I. INTRODUCTION

High-resistivity (HR) short-channel floating-body (FB) partially depleted (PD) silicon-on-insulator (SOI) MOSFETs offer significant advantages for RF integrated circuit (IC) and system-on-chip (SoC) design due to their low source/drain capacitances, low cross-talk noise, and low leakage current ^{[1- 3]}. The BSIMSOI4 (Berkeley Short-Channel IGFET Model Silicon on Insulator 4) ^[4] macro model ^[5] is widely used for large-signal SPICE simulations of RF ICs, where accurate modeling of RF output characteristics is crucial for impedance matching design.

While high-frequency (HF) operation in the GHz range is often emphasized, accurate modeling at MHz frequencies is also critical. In typical RF receiver architectures, an RF signal in the GHz range is downconverted by the mixer to an intermediate frequency (IF), typically ranging from a few MHz to several hundred MHz. Key receiver blocks such as baseband amplifiers and channel filters then operate in this IF range, making accurate low-frequency (LF) modeling essential for predicting overall system performance ^[6].

Therefore, accurate modeling in the full frequency region from DC to tens of GHz is essential for reliable IC design, particularly for short-channel SOI MOSFETs with frequency-dependent behavior.

At low $V_{DS}$, thermally assisted impact ionization holes accumulate in the FB, causing an increase in the drain current known as the low-voltage kink effect ^[7]. However, DC simulation of the kink effect using the BSIMSOI4 model ^[4] is inaccurate due to the lack of a reliable kink effect model.

In SOI MOSFETs, the self-heating effect (SHE) occurs due to the buried oxide (BOX) layer, which thermally isolates the top silicon from the substrate, causing a rise in lattice temperature under high voltage and current bias ^[8]. As temperature increases, the carrier mobility decreases due to increased lattice scattering, reducing drain current. This effect intensifies with more multi-finger devices as heat generation scales with active area. The BSIMSOI4 model provides parameters such as thermal resistance ($R_{th}$) to represent this effect in the DC domain ^[4]. However, in FB devices, it is very difficult to accurately extract $R_{th}$ from the measured DC I-V data, because the low-voltage kink effect overlaps with the SHE on the same DC I-V characteristics in multi-finger devices.

Thus, in this paper, to solve these previous modeling problems, each macro current source for the kink effect and SHE is determined separately by the following method: the current variation caused by the low-voltage kink effect is first modeled using single-finger devices in which the SHE is neglected. Subsequently, the current reduction induced by the SHE is modeled using multi-finger devices, which clearly show the SHE. Two macro current sources based on empirical equations are connected in parallel with the BSIMSOI model. This new method effectively models the non-ideal behavior in the DC I–V characteristics caused by the two effects.

These effects primarily influence DC characteristics and diminish beyond their respective cutoff frequencies ($f_c$) ^{[9- 11]}. Therefore, these SHE and kink effects must be isolated from RF simulations to maintain accuracy in HF behavior by modeling each $f_c$ separately.

In the saturation region, the $S_{21}$ and $S_{22}$-parameters exhibits clockwise rotation on the smith chart in the lower and upper half-planes, respectively, as the frequency increases. This RF inductive effect originating from negative capacitance must be considered when designing RF integrated circuits ^{[5, 12]}. In a previous study ^[5], the RF inductive effect was modeled by combining an empirically defined current source ($I_k$) with an effective inductance ($L_k$).

On the other hand, an abrupt change in the intrinsic output capacitance ($C_{oi}$) and conductance ($G_{oi}$) in the saturation region has been observed in the LF region, which is called LF effect ^{[13, 14]}, and therefore must be considered to accurately model the RF output characteristics. In a previous study ^[5], this LF effect in the channel area was modeled by adding a series RC network to the output of the BSIMSOI4 model. Additionally, a parameter extraction method for RF channel resistance ($R_c$) and drain-source depletion capacitance ($C_{ds}$) has also been studied ^[13].

Although a series RC circuit is traditionally used to model the LF effect in PD-SOI MOSFETs, it has several notable drawbacks. A sharp variation in $C_{oi}$ and $G_{oi}$ below 1 GHz cannot be accurately simulated by a simple RC network ^[13]. Adding more RC components improves modeling accuracy but leads to complex circuit topology and complicated parameter extraction. To solve this problem, the parallel network of $C_{oi}(f)$ and $G_{oi}(f)$ with frequency-dependent empirical equations is used ^[14] to accurately simulate output admittance changes in the LF region.

However, in FB devices, both LF effects and RF inductive effects appear simultaneously in the LF region of the output characteristics within the widely used saturation bias range. Therefore, extracting $R_c$, $C_{ds}$, $I_k$, and $L_k$ independently becomes difficult because two overlapping effects in the LF region exhibit opposite trends in $G_{oi}$ and $C_{oi}$, making accurate modeling of $Y_{22}$-parameters challenging.

Thus, we propose an extended empirical model that modifies previous frequency-dependent equations of $G_{oi}(f)$ and $C_{oi}(f)$ ^[14] to include both LF and RF inductive effects. This unified approach can model overlapping behaviors in the LF region using a single expression, enabling more accurate modeling of output characteristics.

As a result, this work can accurately simulate kink, SHE, LF, and RF inductive effects over the full frequency range from DC to RF by using the macro current source and unified frequency-dependent $C_{oi}(f)$ and $G_{oi}(f)$ equations.

In RF switch ICs using FB devices, the insertion loss is affected mainly by AC leakage current through the substrate resistance ($R_{sub}$) because of no body leakage component. However, this effect is not considered in BSIMSOI4, which leads to inaccurate HF S-parameter simulations. Thus, in this paper, $R_{sub}$ is externally connected to the macro model to improve modeling accuracy.

Conventional C–V measurements using MHz LCR meters are used to extract parasitic capacitance parameters in the BSIMSOI4 model. However, C–V measurements in short-channel devices show inaccuracies due to small capacitance values. Moreover, conventional C-V extraction methods require additional large C-V test structures, complicating the extraction process. Therefore, an RF C–V extraction method ^[15] based on GHz S-parameter measurements on actual small devices is used under HF operating conditions, thereby improving RF modeling accuracy and reducing extraction complexity ^{[15, 16]}.

Therefore, in this paper, we propose a new BSIMSOI4 macro SPICE model that incorporates all the aforementioned effects for FB PD-SOI n-MOSFETs, along with an improved RF capacitance parameter extraction method compared to previous studies.

II. FREQUENCY DEPENDENCE OF $G_{oi}$

The useful SPICE model effectively captures the SHE, kink, LF, and RF inductive effects by reflecting their relative dominance across the frequency spectrum. The SHE and kink effects primarily influence DC characteristics and diminish beyond their respective $f_c$. In previous studies of SOI MOSFETs, the $f_c$ of the SHE ($f_{SHE}$) is typically below 1 MHz ^{[9, 10]}, while the kink-induced decrease in $G_{oi}$ appears at $f_{Kink} = 1\text{ kHz} \sim 100\text{ kHz}$ ^{[9, 11]}, beyond which the effect diminishes in the RF region. The $f_c$ of the LF effect ($f_{LF}$) has been reported to be less than 50 MHz ^[13]. In the case of the RF inductive effect, $f_c$ ranges from 10 MHz to 1 GHz. This $f_c$ ($f_{IN}$) increases with higher $V_{DS}$ because the body-source conductance increases in FB devices ^[17].

As frequency increases, these effects diminish sequentially, each governed by its own physical mechanism: first the kink and then SHE, followed by the LF effect, and finally the RF inductive effect. Fig. 1 shows how each effect in FB PD-SOI n-MOSFET dominates different frequency ranges and explains the rise and fall characteristics of $G_{oi}$ as the frequency increases. The five output conductance components consist of the frequency-independent drain–source conductance ($g_{dso}$) and the frequency-dependent conductances associated with kink effect ($g_{kink}$), SHE ($g_{SHE}$), LF effect ($g_{LF}$), and RF inductive effect ($g_{IN}$).

The $g_{kink}$ induced by the kink effect rises as the channel current increases due to the impact ionized hole accumulation in the FB. In the HF region, rapid signal transitions prevent this hole charge buildup, suppressing the kink effect. As a result, the conductance gradually decreases and saturates to zero above 10 kHz ^[9].

The negative $g_{SHE}$ indicates a decrease in drain current as the drain voltage increases in the I-V output characteristic curve ^[9]. This SHE is due to channel mobility degradation caused by the increase in lattice temperature at higher $V_{DS}$ and $V_{GS}$ ^[10]. The SHE becomes negligible in the HF region, because the thermal processes cannot respond to fast signal variations, causing its effect to disappear in the HF region. As the frequency approaches 1 MHz, this thermal effect diminishes, and $g_{SHE}$ gradually converges to zero ^{[9, 10]}.

The $g_{LF}$ represented by the series RC network in the saturation region shows an increase in $G_{oi}$ in the LF region below 50 MHz ^[13]. As the frequency increases, the impedance of $C_{ds}$ drops significantly, and $R_c$ becomes dominant, leading to gradually saturated $G_{oi}$. The $g_{IN}$ remains high in the LF range. However, beyond $f_{IN}$, the inductive effect fades; $g_{IN}$ gradually decreases and disappears ^[17].

In summary, the kink, SHE, LF, and RF inductive effects vanish beyond their respective $f_c$, resulting in the overall frequency-dependent behavior of $G_{oi}$ shown in Fig. 1. Therefore, accurately capturing the influence of these effects with an empirical model is essential for predicting the frequency-dependent output behavior of FB PD-SOI MOSFETs.

III. MODEL AND PARAMETER EXTRACTION

On-wafer S-parameters were measured over the range of 10 MHz to 20 GHz on HR FB PD-SOI n-MOSFETs with a multi-finger layout (unit gate length $L_g = 0.1\ \mu\text{m}$, unit gate finger width $W_u = 5\ \mu\text{m}$, and number of gate fingers $N_f = 16$). Fig. 2 shows a newly proposed SPICE macro model of FB PD-SOI n-MOSFETs. $I_{K,SHE,DC}$ is the DC current source defined as the sum of the increased current due to the kink effect ($I_{Kink,DC}$) and the reduced current due to SHE ($I_{SHE,DC}$). $I_{Kink,DC}$ and $I_{SHE,DC}$ are connected in opposite directions in series with the coupling capacitors ($C_{rf1}$, $C_{rf2}$). $G_{oix}(f)$ and $C_{oix}(f)$ are frequency-dependent empirical equations that represent the LF and RF inductive effects, $C_{gsx}$ is the external gate-source capacitance compensating for the possible modeling errors in the internal BSIMSOI4 gate-source capacitance, and $R_{sub}$ is the substrate resistance for HF modeling.

For DC modeling, the DC I–V characteristics of single-finger FB devices are first measured at $V_{DS}$ below the kink voltage to obtain non-kink I–V data, and the DC parameter extraction for the BSIMSOI4 model is performed using the standard extraction routine ^[4].

The influence of SHE can be neglected in the measured DC I–V curves of single gate finger devices because $I_{DS}$ is minimized. Thus, it is possible to extract DC parameters for the BSIMSOI4 model without the SHE using a single finger with the same $L_g$ and $W_u$.

The non-kink current ($I_{nonkink}$) of the multi-finger device simulated by this BSIMSOI4 model is subtracted from the measured multi-finger DC I–V data to extract $I_{K,SHE,DC}$, which includes both the kink effect and SHE.

After the simulated $I_{nonkink}$ of the single-finger device is subtracted from the measured single-finger DC I–V data, the resulting current is multiplied by $N_f$ to obtain $I_{Kink,DC}$ of the multi-finger device, with SHE removed. Finally, the current reduction due to SHE ($I_{SHE,DC}$) is extracted by subtracting the $I_{Kink,DC}$ data from the $I_{K,SHE,DC}$ ones of multi-finger devices exhibiting both the kink effect and SHE .

To model the extracted $I_{Kink,DC}$ data, following voltage-dependent empirical equations are used:

where

The $I_{SHE,DC}$ (mA) data are also modeled using the same equations as Eqs. (1)-(5), but with different parameter values. The extracted parameter values of $I_{Kink,DC}$ and $I_{SHE,DC}$ are listed in Tables 1 and 2, respectively.

In this study, we select functions that best model the physical voltage-dependent behavior, and the hyperbolic tangent ($\tanh$) function often provides the most suitable fit. Thus, we applied it in several equations, as it not only matches the observed trends but is also easily differentiable ^[18], making it versatile for modeling.

At DC, the modeled $I_{K,SHE,DC}$ for both the kink effect and SHE is connected in parallel with the BSIMSOI4, which simulates $I_{nonkink}$ in Fig. 2. This parallel configuration simulating $I_{nonkink}+I_{K,SHE,DC}$ accurately models the measured DC I-V characteristics, showing good agreement with the data in Fig. 3.

To isolate $I_{K,SHE,DC}$ from RF simulations, $I_{SHE,DC}$ and $I_{Kink,DC}$ are connected in parallel with $I_{K,SHE,DC}$, but in the opposite direction, through coupling capacitors ($C_{rf1}$, $C_{rf2}$) in series. During DC simulation, $C_{rf1}$ and $C_{rf2}$ block these current sources, allowing only original $I_{K,SHE,DC}$ to be simulated. In contrast, during the RF simulation, $C_{rf1}$ and $C_{rf2}$ allow the current sources to flow, effectively canceling out $I_{Kink,DC}$ and $I_{SHE,DC}$ in $I_{K,SHE,DC}$, respectively. This configuration ensures that the SHE and kink effect do not influence the RF simulation results.

If both effects are suppressed separately using different $C_{rf1}$ and $C_{rf2}$ in Fig. 1, their $f_c$ difference ($f_{Kink} = 1\text{ kHz}$, $f_{SHE} = 0.5\text{ MHz}$) ^{[9- 11]} can be modeled. Thus, the values of $C_{rf1}(= 1.72\ \mu\text{F})$ and $C_{rf2}(= 0.5\text{ nF})$ are extracted so that each effect is suppressed at its respective $f_c$, greatly improving modeling accuracy in the kHz to MHz range.

To model the LF effect, $G_{oi}$ and $C_{oi}$ are measured by the following equations respectively:

In the saturation region, the LF effect causes a sharp rise in $G_{oi}$, as shown in Fig. 4. In the conventional approach using a series RC network, $R_c$ and $C_{ds}$ are extracted through a curve-fitting process based on initially extracted values ^[13]. However, large errors are observed in the LF region, indicating poor accuracy in modeling the abrupt increase in $G_{oi}$ below 1 GHz ^[14].

To address this issue and improve the modeling accuracy of the LF effect on $C_{oi}$ and $G_{oi}$, a frequency-dependent empirical model, modified from reference ^[14], is used for a simple parallel network of $C_{oix}(f)$ and $G_{oix}(f)$ in Fig. 2, and is described by the following equations:

where $C_o$ is the drain–source BOX capacitance.

Unlike the previous work ^[14], the exponent of $f$ in (8) is modified from 1 to 0.5, because it best fits the abrupt increasing trend in the LF data of $G_{oi}$ as shown in Fig. 4. The value of $g_{dso}$ in (8) is calculated from the conductance of the non-kink DC I–V curve modeled by BSIMSOI4. The value of $C_o$ is determined to be 110 fF from the average of the extracted values under various biases to minimize modeling error.

Using a simple curve-fitting of Eqs. (8) and (9) to the measured $G_{oi}$ and $C_{oi}$ data, in this work respectively, the voltage-dependent parameters $G_a$, $e$, $C_a$, $C_o$, and $h$ are extracted under various bias conditions ($V_{DS}$, $V_{GS}$).

Figs. 4 and 5 show the comparison of modeled $G_{oi}$ and $C_{oi}$ using Eqs. (8) and (9) with the measured data, respectively, clearly confirming that the empirical model offers excellent accuracy in modeling the LF effect.

As $V_{DS}$ increases, the RF inductive effect becomes more dominant than the LF effect, resulting in a significant increase of $G_{oi}$ in LF, which then decreases after $f_{IN}$, as shown in Fig. 1. However, since Eq. (8) was originally developed to model only the LF effect, it is unable to fit the altered trends of $G_{oi}$ caused by the RF inductive effect. Therefore, to enable empirical modeling for both effects, it is necessary to modify Eq. (8) by multiplying it with an additional function, as shown in the following new equation:

Although the RF inductive effect causes $C_{oi}$ to become negative in the LF region ^{[12, 17]}, accurate empirical modeling of both LF and inductive effects is still possible using Eq. (9), as shown in Fig. 6. Thus, the equation of $C_{oix}(f)$ in Eq. (9) remains unchanged.

In Fig. 7, $G_{oi}$ initially increases sharply from DC to 10 MHz due to the SHE, LF, and RF inductive effects, then decreases and saturates due to the suppression of the RF inductive effect as the frequency increases.

To model the increase in $G_{oi}$ using the new Eq. (10), $G_a$ is extracted with $e$, which adjusts the saturation level. Subsequently, to model the decreasing behavior of $G_{oi}$, Eq. (8) is multiplied by an additional function containing single pole and zero. The parameters $k$, $l$, and $m$ are extracted under the condition that the pole frequency is lower than the zero frequency, ensuring that the empirical equation (10) matches well with the measured $G_{oi}$ data in Fig. 7. This modeling cannot be regarded as providing physical insight into the LF and RF inductive effects, because Eqs. (9) and (10) empirically model the frequency-dependent tendencies through the curve-fitting process.

Fig. 8 compares the measured $G_{oi}$ data under the two bias conditions. When $V_{DS}$ increases from 0.8 V to 1.2 V, $G_{oi}$ in the LF region rises from 13 mS to 15 mS and then decreases to 12.65 mS beyond $f_{IN}$ due to the RF inductive effect. In the HF region, the 0.6 mS difference in $G_{oi}$ is attributed to a reduction in $g_{dso}$ with increasing $V_{DS}$. In Fig. 9, the extracted data of $G_a$, $e$, $k$, $l$, $m$, $C_a$, and $h$, defined in (9) and (10), are modeled as functions of $V_{DS}$ and $V_{GS}$ using a curve-fitting technique.

To accurately extract extrinsic $C_{gsx}$ and BSIMSOI4 capacitances in Fig. 2, an RF C–V extraction method based on S-parameter measurements in the GHz frequency range is used as follows:

By using the curve-fitting for $(-1/\omega)\text{Imag}(Y_{12})$ versus $V_{DG}$ obtained from measured S-parameters, the gate-drain overlap capacitance parameters ($C_{gdo}$, $C_{gdl}$, $C_{kappa}$) in the BSIMSOI4 model ^[4] are extracted. To extract them accurately, the bias of $V_{GS} = 0\text{ V}$ is used to minimize the influence of other intrinsic capacitances. As shown in Fig. 10(a), the extracted capacitance values match well with the modeled curves as a function of $V_{DG}$. The gate-source overlap capacitance parameters are the same as the gate-drain ones due to the symmetrical source/drain structure.

In SOI MOSFETs, the contribution of the bottom junction capacitance is suppressed by the presence of the buried oxide (BOX). Therefore, only the sidewall junction capacitance is modeled in BSIMSOI4 ^{[4, 19]}. Additionally, junction capacitance cannot be directly measured in FB devices due to the absence of a body terminal. Therefore, body-contacted devices with the same size as FB devices are employed to obtain the sidewall junction capacitance. To extract the sidewall junction capacitance parameters ($C_{jswg}$, $M_{jswg}$, $P_{bswg}$) in the BSIMSOI4 model ^[4], $C_{jswg}/(1+V_{DB}/P_{bswg})^{M_{jswg}} + C_{box}$ is fitted to the measured data of $(1/\omega)\text{Imag}(Y_{22}+Y_{12})$ versus $V_{DB}$, as shown in Fig. 10(b).

In Fig. 2, since $R_{sub}$ is known to be voltage-independent ^[20], it is extracted as a fixed value of 550 $\Omega$. Specifically, $R_{sub}$ is extracted by fitting the modeled magnitude of $S_{22}$ to the measured magnitude with the least mean error. By using $R_{sub}$, the magnitude of $S_{22}$ is accurately modeled to match the measured data. Therefore, the externally connected $R_{sub}$ to the BSIMSOI4 model helps improve the accuracy of $S_{22}$ modeling.

The $C_{gsx}$ values in Fig. 2 are extracted by fitting the modeled $(1/\omega)\text{Imag}(Y_{11})$ versus frequency to agree with the modeled curves over a wide range of $V_{DS}$ and $V_{GS}$.

This $C_{gsx}$ is used to compensate for modeling errors in the internal capacitances of BSIMSOI4 ^[4]. Since the extracted $C_{gsx}$ shows bias dependence in Fig. 11, it is modeled by the following empirical equation:

where $C_{gsxa}$, $C_{gsxb}$, $V_a$, $C_{gsxc}$, $C_{gsxd}$, $V_b$ and $C_{gsxe}$ are voltage-independent. Table 3 shows the extracted parameter values from the curve-fitting of Eq. (11).

To extract gate resistance parameters (RSHG, XRCRG1) in BSIMSOI4 ^[4], the modeled $S_{11}$ magnitude is fitted to the measured data in the HF region over a wide bias range. By extracting $C_{gsx}$, RSHG, and XRCRG1, the magnitude and phase of $S_{11}$ are accurately modeled to match the measured data.

After the parameter extraction process for Fig. 2 is finished, the accuracy of the proposed model and extraction method is confirmed by observing the very close match between simulated and measured S-parameters across a wide range of bias conditions, as shown in Figs. 12 and 13.

IV. CONCLUSIONS

An improved SPICE macro model using BSIMSOI4 is proposed to accurately predict the I-V and bias-dependent RF characteristics of short-channel multi-finger FB PD-SOI MOSFETs across the full frequency range from DC to 20 GHz. Unlike conventional BSIMSOI4 models, the proposed model incorporates new empirical equations that reflect the frequency-dependent behavior of intrinsic output capacitance and conductance. To address the overlapping influence of LF and RF inductive effects in the frequency domain, a unified frequency-dependent empirical model is applied without separating the two effects, simplifying the modeling procedure while maintaining high accuracy in the LF range below 0.5 GHz. Additionally, the SHE and kink effects are modeled individually in the DC domain using separate macro current sources. By modeling these two effects separately using different coupling capacitors, the proposed approach improves modeling accuracy of the kHz to MHz frequency range associated with their respective cutoff frequencies. The substrate resistance, which is not included in BSIMSOI4, is externally added to account for the AC substrate loss, thereby improving the accuracy in high-frequency S-parameter modeling. The newly proposed model reduces DC I–V simulation errors and improves S-parameter simulation accuracy across low and high frequency regions. Verification against measured DC I-V and S-parameter data at $L_g = 0.1\ \mu\text{m}$ confirms the accuracy of the improved model over a wide range of bias and frequency, offering a practical solution for SPICE simulation of FB SOI MOSFETs in RF and mixed-signal applications.