Oscillatory effective mass in the two-dimensional electron gas from Shubnikov–de Haas measurements C. Diaz-Paniagua a, * , M.A. Hidalgo b , A.F. Bran ˜a a , A. Urbina a , F. Batallan a , S. Fernandez de Avila c,² , F. Gonzalez-Sanz c a Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Cientı ´ficas, Cantoblanco, 28049 Madrid, Spain b Departamento de Fı ´sica, Facultad de Ciencias, Universidad de Alcala ´ de Henares. Apartado 20, 28871 Alcala ´ de Henares, Madrid, Spain c Departamento de Ingenierı ´a Electro ´nica, Escuela Te ´cnica Superior de Ingenieros de Telecomunicacio ´n, Universidad Polite ´cnica de Madrid, Ciudad Universitaria, 28040 Madrid, Spain Received 15 December 1998; accepted 4 November 1999 by P. Burlet Abstract The effective mass in the two-dimensional electron gas of a delta-doped In x Ga 1-x As HEMT structure from the variation of the amplitude of the Shubnikov–de Haas oscillations was determined; with the temperature from measurements obtained as a function of the magnetic field and the gate voltage. The effective mass shows at intermediate magnetic fields an oscillatory behaviour, periodic with the filling factor and with maximum amplitude for even factors. Its relation to the oscillatory behaviour of the cyclotron effective mass and the effective g factor is discussed. The effective mass increases with the electron density and the inversion of the magnetic field.  1999 Elsevier Science Ltd. All rights reserved. Keywords: A. Quantum wells; A. Semiconductors; D. Electronic transport; D. Galvanomagnetic effects The effective mass is an important parameter in the characterisation of the two-dimensional electron gas (2DEG) which incorporates information not only about the electronic band but also about many-body effects [1]. The effective mass is obtained from experimental techniques like the Shubnikov–de Haas (SdH) oscillations, the cyclotron resonance and the magnetoluminescence. From SdH oscillations, the effective mass (m*) is determined from the tempera- ture dependence of the SdH oscillations amplitude [2]. However, in the 2DEG the temperature variation depends on the nature of the electronic states even- tually affecting the effective mass determination. Several authors have remarked on these difficulties [3,4] and interpreted the experimental results on the alternative basis of activation plots. These kinds of analyses are particularly useful for low even filling factors where the localised nature of electrons must be taken into account. In the 2DEG the cyclotron effective mass (m c ), obtained from cyclotron reso- nance measurements, shows an oscillatory behaviour as a function of the magnetic field [5–10]. The effec- tive g factor (g*) obtained from SdH oscillations shows also an oscillatory behaviour with the magnetic field [11–13]. However, maxima of the oscillations correspond to even filling factors for m c and to odd filling factors for g*. While the oscillatory behaviour of g*, attributed to an exchange coupling between the Solid State Communications 109 (1999) 785–790 SSC 4597 0038-1098/99/$ - see front matter  1999 Elsevier Science Ltd. All rights reserved. PII: S0038-1098(99)00036-8 PERGAMON * Corresponding author. Tel.: 07-34-1-3349000; fax: 07-34-1- 37-20623 E-mail: panidi@icmm.csic.es (C. Diaz-Paniagua) ² Present address: Departamento de Cienca y Technologı ´a de Materiales, Universidad Miguel Herna ´ndez, 03202 Elche, Alicante, Spain.