On the angular dependence of InP high electron mobility transistors for cryogenic low noise amplifiers in a magnetic field

In many sensitive detection systems, high electron mobility transistor (HEMT) low-noise amplifiers (LNAs) at cryogenic temperatures (1-10 K) are used to read out tiny microwave signals. Some of these systems rely on the presence of a strong magnetic field, e.g. in mass spectrometry¹ or detection of dark matter.^2,3 A potential application for cryogenic LNAs in a magnetic field is magnetic resonance imaging.⁴ A problem prevalent in these detectors is that amplifier properties such as gain and noise figure are negatively affected by the magnetic field. The situation is most unfavorable for the LNA oriented perpendicular to the magnetic field (because of the Lorentz force acting on the current). As a result, scientists always strive to mount the LNA away from the magnetic field using coaxial cables alternatively to align the LNA parallel to the magnetic field lines. While the former solution is not preferable because of losses and reduced sensitivity, the latter gives rise to the issue on the degree of alignment of the LNA in the field. This is related to the orientation of the HEMT (and the 2DEG transport current) in a magnetic field. Here we report the angular dependence of the output current for the cryogenic InGaAs-InAlAs-InP (InP) HEMT in a magnetic field. It is shown that the InP HEMT output current is limited by a strong geometrical magnetoresistance effect (gMR) as a function of angle and magnetic field. We also confirm that the gain and noise properties for the cryogenic InP HEMT LNA are very prone for degradation when exposed to a magnetic field. The strong angular field dependence demonstrated for the cryogenic InP HEMT output current suggests that even small misalignment of the cryogenic InP HEMT LNA in a magnetic environment is detrimental to read-out sensitivity.

We first examined the sensitivity of the cryogenic InP HEMT LNA in a magnetic field using a 10 T superconducting magnet. The LNA was a monolithic microwave integrated circuit (MMIC) chip consisting of three InP HEMT stages and passive components mounted in a gold-plated aluminum module. Neither the LNA module nor in-going passives exhibited any magnetic-field dependence as verified by additional experiments. The amplifier was a broadband design ranging from 0.3 to 14 GHz with a gain of 42 dB and average noise temperature of 4.2 K (0.06 dB) at 6 K ambient temperature.⁵ The LNA was mounted at the centre of the magnet on the 2 K stage of an Oxford Instruments Triton 200 dilution refrigerator. The setup only permitted the LNA module to be oriented perpendicular to the magnetic field. In Fig. 1 the gain and noise temperature at 3, 5 and 8 GHz are presented for the cryogenic InP HEMT LNA at 2 K when exposed to static magnetic fields up to 1.5 T. For all three measured frequencies, the LNA gain and noise temperature started to be affected around 0.25 T. Compared to an earlier study for a GaAs HEMT LNA,⁶ the degradation for the InP HEMT LNA in the presence of a magnetic field is much stronger. This is connected to the higher electron mobility and sheet density of the two-dimensional electron gas (2DEG) in the InP HEMT compared to the GaAs HEMT used in Ref. 6.

The very strong degradation of the cryogenic InP HEMT LNA illustrated in Fig. 1 motivated the investigation of the InP HEMT as a function of angle and magnetic field. DC measurements were conducted on individual transistors at low temperature. The discrete InP HEMTs were fabricated in the same transistor technology⁷ used for the cryogenic InP HEMT LNA measured in Fig. 1. We have fabricated two-finger device layouts with gate width W_g ranging from 10 to 100 μm and gate length L_g from 60 to 250 nm. The DC-characterization was carried out in a Quantum Design Physical Property Measurement System (PPMS). The transistor was electrically connected through wire bonding and mounted in a matched LC-network on a sample holder in the vacuum chamber of the cryostat and cooled down to 2 K. A static magnetic field ranging up to 14 T was then applied and DC measurements were performed using a Keithley 2604B source meter.

The measurement setup in PPMS allows for sample rotation in the B-field. In Fig. 2, the geometry of the DC experiment is shown. A static magnetic field was applied in the z-direction. Fig. 2 presents a top view and side view of the two-finger InP HEMT where an angle of rotation θ is defined with respect to the magnetic field. θ could be varied between 0° and 180° degrees where 0° (180°) and 90° corresponded to measurements of the InP HEMT oriented parallel and perpendicular to the magnetic field, respectively.

The cryogenic InP HEMT output current was first measured for θ = 90°. Figure 3 shows the source-drain current I_ds versus source-drain voltage V_ds for different gate-source voltage V_gs under a magnetic field of 0 T and 10 T. The device was a 2x50 μm InP HEMT with L_g=100 nm. Figure 3(a) illustrates a typical InP HEMT measured under cryogenic conditions in the absence of a magnetic field. The kink behavior at high current level around V_ds=0.4 V originates from electron traps in the interface layers of the heterostructure and is characteristic for these type of devices measured at low temperature.⁸ Since the LC network in the sample holder did not provide a perfect 50 Ω impedance environment for the transistor, oscillations occurred for lower I_ds showing up as small current jumps at V_gs < -0.2 V, which do not influence the interpretations in this study. In Fig. 3(b), the same measurement was repeated under a magnetic field of 10 T. It stands clear that I_ds is extremely suppressed for θ = 90° when exposed to the magnetic field. Comparing Fig. 3(a) and (b), the maximum I_ds (V_ds=1 V) was reduced by almost a factor of 100. The device still behaves as a transistor but with a much larger on-resistance and strongly reduced transconductance.

Measurements for the InP HEMT shown in Fig. 3 for θ = 0° and θ = 90° in a magnetic field up to 14 T are summarized in Fig. 4. I_ds was measured under saturation for two biases V_ds=0.4 and 0.6 V and normalized with respect to zero field. The strong suppression in output current for θ = 90° is visualized in Fig. 4. As comparison, the effect in I_ds from the magnetic field for θ = 0° is almost negligible (a minor reduction beyond 10 T may be due to a slight mis-orientation of the HEMT in the field). No difference with regard to V_ds is noted in Fig. 4.

We also observe in Fig. 4 that for θ = 90°, the normalized I_ds varies as B².

Moreover, it was confirmed that this dependence was the same for a range of various device sizes L_g (60, 100, 250 nm) and W_g (2x10, 2x50, 2x100 μm), see Fig. 5. In our experimental setup, the Hall effect (voltage) is negligible because of the device geometry with W_g > > L_g.⁹ The output current transport in the InP HEMT is therefore limited by gMR,¹⁰ which occurs due to the effect of the Lorentz force on the 2DEG in devices where W_g > > L_g. gMR is expected to be large under the experimental circumstances here, i.e. high channel mobility in the 2DEG and a strong magnetic field.

The angular dependence of the cryogenic InP HEMT output current in a magnetic field was investigated by rotating the transistor in the magnetic field. θ was increased from 0° to 180° using a step size of 1°. In Fig. 6, I_ds is plotted as a function of θ up to 10 T. It is noted that the I_ds is clearly dependent on θ and that this dependence becomes larger with higher magnetic field. Irrespectively of the applied field strength, we observe no change in the output current when (the 2DEG channel of) the transistor has a 0° or 180° rotation. A significant reduction (∼ 20%) in I_ds for rotations as small as 15° occurs at an applied field of 3 T. With increasing magnetic field, the alignment of the InP HEMT becomes even more crucial and the I_ds is reduced by a minor tilt in θ of a few degrees.

For a transistor layout with W_g > > L_g, the gMR in the channel is expected to vary as 1 + μ²B², where μ is the electron mobility in the channel.^9,10 Taking the angular dependence in Fig. 2 into account for a transistor output current in an electrical field subject to a Lorentz force leads to

where R₀ is a resistance term (including channel and access resistance contributions in the InP HEMT). Fitting the data to Eq. 1 gives R₀ = 11 Ω and μ = 10, 500 cm²/Vs, which is in excellent agreement for the full range of measured θ and B in Fig. 6 reflecting the symmetrical angular dependence in I_ds around θ = 90°.

The transconductance and on-resistance are two HEMT parameters fundamental for the design of a cryogenic LNA. The maximum transconductance g_m,max at 2 K of the cryogenic InP HEMT is plotted in Fig. 7(a) as a function of the applied magnetic field up to 14 T for various angles θ. The g_m,max is around 1.9 S/mm at zero field and strongly decreases as a function of magnetic field for θ = 30° and above. Already at 1 T, the g_m,max is reduced with 40% (60%) for θ = 30° (90°). Field-effect transistor transconductance versus magnetic field for θ = 90° has been reported in Refs. 6 and 11 for GaAs and silicon devices at cryogenic and room-temperature conditions, respectively. The dependence on magnetic field is much stronger for the InP HEMTs investigated in this study. In contrast to Ref. 6, the g_m,max here is directly calculated from measured I-V data for the transistor at cryogenic temperature in a magnetic field. Compared to Fig. 7(a), Ref. 11 shows a much weaker dependence which is probably related to the silicon-based transistor subject to study, a device normally not used in cryogenic LNAs. The on-resistance for the InP HEMT (at 2 K) as a function of B for various θ is presented in Fig. 7(b). For B=0 T, the R_on is around 0.7 Ωmm independent of B for θ = 0°. As expected from Figs. 3 and 4, R_on increases rapidly with B for θ = 90°, two orders of magnitude at 5 T. This dependence is also strong at smaller angles as illustrated for θ = 30° in Fig. 7(b). R_on is found to vary in a similar way as the denominator in Eq. (1): R_on = R₀(1 + μ²B²sin²θ). Fig. 7 demonstrates that transistor parameters crucial for the design of a cryogenic LNA are highly sensitive to the alignment of the InP HEMT in a magnetic field at 2 K. This explains the strong degradation of the LNA gain and average noise temperature (measured for θ = 90°) observed in Fig. 1.

In conclusion, we have investigated the angular dependence of the output current of cryogenic InP HEMTs in magnetic fields up to 14 T and found that it is greatly attenuated, not only at θ = 90°, but also at small θ. The physical reason is the very strong gMR occurring for I_ds in the cryogenic InP HEMT. This was validated by an accurate fitting of experimental I_ds data with an equation describing the gMR as a function of B and θ. Furthermore, we have shown the strong influence from θ for the transistor parameters g_m,max and R_on when the cryogenic InP HEMT is exposed to a magnetic field. As a result, the alignment of cryogenic InP HEMT LNAs with respect to a magnetic field is critical in sensitive microwave detection systems: even small deviation from θ = 0° (180°) leads to significantly lower gain and higher average noise temperature.

This work was performed in GigaHertz Centre in a joint research project between Chalmers University of Technology, Low Noise Factory AB, Wasa Millimeter Wave AB, Omnisys Instruments AB and RISE Research Institutes of Sweden. We are grateful to Serguei Cherednichenko for valuable assistance in the noise measurements and Niklas Wadefalk for the LNA design.