Determination of optical constants: Derivative spectra from ellipsometric data

Self Cite

The energy-derivative spectra of the real and imaginary part of the dielectric function E ( W ) = -c1 + ic, in the range of critical interband transitions can be used to determine a parameter which describes the influence of many-particle effects. Afterwards the computation of the oneelectron spectra becomes possible from experimental spectra, which are modified by many-particle interactions. The application of this procedure to ellipsometrically determined spectra of GaP and GaAs for the El-transition results in the predominant influence of the continuum-exciton effect in accordance with theoretical predictions of Hanke and Sham. Die energieabgeleiteten Spektren des Real-und Imaginiirteils der dielektrischen Funktion E ( W ) F= el + is, im Gebiet kritischer Punkte konnen benutzt werden, einen Parameter zu bestimmen, welcher den EinfluB von Vielteilcheneffekten beschreibt. Durch Vielteilchenwechselwirkung modifizierte, experimentelle Spektren konnen damit auf Einelektronen-Spektren umgerechnet werden.Die Anwendung dieses Verfahrens auf ellipsometrisch bestimmte Spektren des GaP und GaAs ergibt in der Umgebung des E,-Ubergangs den iiberwiegenden EinfluD des Kontinuum-ExzitonEffekts in Ubereinstimmung mit theoretischen Voraussagen von Hanke und Sham.

Section: Analogous Changes Will Results For the Other Types Of Criticamentioning

confidence: 99%

“…into the electronic part of the dielectric function (see e.g. [15 to IS]) finally lead to a modification which can roughly be approximated by [19] wavelength modulation spectra using a Kramers-Kronig analysis or (better) from ellipsometric data [20] in the region of critical points.…”

Section: The Modified Lineshape and A Simple Fitting Proceduresmentioning

confidence: 99%

On the Experimental Determination of Many‐Particle Effects at Interband Transitions

Jungk¹

1981

Self Cite

Determination of Optical Constants: Au

Jungk¹,

Gründler²

1976

Self Cite

The dielectric function E = E, + ie, of Au films is measured a t room temperature in the spectral range 1.6 5 E 4.6 eV with an ellipsometric null method. Numerical consideration of the free-electron like part allows the computation of the interband dielectric function and its energy derivatives above 2 eV. The mathematical lineshape analysis of the derivative spectra of el and ez leads to critical points a t 2.54 f 0.02,3.28 0.01, 3.64 0.01, and roughly 4.5 eV of M,, M,, M,, and M2 type, respectively, and a rough estimate of the relative oscillator strengths.Die dielektrische Funktion e = el + is, von Goldschichten wird im Spektralgebiet 1,6 I_ E 5 4,6 eV mit einer ellipsometrischen Nullmethode bei Zimniertemperatur untersucht.Durch numerische Beriicksichtigung des Anteils freier Elektronen konnen der Interbandanteil von e und seine Ableitungen nach der Photonenenergie im Gebiet oberhalb 2 eV berechnet werden. Die rechnerische Linienformanalyse der Ableitungsspektren von el umd e2 ergibt kritische Punkte bei 2,54 f 0,02; 3,28 & 0,01; 3,64 f 0,01 und etwa 4,5 eV der Typen M,, M,, M,, M, sowie eine Abschatzung der relativen Oszillatorstarken.

Short Notes

Jungk¹

1977

Energy derivatives of accurate, ellipsometrically measured C1-and C -2 spectra allow the unique determination of three critical points in the E' -region of Ge: 3 . 0 1 (M ), 3 . 2 2 (M1), and 3 . 6 1 eV (M1). Two possible models are presented and compared with recent bmd structures from non-local pseudopotential calculations.Until now the weak Elstructure of semiconductors was mainly investigated by modulation spectroscopic methods /1 to 7/, thus giving the known difficulties for the unique determination of the type of the critical points in question /8/. Recent developments in ellipsometry allow, however, not only the accurate determination of 0 0 0 &and & -spectra, but the numerical calculation of the energy derivatives, too 1 2 / 9 to 12/. Fig. 1 gives the L ( w)-spectra, Fig. 2 the measurements on a Ge single crystal a t room temperature with a modification of a rotating analyzer ellipsometer /13/. The line-shape analysis was performed using the complete Rabii-Fischer formalism /14/ in a manner described in some detail in /15/. The fitting procedure unequivocally gives the type of the assumed threedimensional critical points and the energy parameters with an accuracy of -20 meV .The results a r e compiled in Table 1. ( a / d w ) & ( w)-spectra from+ F o r comparison with band structure calculations the energy scheme for the I 'region in Ge for two directions in the ;-space is sketched in Fig. 3. Two possible interpretations appear: -b 1. All transitions occur a t k = 0. Because these iransitions should have M -character, the above determined 0 Fig. 1 . Spectra of the real and imaginary part of the die-7 8 1 9 4 , 1 -2 lectric function of Ge between 2 . 8 and 4.0 eV 2.5 30 35 I0 photon energy (el/) -1) DDR-108 Berlin, Mohrenstr. 40/41, DDR.