Cyclotron Resonance of Holes in Si

Abstract

Hole resonances are studied in 3900 SZcm p-type Si samples a t temperatures from 1.2 to 5.0 OK. Measurements are performed a t 45 GHz using magnetic inductions B up to 10 kG corresponding to a maximum value of m*/rn, = 0.62, and a few resonances not reported previously are observed. The experimental data are in reasonably good agreement with the Luttinger theory [l] of Landau levels in the valence band of semiconductors when a suitable set of band parameters are chosen. Numerical calculations of the levels and the matrix elements for transitions between the levels are carried out for B pointing in the crystallographic directions [001], [ l l l ] and [110]. The variation of the level positions and of t,he matrix elements as a function of the band parameters is examined in order to find the parameters providing the best fit to the experimental data. Locher-Resonanzen in p-Ieitendem 3900 Rcm Si sind bei Temperaturen von 1.2 bis 5.0 "K untersucht worden. Die Messungen wurden bei 45 GHz bei magnetischen Induktionen B bis zu 10 kG entsprechend einem Maximalwert von m*/rn, = 0.62 durchgefiihrt. Einige Resonanzen, von denen bisher nicht berichtet worden ist, sind beobachtet worden. Die experimentellen Daten stimmen recht gut mit der Lut'tinger-Theorie [l] der Landau-Niveaus im Valenzband von Halbleitern iiberein, wenn ein passender Satz Band-Parameter gewahlt wird. n'umerische Berechnungen der Niveaus und der Matrixelemente fur obergange zwischen den Kiveaus sind fur B in den kristallographischen Richtungen [001], [111] und [110] durchgefiihrt worden. Die Anderungen der Kiveaus und der Matrixelemente als Funktion der Bandparameter sind untersucht worden, um die Parameter zu ermitteln, die mit den experimentellen Daten die beste Ubereinstimmnng ergeben.14*

The dependence of hole resonances in Si on the wave vector component along the direction of magnetic induction (I)

“…According t o reference [7] the Landau levels in diamond structure semiconductors should be determined from the Hamiltonian The significance of the symbols are as stated in [7] and [8]. Application of a coordinate transformation x, y, z + 1, 2, 3, where the %axis is in the direction of B and the 2-axis is perpendicular to the (110) plane, gives the Hamiltonian on a form suited for calculations corresponding to B parallel to the (110) plane.…”

“…The transformed Hamiltonian contains the angle 8 between the [OOl] direction and the direction of B as a parameter. Since k, and k, do not commute, they can be substituted by the creation and annihilation operators a+ and a defined in [8]. Following the notation of references [2], [3], [5], and [ti] k3 is substituted bv t :…”

“…The minimized RMS mass deviation obtained in the fit was 0.003. The RMS mass deviation of the eight experimental peaks common for references [8] and [lo] was also 0.003. Hence it is believed that the theory on which the calculations are based and the interpretation of the absorption peaks are correct, and that the least RMS mass deviation is solely of statistical nature.…”