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ELECTROREFLECTANCE OF IV-VI COMPOUNDS
B. Seraphin
To cite this version:
B. Seraphin. ELECTROREFLECTANCE OF IV-VI COMPOUNDS. Journal de Physique Colloques,
1968, 29 (C4), pp.C4-95-C4-98. �10.1051/jphyscol:1968413�. �jpa-00213617�
JOURNAL DE PHYSIQUE Colloque C 4 , supple'ment au no 11-12, Tome 29, Novembre-Be'cembre 1968, page
C 4 -
95ELECTROREFLECTANCE OF IV-VI COMPOUNDS
by
B. 0.
SERAPHINMichelson Laboratory, China Lake, California 93555
Rbsumb.
-
La modulation par un champ klectrique exagere considkrablement la structure de la reflectance d'un solide. Outre une plus grande sensibilite, le fait que le parametre de modula- tion detruise les symktries, donne, sur ces symktries, des renseignements utiles pour l'identification des points critiques. Les transitions interbandes, les excitations excitoniques, et les interactions entre les porteurs et le reseau peuvent, en principe, &tre kvaluees pour ce qui est de leurs contribu- tions relatives au processus de l'absorption optique.Jusqu'ici, peu de mesures d'klectror6flectance ont kt6 faites sur les compos6s IV-VI. Comme pour tous les autres matbiaux, la structure existant dans les mesures optiques statiques se trouve renforcee. On trouve aussi une structure nouvelle qui ne se relie pas a des transitions observees auparavant
.
Certaines proprietes caracteristiques des IV-VI rendent les mesures et l'interpretation des spectres d'klectroreflectance difficiles.
Une forte concentration de porteurs de charge amkne la compression des regions de charge d'espace qui sont plus petites que la profondeur de pknktration de la lumiere reflkchie. I1 faut ainsi modifier l'analyse. La forte constante diklectrique deforme la forme de l'onde par l'inter- mkdiaire de retards de phase entre la modulation et la rkponse. Les klectrolytes faibles non-aqueux nkcessaires pour l'infrarouge, en presence de substrats solubles ajoutent des effets parasites de charge d'espace.
Tous ces facteurs compliquent l'interprktation qualitative du profil des raies. Au moment present une analyse de points critiques ne peut &re qu'un essai ; cependant, on peut relier certains rksultats expQimentaux aux calculs de structure de bande existants. En general, il y a accord.
Certains aspects des resultats expkrimentaux suggerent que l'klectroreflectance dans les composes IV-VI comme SnTe n'est pas un phknomkne dCi aux points critiques. Les spectres de la skrie des cristaux mixtes PbzSnl-%Te changent de faqon tres nette d'un bout a I'autre de I'echelle des concen- trations. Bien qu'elle renforce encore la structure observke par les methodes optiques statiques, il est possible que l'klectror6flectance offre des possibilitks limitkes, quant aux phenom8nes dus aux points critiques, dans des materiaux dkgknkres.
Abstract.
-
Electric-field modulation considerably enhances structure in the reflectance of a solid. In addition to the greater sensitivity, the symmetry-breaking effect of the modulation para- meter provides symmetry information useful in the identification of critical points. Interband transitions, excitonic excitations and interactions between carriers and lattice can, in principle, be evaluated in their relative contributions to the optical absorption process. The present status of theory and experiment is briefly reviewed in this respect.So far few electroreflectance measurements have been performed on IV-VI compounds. AS for all other materials the existing structure in static optical measurements is enhanced. Some new structure does not relate to formerly observed transitions.
Properties characteristic for IV-VI compounds make measurements and interpretation of their electroreflectance spectra difficult. A high-carrier concentration results in compressed space- charge layers which are smaller than the penetration depth of the reflected light. This requires a modified analysis. A large dielectric constant distorts the waveform through phase-lags between modulation and response. Weak nonaqueous electrolytes required in the infrared and in the presence of soluble substrates add parasitary space-charge effects.
All these factors complicate quantitative line-shape discussions. At present, a critical-point analysis can only be tentative ; however, some of the experimental results can be correlated to existing band-structure calculations and, in general, support their claims.
Some features of the experimental results suggest that electroreflectance in degenerate IV-VI compounds, such as SnTe, is not a critical-point phenomenon. Spectra of the mixed-crystal series PbZSn~-zTe change from one type at one end to a markedly different type at the other. Although still enhancing the structure of static optical techniques, electroreflectance is probably restricted as a critical-point phenomenon in these degenerate materials.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1968413
C 4 - 9 6 B. 0. SERAPHIN
Many interesting features of the IV-VI compounds
are based on their peculiar band structure. Its explora- tion by means of electroreflectance studies should therefore be particularly profitable.
However, the few available results indicate that interpretation in terms of the band structure must be made cautiously. In addition to difficulties of line shape discussions encountered in other materials, an unusually strong sensitivity of the electroreflectance spectrum to changes in dc bias, carrier concentration, temperature, and modulation amplitude and frequency is observed in most IV-VI compounds. A drastically different appearance of the spectrum can be obtained through only minute changes in any of these parame- ters.
The strong variations are probably caused by the predominance of bandfilling effects. Large carrier concentration and a high dielectric constant further aggravate the difficulties.
In first studies on the Lead salts [I] and on SnTe and GeTe [2], Aspnes and Cardona observed the different character of IV-VI electroreflectance spectra as well as the difficulties in measuring and interpreting them. In a separate study, Aspnes
[3]explored the consequences of modulation by means of a space- charge layer extending over a small fraction of the light penetration depth only. The spectral functions for the coefficients
aand fl in the derivative of Fresnel's reflection equation [4] are then different from the previously considered case of a space-charge layer extending further than the light. Since the light ((sees
Dan electric field over only a fraction of the penetra- tion depth, the modulation is much smaller in mate- rials in which a large carrier concentration compresses the space-charge layer. Reflectance modulation of only
lo-'are typical in the IV-VI compounds. This is close to the detection level and requires careful experimentation.
The large dielectric constant causes phase lag between external modulation and space-charge field, further complicating the correlation between electrical input and optical output.
Band population effects, which Aspnes first postu- lated for the interpretation of the SnTe and GeTe spec- trum seem to establish a fundamental difference of the basic mechanism. In ouf work we therefore concentra- ted on two series of investigations in which a drastic variation of such effects could be expected
:We recor- ded the electroreflectance spectra of a series of PbTe samples of carrier concentrations varying from 2 x 10'' to 9 x 10'' ~ m - ~ , passing the point of degeneracy inside this range. We also observed the
spectra of five samples of the type Pb,Snl-,Te, the PbTe sample x
=1 being the 9 x 1019 cm-3 end of the previous series and the carrier concentration increa- sing to 8 x 10'' cmP3 at the SnTe end.
In both series, the spectra consisted of well-resolved structure, broader than in other materials, but distinct and without large background. The influence of band filling effects is apparent throughout both ranges, however, and probably explains the strong variations in the appearance of the spectra.
Population effects in the surface region where the bands are bent should be observed in essentially three different ways, for accumulation as well as depletion layers.
1. Inversion of the reflectance response (flip-flop) with inversion of the dc bias of half the ac modulation amplitude results when the Fermi level is riding on or is very close to the band edge involved in an optical transition.
2. When the Fermi level has shallowly penetrated the band, structure shifts to larger photon energies upon inversion of the dc from bias positive to negative values.
3. If the Fermi level lies deep inside the band or if the transition involves a band far away from the Fermi level, the structure is insensitive to changes of dc bias.
The dc bias effect will further be determined by the penetration depth of the light
:Large penetration depths will result in small dependance on dc bias, expected in the near infrared and the ultraviolet for most IV-VI compounds since their
E,peaks in the visible region of the spectrum.
The three categories of response to changes in dc bias
-flip-flop, blue shift, or no response
-are actually observed. In spite of the drastic variations of the line shape, they establish a systematic pattern.
The variations can be interpreted consistently in terms
of a shift of the Fermi level up or down, as carrier
concentration, fractional composition, or temperature
are changed. If one part of the spectrum first shows
inversion of sign with dc bias inversion, then shifts
into the blue, and finally becomes intensitive, indica-
ting a downward penetration of the Fermi level into
the band, all parts of the structure show similar
behavior consistent with such a shift of the Fermi
level. We therefore believe that this establishes a
criterion that indicates the location of the initial band
(all samples were p-type) with respect to the Fermi
level. We furthermore believe that this is presently
ELECTROREFLECTANCE
OF
IV-VI COMPOUNDS C 4 - 9 7the only band structure feature that can be extracted
from spectra that vary so strongly with a variety of parameters.
All measurements were taken in the field-effect configuration [5] a t 200 K - a temperature sufficien- tly low to make changes of dc bias effective in the space-charge layer; ac modulation and dc bias were kept at a 2 : 1 ratio, so that the modulation swing touches the zero line. All but one sample were poly- crystals Czrochalski-grown by Wagner and Willard- son [6], the 2 x lot7 ~ m PbTe annealed single- - ~ crystal being the only exception [7].
The spectra of all samples are basically alike, indica- ting a similar band structure in PbTe as well as in Pb,Snl-,Te. A reflectance response in the order of
ARIR =is observed in three spectral regions
:a first group of structure (I) between 0.6 and 0.9 eV, a second one (11) between 3.0 and 3.5 eV, and a third group (111) between 4.0 and 4.5 eV. No distinctive response above the noise level of 1 x is observed in the spectral regions in between.
In the PbTe series, all three groups change as a function of carrier concentration in a manner consistent with a downward shift of the Fermi level (Burstein shift [8]). Starting out in the 2 x 1017 cm-3 sample at 0.6 eV, structure 1 shifts to 0.88 eV in the 9 x 1019 cm-3 sample, jumping abruptly from 0.75 eV to 0.88 eV between 9 x 1018 and 9 x loL9 cmP3. Slope discontinuities of other parameters in this range of carrier concentrations have previously been observed [9] and are correlated to the existence of a second, lower, valence band [lo]. Except for the Burstein shift and a gradual growth toward larger carrier concen- trations, structure I is little affected by changes in dc bias. According to our scheme, this classifies structure I as relating to a transition from inside a band.
Structure I1 between 3.0 and 3.5 eV inverts its sign upon inversion of dc bias (flip-flop) for small carrier concentrations. At higher concentrations, the flip- flop goes over into a blue shift upon change from positive to negative bias, consistent with the downward shift of the Fermi level indicated by the Burstein shift of structure I. Structure I1 apparently correlates to a transition from a band on the edge of which the Fermi level rides at low concentrations and into which it penetrates toward higher concentrations.
Structure 111 between 4.0 and 4.5 eV is little affected by changes in dc bias. This structure probably relates to a transition starting farther away from the Fermi level.
In the Pb,Snl-,Te series, structure I shifts back to
smaller photon energies as the Sn end is approached.
Since the carrier concentration increases from 9 x 1019 cm-3 (PbTe) to 8
x10'' cm3 (SnTe) over the fractional range 1 > x > 0, the Burstein shift seems inverted. An alternate mechanism connected to the existence of lower valence bands apparently overcompensates the Burstein shift, moving the Fermi level upward from PbTe to SnTe, in spite of the increa- sing carrier concentration. Structure I1 and I11 confirm this shift in a consistent manner
:Structure I1 shows a blue shift with dc bias at the Pb end, going over to bias flip-flop at the Sn end. Structure 111 is insensitive to dc bias in PbTe and acquires a blue shift toward SnTe. The correlated transition, sufficient by far away from the Fermi level in PbTe, is apparently approached by the Fermi level near SnTe.
From our observations along the two coordinates PbTe (low carrier concentration)
-+PbTe (high carrier concentration) and PbTe -+ SnTe, we derive the follo- wing tentative conclusions
:1.
A basically similar electroreflectance spectrumsuggests a similar band structure along the two coordi- nates.
2.
The position of the Fermi level with respect to the edge of the initial band determines appearance of the electroreflectance spectrum and its response to dc bias and temperature (band-filling effects).
3. An inverted Burstein shift in Pb,Sn,-,Te confirms the existence of a second, lower, valence band at nearly constant separation from the lowest conduc- tion band edge. The position of the Fermi level inside this lower valence band is determined by the number of states available in the upper band above the Fermi level. Since this number varies strongly over the compositional range, the separation of the Fermi level from the conduction band edge varies accordingly probably overcompensating the simultaneous Burstein shift. If this is accepted, we must conclude from the magnitude of the spectral shift that the density-of- states mass of the lower valence band is comparable to or smaller than that of the upper band [l 1, 121.
4. The consistent behavior of structure 111 suggests that a third valence band could contribute to the generation of the spectrum. With the Fermi level deep inside the valence bands for all samples of the series Pb,Snl-,Te, it cannot be expected that a possible closure of the thermal band gap at some x of the compositional range would drastically affect the electroreflectance spectrum. No evidence for or against
7
such a closure can presently be derived from the electroreflectance spectrum.
5. Our observations support existing band structure calculations
[13]. Two lower valence band maximaare predicted within a few tenths of one eV of the highest valence band maximum a t L, one along the Z-and one along the A-direction. Breaking of selection rules by the electric field may enhance the oscillator strength of transitions from these bands [14]. Move- ment of the Fermi level near these two lower maxima as determined by the strongly variable upper maximum could explain most features of the spectra. Herman's [I51 calculations suggest a separation of these maxima in going from PbTe to SnTe
-in agreement with the postulated upward shift of the Fermi level in our Pb,Sn, -,Te series for decreasing
x.6. Our observations seem to provide a probe for the location of initial states with respect to Fermi level and band edge. Further conclusions with respect to the nature and location of the initial states must await investigations more complete with respect to the range of carrier concentrations, fractional composition, and temperature as well as modulation amplitude and bias.
References
[I]
ASPNES (D.
E.)and CARDONA (M.)
Phys. Rev., 1968, 173, 714.[2]
ASPNES (D. E.) and CARDONA
(M.) Bull. Am. Phys.Soc., 1968, 13, 27.
[3]
ASPNES (D. E.) and FROVA (A.) (to be published).
[4]
SERAPHIN
(B.0.) and BOTTKA
(N.), Phys. Rev., 1966, 145, 628.[5]
SERAPHIN (B. 0.) and HESS (R. B.),
Phys. Rev. Lett., 1965, 14, 138.[6]
WAGNER (J. W.) and WILLARDSON (R. K.),
nuns.Met. Soc. AZME, 1968,242,366.
[7]
This crystal was received from Dr. HOUSTON
(B.)of the Naval Ordnance Laboratory, White Oak, Maryland.
[8]
BURSTEIN (E.),
Phys. Rev., 1954,93, 632.[9]
DIXON
(J.R.) and RIEDL (H. R.),
Phys. Rev., 1965, 138, A873.RIEDL (H. R.), DIXON (J. R.) and SCHOOLAR (R. B.),
Phys. Rev., 1967, 162, 692.[lo]
ALLGAIER
(R. S.), J. Appl. Phys., 1961, Suppl. 32, 2185.RIEDL (H. R.),
Phys. Rev., 1962, 127, 162.ALLGAIER (R. S.) and HOUSTON (B. B.),
J. Appl. Phys., 1966, 37, 302.TAUBER (R.
N.),MACHONIS (A.
A.)and CADOFF
(I.B.),
J. Appl. Phys., 1966J37, 4855.OCIO (M.) and ALBANY (H. J.),
Phys. Letters, 1968, 27A, 72.[ l l ]
HOWARD
(W.E.)x(this conference).
1121
ANDREEV (A. A.)i(this conference).
[13]
LIN (P. J.) and KLEINMAN (L.),
Phys. Rev., 1966, 142, 478.MITCHELL (D. L.) and WALLIS (R. F.),
Phys. Rev., 1966,151,581.LEV (P. J.), SASLOW (W.) and COHEN
(M.L.),
Solid State Commun., 1967, 5, 893.[14]
COHEN (M. L.) (this conference).
[15]
