VOLUME 54, NUMBER 16 PHYSICAL REVIEW LETTERS 22 APRIL 1985 Specific Heat of Two-Dimensional Electrons in GaAs-GaA1As Multilayers E. Gornik, R. Lassnig, and G. Strasser Institut fur Experimentalphysik, Universitat Innsbruck, 6020 Innsbruck, Austria and H. L. Stormer, A. C. Gossard, and W. Wiegmann A TAT Bell Laboratories, Murray Hill, New Jersey 07974 (Received 15 January 1985) We report the first observation of the magnetic-field — dependent electronic specific heat in GaAs-GaAs multilayers. With a heat-pulse technique oscillations of the sample temperature on the order of millikelvins werc observed. Both intra- and inter-Landau-level contributions could be dis- tinguished. Theoretical fits to the data reveal a density of states consisting of Gaussian peaks on a flat background. PACS numbers: 65. 40.Em, 71. 25.Hc, 73. 40.Lq Electrons confined to quasi two-dimensional (2D) motion due to electric fields in heterojunctions or mul- tilayers are known to show interesting phenomena. In particular, if an external magnetic field is applied per- pendicular to the interface, the density of electronic states at high magnetic fields is then characterized by peaks in the vicinity of Landau levels and by almost zero values between them. This results in a pro- nounced oscillatory character of practically all physical phenomena including electrical, magnetic, and thermal properties. In all physical properties which are measured via transport effects, pinning of the Fermi level takes place in regions of localized states which do not con- duct the current. However, for equilibrium properties such as the specific heat or the magnetization the difference between localized and nonlocalized states is of no importance. Therefore equilibrium properties reveal the total density of states. Zawadzki and Lassnig2 have recently shown that the specific heat for 2D electrons in GaAs shows a pro- nounced oscillatory character for a Gaussian density of states. It consists of intra- and inter-Landau-level con- tributions. The temperature dependence of the intra- level specific heat shows a maximum for a level width I to kTratio of — 5. Previously Kunzler, Hsu, and Boyle have investi- gated temperature oscillations of oriented Bi samples as a function of the magnetic field. Oscillations of mil- likelvins were found at 1. 3 K, indicating a change of the electronic specific heat due to a variation of the density of states in the magnetic field. Magnetother- mal oscillations were employed to analyze the Landau and spin level splittings at the Fermi energy. In this paper we report the first measurements of the magnetic-field — dependent specific heat for 2D electrons in GaAs-GaA1As multilayers. We will show that quite conclusive results about the form of the density of states can be obtained by comparing the ex- perimental results with calculations for different types of densities of states (Gaussian, Lorentzian, and Gaussian with constant background). We have applied a heat-pulse technique to deter- mine the electronic specific heat. In this technique a short-duration heat pulse is applied at one point of the sample, increasing the sample temperature by AT. Thermal isolation is achieved by hanging the sample on four S-p, m-thick superconducting wires, which con- nect the sample with the heat bath and serve as electri- cal connections. The wires remain superconducting in the investigated magnetic field range. The resistance variation due to 6 T of a detector film is measured at a different point of the sample. The contributions of the electronic specific heat lead to an oscillatory resistance variation as a function of magnetic field. The experiments were performed on two different multilayer materials: Sample 1 consisted of 172 dou- ble layers of 200-A GaAs and 200-A GaAlAs and resi- dual buffer layers of 1. 2-p, m GaAlAs on both surfaces, grown on a semi-insulating GaAs substrate. The sub- strate was etched away to a total sample thickness of — 10 p, m. The mobility at 4.2 K varied between 30 000 and 40 000 cm2/V s for different sample pieces. The density was n, = (6.3 + 0. 4) x 10" cm Sample 2 consisted of 94 layers of 220-A GaAs and 500-A GaA1As. The mobility at 4. 2 K was — 80 000 cm2/V s, and the density was n, = (7. 7 + 0.3) && 10" cm . Samples are prepared by polishing and etching the material down to a total sample thickness of 20 p, m. As a temperature detector a 1000- to 2000-A-thick Au-Ge (8'/o-Au) film, which was evaporated on the sample surface, was used. The Au-Ge films were prepared in such a way that they showed an exponen- tial temperature dependence with the same exponent over the whole temperature range between 1. 5 K and 300 K. The major advantage of these films is that they show a very small resistance change in magnetic fields up to 10 T (between 0.5'/o and 1'/o). A second 100-A-thick Ni-Cr film was deposited on 1820 1985 The American Physical Society