition occurs) is taken [8] :
d(E” e2)= xf(e2).
(6)
So far both the up- and down-transitions are given in histogram form. The life-time broadening of the valence states, assuming a lorentzian line shape (with an energy-dependent halfwidth r(E)), can be taken into account analytically using the procedure of Goodings and Harris [9] as described in ref. [2]. The broa’dened up-transition is then given by
’ For recent :eviews see refs. [4,5].
U(E) = ~-l Cr” (Ei) i ’
’
E-Ei+q
E-Ei-q
arctg r(Ei)/2
- arctg r&i)/2
C
(7)
where 2s is the width of the histogram blocks. The sum over i is carried out over all histogram blocks (centred around Ei), which he above E, _The broadened down-transition a is obtained similarly. Eq. (4) can thus be rewritten as 0
EsOrEf
+=Eb)
P(Ep)=rSL(E”-Ep)dE” -w
Eb
Fig. 1. Schematic one-electron energy Ievei iliag~m
s +(E’-Eb)dE’ -E”
E’+E” for A?%
x ,f ii (E;) l7(e’+ E”0
312.
1’
El) dq.
Volume 3 1,
~Umbei
CHEMICAL PHYSICS LETFJZRS
2
15 July 1976
ments cFnf?umed that this pretieatment
1,. 0 energy
, , , lo
above
20 threshold.
.c
eV
Fii. 2. Experimental (solid lint) and calculated carbon-K APS spectrum for vanadium carbide. lated spectrum the following halfwidths for the functions were used: core = 0.25 eV, thermal + 0.4 eV and valence, r(E) = Z y2 eV.
(broken line) For the calcubroadening instrument =
The theoretical APS spectrum is given by the energy derivative of P(Ep). The experimental APS spectra were taken in a compact spectrometer with a KC1 photocathode described previously [lo]. The (lOO)-oriented surface of the
vanadium carbide crystal (nominal composition VCo 85) was bombarded for several hours with argon ions-to remove the oxide layer. A light annealing at 400 K produced an APS spectrum, which is judged characteristic of a carbide [ 111. Later XPS measure-
produced a clean vanadium carbide surface [lo]. Fig. ~-&LOWSthe experimental C-K APS spectrum toiether with the calculated spectrum and fig- 3 the corresponding V-I.,,, spectra. The details of the spectra depend to a certain extent on the particular choice ofbroadening functions, the main features remain however and agree well with experiment. If tke up-transition is not approximated with the local DOS but is treated analogously to SXS using optical selection rules according to (2) or (3), tie computed spectra are very similar to those shown in figs. 2 and 3. However for the V-K spectrum, which could not be measured experimentally, there would be ii significant difference.
The experimental valence band XFS spectrum of vanadium carbide was measured with an AEI 20OA photoeIectron spectrometer using a Mg Kcr source. The same cleaning procedures were used as in the APS experiment described above. The spectrum is shown in fig. 4 together with the calculated spectrum, for which the total DOS from the APW calcu?ation was convoluted with an asymmetric broadening function. (It is assumed that in the XPS experiment all fdled k states in the Brillouin zone contribute with the same weight.) The broadening function used was the C-K core level profde from pyrolytic graphite (without loss structure) which, with a halfwidth of z 1.0 eV, was considered to be a good approximation to the instrument function. ‘The separation between the carbon s-band (at i= - 12 eV) and the carbon p-band (at = -5 eV) [l] is about 1.5 eV smaller in the theoretical than in the experimental spectrum. The relative intensities of the different bands are well reproduced, which implies that differences in the
t
0
10
energy above
20‘ threshold,
30 eV
Fig. 3. Experimental (solid line) and calculated (broken line) vanadium-L1lI1ll APS spectrum (in arbitrary units) for vanadium carblde. For the calculated spectrum the following halfwidths for the broadening functions were used: core = 0.7 eV, thermal + instrument = 0.4 eV and valence, JT(.!?) = E ‘I* eV. The separation of the superimposed L~II and LIE spectra was taken from the experiment to be 7.5 eV and the intensity ratio 0.9.
Fig. 4. Experimental (solid line) and calculated (broken tine) v&??~ band XPS spectrum of vanadium carbide.
313
Vcttumel 1, number 2
CHEMICAL PHYSICS LETTERS
ion&&ion cross secti+s are not very pronounced at this @n-titular excitation energy (1254 eV)_ T&e present results indicate that the APW calcnlation predicts a realistic band structure for vandium carbide, ex&pt for the separation of the carbon sand p-bands_ S&e the samk discrepancy is found in SXS 1223the deviation is most likely to be due to the band structure rather than the one-electron, ground state wavefunction models used foi describing the experiments_.The fact &at the experiments were performed on non-stqichiometric VC, f-umay even have been below 0.85 in the surface region after cl,“aning) is not considered to alter this conclusion. As Neckel et al. [I21 have &own, different VC, phases exhbit a fairly “rigid band structure”. The authors are grateful to E. Wimmer for extending the AF’Wcalculation to higher energies necessary for the calculation of the APS spectrum and to U. Krause for assistance with experimental work.
314
15 July 1976
References [l] A. Neckel, P. Rastl, R. Eibler, P. Weinberger and K. Schwan, J. Phys C 9 (1976) 579; A. Neckel. K. Schwae, P. W&nberBer, R. Erbler and P. Rest& Ber. Bunsenges Physik- Chem. 79 (1975) 1053. 121 K. Schwarz and A. Neckel, Ber. Bunsenger Physik, Chem. 79 (197.5) 1071. _ [3; R-I,. F%uk,J.E. Houston and D.G. Schreiner, Rev. Sci. Instr.-441 (1970) 1810. f41 A.M. Bradshaw, Snrfam and Defect Properties of Solids 3 (1974) 153. [S) R-L. Park,Surface Sci 48 (1975) 80. [6] R-L. Park and J-E. Houston, Phys. Rev. B6 (1972) 1073. [7] C. Webb and P.M. Williams, Phys. Rev. BI 1 (1975) 2082. [S] J.C. Tracy, J. Appt Phys 43 (1972) 4164. [9] D.A. Coodings and R Harris, J. Phys. C.2 (1969) 1808. [ 101 A.M. Bradshaw and U. Krause, Ber. Bunsenges. Physik. Chem. 79 (1975) 1095. [ll] J-E. Houston and R-E. Park. J_ Vacuum Sci. Technol. 8 (1971) 91. [ 121 A. Neckel, P. Rasti, K. Schwaa and R. Eibler-Mechffer, Z. Naturforsch. 29a (1974) 107.