Microwave noise temperature versus bias and frequency

Chapter III: Measurement results, device modeling, and interpretations

3.1 Microwave noise temperature versus bias and frequency

Figure3.1shows the noise temperature𝑇_eand gain𝐺 versus bias power𝑃_DC taken at a fixed frequency of 𝑓 =4.55 GHz, the frequency at which the device exhibited its noise minimum as determined by the IMN, and in several different cryogenic environments. Here,𝑃_DCwas varied by changing𝑉_DSfor a fixed𝑉_GS. In Fig.3.1(a), 𝑉_DSranged from 0.21 V to 0.99 V yielding current densities𝐼_DSfrom 57.9 mA mm⁻¹ to 241.6 mA mm⁻¹, with a peak gain of𝐺 = 27.5 at biases above 𝑃_DC = 50 mW mm⁻¹. In Fig.3.1(b),𝑉_DS ranged from 0.15 V to 1.25 V yielding current densities 𝐼_DS from 29.2 mA mm⁻¹ to 190.5 mA mm⁻¹, with a peak gain of𝐺 = 31.5 dB at biases above𝑃_DC =75 mW mm⁻¹. In Fig.3.1(c),𝑉_DSranged from 0.19 V to 1.35 V yielding current densities𝐼_DSfrom 21.3 mA mm⁻¹to 169.0 mA mm⁻¹, with the same peak gain of𝐺 =31.5 dB at biases above𝑃_DC =75 mW mm⁻¹. The data taken with the DUT immersed in vapor environments was taken in the second measurement dewar, where each sweep was taken up to a smaller maximum power. The gain varies by less than 0.5 dB across all temperatures, indicating consistent biasing across each measurement dewar and cryogenic environment. The dependence of both𝐺and𝑇_eon𝑃_DCand𝑇_physis qualitatively similar for each fixed𝑉_GS. As bias is

increased,𝑇_einitially decreases as𝐺increases. The noise temperature then bottoms out as the gain saturates, before𝑇_ebegins to increase with bias. Across all cryogenic environments, the minimum noise temperature occurs between 1.96 K (𝑉_GS =−2.8 V and𝑇_phys = 1.6 K in He II, as seen in Fig. 3.1(b)) and 2.81 K (𝑉_GS = −3.2 V and𝑇_phys =33.8 K in vacuum, as seen in Fig.3.1(c)), an indication that cryogenic environment did not play a significant role in mitigating self-heating at these biases.

A divergence in𝑇_ebetween different physical temperatures is observed beginning at 𝑃_DC =50 mW mm⁻¹in Fig.3.1(a)and at𝑃_DC =75 mW mm⁻¹in both Figs.3.1(b) and3.1(c). The reason for this divergence is unclear, although we suspect that it is related to a changing thermal resistance between the channel, gate, and substrate, and not due to self-heating mitigation by the liquid cryogens.

Figure3.2shows𝑇_eand𝐺versus drain-source current𝐼_DStaken at a fixed frequency 𝑓 =4.55 GHz in several different cryogenic environments, where𝐼_DSwas varied by changing𝑉_GSfor a fixed voltage𝑉^PS

DSoutput by the biasing power supply. Converting 𝐼_DS to 𝑃_DC was not possible for this data due to complications arising from an asymmetry in the biasing circuits between the two stages, which led to an uncertainty in the true𝑉_DS across each transistor. Although this uncertainty was also present in the data shown in Fig. 3.1, in that case since the gate voltage was fixed, the offset of𝑉_DS caused by the bias asymmetry did not change between data points.

For measurements taken in the first measurement dewar (He II, He I, and vacuum) the gate-source voltage was swept from𝑉_GS = −4.1 V to𝑉_GS = −1.0 V, whereas for measurements taken in the second measurement dewar (vapor) this voltage was swept from𝑉_GS =−4.0 V to𝑉_GS = −2.0 V. In Fig. 3.2(a)the drain-source voltage output by the power supply was𝑉_DS =1.0 V. The gain and noise remain relatively flat with increasing𝐼_DS, with𝑇_evarying by less than 1.5 K and𝐺varying by less than 5 dB until a critical bias of_DS=110 mA mm⁻¹when the gate becomes sufficiently open that the gain decreases and the noise temperature increases rapidly. The noise temperature in the flat region varies by less than 1.8 K for the same bias across different physical temperatures. In Fig. 3.2(b) the drain-source voltage output by the power supply was𝑉_DS = 1.4 V. In this case, there was a larger spread in𝑇_e versus 𝑇_phys with a maximum difference of 4.2 K between the noise measured in vacuum and He II at a bias of 99.9 mA mm⁻¹, and a bump in noise temperature is also observed between the flat region and the region of rapidly decreasing gain.

The origin of this bump is presently unclear, and is suspected to be associated with asymmetric biasing.

Fig. 3.1: Noise temperature (left axis) and gain (right axis) versus bias measured at a fixed frequency of 𝑓 =4.55 GHz in the following cryogenic environments: 1.6 K He II (blue triangles), 4.2 K He I (cyan triangles), 8.0 K vapor (green diamonds), 19.7 K vapor (green squares), and 33.8 K vacuum (purple circles). The bias was varied by changing the drain-source voltage for a fixed gate-source voltage of (a) 𝑉_GS = −2.2 V,(b)𝑉_GS = −2.8 V, and (c)𝑉_GS = −3.2 V. For each fixed𝑉_GS the low-noise bias shifts by less than 10 mW mm⁻¹ and the noise temperature at the low-noise bias changes by less than 1 K across all physical temperatures.

Figure3.3(a)shows𝑇_eand𝐺versus microwave frequency 𝑓 with the device biased at its low-noise bias 𝑃_DC = 24.5 mW mm⁻¹ and immersed in five different bath conditions ranging from 1.6 K He II to 35.9 K vacuum. The noise varies by less

Fig. 3.2: Noise temperature (left axis) and gain (right axis) versus drain-source current measured at a fixed frequency of 𝑓 = 4.55 GHz in the same cryogenic environments as in Fig. 3.1. The bias was varied by changing the gate-source voltage for a fixed drain-source voltage output by the power supply of(a)𝑉^PS=1.0

DS V

and(b)𝑉^PS=1.4

DS V.

than 2 K across all measured frequencies and temperatures at this bias. The noise increases monotonically with increasing physical temperature regardless of bath condition. The gain varies by approximately 4 dB over the measured frequency range, peaking at 𝑓 =4 GHz. The gain variation with physical temperature is less than 0.5 dB at fixed 𝑓 and𝑃_DC.

Figure 3.3(b) shows 𝑇_e and 𝐺 versus 𝑓 with the device immersed in 1.6 K He II at three different device biases of 𝑃_DC = 24.5 mW mm⁻¹, 𝑃_DC = 79.5 mW mm⁻¹ and 𝑃_DC = 120 mW mm⁻¹. At biases below 𝑃_DC = 79.5 mW mm⁻¹ the noise temperature varies by less than 1.5 K for all frequencies, while above 𝑃_DC = 79.5 mW mm⁻¹ the noise increases more rapidly with bias. The gain

increases monotonically with increasing bias while retaining the same shape versus frequency, but it appears to asymptotically plateau at approximately the highest gain shown here, at a bias of𝑃_DC =120 mW mm⁻¹.