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Effective correlation energies for defects in a-C:H from a comparison of photelectron yield and electron spin resonance experiments
Diamond and Related Materials 4 (1995) 508-516
Effective correlation energies for defects in a-C:H from a comparison photelectron yield and electron spin resonance experiments
of
J. Ristein, J. Schgfer, L. Ley Inzstitutfb
Technische
Physik,
Universitiit
Erlangen,
Erwin-Rommel-StraJe
1, D-91058
Erlangen,
Germany
Abstract Amorphous hydrogenated carbon films (a-C:H) were deposited by r.f. plasma CVD from methane, varying the self bias potential of the substrate electrode by means of the r.f. power coupled into the discharge. Films were characterized by IR and optical spectroscopy, confirming a transition from polymer-like to diamond-like (DLC) material with increasing self bias. One set of samples was investigated in situ by photoelectron and photoelectron yield spectroscopy, from which the density of gap states and their spectral distribution was derived. An identical set of samples was then examined by electron spin resonance to determine the density of paramagnetic defects. From a comparison of the results of both experiments, a lower limit for the effective correlation energy of the defect states was extracted which gave surprisingly large values for the correlation energy of the DLC material. In addition to the interpretation of the results within a spatially uniform model, the influence of a possible surface band bending on the evaluation of the correlation energies is also discussed. K~JWJ~& Amorphous
hydrogenated
carbon;
Electron
paramagnetic
1. Introduction Hydrogenated amouphous carbon (a-C:H) as prepared by CVD from hydrocarbon gases can be produced with strongly varying mechanical and electronic properties by changing the deposition parameters. When deposited from a capacitively coupled r.f. glow discharge, the most critical parameter has been proven to be the negative bias of the substrate electrode which controls the kinectic energy with which the film-forming radicals from the plasma hit the growing surface. By changing this bias the character of resulting a-C:H films can be gradually changed from soft polymer-like films with a large optical band gap to hard so-called diamond-like films (DLC) with smaller optical band gap which are covering an extending field of applications as protective IR transparent coatings or as passivation layers on semiconductor devices [ 11. The variety of mechanical and optical properties accessible with amorphous carbon thin films is due to the various forms of bonding a carbon atom can adopt and the accompanying changes in hybridization. The transformation from polymer-like to diamond-like a-C:H is accompied by a gradual increase in the sp’ 0925-9635/95/$09.50 0 1995 Elsevier Science S.A. All rights reserved SSDI 0925-9635(94)05272-7
resonance;
Defects
content and a decrease in hydrogen concentration. The electronic states close to the pseudogap of the material are thus derived from the 71electrons which necessarily come along with each sp’ bonded carbon atom. Thus the density of states in the pseudogap including localized defects and also the optical properties depend on the type of interaction of these n electrons. The tailing of valence and conduction band density of states into the gap is observed experimentally to increase with increasing sp2 content, and there are essentially two microscopic mechanisms responsible for this, as reviewed briefly in Section 4. In the following paper we focus on the properties of the gap states in a-C:H using a combination of two complementary experimental techniques, photoelectron yield spectroscopy (photoyield) and electron spin resonance (ESR). The ESR results on a-C:H published so far show as a general tendency an increase in spin density of several orders of magnitude when going from polymer-like to DLC samples [ 2-41. The results, however, depend sensitively on the details of the deposition and preparation process (source gas, deposition and annealing temperature, reactor design, r.f. power etc.). Thus in order to combine photoyield and ESR results, they had to be obtained on identical samples.
J. Ristein et al. JDiamond and Related Materials 4 (199.5) 508-516
2. Experimental
details and sample characterization
32
Identical samples for photoemission and photoyield spectroscopy and for optical and ESR experiments were deposited by r.f. plasma decomposition of methane onto stainless steel and Corning glass 7059 respectively. The substrates were placed at room temperature on the powered electrode of the reactor and the self bias of this electrode was adjusted by an appropriate r.f. power to lie between 0 and 200 V, thereby changing the film character from polymer-like to DLC. X-ray and UV excited photoelectron spectroscopy as well as photoyield experiments were performed in situ as described elsewhere [S]. Optical transmission and ESR experiments were performed on reference samples deposited under identical conditions onto the Corning glass substrates. For the ESR experiments a standard Bruker x-band spectrometer was used at room temperature and the ESR signal was calibrated to a DPPH standard and also to a sputtered amorphous silicon sample of known spin density. We estimate the absolute accuracy obtained by that procedure for the spin densities to be a factor of two. Characteristic parameters of the sample series obtained from photoemission and optical spectroscopy are summarized in Table 1 in order to illustrate the transition from polymer-like to DLC.
28
18
16
14 -1
Fig. 1 shows the occupied density of states (ODOS) as obtained by the derivative of the photoyield spectra [6] with reference to the Fermi level. The spectra of the 50 V and 140 V samples have been omitted and the others offset by a factor of 100 for clearer presentation. Careful calibration of the absolute ODOS values, which is crucial for the type of analysis intended, was performed by comparison with UPS spectra where the 71 band of
from photoelectron
Self bias (V)
sp2 content
0 25 50 90 140 200
14 22 22 30 27 37
(%)
and optical Plasmon 19.5 20.5 21.5 22.3 22.7 23.3
spectroscopy
energy
(eV)
2
’
3
4
Fig. 1. Occupied density of states with respect to the Fermi level as obtained from the derivative of the photoyield spectra on amorphous carbon. The curves are labeled with the self bias with which the samples were prepared and are offset for clarity. For the polymer-like 0 V sample the fit of the three gaussian bands D2, Dl and K to the density of states is also shown. The vertical bars in the spectra indicate up to which binding energy states have to be singly occupied to account for the measured spin densities. The labels at the bars are the corresponding lower limits for the correlation energy (in electronvolts).
spectra
Table 1 Sample characterisation
F
Binding Energy (eV)
3. Results 3.1. Photoyield
o=E
states could be identified unambigously and fitted to a gaussian density of states. From the ratio of the rc and 0 density of states in the UPS spectra the total ratio of rc and 0 electrons in the samples was extracted using photoemission cross-sections which were calibrated by
data Optical 4.00 3.8 3.05 2.45 2.10 1.90
gap E,, (eV)
Refractive 1.53 1.54 1.61 1.74 1.68 1.97
index
Work function
(eV)
2.60 2.15 3.10 3.25 3.40 3.40
Parameters that illustrate the transition from polymer-like to diamond-like amorphous carbon with increasing self bias of the substrate electrode. The sp’ content was determined from analysis of the UV excited photoemission data (UPS) of the n band density of states [S]. The plasmon energy was extracted from photoelectron energy loss spectra and scales with the square root of the density of the material. The optical gap and refractive index were determined from transmission experiments, and the work function from the photoyield spectra.
comparison with graphite. Using that ratio in conjunction with the total valence electron density as obtained from the plasmon energy of the photoelectron energy loss spectra, the density of rr electrons in that band could be derived and compared with the gaussian fit. From this comparison, the density of states at the peak position of the rc band was extracted on an absolute scale and transferred to the ODOS spectra of Fig. 1. The procedure is described in more detail in Ref. [S]. Moreover, the work function of the samples was obtained directly as the photoemission threshold of the photoyield spectra and is also given in Table 1. It ranges from very low values (2.6 eV) for polymer-like samples to approximately 3.4 eV for the DLC material. Owing to the high sensitivity of the photoyield technique, the density of gap states can be measured all the way down to the Fermi level. Besides the tail of the rc band, two other gaussian bands have been fitted to the ODOS whose physical origin is unclear as yet. For the purpose of this paper the fit of those bands can be
.g E
21 -
0” zo-
E
5
=“-
19-
a, +.
D2
18-
-
Self Bias (V) Fig. 2. (a) Band position and (b) total integrated electron density of the three gaussian bands fitted to the ODOS spectra of Fig. 1. In addition, the ESR spin densities of the samples are shown in (b).
Table 2 ESR line parameters Self bias (V)
0
25 50 90 200
and spin densities
for a-C:H
Film thickness
0.30 0.25 0.26 0.74 0.58
(pm)
considered as a pure parameterization of the density of states observed spectroscopically. The parameters of the n band and the two defect bands Dl and D2 are shown in Fig. 2. While the numbers of states under the 71band and the Dl band increase with self bias by a factor of 3 and 5 respectively, the D2 band decreases by almost two orders of magnitude reflecting a decrease in the density of states at the Fermi level. Note that for the 200 V sample this density of states at the Fermi level is of the order of 10lh cmP3 only (Fig. 1).
3.2. Electron spin resonance The results of ESR are listed in Table 2. The g value of the spin signal for all samples was around 2.0035 for the DLC films, with a slight tendency to larger values for the polymer-like films. The peak-to-peak linewidth of the spectra (in their original derivative form) increased from 8.2 G for the 0 V sample to 14.6 G for the 90 V sample and decreased again to 7.3 G for the 200 V sample. A most dramatic change, however, was seen in the spin density which increased from around 5 x 10” cmm3 for polymer-like samples to 1 x 10” cm-.” for DLC. For the samples deposited with bias voltages of 50 V and more, the statistics of the spin signal was sufficient for a line form analysis which revealed a perfect Lorentzian shape. Note that the spin densities of the 90 V and 200 V samples exceed 7.5 x 1015 cm-’ when projected onto the surface or interface of the samples, which is more than the density of surface atoms! This is a clear indication of the bulk character of the paramagnetic centers. For a first comparison with the yield data, the spin densities of Table 2 have been included in Fig. 2(b). Above 100 V self bias the relative contributions of the Dl, D2 and rc band to the density of states as well as the ESR line parameters and spin density show saturation, indicating that the structural transition from polymer-like to DLC is essentially completed at this point. For the latter samples the spin density reaches approximately a quarter of the total density of states in the Dl band, which implies that a considerable part of that band is singly occupied with electrons.
samples ,T value
Line width AH,,
2.0040 2.0044 2.0045 2.0036 2.0036
x.2 8.2 10.0 14.6 7.3
(G)
Spin density (cm-“) 7.3 5.5 2.9 1.30 1.33
x x x x x
10” 10” 10’” lo*” 10Z”
J. Ristein et al/Diamond and Related Materials 4 (1995) 508-516
4. Discussion 4.1. Current understanding
of the gap states in amorphous
carbon
It is generally accepted for amorphous carbon that the density of states at the top of the valence band and the bottom of the conduction band is due to electrons in p-type orbitals on sp’ hybridized atoms (7~electrons) which do not participate in the g bonds of those atoms. The local arrangement of the sp2 atoms determines the interaction of the 71electrons with one another, and it is this interaction which is responsible for the specific form of the density of states at the band edges and within the gap. It is further accepted that p orbitals on adjacent atoms tend to align parallel to maximize their overlap and thus form form 7c bonds. The splitting of bonding and antibonding states for an isolated, perfect n-bond in ethylene is 5.8 eV [7]. Correspondingly the average separation between n and X* states in amorphous carbon is found to be around 6 eV. x and X* density of states, however, form broad bands extending into the band gap. Two qualitatively different mechanisms have been suggested for this broadening and are still discussed controversely. On the one hand, Robertson suggested a pronounced clustering of sp’ atoms to groups of aromatic rings. In a simple Htickel approximation the HOMO-LUMO gap of the eigenvalue spectrum of the 71 electrons decreases for such a model with increasing cluster size [7]. The closing of the optical gap on going from polymer-like to diamond-like carbon is thus interpreted as an increase in the average size of aromatic clusters in the material. Within that model a distinct defect density of states within the gap can be interpreted as isolated orbitals close to the Fermi level of odd numbered clusters, the so called 7~defects [ 71. On the other hand, molecular dynamics calculations of amorphous carbon show no sign of aromatic clustering. Instead, 7c electrons tend to form isolated double bonds or small chain segments [S]. The tailing of the X-Z* bands into the gap in this model is due to a statistical deviation of the p orbital overlap from its maximum value which is enforced by the rigidity of the surrounding network. With the transformation from polymer-like to diamond-like carbon, this tailing is expected to increase, explaining again the closing of the optical gap. Defects in this model now have to be understood as isolated, non-bonding orbitals. Depending on the hybridization of their host atoms they are expected to vary in character between p type (on sp2 sites) and sp3 type (on sp3 sites) which would in the latter case correspond to the classical dangling bond in amorphous silicon. 4.2. The concept of correlation
energies
In the single-electron approximation for the wave functions of a solid, the density of states will in general
511
be filled pairwise by electrons in order of their orbital energy. In this approximation compensation of all electronic spins is expected, which is perfect at zero temperature and only weakly reduced by the Fermi occupation statistics at finite temperature. In order to explain paramagnetic behavior in ESR experiments, correlation effects have to be considered which prevent spin pairing. In its simplest form this can be done by associating a correlation energy U with each electronic state. For the ionization of an electron from a state with orbital energy E thus two cases have to be distinguished. If the electronic state is occupied only by the electron under consideration, the ionization energy is simply the energy difference E,,, - E between the vacuum level and the respective obital. If, however, two electrons reside in that specific state, then the energy necessary to excite one of them into the vacuum is now different from the first case. Since both electrons are indistinguishable this modified value for the ionization energy has to be assigned to both electrons in the state. The correlation energy U is defined as just the difference between the ionization energies in the first case and the second case, thus for the situation of double occupation the ionization as energy is E,,, - E - U. In general, electron-electron well as electron-phonon interactions contribute to the correlation energy and as a consequence U is an effective correlation energy given by the difference of the Coulomb repulsion between the two electrons and the energy gained by lattice relaxation after the second electron is put into the state. Both contributions, of course, depend on the wavefunction of the state. Thus U is generally not a constant. For example, U is expected to be smaller, the larger the spatial extention of the electron state under consideration is, owing to a reduction in Coulomb repulsion. This effect was discussed for example in conjunction with field effect measurements in amorphous silicon by considering a gradually decreasing value for the correlation energy when going from mid gap defect states to valence band tail states, reaching U = 0 at the valence band mobility edge [ 91. In cases of strong electron-phonon coupling U can even be negative, as is found in low coordinated semiconductors with lone pair p electrons (chalcogenides). Since for the other amorphous semiconductors of group IV elements, e.g. silicon and germanium, U is found experimentally to be positive [lo], and only positive U values can explain the ESR results in our experiment, we only consider this case in the following. Making U a function of orbital energy, U(E), as was done in Ref. [9] is strictly speaking also an approximation because even for the same orbital energy, different wavefunctions, different coulomb interaction and electron-phonon coupling will generally result in different correlation energies. In general, therefore, U has to be assigned along with E as a second independent variable to each electronic state. Thus, the density of
J. Ristein et 01. ,‘Diamond and Related Materials
512
states is now to be considered as a two-dimensional distribution function p(E,U). p(E,U)dEdU is the density of electronic states with orbital energies between E and E + dE and correlation energies between U and U + dU. The relative contributions of unoccupied, singly occupied and doubly occupied states to p(E,U) are then ,f,‘,y(E,U) = exp
$$ (
i
[2+TJ(‘-~f “)+exp($$)]P1 ,f~,~(E,U)=2~2+expjli-:1-
(1)
u)+eq[G]]p’
(2) fi$(E,U)
= exp(’
-:i
[2+exp(“+f[
“)
“),exp($$)]-’
(3)
respectively [ 111. Note that the variable E in these and all the formulae following describes single-electron orbital energies, while the energy scales on Figs. 1, 2(a), 3 and 4 refer to binding energies and thus are counted in the opposite direction. The functions above still depend on the chemical potential /L common to all electrons in the system and the temperature T as parameters. We use the terms “chemical potential” and “Fermi energy” as synonyms in the following. From Eqs. ( 1 )-( 3) the average occupation function (n) for p(E,U) follows immediately:
The indices p and T have been omitted for (n), as is done in the following. In most cases the statistical character of U is neglected for simplicity. For example, for amorpous silicon a constant correlation energy U, for deep defects and U =0 for the band tail states is assumed which in the formalism above is translated to p(E,U) = D,(E)G(U)+D,(E)G(UU,), where D,(E) and D,(E) are the conventional tail state and defect densities of states respectively. We later adopt the same level of approximation by replacing conceptually D, by the density of states of the 7~band. To illustrate the formalism and point out its general character we would like to discuss this rc band density of states in a simple tight binding scheme of single 7~ bonds. According to the disorder of the lattice, the
4 i 199.5) 508-516
hybridization of the two atoms 1 and 2 participating in the bond will deviate statistically from sp2, say as The difference 6, ~ 6, sp:+6 and spit6 respectively. results in a statistical difference AE, between the 7~ orbitals on atoms 1 and 2. Depending on the overlap of the p orbitals, a transfer matrix element j will result which together with AE, determines the energies E,, E, and wavefunctions of the bonding and antibonding orbitals of the bond. Owing to the statistical distribution of AE, and j, the energies E, and E, will form the 7~and 7~* bands respectively. The situation is sketched out in the insert of Fig. 3(a) for the limiting case j >>AE,, i.e. a relaxed network with strong n bonds. In this case bonding and antibonding states are clearly seperated in energy, as shown by the (single-electron) density of states D(E) in Fig. 3(a). In the other limit, j <
-
Orbital Energy
EF=m
Binding
Energy
-
Fig. 3. Electrons in a simple tight hinding picture. Depending on the transfer matrix element J either clearly seperated bonding and antibonding states evolve (a) or both types of states merge into a defect band (b). In both cases a correlation U,, (assumed to be constant for this illustration) can be assigned to the smgle electron orbitals which results in an average occupation functions (n)(E.U,) as shown.
J. Ristein et al.!Diamond
and Related Materials
cated in the figure. Essentially the part of the DOS between p and p - U will be occupied with one electron (exact for T=O) and contribute to the spin signal in an ESR experiment which consequently increases with U/AE,. Also for the bonding and antibonding states of Fig. 3(a) a finite correlation energy is expected and for simplicity the same value as in (b) is indicated in the figure. However, if splitting of bonding and antibonding density of states is considerably larger than U, the bonding states will essentially be doubly occupied and the antibonding states will be empty; no ESR signal is expected in this case. It should be stressed explicitly that in this framework isolated defects and covalent bonds are just limiting cases of the same general concept. Depending on j and AE,, situations in between can result. The distinction between the tails of the n and n* bands and dangling bond defects eventually becomes meaningless; only the orbital energy E and correlation energy U characterize the states and determine their occupation with electrons. Note that the concept of orbital energy and correlation energy can, of course, also be applied to the gap states in the aromatic cluster model, although wavefunctions are in this case expected to be less localized and correlation energies should be smaller.
4 (1995) 508-516
The ESR spin density N, is just amount of singly occupied states 00
The photoyield experiment probes occupied electronic states by excitation of electrons to the vacuum level and monitoring of the total photoelectron yield as a function of the photon energy used. Assuming a constant matrix element for the transitions into states close to the vacuum level, the derivative of the photoyield spectrum equals the spectrum S(E) of electron energies with respect to the vacuum level (ODOS). In the framework of a singleparticle density of states with correlation energies sketched out above, this spectrum is given by
s
Cf:,?(E,UME,U)
0
+2fj,y (E - U,U)p(E - U,U)]dU
(5)
The first term in the integral stands for singly occupied and the second for doubly occupied states, which are seen twice as efficiently and at higher energies U compared with the singly occupied states. For the special case of a single correlation energy U. for all states, i.e. p(E,U,)=D(E)G(U - U,), Eq. (5) reduces to S(E)=f:,~(E,Uo)D(E)+2f:,~(E
by the total
Cf:,y
W%@,WdU
dE
(7)
i
,ij -CR 0 which again reduces
for constant
U = U. to
cc
-00
In the low temperature limitf:,? (E,U,) is a box function, i.e. it equals 1 for energies between ,LL - U. and p, and is 0 elsewhere (compare also (n(E)) in Fig. 3). N, is thus essentially given by the integral of the density of states D(E) extending from the Fermi energy to an energy that is lower by the correlation energy. From Eq. (6) S(E) is seen to be an upper limit for the integrand in Eq. (8), S(E) >fi,y (E,U,)D(E). Thus a strict lower limit UO,min for the correlation energy U, can be readily obtained from the ODOS spectra S(E) of Fig. 1 and the spin densities N, by m N, =
i
S(E)dE
(9)
Cl,, min
The lower limits for the correlation energy (assumed to be constant) as obtained from Eq. (9) are indicated by labeled vertical bars in the spectra of Fig. 1. While for the polymer-like samples lower values of about 0.2 eV are found, the very high spin densities in the diamondlike material along with the fairly low occupied density of states close to the Fermi level (see Fig. l), require correlation energies of at least 1.5 eV. Although this estimate has to be reduced in the case of band bending (see Section 4.5), unusually high correlation energies for the defects in DLC are already expected from this coarse evaluation of the raw data. 4.4. Fitting of the spectroscopic density of states curves
co
S(E) =
given
co
N, =
p4.3. Photoyield spectra and electron spin resonance signal
513
- Uo,Uo)D(E
- Uo) (6)
In the last section a lower limit for the correlation energy was obtained directly from the ODOS spectra of Fig. 1 and a rather large value for the DLC samples around 1.5 eV was found. In the following we want to analyze the spectrum of the 200 V sample further under the assumption that the spin signal originates from a gaussian defect band with fixed correlation energy U,. Following Eq. (6) it is easily seen that besides the singly occupied density of states with orbital energy E = p, the density of states at E = p - U, also contributes to the ODOS spectrum S(E) at the Fermi level. The value of the order of 1016 cmP3 (Fig. 1) implies that the density of states of the defect band at y - U. is of approximately that magnitude as well. Thus we have qualitatively three
J. Ristein et ~l.!Diornond und Rehted
514
Muteriu1.y 4 i 1995) 50X-SI6
Fig. 4(a) shows a fit to the ODOS spectrum of the 200 V sample which fulfils these requirements. A single gaussian band, centered at 1.65 eV below the Fermi level with an FWHM of 0.7 eV and a peak amplitude of 4 x 10” cm-’ eV3 was used for the defect density of states D,(E). Note that the parameters of this band are close to those of the Dl band originally fitted phenomenologically to the ODOS spectrum. A second broader gaussian band centered at 4 eV below the Fermi level was used to simulate the density of states D,(E) of the 71 and Dl bands. The superposition of both bands, i.e. the total density of states D(E) = D,(E) + D,(E), is shown as the dotted curve in Fig. 4(a). A constant U, was then assigned to the defect band D,(E) and no correlation
restrictions for the defect band to explain the ODOS spectra and the spin densities of the diamond-like samples simultaneously. (1) The integrated density of states in the band has to be high enough to explain the large ESR signal of the order of (10” crne3 ), thus a peak amplitude 10” crn3 eV1 is expected. (2) Considering its large amplitude, the peak position of the band has to be far enough below the Fermi level to be consistent with the observed ODOS spectrum S(E). (3) The correlation energy has to be high enough to guarantee single occupation of the band and sufficiently low density of doubly occupied states at p - U, which are shifted spectroscopically to the Fermi level.
experimental ODOS
S(E)_
2. .=
E &
16
14
3
experimental
o=E,
1
ODOS
2
3
4
Binding Energy (eV) Fig. 4. Two fits to the ODOS including a downward surface
spectrum of the diamond-like band bending and a constant
200 V sample: (a) homogeneous model with singly occupied defect band, (b) model correlation energy assigned to the complete density of gap states. For details see text.
J. Ristein et al./Diamond
and Related Materials
tE
“r-_-n*
probe depth for photoyield Fig. 5. Illustration of the effect of possible surface band bending on determination of the correlation energies from photoyield and ESR experiments. Band bending leads to a difference in energy position of the Fermi level within the DOS at the surface and in the bulk which has to be taken into account. For details see text.
energy (U =0) to the rt and D2 density of states, thus p(E,U) = D,(E)& U) + D,(E)@ U - U,). Within this model the spin density according to Eq. (7) and the ODOS spectrum S(E) according to Eq. (5) were then calculated. In order to fit both experimental quantities a correlation energy of U,= 3.0 eV turned out to be necessary. The resulting fitted curve S(E) as well as the singly occupied density of stages n’(E) =f$j (E,U,)D,(E) (dashed curve) are also shown in Fig. 5(a). The integral over n’(E), was within a factor of 2 consistent, however at the expense of an unusually high correlation energy which exceeds the lower limit estimate (see Section 4.3.) roughly by a factor of 2. 4.5. The effect of band bending The very large correlation energies necessary in the analysis for the DLC samples above are the result of a conflict between two experimental results: on the one hand a very high spin density and on the other hand a comparatively low density of states at the Fermi level. A possible mechanism which de-escalates that conflict could be a surface band bending in the DLC samples as scetched out in Fig. 5. The photoyield experiment probes the sample volume close to the surface (10 nm) while the ESR experiment as an integrating technique is dominated by the bulk properties. Surface band bending locally leads to a different energetic position of the Fermi level within the density of states. If a downward band bending V as indicated in the figure is present, the minimum correlation energy necessary to guarantee single occupation of enough states is reduced in the bulk by V compared with the surface. To estimate this influence, a second fit of the ODOS spectrum of the 200 V sample is given in Fig. 4(b). The density of states D(E)
4 (1995) 508-516
515
is modeled again by the two gaussian bands D,(E) and D,(E) as in Fig. 4(a); this time, however, a finite correlation energy UO= 1.5 eV is assigned to both of them, p(E) = D(E)G(U - U,). Owing to the steep increase in D(E) with increasing binding energy, the occupied density of states is essentially S(E)=2f$,q (E - U,,U,)D(EU,) (Eq. (6)). Thus S(E) is simply given by D(E), but shifted by U0 towards lower binding energy and multiplied by a factor of two (indicated in the figure). Remember that the variable E in the formulae describes single electron orbital energies while the energy scales on the figures refer to binding energies and are counted in the opposite direction. This shift and scaling was compensated by shifting the complete density of states D(E) by the correlation energy towards higher binding energy and decreasing D,(E) by a factor of 2, both in comparison with the fit of Fig. 4(a). With this model an equally good fit of the ODOS spectra is obtained in Fig. 4(b), albeit this time with half the correlation energy! The spin density in this case, however, is only 4 x 1014 cmP3, inconsistent with the experimental result. Note that the situation analyzed so far corresponds to the surface region of the sample probed by the photoyield (Fig. 5). If a downward surface band bending of V is assumed, the Fermi level in the bulk is closer by V to the valence band edge, i.e. at a binding energy V larger. The singly occupied density of states in the bulk is again readily calculated as r~‘(E)=f~~,)~ (E,U,D(E) by just using the modified value pg for the bulk Fermi level (dashed curve in Fig. 4(b)). Taking (as an estimate for an upper limit) a band bending of 1.5 eV into account, a spin density of 7 x 10” cme3 results, which is again consistent with the experimental value within a factor of 2. Comparing the two fits of Fig. 4 shows that part of the correlation energy necessary to explain ESR and photoyield in a spatially homogeneous model for DLC (3.0 eV in our case) can be substituted by a downward surface band bending (1.5 eV). It should be mentioned that exactly the same effect of a different position of the Fermi level seen by the photoyield and the ESR experiment can also be the result of formation of a Schottky barrier at the stainless steel substrates of our comparatively thin a-C:H samples (100 nm) used for the photoemission experiments.
5. Conclusions From the comparison of ESR and photoyield results on identical a-C:H samples whose character varied from polymer-like to diamond-like, a lower limit for the correlation energy of the gap states in the material can be obtained. While for the polymer-like samples this limit is set around 0.25 eV, DLC samples require unusually high correlation energies to explain the low density
516
J. Ristein et allDiamond and Related Materials 4 (199.5) 508-516
of states at the Fermi level and the large spin density. Even if part of this effect is explained by surface band bending, values for U, in excess of 1 eV are necessary to fit the spectroscopic photoyield densities of states and the spin densities simultaneously. This result may either point to a large Coulomb contribution to the effective correlation energy, possibly due to strong localization of the defect states, or to a strong supression of lattice relaxation in diamond-like carbon.
References [l] [2] [3] [4] [S] [6] [7] [S]
Acknowledgement [9]
We thank Professor M. Stutzmann and Dr. S. Schtitte for performing the ESR experiments on our samples discussed in this work.
[lo] [l l]
M. Frischholz, Th. Mandel, R. Helbig, G. Schmidt and A. Hammerschmidt, Diamond Relat. Mater., 2 (1993) 778. D. Dasgupta, F. Demichelis, C.F. Pirri and A. Tagliaferro, Phys. Reo. B, 43 (1991) 2131. A. Reyes-Mena, R. Asomoza, J. Gonzalez-Hernandez and S.S. Chao, J. Non-Cryst. Solids, 114 (1989) 310. K. Fabisiak, F. Rozploch and J. Wieczorek, J. Phys. D, 21 (1988) 995. J. Schafer, J. Ristein and L. Ley, Diamond Relat. Mater., 3 (1994) 861. K. Winer and L. Ley, PhJx Reo. B, 36 (1987) 6072. J. Robertson and E.P. O’Reilly, Phys. Rec. B, 35 (1987) 2946. U. Stephan, Th. Frauenheim, P. Blaudeck and G. Jungnickel, Phys. Rec. B, 49 (1994) 1489. L. Schweitzer, M. Griinewald and H. Dersch, Solid State Cornmun.,39 (1981) 355. J. Stuke, J. Non-Cryst. Solids, 97-98 (1987) 1. H. Okamoto and Y. Hamakawa, Solid State Commun., 24 (1977) 23.
Effective correlation energies for defects in a-C:H from a comparison photelectron yield and electron spin resonance experiments
of
J. Ristein, J. Schgfer, L. Ley Inzstitutfb
Technische
Physik,
Universitiit
Erlangen,
Erwin-Rommel-StraJe
1, D-91058
Erlangen,
Germany
Abstract Amorphous hydrogenated carbon films (a-C:H) were deposited by r.f. plasma CVD from methane, varying the self bias potential of the substrate electrode by means of the r.f. power coupled into the discharge. Films were characterized by IR and optical spectroscopy, confirming a transition from polymer-like to diamond-like (DLC) material with increasing self bias. One set of samples was investigated in situ by photoelectron and photoelectron yield spectroscopy, from which the density of gap states and their spectral distribution was derived. An identical set of samples was then examined by electron spin resonance to determine the density of paramagnetic defects. From a comparison of the results of both experiments, a lower limit for the effective correlation energy of the defect states was extracted which gave surprisingly large values for the correlation energy of the DLC material. In addition to the interpretation of the results within a spatially uniform model, the influence of a possible surface band bending on the evaluation of the correlation energies is also discussed. K~JWJ~& Amorphous
hydrogenated
carbon;
Electron
paramagnetic
1. Introduction Hydrogenated amouphous carbon (a-C:H) as prepared by CVD from hydrocarbon gases can be produced with strongly varying mechanical and electronic properties by changing the deposition parameters. When deposited from a capacitively coupled r.f. glow discharge, the most critical parameter has been proven to be the negative bias of the substrate electrode which controls the kinectic energy with which the film-forming radicals from the plasma hit the growing surface. By changing this bias the character of resulting a-C:H films can be gradually changed from soft polymer-like films with a large optical band gap to hard so-called diamond-like films (DLC) with smaller optical band gap which are covering an extending field of applications as protective IR transparent coatings or as passivation layers on semiconductor devices [ 11. The variety of mechanical and optical properties accessible with amorphous carbon thin films is due to the various forms of bonding a carbon atom can adopt and the accompanying changes in hybridization. The transformation from polymer-like to diamond-like a-C:H is accompied by a gradual increase in the sp’ 0925-9635/95/$09.50 0 1995 Elsevier Science S.A. All rights reserved SSDI 0925-9635(94)05272-7
resonance;
Defects
content and a decrease in hydrogen concentration. The electronic states close to the pseudogap of the material are thus derived from the 71electrons which necessarily come along with each sp’ bonded carbon atom. Thus the density of states in the pseudogap including localized defects and also the optical properties depend on the type of interaction of these n electrons. The tailing of valence and conduction band density of states into the gap is observed experimentally to increase with increasing sp2 content, and there are essentially two microscopic mechanisms responsible for this, as reviewed briefly in Section 4. In the following paper we focus on the properties of the gap states in a-C:H using a combination of two complementary experimental techniques, photoelectron yield spectroscopy (photoyield) and electron spin resonance (ESR). The ESR results on a-C:H published so far show as a general tendency an increase in spin density of several orders of magnitude when going from polymer-like to DLC samples [ 2-41. The results, however, depend sensitively on the details of the deposition and preparation process (source gas, deposition and annealing temperature, reactor design, r.f. power etc.). Thus in order to combine photoyield and ESR results, they had to be obtained on identical samples.
J. Ristein et al. JDiamond and Related Materials 4 (199.5) 508-516
2. Experimental
details and sample characterization
32
Identical samples for photoemission and photoyield spectroscopy and for optical and ESR experiments were deposited by r.f. plasma decomposition of methane onto stainless steel and Corning glass 7059 respectively. The substrates were placed at room temperature on the powered electrode of the reactor and the self bias of this electrode was adjusted by an appropriate r.f. power to lie between 0 and 200 V, thereby changing the film character from polymer-like to DLC. X-ray and UV excited photoelectron spectroscopy as well as photoyield experiments were performed in situ as described elsewhere [S]. Optical transmission and ESR experiments were performed on reference samples deposited under identical conditions onto the Corning glass substrates. For the ESR experiments a standard Bruker x-band spectrometer was used at room temperature and the ESR signal was calibrated to a DPPH standard and also to a sputtered amorphous silicon sample of known spin density. We estimate the absolute accuracy obtained by that procedure for the spin densities to be a factor of two. Characteristic parameters of the sample series obtained from photoemission and optical spectroscopy are summarized in Table 1 in order to illustrate the transition from polymer-like to DLC.
28
18
16
14 -1
Fig. 1 shows the occupied density of states (ODOS) as obtained by the derivative of the photoyield spectra [6] with reference to the Fermi level. The spectra of the 50 V and 140 V samples have been omitted and the others offset by a factor of 100 for clearer presentation. Careful calibration of the absolute ODOS values, which is crucial for the type of analysis intended, was performed by comparison with UPS spectra where the 71 band of
from photoelectron
Self bias (V)
sp2 content
0 25 50 90 140 200
14 22 22 30 27 37
(%)
and optical Plasmon 19.5 20.5 21.5 22.3 22.7 23.3
spectroscopy
energy
(eV)
2
’
3
4
Fig. 1. Occupied density of states with respect to the Fermi level as obtained from the derivative of the photoyield spectra on amorphous carbon. The curves are labeled with the self bias with which the samples were prepared and are offset for clarity. For the polymer-like 0 V sample the fit of the three gaussian bands D2, Dl and K to the density of states is also shown. The vertical bars in the spectra indicate up to which binding energy states have to be singly occupied to account for the measured spin densities. The labels at the bars are the corresponding lower limits for the correlation energy (in electronvolts).
spectra
Table 1 Sample characterisation
F
Binding Energy (eV)
3. Results 3.1. Photoyield
o=E
states could be identified unambigously and fitted to a gaussian density of states. From the ratio of the rc and 0 density of states in the UPS spectra the total ratio of rc and 0 electrons in the samples was extracted using photoemission cross-sections which were calibrated by
data Optical 4.00 3.8 3.05 2.45 2.10 1.90
gap E,, (eV)
Refractive 1.53 1.54 1.61 1.74 1.68 1.97
index
Work function
(eV)
2.60 2.15 3.10 3.25 3.40 3.40
Parameters that illustrate the transition from polymer-like to diamond-like amorphous carbon with increasing self bias of the substrate electrode. The sp’ content was determined from analysis of the UV excited photoemission data (UPS) of the n band density of states [S]. The plasmon energy was extracted from photoelectron energy loss spectra and scales with the square root of the density of the material. The optical gap and refractive index were determined from transmission experiments, and the work function from the photoyield spectra.
comparison with graphite. Using that ratio in conjunction with the total valence electron density as obtained from the plasmon energy of the photoelectron energy loss spectra, the density of rr electrons in that band could be derived and compared with the gaussian fit. From this comparison, the density of states at the peak position of the rc band was extracted on an absolute scale and transferred to the ODOS spectra of Fig. 1. The procedure is described in more detail in Ref. [S]. Moreover, the work function of the samples was obtained directly as the photoemission threshold of the photoyield spectra and is also given in Table 1. It ranges from very low values (2.6 eV) for polymer-like samples to approximately 3.4 eV for the DLC material. Owing to the high sensitivity of the photoyield technique, the density of gap states can be measured all the way down to the Fermi level. Besides the tail of the rc band, two other gaussian bands have been fitted to the ODOS whose physical origin is unclear as yet. For the purpose of this paper the fit of those bands can be
.g E
21 -
0” zo-
E
5
=“-
19-
a, +.
D2
18-
-
Self Bias (V) Fig. 2. (a) Band position and (b) total integrated electron density of the three gaussian bands fitted to the ODOS spectra of Fig. 1. In addition, the ESR spin densities of the samples are shown in (b).
Table 2 ESR line parameters Self bias (V)
0
25 50 90 200
and spin densities
for a-C:H
Film thickness
0.30 0.25 0.26 0.74 0.58
(pm)
considered as a pure parameterization of the density of states observed spectroscopically. The parameters of the n band and the two defect bands Dl and D2 are shown in Fig. 2. While the numbers of states under the 71band and the Dl band increase with self bias by a factor of 3 and 5 respectively, the D2 band decreases by almost two orders of magnitude reflecting a decrease in the density of states at the Fermi level. Note that for the 200 V sample this density of states at the Fermi level is of the order of 10lh cmP3 only (Fig. 1).
3.2. Electron spin resonance The results of ESR are listed in Table 2. The g value of the spin signal for all samples was around 2.0035 for the DLC films, with a slight tendency to larger values for the polymer-like films. The peak-to-peak linewidth of the spectra (in their original derivative form) increased from 8.2 G for the 0 V sample to 14.6 G for the 90 V sample and decreased again to 7.3 G for the 200 V sample. A most dramatic change, however, was seen in the spin density which increased from around 5 x 10” cmm3 for polymer-like samples to 1 x 10” cm-.” for DLC. For the samples deposited with bias voltages of 50 V and more, the statistics of the spin signal was sufficient for a line form analysis which revealed a perfect Lorentzian shape. Note that the spin densities of the 90 V and 200 V samples exceed 7.5 x 1015 cm-’ when projected onto the surface or interface of the samples, which is more than the density of surface atoms! This is a clear indication of the bulk character of the paramagnetic centers. For a first comparison with the yield data, the spin densities of Table 2 have been included in Fig. 2(b). Above 100 V self bias the relative contributions of the Dl, D2 and rc band to the density of states as well as the ESR line parameters and spin density show saturation, indicating that the structural transition from polymer-like to DLC is essentially completed at this point. For the latter samples the spin density reaches approximately a quarter of the total density of states in the Dl band, which implies that a considerable part of that band is singly occupied with electrons.
samples ,T value
Line width AH,,
2.0040 2.0044 2.0045 2.0036 2.0036
x.2 8.2 10.0 14.6 7.3
(G)
Spin density (cm-“) 7.3 5.5 2.9 1.30 1.33
x x x x x
10” 10” 10’” lo*” 10Z”
J. Ristein et al/Diamond and Related Materials 4 (1995) 508-516
4. Discussion 4.1. Current understanding
of the gap states in amorphous
carbon
It is generally accepted for amorphous carbon that the density of states at the top of the valence band and the bottom of the conduction band is due to electrons in p-type orbitals on sp’ hybridized atoms (7~electrons) which do not participate in the g bonds of those atoms. The local arrangement of the sp2 atoms determines the interaction of the 71electrons with one another, and it is this interaction which is responsible for the specific form of the density of states at the band edges and within the gap. It is further accepted that p orbitals on adjacent atoms tend to align parallel to maximize their overlap and thus form form 7c bonds. The splitting of bonding and antibonding states for an isolated, perfect n-bond in ethylene is 5.8 eV [7]. Correspondingly the average separation between n and X* states in amorphous carbon is found to be around 6 eV. x and X* density of states, however, form broad bands extending into the band gap. Two qualitatively different mechanisms have been suggested for this broadening and are still discussed controversely. On the one hand, Robertson suggested a pronounced clustering of sp’ atoms to groups of aromatic rings. In a simple Htickel approximation the HOMO-LUMO gap of the eigenvalue spectrum of the 71 electrons decreases for such a model with increasing cluster size [7]. The closing of the optical gap on going from polymer-like to diamond-like carbon is thus interpreted as an increase in the average size of aromatic clusters in the material. Within that model a distinct defect density of states within the gap can be interpreted as isolated orbitals close to the Fermi level of odd numbered clusters, the so called 7~defects [ 71. On the other hand, molecular dynamics calculations of amorphous carbon show no sign of aromatic clustering. Instead, 7c electrons tend to form isolated double bonds or small chain segments [S]. The tailing of the X-Z* bands into the gap in this model is due to a statistical deviation of the p orbital overlap from its maximum value which is enforced by the rigidity of the surrounding network. With the transformation from polymer-like to diamond-like carbon, this tailing is expected to increase, explaining again the closing of the optical gap. Defects in this model now have to be understood as isolated, non-bonding orbitals. Depending on the hybridization of their host atoms they are expected to vary in character between p type (on sp2 sites) and sp3 type (on sp3 sites) which would in the latter case correspond to the classical dangling bond in amorphous silicon. 4.2. The concept of correlation
energies
In the single-electron approximation for the wave functions of a solid, the density of states will in general
511
be filled pairwise by electrons in order of their orbital energy. In this approximation compensation of all electronic spins is expected, which is perfect at zero temperature and only weakly reduced by the Fermi occupation statistics at finite temperature. In order to explain paramagnetic behavior in ESR experiments, correlation effects have to be considered which prevent spin pairing. In its simplest form this can be done by associating a correlation energy U with each electronic state. For the ionization of an electron from a state with orbital energy E thus two cases have to be distinguished. If the electronic state is occupied only by the electron under consideration, the ionization energy is simply the energy difference E,,, - E between the vacuum level and the respective obital. If, however, two electrons reside in that specific state, then the energy necessary to excite one of them into the vacuum is now different from the first case. Since both electrons are indistinguishable this modified value for the ionization energy has to be assigned to both electrons in the state. The correlation energy U is defined as just the difference between the ionization energies in the first case and the second case, thus for the situation of double occupation the ionization as energy is E,,, - E - U. In general, electron-electron well as electron-phonon interactions contribute to the correlation energy and as a consequence U is an effective correlation energy given by the difference of the Coulomb repulsion between the two electrons and the energy gained by lattice relaxation after the second electron is put into the state. Both contributions, of course, depend on the wavefunction of the state. Thus U is generally not a constant. For example, U is expected to be smaller, the larger the spatial extention of the electron state under consideration is, owing to a reduction in Coulomb repulsion. This effect was discussed for example in conjunction with field effect measurements in amorphous silicon by considering a gradually decreasing value for the correlation energy when going from mid gap defect states to valence band tail states, reaching U = 0 at the valence band mobility edge [ 91. In cases of strong electron-phonon coupling U can even be negative, as is found in low coordinated semiconductors with lone pair p electrons (chalcogenides). Since for the other amorphous semiconductors of group IV elements, e.g. silicon and germanium, U is found experimentally to be positive [lo], and only positive U values can explain the ESR results in our experiment, we only consider this case in the following. Making U a function of orbital energy, U(E), as was done in Ref. [9] is strictly speaking also an approximation because even for the same orbital energy, different wavefunctions, different coulomb interaction and electron-phonon coupling will generally result in different correlation energies. In general, therefore, U has to be assigned along with E as a second independent variable to each electronic state. Thus, the density of
J. Ristein et 01. ,‘Diamond and Related Materials
512
states is now to be considered as a two-dimensional distribution function p(E,U). p(E,U)dEdU is the density of electronic states with orbital energies between E and E + dE and correlation energies between U and U + dU. The relative contributions of unoccupied, singly occupied and doubly occupied states to p(E,U) are then ,f,‘,y(E,U) = exp
$$ (
i
[2+TJ(‘-~f “)+exp($$)]P1 ,f~,~(E,U)=2~2+expjli-:1-
(1)
u)+eq[G]]p’
(2) fi$(E,U)
= exp(’
-:i
[2+exp(“+f[
“)
“),exp($$)]-’
(3)
respectively [ 111. Note that the variable E in these and all the formulae following describes single-electron orbital energies, while the energy scales on Figs. 1, 2(a), 3 and 4 refer to binding energies and thus are counted in the opposite direction. The functions above still depend on the chemical potential /L common to all electrons in the system and the temperature T as parameters. We use the terms “chemical potential” and “Fermi energy” as synonyms in the following. From Eqs. ( 1 )-( 3) the average occupation function (n) for p(E,U) follows immediately:
The indices p and T have been omitted for (n), as is done in the following. In most cases the statistical character of U is neglected for simplicity. For example, for amorpous silicon a constant correlation energy U, for deep defects and U =0 for the band tail states is assumed which in the formalism above is translated to p(E,U) = D,(E)G(U)+D,(E)G(UU,), where D,(E) and D,(E) are the conventional tail state and defect densities of states respectively. We later adopt the same level of approximation by replacing conceptually D, by the density of states of the 7~band. To illustrate the formalism and point out its general character we would like to discuss this rc band density of states in a simple tight binding scheme of single 7~ bonds. According to the disorder of the lattice, the
4 i 199.5) 508-516
hybridization of the two atoms 1 and 2 participating in the bond will deviate statistically from sp2, say as The difference 6, ~ 6, sp:+6 and spit6 respectively. results in a statistical difference AE, between the 7~ orbitals on atoms 1 and 2. Depending on the overlap of the p orbitals, a transfer matrix element j will result which together with AE, determines the energies E,, E, and wavefunctions of the bonding and antibonding orbitals of the bond. Owing to the statistical distribution of AE, and j, the energies E, and E, will form the 7~and 7~* bands respectively. The situation is sketched out in the insert of Fig. 3(a) for the limiting case j >>AE,, i.e. a relaxed network with strong n bonds. In this case bonding and antibonding states are clearly seperated in energy, as shown by the (single-electron) density of states D(E) in Fig. 3(a). In the other limit, j <
-
Orbital Energy
EF=m
Binding
Energy
-
Fig. 3. Electrons in a simple tight hinding picture. Depending on the transfer matrix element J either clearly seperated bonding and antibonding states evolve (a) or both types of states merge into a defect band (b). In both cases a correlation U,, (assumed to be constant for this illustration) can be assigned to the smgle electron orbitals which results in an average occupation functions (n)(E.U,) as shown.
J. Ristein et al.!Diamond
and Related Materials
cated in the figure. Essentially the part of the DOS between p and p - U will be occupied with one electron (exact for T=O) and contribute to the spin signal in an ESR experiment which consequently increases with U/AE,. Also for the bonding and antibonding states of Fig. 3(a) a finite correlation energy is expected and for simplicity the same value as in (b) is indicated in the figure. However, if splitting of bonding and antibonding density of states is considerably larger than U, the bonding states will essentially be doubly occupied and the antibonding states will be empty; no ESR signal is expected in this case. It should be stressed explicitly that in this framework isolated defects and covalent bonds are just limiting cases of the same general concept. Depending on j and AE,, situations in between can result. The distinction between the tails of the n and n* bands and dangling bond defects eventually becomes meaningless; only the orbital energy E and correlation energy U characterize the states and determine their occupation with electrons. Note that the concept of orbital energy and correlation energy can, of course, also be applied to the gap states in the aromatic cluster model, although wavefunctions are in this case expected to be less localized and correlation energies should be smaller.
4 (1995) 508-516
The ESR spin density N, is just amount of singly occupied states 00
The photoyield experiment probes occupied electronic states by excitation of electrons to the vacuum level and monitoring of the total photoelectron yield as a function of the photon energy used. Assuming a constant matrix element for the transitions into states close to the vacuum level, the derivative of the photoyield spectrum equals the spectrum S(E) of electron energies with respect to the vacuum level (ODOS). In the framework of a singleparticle density of states with correlation energies sketched out above, this spectrum is given by
s
Cf:,?(E,UME,U)
0
+2fj,y (E - U,U)p(E - U,U)]dU
(5)
The first term in the integral stands for singly occupied and the second for doubly occupied states, which are seen twice as efficiently and at higher energies U compared with the singly occupied states. For the special case of a single correlation energy U. for all states, i.e. p(E,U,)=D(E)G(U - U,), Eq. (5) reduces to S(E)=f:,~(E,Uo)D(E)+2f:,~(E
by the total
Cf:,y
W%@,WdU
dE
(7)
i
,ij -CR 0 which again reduces
for constant
U = U. to
cc
-00
In the low temperature limitf:,? (E,U,) is a box function, i.e. it equals 1 for energies between ,LL - U. and p, and is 0 elsewhere (compare also (n(E)) in Fig. 3). N, is thus essentially given by the integral of the density of states D(E) extending from the Fermi energy to an energy that is lower by the correlation energy. From Eq. (6) S(E) is seen to be an upper limit for the integrand in Eq. (8), S(E) >fi,y (E,U,)D(E). Thus a strict lower limit UO,min for the correlation energy U, can be readily obtained from the ODOS spectra S(E) of Fig. 1 and the spin densities N, by m N, =
i
S(E)dE
(9)
Cl,, min
The lower limits for the correlation energy (assumed to be constant) as obtained from Eq. (9) are indicated by labeled vertical bars in the spectra of Fig. 1. While for the polymer-like samples lower values of about 0.2 eV are found, the very high spin densities in the diamondlike material along with the fairly low occupied density of states close to the Fermi level (see Fig. l), require correlation energies of at least 1.5 eV. Although this estimate has to be reduced in the case of band bending (see Section 4.5), unusually high correlation energies for the defects in DLC are already expected from this coarse evaluation of the raw data. 4.4. Fitting of the spectroscopic density of states curves
co
S(E) =
given
co
N, =
p4.3. Photoyield spectra and electron spin resonance signal
513
- Uo,Uo)D(E
- Uo) (6)
In the last section a lower limit for the correlation energy was obtained directly from the ODOS spectra of Fig. 1 and a rather large value for the DLC samples around 1.5 eV was found. In the following we want to analyze the spectrum of the 200 V sample further under the assumption that the spin signal originates from a gaussian defect band with fixed correlation energy U,. Following Eq. (6) it is easily seen that besides the singly occupied density of states with orbital energy E = p, the density of states at E = p - U, also contributes to the ODOS spectrum S(E) at the Fermi level. The value of the order of 1016 cmP3 (Fig. 1) implies that the density of states of the defect band at y - U. is of approximately that magnitude as well. Thus we have qualitatively three
J. Ristein et ~l.!Diornond und Rehted
514
Muteriu1.y 4 i 1995) 50X-SI6
Fig. 4(a) shows a fit to the ODOS spectrum of the 200 V sample which fulfils these requirements. A single gaussian band, centered at 1.65 eV below the Fermi level with an FWHM of 0.7 eV and a peak amplitude of 4 x 10” cm-’ eV3 was used for the defect density of states D,(E). Note that the parameters of this band are close to those of the Dl band originally fitted phenomenologically to the ODOS spectrum. A second broader gaussian band centered at 4 eV below the Fermi level was used to simulate the density of states D,(E) of the 71 and Dl bands. The superposition of both bands, i.e. the total density of states D(E) = D,(E) + D,(E), is shown as the dotted curve in Fig. 4(a). A constant U, was then assigned to the defect band D,(E) and no correlation
restrictions for the defect band to explain the ODOS spectra and the spin densities of the diamond-like samples simultaneously. (1) The integrated density of states in the band has to be high enough to explain the large ESR signal of the order of (10” crne3 ), thus a peak amplitude 10” crn3 eV1 is expected. (2) Considering its large amplitude, the peak position of the band has to be far enough below the Fermi level to be consistent with the observed ODOS spectrum S(E). (3) The correlation energy has to be high enough to guarantee single occupation of the band and sufficiently low density of doubly occupied states at p - U, which are shifted spectroscopically to the Fermi level.
experimental ODOS
S(E)_
2. .=
E &
16
14
3
experimental
o=E,
1
ODOS
2
3
4
Binding Energy (eV) Fig. 4. Two fits to the ODOS including a downward surface
spectrum of the diamond-like band bending and a constant
200 V sample: (a) homogeneous model with singly occupied defect band, (b) model correlation energy assigned to the complete density of gap states. For details see text.
J. Ristein et al./Diamond
and Related Materials
tE
“r-_-n*
probe depth for photoyield Fig. 5. Illustration of the effect of possible surface band bending on determination of the correlation energies from photoyield and ESR experiments. Band bending leads to a difference in energy position of the Fermi level within the DOS at the surface and in the bulk which has to be taken into account. For details see text.
energy (U =0) to the rt and D2 density of states, thus p(E,U) = D,(E)& U) + D,(E)@ U - U,). Within this model the spin density according to Eq. (7) and the ODOS spectrum S(E) according to Eq. (5) were then calculated. In order to fit both experimental quantities a correlation energy of U,= 3.0 eV turned out to be necessary. The resulting fitted curve S(E) as well as the singly occupied density of stages n’(E) =f$j (E,U,)D,(E) (dashed curve) are also shown in Fig. 5(a). The integral over n’(E), was within a factor of 2 consistent, however at the expense of an unusually high correlation energy which exceeds the lower limit estimate (see Section 4.3.) roughly by a factor of 2. 4.5. The effect of band bending The very large correlation energies necessary in the analysis for the DLC samples above are the result of a conflict between two experimental results: on the one hand a very high spin density and on the other hand a comparatively low density of states at the Fermi level. A possible mechanism which de-escalates that conflict could be a surface band bending in the DLC samples as scetched out in Fig. 5. The photoyield experiment probes the sample volume close to the surface (10 nm) while the ESR experiment as an integrating technique is dominated by the bulk properties. Surface band bending locally leads to a different energetic position of the Fermi level within the density of states. If a downward band bending V as indicated in the figure is present, the minimum correlation energy necessary to guarantee single occupation of enough states is reduced in the bulk by V compared with the surface. To estimate this influence, a second fit of the ODOS spectrum of the 200 V sample is given in Fig. 4(b). The density of states D(E)
4 (1995) 508-516
515
is modeled again by the two gaussian bands D,(E) and D,(E) as in Fig. 4(a); this time, however, a finite correlation energy UO= 1.5 eV is assigned to both of them, p(E) = D(E)G(U - U,). Owing to the steep increase in D(E) with increasing binding energy, the occupied density of states is essentially S(E)=2f$,q (E - U,,U,)D(EU,) (Eq. (6)). Thus S(E) is simply given by D(E), but shifted by U0 towards lower binding energy and multiplied by a factor of two (indicated in the figure). Remember that the variable E in the formulae describes single electron orbital energies while the energy scales on the figures refer to binding energies and are counted in the opposite direction. This shift and scaling was compensated by shifting the complete density of states D(E) by the correlation energy towards higher binding energy and decreasing D,(E) by a factor of 2, both in comparison with the fit of Fig. 4(a). With this model an equally good fit of the ODOS spectra is obtained in Fig. 4(b), albeit this time with half the correlation energy! The spin density in this case, however, is only 4 x 1014 cmP3, inconsistent with the experimental result. Note that the situation analyzed so far corresponds to the surface region of the sample probed by the photoyield (Fig. 5). If a downward surface band bending of V is assumed, the Fermi level in the bulk is closer by V to the valence band edge, i.e. at a binding energy V larger. The singly occupied density of states in the bulk is again readily calculated as r~‘(E)=f~~,)~ (E,U,D(E) by just using the modified value pg for the bulk Fermi level (dashed curve in Fig. 4(b)). Taking (as an estimate for an upper limit) a band bending of 1.5 eV into account, a spin density of 7 x 10” cme3 results, which is again consistent with the experimental value within a factor of 2. Comparing the two fits of Fig. 4 shows that part of the correlation energy necessary to explain ESR and photoyield in a spatially homogeneous model for DLC (3.0 eV in our case) can be substituted by a downward surface band bending (1.5 eV). It should be mentioned that exactly the same effect of a different position of the Fermi level seen by the photoyield and the ESR experiment can also be the result of formation of a Schottky barrier at the stainless steel substrates of our comparatively thin a-C:H samples (100 nm) used for the photoemission experiments.
5. Conclusions From the comparison of ESR and photoyield results on identical a-C:H samples whose character varied from polymer-like to diamond-like, a lower limit for the correlation energy of the gap states in the material can be obtained. While for the polymer-like samples this limit is set around 0.25 eV, DLC samples require unusually high correlation energies to explain the low density
516
J. Ristein et allDiamond and Related Materials 4 (199.5) 508-516
of states at the Fermi level and the large spin density. Even if part of this effect is explained by surface band bending, values for U, in excess of 1 eV are necessary to fit the spectroscopic photoyield densities of states and the spin densities simultaneously. This result may either point to a large Coulomb contribution to the effective correlation energy, possibly due to strong localization of the defect states, or to a strong supression of lattice relaxation in diamond-like carbon.
References [l] [2] [3] [4] [S] [6] [7] [S]
Acknowledgement [9]
We thank Professor M. Stutzmann and Dr. S. Schtitte for performing the ESR experiments on our samples discussed in this work.
[lo] [l l]
M. Frischholz, Th. Mandel, R. Helbig, G. Schmidt and A. Hammerschmidt, Diamond Relat. Mater., 2 (1993) 778. D. Dasgupta, F. Demichelis, C.F. Pirri and A. Tagliaferro, Phys. Reo. B, 43 (1991) 2131. A. Reyes-Mena, R. Asomoza, J. Gonzalez-Hernandez and S.S. Chao, J. Non-Cryst. Solids, 114 (1989) 310. K. Fabisiak, F. Rozploch and J. Wieczorek, J. Phys. D, 21 (1988) 995. J. Schafer, J. Ristein and L. Ley, Diamond Relat. Mater., 3 (1994) 861. K. Winer and L. Ley, PhJx Reo. B, 36 (1987) 6072. J. Robertson and E.P. O’Reilly, Phys. Rec. B, 35 (1987) 2946. U. Stephan, Th. Frauenheim, P. Blaudeck and G. Jungnickel, Phys. Rec. B, 49 (1994) 1489. L. Schweitzer, M. Griinewald and H. Dersch, Solid State Cornmun.,39 (1981) 355. J. Stuke, J. Non-Cryst. Solids, 97-98 (1987) 1. H. Okamoto and Y. Hamakawa, Solid State Commun., 24 (1977) 23.