Volume 5 1A, number 5 PHYSICS LETTERS 24 March 1975 DETERMINATION OF THE HOLE BAND GAP IN BISMUTH BY FAR-INFRARED MAGNET-TRANSMISSION * B.T. SMITH and A.J. SIEVERS Laboratory of Atomic and Solid State Physics and Materials Science Center, Cornell University, Ithaca, New York 14853, USA Received 27 January 1975 In the context of a two-band model the hole gap-energy is determined to be 720 f 160 meV. Far-infrared Alfven-wave transmission through bulk samples of bismuth in the extreme quantum limit has proven to be a very sensitive experimental technique for studying specific features of the hole- like carriers [ 1,2]. In this letter we report on our de- termination of the hole band gap from a study of the magnetic field dependence of the far-infrared cyclo- tron resonance absorption. Previous investigators have either assumed that the hole band gap in bismuth is infinite or have reported values which differ by more than an order of magnitude from each other. A summary of the values of the band gap obtained from the literature as well as the value we have deter- mined is given in table 1. All far-infrared spectra were recorded by conven- tional Fourier transform spectroscopic techniques using a helium-3 cooled bolometer detector. A modi- fied Bridgeman technique was used to grow the Bi crystals from six-nines pure starting material. Our measured values of the cyclotron resonance frequen- cy of the holes versus magnetic field are shown as open circles in fig. 1. Data were taken for fields be- tween 40 and 97 kOe. The applied magnetic field is nearly parallel to the crystal bisectrix axis and the sample temperature is 4.2 K. The instrument resolu- tion is 1 cm-l. The nonlinearity of the cyclotron resonance with field gives a measure of the interaction between hole bands which we now consider in more detail. * This work has been supported by the US Atomic Energy Commission under Contract No. AT(ll-l)-3151, Technical Report No. COO3151-51. Additional support was received from the National Science Foundation under Grant #GH- 33637 through the Cornell Materials Science Center, Report #2377. In general the energy levels of the hole-like carriers are designated by three quantum numbers, n, s and kH, where the orbital quantum number, n = 0, 1,2, ... the spin quantum number, s = f 1; and kH is the com- ponent of crystal momentum parallel to the magnetic field. When considering optical transitions, the kH dependence can be ignored because the density of states of each Landau level at kH = 0 exhibits a singu- larity so that the absorption is peaked as if the kH = 0 point of the Landau level represents a discrete level [4]. For the special configuration which we have measured where the magnetic field is along the bisec- trix axis, the spin-dependent energy term is zero [7]; therefore, we need consider only the n dependence of the energy levels. The energy of the observed cyclo- tron resonance is the energy difference between neigh- -;; 30 v E 5 25 820 E 8 I5 u % IO 0 0 IO 20 30 40 50 so 70 80 so I magnetic field (ItOe) ‘0 Fig. 1. Observed cyclotron frequency versus applied magnetic field strength. The field is parallel to the crystal bisectrix axis. Sample temperature is 4.2 K. The instrument resolution is 1 cm-‘. The upper solid curve is calculated using Eg = 920, the lower for Eg = 520 meV. 273 dF-PLA1958-