High electron mobility transistors are widely used as microwave amplifiers owing to their low microwave noise figure. Electronic noise in these devices is typically modeled by noise sources at the gate and drain. While consensus exists regarding the origin of the gate noise, that of drain noise is a topic of debate. Here, we report a theory of drain noise as a type of partition noise arising from real-space transfer of hot electrons from the channel to the barrier. The theory accounts for the magnitude and dependencies of the drain temperature and suggests strategies to realize devices with lower noise figure.

Low noise microwave amplifiers based on high electron mobility transistors (HEMTs) are widely used in scientific applications ranging from radio astronomy1 to quantum computing.2,3 Decades of progress in device fabrication have yielded significant advances in figures of merit, such as transconductance,4–6 gain,7 unity gain cutoff frequency,8–10 maximum oscillation frequency,11 and power consumption.9,12,13 The resulting devices exhibit excellent noise performance, with minimum reported noise figures of HEMTs around a factor of 5 above the standard quantum limit in the 1–100 GHz frequency range.7,14–18

Further improvements in the noise performance of HEMTs require a physical understanding of the microscopic origin of electronic noise. The Pospieszalski model19 describes the noise using noise generators at the gate and drain. The gate noise is generally attributed to thermal noise of the gate metal,1,20 but the physical origin of the drain noise remains unclear. The earliest treatment of electronic noise in HEMTs by Pucel et al.21 described noise in the saturated region as originating from the generation of dipole layers. More recently, drain noise has been attributed to a suppressed shot noise mechanism.22,23 Experimentally, drain noise is reported to exhibit a dependence on drain current1 and physical temperature,24–26 although the temperature dependence is disputed.27 Recent work has reported the dependence of drain noise on drain current and drain voltage, with the former being dominant but the latter being non-negligible in devices with 35 nm gate length.28 

A separate body of literature has extensively investigated high-field transport,29–31 energy relaxation,32–38 microwave noise,39,40 and related properties in 2D quantum wells.41–45 The physical picture of high-field transport obtained from these studies is that electrons are heated by the electric field and lose energy primarily by optical phonon emission. Photoluminescence experiments provide evidence that electrons heated by the field scatter rapidly enough with each other to maintain a distribution characterized by a temperature that is higher than the lattice temperature.30 If the electron temperature is sufficiently high, electrons may thermionically emit over the confining potential at the heterointerface between the channel and the barrier and thereby leave the channel in a process known as real-space transfer (RST). This process was originally proposed as a means to realize heterostructure devices exhibiting negative differential resistance (NDR), where the NDR originates from an increased electron population in the lower mobility barrier layer as the drain voltage is increased.46 Devices exploiting the effect, such as charge injection transistors47 and negative resistance field effect transistors,48 were reported shortly thereafter. RST has also been observed in HEMTs under forward gate bias and high drain voltage.49,50

Observing NDR in a HEMT requires a non-negligible fraction of channel electrons to emit into the low-mobility barrier layer. However, even if RST is not evident in current–voltage characteristics, it may contribute to microwave noise as a type of partition noise between two dissimilar current paths, similar to intervalley noise.51,52 Microwave noise in semiconductor quantum wells and devices has been previously attributed to RST. For instance, Aninkevicius et al. concluded that RST was the origin of noise in an AlGaAs/GaAs heterostructure at 80 K based on the measured dependencies of noise temperature on electric field and conduction band offset, and they further attributed intervalley noise suppression to RST at high fields.39 In HEMTs, Feng et al. attributed drain noise partially to RST,53 although evidence supporting the claim was not provided. Other works reported on an RST process dominating low-frequency noise characteristics of AlGaAs/InGaAs HEMTs.54 Monte Carlo simulations have reported RST to affect the transit time55 and contribute to gate noise.56 Despite these prior studies in which noise in HEMTs was attributed to RST, a systematic examination of whether RST can account for the reported magnitude and trend of microwave drain noise in the context of the Pospieszalski model is lacking.

Here, we report an analytical theory of drain noise in HEMTs based on microwave partition noise arising from real-space transfer. The theory yields an expression for the drain noise temperature of the Pospieszalski model in which the peak electron temperature and the conduction band offset are key parameters. The theory explains the reported dependencies of the drain temperature and makes predictions about how to reduce its magnitude. Our work may guide the development of HEMTs with improved noise performance.

Consider a two-dimensional electron gas (2DEG) with an applied longitudinal electric field between the source and drain contacts such that electrons flow from the source to drain. We may focus only on the region under the gate by incorporating the other regions as access resistances.57 At the low-noise bias VGS0.1 V, the channel is pinched off, leading to an electric field with a peak value of 100 kV cm1(Ref. 58) under the drain side of the gate to maintain the current of around tens of mA mm1.15 The electric field heats the electrons to a temperature that may be sufficient for electrons to thermionically emit out of the channel; if so, the current will flow through both the channel and the barrier to the drain contact. The barrier is typically of much lower mobility than the channel owing to ionized impurity scattering by the dopants, and therefore, NDR will result from RST if a sufficiently large fraction of electrons transfer to the barrier.

Even if no changes in the IDSVDS characteristics due to RST can be detected, non-negligible current noise may still be generated by RST. The generated noise can be viewed as a type of partition noise owing to the different mobilities of the channel and the barrier. As given in Eq. (4.21) of Ref. 31, the spectral noise power of this mechanism can be expressed in terms of frequency ω and electric field E by

Sj(ω,E)=4e2n1n2(vd1vd2)2τV0n(1+ωτ)2,
(1)

where τ is the characteristic time for electrons to transfer from the channel to the barrier; n1, n2, vd1, and vd2 are average carrier concentrations and velocity in the channel (index 1) and barrier (index 2), respectively; n=n1+n2; and V0 is the 2DEG volume.

Equation (1) can be simplified further with the following considerations. First, we take n2n1 because NDR is not observed at the low-noise bias, constraining the maximum magnitude of n2. Second, vd2vd1 since the spacer mobility is much less than the channel mobility. Finally, ωτ1 in microwave applications so that Eq. (1) becomes

Sj(E)=4e2n2vd12τV0.
(2)

Let V0=LWd, where W and d are the gate width and 2DEG thickness, respectively, and L is a characteristic length over which electrons are hot enough to undergo RST. To facilitate comparison with the Pospieszalski model, we note that the spectral density of current fluctuations (SI) is related to that of current density fluctuations (Sj) as SI=A2Sj where A=Wd. Then, SI can be expressed as

SI(E)=4e2ns2vd12WτL,
(3)

where ns2=dn2 is the barrier sheet density and we have assumed that d is on the order of the barrier thickness.

This partition noise is added at the output of the HEMT. In the Pospieszalski model, the output spectral noise power SI=4kBTdgDS is parametrized by a drain temperature, Td, of the drain conductance gDS. To connect Eq. (3) to the Pospieszalski model, we equate the spectral noise powers and solve for Td. A simple expression for the drain temperature can then be obtained as

Td=e2vd12ns2τkBgDSL,
(4)

where gDS=gDS/W is the drain conductance per width. From Eq. (4), Td is observed to depend on ns2, showing a direct relationship between the fraction of electrons transferred into the barrier and Td. ns2, in turn, depends on the electron temperature, the conduction band offset between the channel and the barrier, and the probability for a hot electron to emit out of the channel. We note that Td should be regarded as the additional noise contribution from RST over that contributed by the channel resistance, which could be computed using the methods of Ref. 59.

We assess the validity of the theory by first presenting experimental evidence of the RST process in modern HEMTs at cryogenic temperatures. Current–voltage characteristics of an InP HEMT studied in Ref. 9 were measured at 5 K. The data, courtesy of Junjie Li and Jan Grahn at Chalmers University of Technology, are shown in Fig. 1(a) for 0.42VVGS1.14 V. Typical IV curves are observed for most values of VGS, including those corresponding to depletion (VGS0.1 V) at the low noise bias. In particular, a positive output conductance, gDS>0, is observed for VGS<1 V.

FIG. 1.

(a) IDSVDS characteristics of a 2×100μm gate width, 150 nm gate length InP HEMT at 5 K for several VGS. (b) Magnified view of current–voltage characteristics in (a) under forward bias. NDR is observed for VGS ≳ 1.05 V and VDS ≳ 1.1 V. Data courtesy of Junjie Li and Jan Grahn, Chalmers University of Technology.

FIG. 1.

(a) IDSVDS characteristics of a 2×100μm gate width, 150 nm gate length InP HEMT at 5 K for several VGS. (b) Magnified view of current–voltage characteristics in (a) under forward bias. NDR is observed for VGS ≳ 1.05 V and VDS ≳ 1.1 V. Data courtesy of Junjie Li and Jan Grahn, Chalmers University of Technology.

Close modal

As VGS increases above 1 V for VDS1.1 V, gDS<0 is observed. A magnified view of these characteristics is shown in Fig. 1(b), in which NDR is clearly present. Self-heating can be excluded as the origin as the three curves in Fig. 1(b) differ in dissipated power by only a few percent yet exhibit qualitatively different IV trends, depending on the value of VGS.

On the other hand, the observed trends qualitatively agree with those reported in prior studies of NDR devices60–62 and HEMTs50,63 at similar bias. In the case of HEMTs, a negative output conductance at forward gate bias and high VDS1 V was attributed to heating of electrons by the source–drain voltage, leading to increased emission of channel electrons into the barrier and through the gate terminal as VDS increased. As a result, the drain current decreased with increasing VDS, leading to a negative output conductance.50,63 The forward-biased gate voltage VGS allows a sufficient number of electrons to be emitted into the barrier so that the negative output conductance is observed. Although we have presented measurements on one HEMT in this study, the measurements are in qualitative agreement with trends reported previously,50,63 suggesting that similar results are observable in HEMTs more generally. These considerations, therefore, support the hypothesis that RST occurs and could also produce partition noise in modern HEMTs.

We now examine the predictions of the theory and how they compare to the reported magnitude and dependencies of drain noise. First, to estimate the magnitude of Td from Eq. (4), we must specify numerical values of the various parameters. We choose L100nm and gDS50mSmm1.15 The channel–barrier transit time, τ, has been estimated to be on the order of picoseconds by analyzing current reduction in a test structure devised to measure switching and storage effects in GaAs/AlGaAs heterojunctions.64 Following Eq. (5.15) in Ref. 45, we choose τ1 ps as a characteristic time for the emission process.

Next, the sheet density in the barrier due to transferred electrons, ns2, is required. This parameter depends on the channel sheet density in the pinched off region under the gate ns1; the hot electron fraction η or the fraction of electrons that are energetic enough to thermionically emit over the barrier; and the probability for a hot electron to actually emit, γ, as ns2γηns1. The typical sheet density obtained from Hall measurements is 3×1012cm2.14 However, the sheet density of relevance to RST is that near the pinchoff region of the gate where the electron temperature is highest. This value can be estimated using the typical current at the low-noise bias and the saturated drift velocity. Monte Carlo simulations have reported the saturated electron velocity to be vd15×107cms1 for InGaAs HEMTs.65,66 Using a value of IDS75mAmm1, a typical value at the low-noise bias,15 we obtain ns11011cm2. For simplicity, we assume that all electrons with sufficient energy jump the barrier so that γ=1.

The hot electron fraction η is determined by the conduction band offset ΔEc and VGS for a given electron temperature Te. This fraction can be obtained using standard theory for the current across a Schottky barrier [see Eq. (61) in Chapter 3 of Ref. 67] as η=exp((ΔEcqVGS)/kBTe).

Due to the exponential dependence of η on VGS, we neglect the weaker dependence of ns1 on VGS in our analysis. To compute η, we must specify Te in the channel. We obtained a numerical estimate of its magnitude for a 100 nm gate InAlAs/InGaAs HEMT with VDS=0.5 V, VGS=0 V at a lattice temperature of 300 K using Synopsys TCAD to solve the hydrodynamic and Poisson equations in a provided template structure.68 The result is shown in Fig. 2. We observe that Te equals the lattice temperature at the source, increases to a peak value at the drain side of the gate edge due to heating by the electric field, and decreases toward the drain as electrons lose energy by optical phonon emission. This calculation shows that peak electron temperatures in the HEMT are on the order of 1000 K around the low-noise bias point, although this value could vary by several hundred K depending on the device and bias conditions. With Te estimated, we can now compute η. For ΔEc0.5 eV57 and Te1000 K, we find η0.3%.

FIG. 2.

Electron temperature Te vs position along the channel computed using Sentaurus TCAD for VDS=0.5 V, VGS=0 V. Te peaks at the drain edge of the gate and decreases toward the drain as electrons lose energy by optical phonon emission.

FIG. 2.

Electron temperature Te vs position along the channel computed using Sentaurus TCAD for VDS=0.5 V, VGS=0 V. Te peaks at the drain edge of the gate and decreases toward the drain as electrons lose energy by optical phonon emission.

Close modal

Using these numerical parameters, we can now use Eq. (4) to estimate Td. We find Td260 K. This value is of the same order as those reported in modern HEMTs.15,28 Due to uncertainties regarding the exact values of the parameters in Eq. (4), we note that this value of Td should be regarded as an order of magnitude estimate rather than a precise value. At a qualitative level, this estimation shows that a relatively small portion of the electron population appears capable of explaining an appreciable portion of the drain noise measured experimentally. At the same time, the effect of RST on mobility would likely not be observable in a HEMT under normal operating conditions due to the small value of η.

We now examine the dependencies of Td predicted from Eq. (4). Previous works have reported a dependence of Td on IDS1,28 and physical temperature.24–26 The present theory predicts a dependence of Td on VGS since VGS changes the Fermi level of the electrons under the gate, thus altering the population of hot electrons able to thermionically emit out of the channel as experimentally shown in Fig. 1(b).

To verify that this dependence is predicted by the model, we plot Td vs IDS in Fig. 3(a). The values of IDS are estimated from the transfer characteristics of an InP HEMT for VDS=0.5 V.15 We observe a dependence of Td on IDS, which compares reasonably with experiments (see Fig. 5 of Ref. 1, Figs. 4 and 5 of Ref. 28). In addition to qualitatively reproducing the experimental drain temperature–drain current relationship, the theory offers a physical explanation for this dependence as arising from the dependence of the hot electron fraction on Fermi level, which is controlled by VGS.

FIG. 3.

(a) Drain noise temperature Td vs IDS. Increasing VGS and, hence, IDS lowers the energy barrier for thermionic emission, leading to higher Td. Transfer characteristics were obtained from Fig. 4.1 of Ref. 15. (b) Td vs physical temperature T for ΔT=1000 K. The occupation of electronic states above the Fermi energy increases with temperature, and consequently, Td increases with T as the hot electron fraction η increases.

FIG. 3.

(a) Drain noise temperature Td vs IDS. Increasing VGS and, hence, IDS lowers the energy barrier for thermionic emission, leading to higher Td. Transfer characteristics were obtained from Fig. 4.1 of Ref. 15. (b) Td vs physical temperature T for ΔT=1000 K. The occupation of electronic states above the Fermi energy increases with temperature, and consequently, Td increases with T as the hot electron fraction η increases.

Close modal

We next examine the dependence of Td on physical temperature. Several authors have reported a temperature dependence of Td, as in Fig. 8 of Ref. 24, Fig. 8 of Ref. 25, and Fig. 3 of Ref. 26. On the other hand, other noise measurements were reported to be consistent with a temperature-independent Td.27Figure 3(b) illustrates how a dependence of Td on physical temperature may arise based on RST. For a non-degenerate electron gas, the electronic heat capacity is constant69 so that Te=T+ΔT, where ΔT denotes the electron temperature increase and is independent of T. In this figure, ΔT was chosen as 1000 K so that the computed Td is consistent with reported cryogenic values in modern HEMTs (see Fig. 10 of Ref. 70). The figure shows that Td can vary with physical temperature because Te varies linearly with physical temperature, which, in turn, affects Td through η. We observe that this dependence is more pronounced at higher physical temperatures, the parameter range studied in Ref. 25. At lower temperatures below 100 K, the dependence is weaker and may be more difficult to discern experimentally relative to room temperature measurements considering the challenge of accurately extracting the drain temperature from microwave noise data. The weaker dependence below 100 K may also account for the conclusions of Ref. 27 that Td is independent of temperature because that study did not consider temperatures above 100 K. A quantitative comparison of the calculated dependence to experiment is difficult because Td data are often reported with IDS held constant, requiring shifts in VGS to compensate for changes in mobility, conduction band offset, threshold voltage, and related quantities with temperature. Due to the lack of availability of certain data, particularly the variation of conduction band offset with temperature, such changes are not included in the present calculation and will be addressed in future work.

We have presented evidence that drain noise in HEMTs can be attributed to the partition noise arising from RST of electrons from the channel to the barrier. We now discuss this finding in the context of prior explanations of drain noise. The first explanation for drain noise in the saturated region was due to Pucel et al.,71 who described the noise current in terms of the generation of dipole layers formed by random electron scattering events. However, their theory did not make testable predictions and so obtaining evidence to support it is difficult. Other authors have attributed noise in GaAs FETs72,73 and Si MOSFETs74 to intervalley scattering. However, in modern InP HEMTs, the ΓL separation in the InxGa1xAs channel (0.55 eV at 300 K and x=0.5375) exceeds the conduction band offset so that RST is expected to occur prior to intervalley transfer. Experimental evidence for this expectation has been reported in AlGaAs/GaAs heterostructures, where noise at intermediate fields, below the threshold for intervalley transfer, is attributed to RST.39 

Several works have suggested that drain noise can be attributed to a suppressed shot noise mechanism in which electrons travel quasiballistically from the source to drain.22,23 However, various studies of electron transport in quantum wells indicate that the electron mean free path is sufficiently short that the transport is not quasi-ballistic as required for the suppressed shot noise mechanism. For instance, time-resolved differential transmission spectra indicate that photo-excited electrons thermalize within around 200 fs, implying that electron-electron scattering is several times faster than this timescale.37 Taking the electron–electron scattering time as around 20 fs, the corresponding mean free path is around 40 nm, nearly two orders of magnitude smaller than the 1 μm source–drain spacing of modern HEMTs. Furthermore, hot electrons lose energy to the lattice on the drain side of the gate by optical phonon emission with a mean free path of tens of nanometers,35 further disrupting quasiballistic transport across the channel. These considerations suggest that electrons undergo sufficient scattering events to prevent the suppressed shot noise mechanism from contributing to drain noise.

Finally, we consider the predictions of the theory regarding how drain noise may be suppressed. A large ΔEc is desired in HEMTs to maximize the channel sheet density.57 Our theory predicts that ΔEc is also important to suppress RST and hence drain noise. Minimizing RST requires increasing ΔEc/kBTe so that the hot electron fraction decreases. A lower Te can be achieved by decreasing the InAs content of the channel and hence increasing the effective mass, but this change must be balanced against the need for high mobility and hence higher InAs content. An increase in conduction band offset, on the other hand, can be achieved without affecting the channel by reducing the InAs mole fraction of the barrier. Studies of HEMTs with barrier composition (InAs)x, 0.3<x<0.5, reported decreased RST in devices for smaller x.76 However, x must be chosen accounting for the lattice mismatch between the channel and the barrier that can lead to the formation of misfit dislocations that negatively impact the noise.

We quantify the impact of varied InAs mole fraction in the barrier on Td by obtaining ΔEc for each x,76 using these values to calculate the sheet density in the barrier, and following the same analysis as described in Sec. III. The result is shown in Fig. 4. We observe a marked decrease in Td as x is reduced from its lattice-matched value of 0.52 to 0.46, followed by a slower decrease from 0.46 to 0.4. Following Pospieszalski’s noise model, specifically Eq. (26) in Ref. 19, a factor of 2 reduction in Td as seen when x changes from 0.52 to 0.46 translates to a factor of 1.4 reduction in the minimum noise temperature. This analysis suggests that further improvements to the noise figure of HEMTs can be realized by optimizing the barrier InAs mole fraction.

FIG. 4.

Drain temperature vs barrier mole fraction, x in InxAl1xAs. A reduction in Td is observed as x is decreased due to an increase in ΔEc.

FIG. 4.

Drain temperature vs barrier mole fraction, x in InxAl1xAs. A reduction in Td is observed as x is decreased due to an increase in ΔEc.

Close modal

We have reported a theory of drain noise in high electron mobility transistors based on microwave partition noise arising from real-space transfer of electrons from the channel to the barrier. The theory successfully explains the reported magnitude and dependencies of Td. The theory predicts that Td can be decreased by altering the barrier composition to increase the conduction band offset and, thus, decrease the occurrence of RST. A reduction in the drain temperature of a HEMT leads to a corresponding decrease in the minimum noise temperature. Our results may, therefore, guide the design of HEMTs with a lower microwave noise figure.

The authors thank Jan Grahn and Junjie Li at Chalmers University of Technology for useful discussions and providing the data shown in Fig. 1. I.E. was supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1745301. A.Y.C. and A.J.M. were supported by the National Science Foundation (NSF) under Grant No. 1911220. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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