PL was excited with an argon ion laser (514 nm), dispersed with a 0.5-m monochromator and detected with a thermo-cooled GaInAs photodetector. Results and discussion Figure 1a shows the experimental data of magnetoresistance measurements at various temperatures for one set of the N-containing and N-free as-grown samples. It is known that SdH oscillations can be observed in high magnetic fields (μB > 1) in low mobility samples and at low temperatures (k B T < ℏω C ). Since doping amount is the same in all samples, carrier mobility is an important factor to be able to observe SdH oscillations. As seen in Figure 1, the SdH oscillations start at lower magnetic fields for N-free samples

as an indication of higher carrier mobility in N-free samples. It is worth noting that we observed higher mobility in N-free samples in a previous work (see [8]). Figure 1 SdH oscillations. (a) Raw experimental magnetoresistance Akt inhibitor in vivo data and (b) second derivative of the SdH oscillations at different temperatures for the as-grown N-free (y = 0) and N-containing (y = 0.009) samples. The observed decrease of the amplitude of SdH oscillations with increasing temperature can be expressed by an analytical function [17–19]: (1) (2) (3) (4) (5) where Δρ xx ,  ρ 0,  E F,  E 1,  ω c ,  m *,  τ q , and μ q are the oscillatory magnetoresistivity, zero-field

resistivity, Fermi energy, first subband energy, cyclotron Endonuclease frequency, effective mass, quantum lifetime of 2D carriers, and carrier mobility, respectively. The i represents the subbands. In Equation 1, the temperature dependence click here of the amplitude of the oscillations is included in the function D(χ). The exponential function in Equation 1

represents the damping of the oscillations due to the collision-induced broadening of Landau levels. The contribution of the higher subbands appears in SdH oscillations with different periodicity. We observed that the SdH oscillations has only one period, indicating that only the lowest subband is occupied. The observation of diminishing minima is an indication of absence of background magnetoresistance and presence of 2D carrier gas. As seen in Figure 1a, the SdH oscillations are suppressed by either a positive (for N-free sample) or a negative (especially for n-type N-containing sample) background magnetoresistance. The minima of SdH oscillations decrease as the magnetic field increases for p-type N-containing samples due to negligible negative magnetoresistance than that of n-type sample. As for N-free samples, a pronounced positive magnetoresistance causes minima to increase with the magnetic field. The origin of the positive magnetoresistance is parallel conduction due to undepleted carriers in barrier layer, herein GaAs. On the other hand, the weak localization effect leads to negative magnetoresistance [19, 20].