Growth temperature

The influence of the growth temperature for LaAlO₃films on the transport properties of the LaAlO3/SrTiO3interface can be clearly seen in Fig.3.1. Here we further perform a systematic magneto-transport study to investigate the role of the growth temperature (T_g) [66].

In the top panel of Fig.3.6, the room temperature sheet resistanceRsis plotted as a function ofT_g. We note that upon decreasingT_gdown to 650^◦C,R_sincreases by roughly an order of magnitude. This evolution is mainly attributed to a reduction of the carrier density, with the increase in the Hall mobility (µ) being less than a factor of 2¹. The lower panel of Fig.3.6shows that asT_gis reduced from 900 to 650^◦C, a large

1The estimation of the carrier density is obtained from the Hall constant at 296 K where the Hall resistance is linear in magnetic field.

increase in the electron mobility (µ) at low temperatures is observed:µgoes from 600 to 8000 cm²V⁻¹s⁻¹at 1.5 K.

In the left panels of Fig.3.7, we plot the Hall resistanceRxy measured at 1.5 K as a function of the magnetic field (B). In the right panels we plot in colour code the field derivative of the Hall resistance (^∂R_∂B^xy) with respect to the magnetic fieldB (vertical axis) and temperatureT (horizontal axis) for heterostructures grown at 650^◦C, 800^◦C and 900^◦C.

Samples grown atT_g= 650^◦C, exhibit a linearR_xy, which is essentially temper-ature independent. For samples grown at 800 and 900^◦C, the Hall resistanceRxy

displays a more complex behaviour. In the 100-300 K temperature range,Rxy is linear in magnetic field and ^∂R_∂B^xy is temperature independent². Below∼100 K, the Hall response becomes a non-linear function of the magnetic field and its low field derivative increases at low temperature. The temperature dependence of the inverse Hall constant estimated atB →0is shown in Fig.3.8.

Analysing the low temperature magnetotransport for samples grown at 900^◦C with a two band model [28] reveals contributions from a band with a low carrier density (1−5×10¹²cm⁻²) and a high mobility (in the range of1000−2000 cm²V⁻¹s⁻¹) and from a band with a higher carrier density (≈5−6×10¹³cm⁻²) and low mobility (in the range of100−200 cm²V⁻¹s⁻¹), in agreement with previous reports [81,153].

The dependence on magnetic field ofRHfor different temperatures can be captured by the same two-band model (see Fig.3.8) taking into account the temperature dependence of the scattering time (1/τ = 1/τ_e+ 1/τ_i,τ_eandτ_ibeing the elastic and the inelastic scattering times respectively andτi∝T^−2.8, see Fig.3.6) while keeping the density of each band constant³. Thus the temperature and field dependencies of the Hall resistance can be quantitatively explained by the presence of carriers with different mobilities in the system. This analysis also suggests that the slope of the Hall effect at high fields can give a better estimation of the total mobile carrier density [154].

The presence of charge carriers with different masses (and thus different mobilities) at the LaAlO3/SrTiO3 interface has been anticipated by ab initiocalculations [69, 71,72,102,142]. As we have seen in Chapter1, both calculations and experimental observations have unveiled an electronic structure of the confined 2DEL characterised by a lifting of thet2g degeneracy of the 3dorbitals. The lowest dxy sub-band has a lower energy than the lowestd_xz/d_yz sub-bands [74]. According to this picture, for low carrier densities only d_xy sub-band with an effective mass m^∗ = 0.7 m_e should contribute to the transport. For large densities, the Fermi level should crossdxy

andd_xz/d_yz (m^∗ = 2.2m_e,m_ebeing the electron mass) sub-bands and then multi-channel conduction can be expected. However, more recently resonant photoemission spectroscopy [75] supported byab initiocalculations have revealed that the electronic band structure is modified when the carrier density is changed. Probably due to a change in the confinement potential [28,144], as we saw in Section 2.5, d_xz/d_yz sub-bands are still observed at low carrier density.

2We note that, depending on the photo-doping level [151,152], some temperature dependence of the Hall effect above 100 K can sometimes be observed.

3The elastic scattering time for each band is calculated from the respective mobility obtained from the two band fit in magnetic field while the inelastic scattering time is considered to be independent of the carrier type.

6 0 0 7 0 0 8 0 0 9 0 0 1 0

1 0

1 0

1 1 0 1 0 0

1 0

1 0

1 0

1 0

1 0

R S a t R T ( k Ω )

T _g (°C)

0 . 1

1

1 0

1 /R H e a t R T ( 1 0 1 3 c m -2 )

T _g =650 °C T _g =800 °C T _g =900 °C

µ ( c m 2 V -1 s -1 )

T (K)

∝ T ^-2.8

Figure 3.6 –Top panel: Evolution of the sheet resistance (left axis) and inverse Hall constant (right axis) measured at room temperature (RT) as a function of the growth temperatureTg. The lines are guides to the eye. Bottom panel: Hall mobility as a function of temperature for samples grown at 650^◦C (blue squares), 800^◦C (gold diamonds) and 900^◦C (brown pentagrams). The dashed line shows a fit assumingµ∝T^αwithαbeing

−2.8. This temperature dependence is also observed in bulk doped-STO.

rescaled

Figure 3.7 –Left-Rxyvs. magnetic fieldB measured at 1.5 K for three growth tem-peratures. right- Derivative ofRxy as a function ofB and temperatureT. For each growth temperature, the value of the derivative has been rescaled by its value at 160 K (^∂R_∂B^xy)|_T/(^∂R_∂B^xy)|_160Kto illustrate the presence of non-linearities.

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0

0 . 1

1

1 0

900°C

800°C 650°C

T(K) 1 /R H e ( 1 0 1 3 c m -2 )

Figure 3.8 –Temperature dependence of the inverse Hall constant estimated forB →0 (calculated as^∂R_∂B^xy|_B→0) for interfaces grown at different temperatures (symbols) and calculated using the two band model described in the text (dashed line).

- 8 - 4 0 4 8

Figure 3.9 – Comparison between the magnetotransport of two interfaces exhibiting the same sheet carrier density but grown at different temperatures:For the interface grown at 800^◦C, electric field effect was used to reduce the carrier density. A low value for the mobility (34 cm²V⁻¹s⁻¹) is observed. The negative magnetoresistance shown here is a sign of weak localisation. For the sample grown at 650^◦C Shubnikov-de Haas oscillations can be observed revealing high mobility.

Figure3.9shows magnetoresistance (^Rxx(B)−R_R ^xx(0)

xx(0) ) at 1.5 K for a sample grown at 650^◦C (µ= 5050 cm²V⁻¹s⁻¹): it increases by 20% for a magnetic field of 7 T.

This large magnetoresistance suggests that, for these low carrier densities, multiple channels also contribute to the transport. Above 4 T, a remarkable Shubnikov-de Haas oscillation can be observed, which were not present in the samples grown at 800 and 900 ^◦C at this magnetic field. Comprehensive analysis of this spectacular magnetoresistance oscillations gives access to study the complex Fermi surface and to shed light on the band structure of the system [48]. Further evidence of the population ofdxz/dyz orbitals in LaAlO3/SrTiO3interfaces grown at 650^◦C and the presence of Rashba type spin-orbit coupling in these orbitals were shown recently by model dependent fittings done on these large Shubnikov-de Haas oscillations [155].

We performed a series of field effect experiments on samples grown at 800^◦C.

In agreement with Bell et al.[84], we find that the dominant effect of the electric field in the back gate geometry is the modulation of the mobility. In Fig.3.9we show also the low temperature magnetoresistance of a sample grown at 800^◦C upon using field effect. The carrier density was tuned to match that of the high mobility sample⁴ (R⁻¹_H e⁻¹ = 8×10¹²cm⁻²). In this case, we observe a reduction of the mobility to 34 cm²V⁻¹s⁻¹. We can clearly see that whereas the high mobility sample displays

4In this carrier density range, the Hall effect is linear in magnetic field for both type of interfaces.

a positive magnetoresistance, the magnetoresistance of the sample grown at 800^◦C is negative and in the scale ofe²/πh. This behaviour has been attributed to weak-localisation phenomena [80]. The strikingly different magnetotransport behaviour in samples compared here with similar carrier densities reveals the low dimensional nature of this conducting system where transport regimes are determined by the characteristic scattering lengths (elastic, phase, spin-orbit) more than their carrier density.

These results emphasise the open question on the origin of the carrier mobility at the LaAlO₃/SrTiO₃ interface : what determines the highµobserved in lowT_gsamples compared with the lowµmeasured in highT_gsamples for the same doping? Since the shape of the confinement potential is considered to be responsible for the proximity of the conducting layer to the interface, any disorder would affect differently the electron mobility depending on the charge profile [84]. In this scenario, the electric field effect results suggest that the charge profile at the same density can be different. On the other hand, if the interface perfection is modified by the growth temperature [156], the same charge profile would generate a different electronic mobility.

3.3 Fabrication of superconducting interfaces between