6.3 Low Frequency Noise

For oscillator applications the low frequency 1/f noise is an extremely important quantity. The upconversion of low frequency noise leads to widening of the frequency spectrum of the oscillators' output signal. It is generally acknowledged [24] that the HEMT shows inferior performance towards the HBT in terms of 1/f noise. However, if a HEMT technology is inferior but available for a given chip set, it is useful to control variations of the 1/f noise level to a certain extent. Similar to CMOS technologies where the 1/f noise levels are part of the SIA Technology Roadmap [252] the 1/f levels are measured with respect to several technology runs or variations. 1/f measurements were performed in a system that was described in [30,154]. Fig. 6.17 shows a typical measurement from an experiment performed:

Figure 6.17: Comparison of the 1/f noise between 0.5 Hz and 10 MHz for various transistor samples.

Nominally identical structures were processes with different test surface treatments after recess etching. A relatively strong scattering is observed using different cleaning procedures. Two conclusions can be drawn. First, the noise levels are subject to the surface treatment, which was also reported in [79]. Second, for device modeling the measurements supply a secondary piece of information: characteristic frequencies, respectively time constants are extracted by the following procedure. To the first order, in [30,154] it was found that a linear fit can be used to model the noise spectrum:

$$S_{V,1/f,lin} = \frac{S_{V,0}}{f^\alpha}$$ (6.1)

which is suitable and indicated in Fig. 6.17. $\alpha$ is the slope, which is close to unity. However, the modeling can be improved. When measuring up to 10 MHz, as done in Fig. 6.17, and after eliminating possible noise sources in the measurement setup [30], specific trap time constants are obtained by means of the following extraction procedure: The spectral noise density $S_{V,1/f,trap}$ is modeled as:

$$S_{V,1/f,trap} = \frac{S_{V,0}}{f^\alpha} + \frac{S_{V,1}}{1+(2\pi f\tau_1)^2} + \frac{S_{V,2}}{(2\pi f\tau_2)^2}$$ (6.2)

$$\ \text {using    } f_n = \frac{1}{2 \pi \tau_t}$$ (6.3)

$$S_{V,1/f,trap} = \frac{S_{V,0}}{f^\alpha} + \frac{S_{V,1}}{1+(f/f_1)^2} + \frac{S_{V,2}}{(f/f_2)^2}$$ (6.4)

The $\tau_t$ are time constants introduced to model the impact of traps. It was found by Bea in [30] that for the HEMTs under investigation adding two time constants is sufficient representing two major traps in order to model the noise voltage in (6.4). This allows to fit the trap contribution superimposed on the linear behavior, as also described by [154]. Thus, characteristic time constants $\tau_t$ are obtained characterizing the dynamic trap behavior for the devices simulated. Dominant trap concentrations are assumed at the SiN/barrier interface, as shown by Fig. 6.17, and in the bulk. Table 6.1 gives typical frequencies obtained from the 1/f measurements, where the inverse supplies time constants of the trap occupation.

Table 6.1: Transient time constants obtained by 1/f measurements.

Material	f [MHz]	Range [MHz]
Al$_{x}$Ga$_{1-x}$As/InGaAs HEMT	1	0.2-4
InAlAs/InGaAs/InP HEMT	0.4	0.02-2