High-field transport in high carrier density GaAs/Ga0.8In0.2As/Ga0.75Al0.25As heterostructures

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High-field transport in high carrier density GaAs/Ga0.8In0.2As/Ga0.75Al0.25As heterostructures
  Physica B 184 (1993) 211-215 North-Holland PHYSIC [ High-field transport in high carrier density GaAs / Gao. 8Ino.2As / Gao. 75 A10.25 AS heterostructures M. van der Burgt , A. Van a 1 sch ', F.M. Peeters b'z, M. Van Hove c, G. Borghs c and F. Herlach a aDepartment of Physics, K.U. Leuven, Belgium bDepartment of Physics, University of Antwerp (UIA), Belgium Clnteruniversity Micro Electronics Center (IMEC), Leuven, Belgium We report magnetotransport experiments in high carrier density GaAs/GaoslnozAs/Gao.75Alo25As heterostructures in magnetic fields up to 50 T. At the lowest electron densities the quantized Hall effect is observed, with one subband occupied. As the density is increased, features indicating the population of the second subband emerge. Further increase of the electron density results in drastic changes in the transport coefficients Pxx and Pry, especially at fields above 30 T. The data cannot be explained by standard models for two-band conduction or magnetic freeze-out. 1. Introduction There is currently a great deal of technological interest in Gal_xlnxAs-based devices because they have a larger electron density as compared to GaAs/Gal_xAlxAS heterostructures, and as a consequence much higher room temperature conductivities are achievable. Up to date very little is known about the subband structure and the electron mobilities in the different subbands in GaAs/Gal_xlnxAs/ Gal_yAlyAs heterostructures. This is mainly due to the low mobilities in these systems at low temperatures, which is limited by cluster scatter- ing and remote ionized impurity scattering in the Gal_xlnxAs layer [1,2]. This prevents Shub- nikov-de Haas (SdH) oscillations from higher subbands to be seen in Pxx. Furthermore high magnetic fields are needed to reach the condition /xB ~> 1, in order to reveal all Landau levels. The results we obtained from a GaAs/ Correspondence to: M. van der Burgt, Clarendon Labora- tory, University of Oxford, Parks Road, Oxford OX1 3PU, UK. 1 Supported by the Onderzoeksraad from the K.U. Leuven. 2 Senior research associate of the National Fund for Scientific Research. Ga0.8In0.2As/Ga0.75A10.35As sample indicate that besides in a first and a second subband, other mechanisms are involved which are dif- ficult to reconcile with parallel conduction in the doped Gal_xAlxAS layer of the sample. 2. Experimental details The experiments were done with a modula- tion-doped pseudomorfic GaAs/Ga0.sln0.2As/ Ga0.75Alo.25As heterostructure grown by mo- lecular beam epitaxy. It consists of a 13 nm thick Ga0.8In0.2As layer grown on a GaAs substrate. In order to obtain the high carrier density, a Si ~-layer (5 × 10 lz cm -2) was included between the Si-doped (5 × 1017 cm -3) Gao.75A10.25As layer of 30 nm thick and the 5 nm wide Ga0.vsA10.25As spacer layer. An n+-GaAs layer on top of the structure was etched away. The thickness of the Ga0.8Ino.2As layer is below the critical thickness above which the strain in the Gao.8In0.2As layer is relieved by the introduction of dislocations [3]. The carrier density of the sample was n s = 1.67× 1012cm-2 and the mobility was ~ = 3.2mE/Vs, when cooled to 4.2 K in the dark. The density could be increased by a factor of 2 0921-4526/93/$06.00 (~) 1993 - Elsevier Science Publishers B.V. All rights reserved  212 M. van der Burgt et al. I High-field transport in GaAslGao.slno.eAs/Gao.75Alo.esAs by illumination with a red LED, mounted 2 cm above the sample. The sample was cooled in a liquid-helium bath cryostat. By letting exchange gas into the vacuum space between the liquid nitrogen and the helium space, measurements could be done at 77 K. The-Hall effect fix , and the longitudinal mag- netoresistance Px, were measured using a con- ventional DC technique in pulsed magnetic fields up to 50 T. Currents in the range 1-10 IxA were used. The field is generated by discharging a 500kJ capacitor bank into a copper solenoid with a 17mm bore; the solenoid is internally reinforced with glass fibre composite in order to contain the Lorentz forces [4] and is precooled with liquid nitrogen. The field pulse is a damped sine wave which reaches its peak after 6-8 ms; by changing the crowbar resistance, the total pulse duration can be varied in the range 15- 40 ms. Pulses up to 50 T can be repeated every 45 minutes. The sample holder is equipped with three small coils: one for the field measurement and two for the compensation of spurious signals induced in the sample wiring by the transient magnetic field. Further reduction of induced vol- tages is achieved by combining two different magnetic field sweeps: one with and one without applied sample current, or one with a positive and one with a negative applied sample current. This was not possible with the illuminated sam- ple since the density in our illuminated sample slowly changes back to the dark value in about 10 hours. 3. Experimental results Figures 1 and 2 show the transport coefficients fxx and fxy at six different illumination doses, resulting in six different densities. For clarity, only the down-sweep of the magnetic field is shown. In the fast up-sweep the Hall effect showed strong distortions due to the capacitive wiring of the probe [5]. The density indicated is the Hall density nil; it is obtained from the low-field slope of the Hall effect: fxr = B/nHe 3 0 3 v 0 3 1 0 .... f , , , (b) / ~ v=2 (e) P=4 (c) Au=2 (f) ~,=4 0 0 2~ ,0 0 10 20 30 4 0 10 20 30 4 0 50 B T) B T) Fig. 1. The longitudinal resistivity Pxx for a GaAs/ Ga0.slno.2As/Gao.75Alo.25As heterostructure for six different Hall densities: (a) nH= 1.67 x 1012 cm-2; (b) n H = 1.74 x 1012cm-2; (c) n n=1.81×1012cm-2; (d) n H=1.83x 1012 cm -2, (e) nit = 1.9 x 1012 cm-2; (f) n. = 2.0 x 1012 cm -2. The Hall mobility /x H is then defined by pxx(B = O) = 1/nHl~ne. At the dark value of the density (n H = 1.67 × 1012 cm -2) the sample showed the quantum Hall effect with one subband occupied (figs. l(a) and 2(a)). The fxy plateau at filling v = 2 extends over 5 T and corresponds to a fxx = 0 minimum of the same width. Bottomed out fxx minima are also seen at u=4and u=6. As the carrier density is increased, the ~ > 2 minima in fxx lift off from the fxx = 0 line (fig. 16 ~,12 ~a ,a. 4- 0 ~12 g8 ~ 4 0 %B Q- ¢ i 2 • / v=2 (b) .~ ..- I ') ' (c) ~. (f) ....... 16 12~, 4. a. 0 '12..-. 8 v 1, 4- Q- 0 ~2~, a~ 4 ~ 0 0 10 20 30 40 0 10 20 30 40 50 B T) B T) Fig. 2. Hall resistivity Pxy for the same densities as in fig. 1. The dashed line represents the classical Hall effect.  M. van der Burgt et al. / High-field transport in GaAs/Gao slno.2As/Gao.75Alo esAs 213 l(b)). Since Pxx remains zero for v = 2, this might be due to conduction in the second subband. however, we do not observe a second frequency in the SdH oscillations srcinating from carriers in the second subband as this is seen in high- mobility GaAs/Gal_xAlxAs heterostructures [6]. The difference between the Pxx = 0 baseline and the minima in Pxx becomes larger when the density is increased further (n,= 1.81× 1012 cm -2, fig. l(c)). At this density an asymmet- ry shows up in the v = 4 minimum at 19 T. This asymmetry becomes more pronounced at n n = 1.83 x 1012 cm -2 (fig. l(d)). At the same den- sities the Hall effect starts to deviate from the classical line ~xy = B/nHe Note the steep drop towards px~ = 0 in fig. l(d) at B = 30-40 T. For fields below 25T the SdH oscillations are superimposed on a rising background. Illuminating further to n H = 1.9 × 1012 cm -2 results in a new v = 4 minimum at B = 35 T (fig. l(e)) together with a plateau at p~y = h/4e z (fig. 2(e)). The structure in Pxx and Pxy corresponding to v = 2 is shifted beyond the available field range. The asymmetric minimum around 20 T hardly changes. As the density is increased to n H=2.0X 1012 cm -2 the v = 4 structure becomes very pro- nounced (figs. l(f) and 2(f)): a broad deep mini- mum is seen in p~ at B = 38 T and a broad plateau is developed in the Hall effect at Pxy = h/4e 2. This structure shifts to fields beyond 50 T with further increasing density (not shown). The minimum in p~ around 20 T then broadens and shifts to 25 T without drastic changes. Although less pronounced, for the u = 2 struc- ture similar changes as described above are ob- served at 77 K. From a series of sweeps to 5 T as a function of density we determined the Hall density nn, the Hall mobility/z H and the SdH density nsd .. The latter is the density of the first subband de- termined from the period of the SdH oscillations versus 1/B. The results are shown in fig. 3. As functions of the Hall density, the Hall mobility stays constant at /ha~3.25m2/Vs as long as n H ~< 1.85 × 1012 cm -2, and then shows a strong decrease. Note that this critical Hall density is the density where the strong changes in the 3.5 ,. 2.4 3o // 22 f % o - ' ~ E o oOo /J 2 0 ,~ • 1.8 t- 1 5 ~ 1.6 1 6 1 8 2 0 2 2 2 4 2 6 nH(1012cm -2) Fig. 3. The Hall mobility ~ (O) and the SdH density nsa H (R) versus Hall density n H. The solid symbols are points taken at 1.5 K, the others at 4.2 K. The dashed line repre- sents the nsa H = n, line. transport data are observed. At the same time nsd H starts to differ from nil, indicating that the total carrier density differs from .the carrier den- sity in the first subband. From the temperature dependence of the am- plitudes of the low-field SdH oscillations we determined the effective mass to be m*= 0.058m 0. This was done by fitting the amplitudes to the expression for the oscillating longitudinal resistivity of a 2DEG derived by Ando et al. [7]. 4. Discussion The value for the effective mass we obtained, m*= 0.058m0, agrees well with the value ob- tained from a linear interpolation between the effective mass values for GaAs, rn* = GaAs 0.067m0, and InAs, rni*nn = 0.023m 0 [8], for an In content of 20%. But our result is consistently lower than found by other groups [1,9], who obtain different values depending on In content and strain. The effective mass we find is used to calculate the Fermi level. With a density nH= 1.74 × 1012 cm -2, the density where the Pxx minima start to lift off from the baseline (fig. l(b)), the Fermi energy with respect to the first subband is E F =  214 M. van der Burgt et al. / High-field transport in GaAs/Gao slno eAs/Gao 75Alo 25As 72 meV. This agrees well with the distance be- tween the first and the second subband, which, from photoluminescence measurements, was found to be E~0 = 74 meV. This indicates that the changes in Pxx as seen in fig. l(b) might be due to conduction in the second subband. However, with these values of m* and El0, it is not possible to derive the v = 4 structure in figs. l(e)~(f) and 2(e)-(f) by drawing the calculated Fermi energy as a function of field in a Landau level fan diagram, e.g. as done in ref. [10] for GalnAs/ AllnAs heterojunctions. In order to obtain the electron densities and the mobilities of the two possible subbands we tried to fit our data to the two-band model [11,12]. In such a model for conduction, the total resistivitytensor for a system with two types of carriers is obtained by inverting the conductivity tensor, which is the sum of the conductivity tensors of the individual carrier types. We fitted this model to low-field data for Pxx and Pxy up to 5 T. We took nSd H = n~, the density of the first subband, as a known parameter. The mobility of the first band, /.q, and the density and mobility of the second band, n 2 and/x 2, are obtained from the fit. The results are summarized in table 1. Note that the Hall density n H gives a weighted sum of the two densities n I and n2, due to the different mobilities of the two types of carriers: nil/. ~ ---- nl/.L 1 + n2~ 2. We see that the second band has a relatively large density (n2) with a very low mobility (/~2)- It is hard to imagine how a second subband could accomodate such a large amount of carriers as compared to the first sub- band. Furthermore, the low mobility of the as- sumed second subband, which is about 40 times lower than the mobility of the first subband, is in strong contrast with results from GaAs/GaA1As heterostructures where the mobility of the sec- ond subband is only a factor 4 smaller [6]. The low mobility and the high carrier density we obtain for the second type of carrier is typical for parallel conduction, which in our case might occur also in the dopant layer inside the Gao.75Alo.25As. Further support in favour of par- allel conduction is the fact that the low-field (B < 15 T) SdH oscillations in figs. l(c)-(f), are superimposed on a rising background and the Hall effect deviates from the classical line (figs. 2(c)-(f) at these densities [13,14]. But, parallel conduction in the Gao.75Alo 25As cannot be reconciled with the high-field transport data. The steep drop of Pxx towards zero at B = 40T (figs. l(d), (f)) and the corresponding plateaux in Pxy (figs. 2(d), (f)) would argue against parallel conduction for B > 30 T. A possible mechanism which may explain this steep drop of px, is magnetic freeze-out of the electrons in the Ga075A10.25As layer. But it is not clear how the electrons could be captured by the deep impurity levels (DX centra) in this layer. Up to date very little is known about it since extreme high fields are needed to study this effect. Furthermore, magnetic freeze-out cannot explain the v = 4 plateau in fig. 2(f) either. From the arguments listed above, we may conclude that the decrease in mobility as shown in fig. 3 cannot be explained as simply arising from parallel conduction or inter-subband scat- tering [15]. Table 1 Densities and mobilities obtained from the low-field ransport data (nil,/~, nsdH) and a fit to the two-band model (/zl, n2,/z2). nn P-n nsdn = nl //'1 n2 /I,2 (10 2 cm -2 ) (m2/V ) (1012 cm -2 ) (m2/V ) (10 x2 cm -2) (m2/V ) 1.67 3.24 1.66 3.31 - - 1.87 3.25 1.84 3.32 0.7 0.02 1.97 3.02 1.88 3.22 0.8 0.08 2.07 2.65 1.95 2.81 1.5 0.06 2.21 2.50 2.01 2.74 2.4 0.06  M. van der Burgt et al. / High-field transport in GaAs/GaoslnoeAs/Gao 75Alo.esAs 215 5. Conclusions We studied transport in GaAs/GaosIno.2As/ Ga0.75A102sAs heterostructures in magnetic fields up to 50 T. Although the transport data at low fields can be interpreted as resulting from parallel conduction, the behaviour of the trans- port coefficients at magnetic fields above 30 T suggests other conduction mechanisms at these fields. The possibility of magnetic freeze-out and conduction in a second subband are discussed. Thus, the conclusions drawn from the low-field data are not supported by the transport be- haviour at very high magnetic fields. References [1] J.K. Luo, H. Ohno, K. Matsuzaki and H. Hasegawa, Jpn. J. Appl. Phys. 27 (1988) 1831. [2] H. Ohno, J.K. Luo, K. Matsuzaki and H. Hasegawa, Appl. Phys. Lett. 54 (1988) 36. [3] J.W. Matthews and A.E. Blakeslee, J. Cryst. Growth 27 (1974) 118. [4] L. Van Bockstal, G. Heremans and F. Herlach, Meas. Sci. Technol. 2 (1991) 1159. [5] M. van der Burgt, P. Thoen, F. Herlach, F.M. Peeters, J.J. Harris and C.T. Foxon, Physica B 177 (1992) 409. [6] H. van Houton, J.G. Williamson, M.E.I. Broekaart, C.T. Foxon and J.J. Harris, Phys. Rev. B 37 (1988) 2756. [7] T. Ando, A.B. Fowler and F. Stern, Rev. Mod. Phys. 54 (1982) 437. [8] G. Ji, D. Huang, U.K. Reddy, T.S. Henderson, R. Houdr6 and H. Morkoq, J. Appl. Phys. 62 (1987) 3366. [9] H. Brugger, H. Miissig, C. W61k, K. Kern and D. Heitmann, Appl. Phys. Lett. 59 (1991) 2739. [10] J.C. Portal, R.J. Nicholas, M.A. Brummell, A.Y. Cho, K.Y. Chen and T.P. Pearsal, Solid State Commun. 43 (1982) 907. [11] M.A. Reed, W.P. Kirk and P.S. Kobiela, IEEE J. Quantum Electron. 22 (1986) 1753. [12] M.J. Kane, N. Apsley, D.A. Anderson, L.L. Taylor and T. Kerr, J. Phys. C 18 (1985) 5629. [13] S. Luryi and A. Kastalsky, Appl. Phys. Lett. 45 (1984) 164. [14] D.A. Syphers, K.P. Martin and R.J. Higgins, Appl. Phys. Lett. 49 (1986) 534. [15] H.L. St6rmer, A.C. Gossard and W. Wiegmann, Solid State Commun. 41 (1982) 707.
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