Scalable Small Signal and Noise Modeling of InP HEMT for THz Application

Scalable small signal and noise modeling for 90nm InP high electron mobility transistor (HEMT) is proposed in this paper. Analytical expressions for the noise parameters of the intrinsic part are derived from an accurate small signal and noise equivalent circuit model. The experimental and theoretical results show that at the same bias condition, good scaling can be achieved between the HEMTs with different gate widths. Model verification is carried out by comparison of measured and simulated S-parameters up to 325 GHz and noise parameters up to 40GHz. Good agreement is obtained for 90 nm gate-length devices of gate widths including <inline-formula> <tex-math notation="LaTeX">$2\times 15\,\,\mu \text{m}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$2\times 20\,\,\mu \text{m}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$2\times 25\,\,\mu \text{m}$ </tex-math></inline-formula> gate width (number of gate fingers <inline-formula> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula>unit gate width <inline-formula> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula>cells). The proposed model can be used to predict the S-parameters and noise performance of HEMTs with different geometry accurately.


I. INTRODUCTION
InP-based high electron mobility transistors are superior in terms of their excellent microwave and noise performance and are good choices for space-based millimeter wave receivers with low DC power consumption [1], [2]. A noise figure as low as 11.1 dB at 850GHz has been achieved as reported in [3].
Most monolithic microwave and millimeter-wave integrated circuits consist of HEMTs with different sizes, the scalable models are powerful computer-aided design tools for optimizing such circuits. Scaling of the small-signal equivalent circuit model dependent on the sizes of gate-length and gate-width regions has been investigated [4], [5], [6]. For a state-of-art process, the most important task is to build a gate-width scalable model, since the reason is the gatelength is fixed normally. Based on the physical scaling rules of small size devices, the performance of large size devices can be evaluated [7], [8], [9], [10] and provide feedback for process control data.
In this paper, the scalable noise and small signal model for InP HEMTs devices have been developed. Based on an improved extrinsic elements extraction procedure has been proposed. The main contribution of this paper is the scalable rules for small signal model and noise parameters up to 325 GHz are given in detail, and three extrinsic resistances can be obtained from the pinch-off (gate-to-source voltage is less than threshold voltage) and zero-biased (gate-to-source voltage is larger than threshold voltage) S-parameters measurements. It can be observed that the HEMTs with different gate width fabricated utilizing the same process can be described by the consistent equivalent circuit model. The proposed model can be used to predict the S-parameters and noise performance of HEMTs with different geometry accurately.
This paper is organized as follows. Section II describes the determination of extrinsic model parameters, and the intrinsic and noise model parameters are given in Section III, and the scaling rules for extrinsic and intrinsic elements are given   in detail. The comparison of gate width scaled small signal and noise parameters with the measured data to verify the validity of the technique. The conclusions are discussed in Section V. Fig. 1 depicts the equivalent circuit model under cutoff bias condition (V gs < V th and V ds = 0V) in the low frequency ranges (less than 3GHz normally). It is obvious that the equivalent circuit exhibits a pure capacitive behavior.

A. PAD CAPACITANCES
The imaginary parts of Y-parameters can be written as: where C pg , C pd and C pgd are the pad capacitances. C gsp , C gdp and C dsp are the gate width normalized intrinsic capacitances under cutoff bias condition. Wis the gate width of the PHEM. C pg , C pd and C pgd can be obtained from the interceptions of the three linear regression lines versus gate width simultaneously, as illustrated in Fig. 2.

B. FEEDLINE INDUCTANCES
The extrinsic network of the HEMT device is displayed in Fig. 3, where L g , L d and L s represent the feedline inductances, respectively. The extrinsic inductances are obtained   directly from the Z-parameters of the short test structure. The extracted feedline inductances versus frequency are given in Fig. 4. Constant values are observed from 1 GHz to 170 GHz with the deviations from the mean values being less than 10% for feedline inductance L g and L d .

C. DETERMINATION OF R S
After de-embedding the pad capacitances and feedline inductances, the equivalent circuit model under V gs = 0 and V ds = 0 bias condition is provided in Fig. 5, where R g , R d and R s are the extrinsic resistances, and R ch is the channel resistance. As gate-to-source voltage V gs becomes larger than the threshold voltage V th (V th less than −1V), the channel inversion charge density increases, which increases the channel conductance.
Since the intrinsic capacitances C gso and C gdo dominate the Y 11 and Y 12 parameters at low frequencies, we have: Note that the impedance of C dso and channel resistance R ch are compatible, hence it is difficult to determine C dso directly.
The real part of Z 12 is given by: The frequency response of Re[Z 12 ] is portrayed in Fig. 6. When the angular frequency is close to zero, the relationship between R s and R ch can be obtained: Select two frequency points with large differences in frequency response amplitude, such as ω 1 and ω 2 . We have: Combining (8) and (9), we have: If ω 2 = 2ω 1 , Eq. (10) can be simplified as follows: Substituting y into Eq. (8), x can be determined directly:  In the frequency of 1-325 GHz, the modeled and measured Re[Z 12 ] versus frequency is plotted in Fig. 7. Good agreement between modeled and measured data is obtained. The extracted R s and R ch versus gatewidth is shown in Fig. 8. As seen, R s and R ch are inversely proportional to the gate width.

D. DETERMINATION OF R D AND R G
The real part of Z 22 can be expressed as follows: At low frequencies, the drain extrinsic resistance R d can be determined: The real part of Z 11 can be expressed as follows: In the high frequency ranges (above 100GHz), the gate resistance is: For three devices with different gate width, the extracted R g + R s in the frequency of ranges 1-170GHz is exhibited in Fig. 9. Furthermore, the extracted R g and R d versus gate   width is illustrated in Fig. 10, it is apparent that R g and R d are inversely proportional to the gate width.

III. DETERMINATION OF INTRINSIC AND NOISE MODEL PARAMETERS
The intrinsic small signal and noise model is sketched in Fig. 11. After de-embedding all the extrinsic elements, three intrinsic capacitances (gate-to-source capacitance C gs , gateto-drain capacitance C gd and drain-to-source capacitance C ds ), as well as transconductance, output conductance, time delay, and intrinsic gate resistance, form the intrinsic small signal part. Noted that, compared with the impedance of C gd , intrinsic feedback resistance R gd is very small, and can be neglected. Fig. 12-Fig. 14 display the extracted results versus gate width, it can be clearly observed that the intrinsic capacitances and transconductance are proportional to the size of device, and the intrinsic resistances are inversely proportional to the size of device. Note that the time delay associated with transconductance remains invariant.   The scaling formulas are determined as: Subscript c denotes the normalized elementary model parameters.
Based on the Pucel et al.'s model (also called PRC model) and the effect of gate leakage, the corresponding admittance  noise correlation matrix can be expressed [11], [12]: where R and P are the gate and drain noise model parameters, C represents the correlation coefficient, k represents Boltzmann's constant, and T o represents the ambient temperature. It can be noticed that the influence of gate leakage currents becomes significant under high drain and gate bias condition. An additional noise current source I gL is needed in parallel with the noise current source at the input port for the PRC noise model [13], [14]. A large size device normally consists of multiple elementary cells with the same gate width connected in parallel [15]:

IV. EXPERIMENTAL VERIFICATION
In order to verify the above results, three 90 nm InP HEMTs with different size 2×15 μm, 2×20 μm and 2×25 μm have been used to demonstrate the proposed model. Microwave S-parameters are carried out on wafer over the frequency range 1-325 GHz, and noise parameter measurements over the frequency range 8-45GHz. The test layout of InP HEMT devices is shown in Fig. 16 [16].

A. SMALL SIGNAL MODEL VERIFICATION
In the frequency range of 1GHz to 325 GHz, Fig. 17 plots the comparison between the measured and modeled Sparameters for the 2×15 μm HEMT device under bias condition of V gs =−0.2V and V ds =1.0V. The good agreement in S-parameters between the measured and the scaled models determined by using the scaling rules for 2×15 μm and 2×25 μm HEMT devices are displayed in Fig. 18 and Fig. 19.

B. NOISE MODEL VERIFICATION
For 2×20μm HEMT device, Fig. 20 shows the modeled noise parameters up to 325 GHz utilizing the whole noise model and without pad and feedline parasitics under bias condition of V gs = −0.2V and V ds =1.0V. It can be found that the effect of the pad and feedline can be neglected in the frequency of 1-30 GHz when the pad capacitances and 352 VOLUME 11,2023 feedline inductances are as small as enough. The modeled noise parameters are also compared with measured data, in the frequency of 8-45GHz, and good agreement is obtained. Fig. 21 depicts the comparison of measured and modeled noise parameters as a function of gate-to-source voltage by utilizing the scaling rules for 2×15μm and 2×25μm HEMT devices under V ds =1.0V bias condition. The noise parameters have been obtained using the tuner-based method. Unfortunately, the optimization techniques may cause ripples in the measured data.

V. CONCLUSION
A scalable noise and small signal model for 90nm InP HEMT is presented in this paper. The experimental and theoretical results show that at the same bias condition, good scaling of the noise and small signal model parameters can be achieved. The validity of the new approach is proven by comparison with measured S-and noise-parameters. The proposed model can be used to predict the S-parameters and noise performance of HEMTs with different geometry accurately.