Infrarotspannungsoptische Untersuchungen an Halbleitereinkristallen

Abstract

Infrarotspannungsoptische Untersuchungen an Halbleitereinkris tallenDer piezooptische Effekt in Kristallen, speziell in Kristallen der Klassen m3m und 33 m des regulciren Systems wird erlciutert. Unter Beachtung der Symmetrieeigenschaften wird eine Methode zur Messung der Spennungsdoppelbrechungskonstanten (qI1 -q12) und q,, an einer einzigen Materialprobe vorgeschlagen und an Siund GaAs-Einkristallen praktisch angewendet. Zur Messung der Spannungsdoppelbrechungskonstanten wurde eine Apparatur entwickelt, die mit grol3er Genauigkeit quantitative Bestimmungen erlaubt. Zur Probenpriiparation wurden mehrere Verfahren untersucht.Die Messungen an verschiedenen Si-bzw. GaAs-Einkristallen ergaben unterschiedliche spannungsoptische Werte, die mit den bisher in der Literatur angegebelien Werten verglichen werden. Es wird gezeigt, daB der Begriff ,,spannungsoptische Konstante" nicht ale Materialkonstante, sondern als kristallindividueller Wert aufgefaBt werden muB. Unter Verwendung der gemessenen spannungsoptischen Werte werden die Restspannungen in kompakten Einkristalleri aus Doppelbrechungsmessungen an dicken Scheiben rekonstruiert.The piezooptic effect in crystals is explained, in particular for cubic classes m3m and 33m. Taking in consideration the properties of symmetry, a method is proposed for measuring the piezobirefringence constants (qll-q12) and q4* in a single sample only, and its application to Si-and GaAs-single crystals is shown. A device was constructed for exact measurement of the piezobirefringence constants. Some methods for the preparation of the samples were examined.The measurements on different Si-and GaAs-single crystals lead to different photoelastic values. These values are discussed in comparision to values published up to now in the literature. It is shown that the terminus ,,photoelastic constant'' cannot be used in the meaning of material constant, because these values are specific for every crystal. Taking into consideration the photoelastic values measured the residual stresses in crystal ingots are reconstructed by birefringence measurements on thick slices.

Mechanical microstresses in dislocation-free floating-zone silicon monocrystals

“…Using (1) for a n optical path difference of Al20, and taking the sample thickness D = 1.5 cm, n o = 3.54 (for 1 = 1.15 pm [ l l ] ) , and rillnl, = 10-le Pa-l [4], we derive To estimate the concentration of defects causing the stress (Z), we make use of Hooke's equation presented in matrix form, g m = Cn,n~n (m, n = 1, 2, ... , 6) ,…”

“…The stresses can be esplairied by an inhomogeneous distribution of intrinsic point defects, impurity atoms, and their clusters in the crystal matrix. With known values of the relative changes in lattice parameter Aa/a, they amount t o 4.5 x x 1 0 -2 4 IS], -6.5 x 10-24 [6], and -1.2 x 10-24N (71 for oxygen, carbon, and phosphorus, respectively ( N is the concentration of atoms per cm3) ; besides, they should have the same order of magnitude for Si interstitial atoms, vacancies, and boron. The sensitivity of methods recording mechanical stresses by using ordinary light sources is restricted by their low intensity in a narrow spectral interval: the minimum level which can be detected in a 15 mm sheet amounts t o approximately 1.5 x 1 0 5 P a (see [S]).…”