Variable-Temperature Noise Characterization of N-MOSFETs Using an In-Situ Broadband Amplifier

—Characterization of broadband noise of MOSFETs from room temperature down to 120 K in fine temperature steps is presented. A MOSFET is mounted on a reusable printed circuit board vehicle with a built-in low-noise amplifier, and the vehicle is loaded into a cryogenic chamber. The vehicle allows noise measurement in the frequency range from 50 kHz to 100 MHz. At low frequencies, it enables extraction of activation energies associated with electron trapping sites. At high frequencies, as has been suggested by noise figure measurements, the white noise of MOSFETs is shown to be dominated by the shot noise, which has much weaker temperature dependence than the thermal noise. The shot noise will a problematic noise source in broadband RF CMOS circuits operating at cryogenic temperatures.


I. INTRODUCTION
Low temperature environment enhances performance of CMOS devices through the improvement of the carrier mobility, subthreshold slope, Cu wire resistance, and thermal noise [1][2][3]. Applications of "cold" CMOS range from high performance computing to space exploration and low temperature physics. Quantum computing is one of the challenging technologies that require that the power of CMOS circuits be made available at cryogenic temperatures. To maintain the coherence time of quantum bits (qubits), such as superconductive qubits [4][5][6] and semiconductor spin qubits [7], a quantum processor comprising several to several tens of qubits is put in a sub-decikelvin cryogenic chamber. At present, peripheral circuits for controlling the quantum processor typically operate at room temperature and are connected to the quantum processor via long RF cables. However, as the number of qubits increases exponentially in the near future, error correction needs to be implemented for maintaining the computation fidelity over the coherence time of qubits. Then, the control latency will be critical for continuous operation of such a quantum processor [8][9][10][11]. Efforts have been made to move low-power RF CMOS controllers into a few-kelvin chamber that encloses the sub-decikelvin chamber [10].
including the saturation value of the drain current ( ! ) and electron mobility improve and, in addition, peculiar phenomena, such as bandgap widening, carrier freeze-out, and self-biasing, appear [14]. Therefore, continuous characterization of MOSFETs at varying temperatures starting from room temperature down to cryogenic temperatures is important for developing physics-based predictive device models. In particular, wideband noise modeling is essential for the development of low-noise circuits.
MOSFETs are known to exhibit flicker noise at low frequencies and white noise at high frequencies. Physical origins of flicker noise and white noise are different, and their power spectral densities are independent of each other. White noise can be further classified into thermal noise and shot noise. These are not completely independent of each other and become indistinguishable under a zero drain bias [15,16]. When a nonzero drain bias is applied, the shot noise becomes dominant [17,18]. White noise from a local oscillator have recently been shown to adversely affect the operation of wideband millimeter-wave circuits [19,20].
The noise figure (NF) measurement is typically used to characterize the white noise of MOSFETs [21,22]. The most commonly used Y-factor method of NF measurement requires a hot noise source. In cryogenic environments, this method is not straightforwardly applicable because noise sources are not commercially available [23]. Therefore, either the cold-source method or the cold-attenuator method is employed, in which several cooling cycles per characterizing a single device under test (DUT) are required for complicated calibration [24]. On the other hand, the maximum measurable frequency of lowfrequency noise measurement systems is usually too low to cover white noise due to parasitic capacitance inherent in such systems.
A proof-of-concept noise probe for on-wafer broadband noise characterization was demonstrated at room temperature, achieving noise measurement from 100 kHz up to 800 MHz [25,26]. This was made possible by reducing the parasitic capacitance by placing a broadband low-noise amplifier (LNA) in the probe itself. At present, an improved version of the noise probe is commercially available [27], details of which were presented in [18]. In this study, we apply the same principle to the development of an in-situ system for variable-temperature broadband noise measurements down to 120 K [28].
Low-frequency noise from a very small MOSFET can reveal individual trapping/detrapping of a single electron to/from a trapping site. Using this capability, low-frequency noise measurement is commonly employed to characterize the quality of gate dielectrics [29]. In this paper, we will also demonstrate low-frequency noise spectroscopy (LFNS) [30][31][32][33], in which, by characterizing temperature-dependent noise intensities of a MOSFET, the activation energy related to electron trapping is extracted.
We will also look at the temperature dependence of white noise, especially shot noise, and the suppression of the latter compared to its theoretical maximum value (full shot noise), through the use of the so-called Fano factor or the shot-noise suppression factor.

II. EXPERIMENTAL SETUP AND MEASUREMENT
We developed a reusable printed circuit board (PCB) vehicle for cryogenic measurements, on which a DUT is mounted. Also on the PCB vehicle is a broadband LNA for in-situ sensing of noise from the DUT. The noise generated by the broadband LNA can be calibrated out by pre-characterizing the LNA by extensive measurements [18]. We applied this calibration approach to variable-temperature measurements so that the PCB vehicle is calibrated at every kelvin over the temperature range from 300 to 120 K. Note that once the variabletemperature calibration of a vehicle is completed through several cooling cycles, measurements of dc and noise characteristics can be conducted in a single cooling cycle.
A DUT is mounted on the vehicle right next to the LNA. The configuration of electrical instruments is similar to that in [18], except that the PCB vehicle is put in a cryogenic helium chamber as schematically shown in Fig. 1. We employed a semiconductor device analyzer (B1500A, Agilent Technologies), equipped with four high-resolution sourcemeasure units (HR-SMUs), for biasing the DUT, and a spectrum analyzer (N9030A, Agilent Technologies) for reading the output from the LNA. The noise generated by the spectrum analyzer is accounted for, in effect, by turning on its Noise Floor Extension option [34]. Custom-built low-pass filters were used to filter out noise from the HR-SMUs.
We characterized N-MOSFETs from a few different semiconductor foundries. Three types of MOSFETs, denoted by A/B/C, were measured. The gate lengths ( ) of type-A/B MOSFETs were 240 nm, and that of type-C was 120 nm. Each of the DUTs had 4 contact pads (gate, drain, source, and substrate electrodes) and was mounted on a PCB vehicle by flip-chip or wire bonding for stable measurements at different temperatures. If one uses a cryogenic probe station, the probe tips shrink in length as decreases, which makes stable continuous variable-measurement very difficult. Therefore, it is beneficial also in this regard to bond a DUT next to an LNA.
DUT temperatures were measured using a silicon diode sensor attached next to the DUT on the PCB vehicle. The temperature ranges examined are from 5 to 300 K for dcmeasurements and 120 to 300 K for noise measurements. The lowest temperature of 120 K of the noise measurement was dictated by the carrier freeze-out of bipolar transistors in the LNA. Figure 2(a) shows ! -" curves at = 5 to 300 K for a type-A DUT under a drain-source voltage, ! , of 0.05 V. The ! -" measurement was carried out at every 1-5 K step. At low temperatures, ! decreases in the subthreshold region and increases in the strong inversion region. The change in the transconductance # is shown in Fig. 2(b). The dependence of the threshold voltage $% on is plotted in Fig. 3(a). $% was extracted by drawing a tangential line on an ! -" curve at the point where # assumes a maximum value. $% shifts from 0.74 V at 300 K to 0.94 V at 5 K. The electron current density is expressed as   where is the concentration of electrons in the inversion layer, & is the electron mobility, is the electric field, and & is the diffusion coefficient, which is proportional to . The diffusioncurrent component of ! decreases as the temperature becomes lower, resulting in higher $% [ Fig. 3(a)] and steeper subthreshold slope [ Fig. 2(a)]. Figure 3

A. Dc Characteristics
⁄ is the normalized (per-unit-drain-current) transconductance, often examined in relation to surface potential fluctuations [35,36]. The peak # values in Fig. 2(a) and the corresponding ! were used to estimate is to be considered later in connection with the dependence of normalized noise intensity on . Figure 4 shows ! -! curves at = 122 to 300 K for a type-A DUT under (a) " = 0.9 and (b) 1.5 V. ! in Fig. 4(a) decreases as decreases, whereas ! in Fig. 4(b) increases, consistent with the behavior observed in Fig. 2(a). The dependence of ! on under a given bias condition is affected by many factors including the process technology node, the structure of the MOSFET, and the impurity concentration [2]. Therefore, continuous variable-temperature characterization is necessary for physics -based predictive device modeling.

B. 1/f Noise in the Saturation Region
Before focusing on white noise, we demonstrate a measurement result using the vehicle in the low-frequency, flicker-noise region. Changes in drain-current noise power spectral density )! for a type-A DUT are shown in Fig. 5(a,b). The bias conditions are (a) " = 0.9 and (b) 1.5 V with ! = 1.0 V in both cases. The corresponding ! values can be found in Fig. 4. )! normalized by ! ' for selected temperatures is shown in Fig. 5(c,d). 1/ * frequency dependence is observed with gradually decreasing in the high-frequency region above 10 MHz, where − is the slope of the noise power spectrum on a log-log plot. The value for " = 0.9 V extracted in the frequency range from 100 kHz to 1 MHz decreases from 1.07 at 300 K to 0.77 at 122 K. As shown in Fig. 3(a), $% is a decreasing function of temperature. We used the gate-source voltage, " , as biasing points in variable-temperature noise measurements. Under the condition of " = 0.9 V, the channel is in strong inversion, and the gate overdrive voltage decreases as decreases. The change in for " = 0.9 V in Fig. 5(a) could be related to a depth-dependent trap profile in the oxide layer [37]. Note that the magnitudes of normalized )! for 122 and 300 K intersect in Fig. 5(c) and the inequality is reversed at 400 kHz. Studies on low frequency noise are typically conducted in a frequency range from 1 Hz to 10 kHz, or at most 100 kHz. It does appear important that the measurement frequency range is significantly extended when trying to develop predictive device noise models valid in various operating conditions, including low temperatures. On the other hand, the values of do not change very much when " = 1.5 V and ! = 1.0 V as shown in Fig. 5(b,d).
Although ! increases as decreases [ Fig. 4(b)], )! (and obviously, normalized )! ) decrease. The relationship between the normalized )! and ( # ( ⁄ ) ' is expressed as [36] + !" , " where is the density of the McWhorter states in the oxide, is the electron wave penetration depth in the oxide, 7 is the Boltzmann constant, 89 is the capacitance of the oxide per unit area, and is the gate width. ( # ! ⁄ ) ' , shown in Fig. 3(b), for the same bias condition also decreases as decreases. This is consistent with the decrease in normalized )! in the lowfrequency region in Fig. 5(d).

C. Low-Frequency Noise Spectroscopy (LFNS)
Next, we conduct an analysis of the physical origin of the observed low-frequency noise. Trapping and detrapping of electrons, typically at the interface between the gate dielectric film and the channel of a MOSFET, result in random telegraph noise (RTN) in the time domain [38]. This is often observed as waveforms exhibiting two discrete levels with a certain time constant of transition between the two levels, corresponding to capture and emission of an electron. In the frequency domain, RTN appears as a Lorentzian-shaped hump at a characteristic frequency : ≈ (2 ) ;< [38]. Figure 6 shows changes in draincurrent noise power spectral density )! for a type-B DUT at different temperatures, exhibiting the Lorentzian behavior with temperature-dependent : . Since the time constant is a function of the activation energy and , the frequency : shifts to higher frequencies as rises. Figure 7(a) shows )! versus temperature extracted at frequencies ranging from 50 kHz to 5 MHz. Two sets of peaks, labeled "Peak 1" and "Peak 2," were observed. The peak temperatures depend on the frequency. For an electron trap in a MOSFET, the relationship between and is expressed as [30] ln ?
where > is the bottom energy of the conduction band, $ is the trap level, and is a constant that includes the capture cross section of the trap and the effective mass of electrons. This allows us to use the Arrhenius method of estimating the activation energy > − $ . Figure 7(b) shows an Arrhenius plot for the peak temperatures and frequencies extracted from Fig. 7(a). The values of > − $ were found to be 0.21 and 0.27 eV for "Peak 1" and "Peak 2," respectively. Identification of trap species, for example, hydrogen, interstitial carbon, and interstitial boron, was reported [32], in which the activation energies ranged from 0.10 to 0.44 eV. To do the same here, further investigation using more DUTs will be required.
In quantum computing, a major cause of decoherence is noise, which is often generated by defects and traps in close proximity to qubits [39]. LFNS is applicable to systems in which current or voltage is affected by trapping phenomena [31]. LFNS could also be employed for studies of improving the coherence time of qubits.

D. Pure Thermal Noise at Zero Drain Voltage
What is unique about using the vehicle with the built-in broadband LNA is the capability to characterize white noise, depending on the bias condition. Figure 8 shows )! versus frequency under zero-drain-bias ( ! = 0 V) conditions with " from 0.8 to 1.6 V at (a) = 300 and (b) 121 K. The frequency range is from 50 kHz to 100 MHz. Note that the maximum measurable frequency in commercially available lowfrequency noise systems is a few tens of MHz at the highest. The observed white noise in Fig. 8 can be regarded either as thermal noise, given by 4 7 / !?@ , where !?@ = ! / ! , or as shot noise [40]. As " increases, !?@ decreases, resulting in higher white noise levels.
Noise measurements were conducted continuously from 120 to 300 K. In Fig. 9, temperature dependence of extracted )! values at 10 MHz for (a) " = 1.0 V and (b) " ranging from 0.8 to 1.6 V are plotted as a function of the theoretical thermal noise intensity $% (= 4 7 / !?@ ). As the temperature becomes low, $% and hence )! decrease. We observed a good linear relationship between $% and )! with a slope of unity. The range of the linear relationship in Fig. 9(b) is from 4 × 10 -'B to 7 × 10 -'C A 2 /Hz, which corresponds to !?@ values from 23 kΩ to 188 Ω.   Frequency (Hz)

E. Shot-Noise Evaluation in the Linear Region
When a nonzero ! is applied, ! starts to increase and shot noise component that cannot be regarded as thermal noise emerges. In order to characterize white noise that consists of thermal and shot noise, noise measurement was conducted in the linear region of MOSFET operation using the type-A DUT, which showed the lowest levels of flicker noise. Figure 10 shows )! for " = 1.5 V and ! = 0, 0.02, 0.04, 0.06, and 0.08 V at (a) = 300, (b) 151, and (c) 121 K. Transitions from flicker noise dominance at low frequencies to white noise dominance at high frequencies are clearly observed. Although the slope of )! ( ) becomes very small at high frequencies, the slope at large ! values is not quite zero. )! ( ) above 1 MHz can be regarded as the sum of white noise and residual flicker noise. We therefore estimated the level of white noise, D , and the corner frequency, > , at which the intensity of flicker noise is equal to that of white noise, by using [18]    where @ is )! at 1 Hz, and ( @ D ) ⁄ </* equals > . Here, a value of averaged over 300 kHz to 1 MHz and )! values at 10 and 30 MHz at each were used to estimate D and > . A straight 1/ * line on a log-log )! -versus-plot is assumed in (4). The accuracy of extraction of D by using (4) is affected by humps due to RTN. For example, this is observed as a broad hump in )! (around 1 MHz) in Fig. 10(c). Hereafter, we will limit the lowest temperature analyzed by using (4) to 150 K because flicker noise below 150 K does not exhibit a good straight 1/ * line due to the appearance of RTN. As shown in Fig. 11, the corner frequency > gradually increases as decreases mainly because the intensity of thermal noise decreases. > is higher for larger ! due to higher flicker noise intensity. Figure 12 shows the dependence of measured )! and the estimated white noise D on ! for (a) = 300 and (b) 151 K. Open circles/squares and solid squares show measured )! at 10/30 MHz and estimated D from (4), respectively. The difference between these values grows as ! increases, resulting from the increase in residual flicker noise (Fig. 10). Thermal noise intensity $% for nonzero-drain-bias conditions is given by [40] where >% = ! / ! is the chord resistance [41]. Note that >% ( ! ) ≠ !?@ ( ! ) unless ! = 0 V. Also plotted in Fig. 12 are the expected thermal noise $% (green dotted line) from (5), full shot noise 2 ! (orange solid line), and the sum of these (blue dot-dashed line). At ! = 0 V, D equals $% and, as ! increases, D increases along but below 2 ! [18]. The latter gives the maximum possible value of shot noise intensity, realized when statistical fluctuation of the carrier number is at its maximum. Thermal noise $% dominates under low drain bias ( ! ≲ 2 7 / ) and shot noise becomes dominant when ! ≳ 2 7 / , as delineated by the red arrows. The values of 2 7 / for = 300 and 151 K are 52 and 26 mK, respectively. Therefore, as clearly observed in Fig. 12, the onset drain voltage of shot noise predominance at low temperature is smaller than that at room temperature. Figure 13 shows the relation between the estimated white noise D and the thermal noise $% at 150 ≤ ≤ 300 K. Although temperatures are not explicitly shown in Fig. 13, decrease in the value of $% (horizontal axis) for each ! corresponds to lowering of . As decreases, D at ! = 0 V (black open squares) decreases, exhibiting a linear relationship with a nearly unity slope as was also seen in Fig. 9. In contrast, D (vertical axis) at ! > 0 V remains higher than the thermal noise $% , clearly demonstrating that shot noise becomes predominant at low temperatures. Shot noise originates from the discrete nature of carrier transport. In MOSFETs, the shot noise is considered to originate primarily from carriers crossing the potential barrier near the source [17,42], and secondarily from quasi-ballistic transport in the pinch-off region, where the inversion carrier density is low [43]. In this experiment, the observed shot noise should have resulted from the former because of the small values of ! .   Shot noise is often characterized by using the so-called Fano factor (≤ 1) [44], given by the actual shot noise intensity divided by the full shot noise intensity, 2 ! . Successful use of for white noise modeling has been demonstrated for shortchannel MOSFETs [45]. A useful expression for measurementbased evaluation of applicable even near and at ! = 0 V, where thermal noise and shot noise become indistinguishable, is [18] = + -'., " M+ )* .
(6) Figure 14 shows temperature dependence of for ! ranging from 0 to 0.08 V. The black line in Fig. 14 is roughly equal to unity, which is the theoretically expected value of at ! = 0 V. At room temperature, as ! is raised from 0 V, quickly falls in the linear region of MOSFET operation and becomes constant in the saturation region [18,45]. In this study, only the beginning of the linear region has been examined because of high > at larger values of ! (Fig. 11). It is noteworthy that, in the linear region with ! from 0.02 to 0.08 V, slightly decreases as decreases (Fig. 14), and its dependence will presumably become weaker as ! increases. However, further measurements at higher ! , including the saturation region [18], and at lower are definitely needed to be sure and for reliable cryogenic device modeling. Simulation with physical modeling, taking Coulomb interaction and the Pauli exclusion principle into consideration, will also be a powerful tool for further study [43,46].
The lowest temperature for noise characterization in this study was limited to 120 K because bipolar transistors were adopted in the LNA. The measurement method proposed here should be applicable down to 4 K by using an LNA composed of MOSFETs or GaAs high electron mobility transistors (HEMTs).

IV. CONCLUSIONS
We have demonstrated variable-temperature characterization of N-MOSFETs, using the precisely calibrated PCB vehicle for broadband noise measurements from the flicker noise region to the white noise region. In order to build physics-based predictive models for MOSFETs, actual temperature-dependent measurements of broadband noise are necessary. Our measurement data show that a cryogenic environment reduces white noise at ! = 0 V as expected, but does not reduce shot noise that much at ! ≠ 0 V. The latter will be a problematic noise source for applications in need of low-noise CMOS circuits.