# Scalable RFCMOS Model for 90 nm Technology

Authors: Ah Fatt Tong; Wei Meng Lim; Choon Beng Sia; Xiaopeng Yu; Wanlan Yang; Kiat Seng Yeo
Journal: International Journal of Microwave Science and Technology
 (2011)

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## Abstract

This paper presents the formation of the parasitic components that exist in the RF MOSFET structure during its high-frequency operation. The parasitic components are extracted from the transistor's S-parameter measurement, and its geometry dependence is studied with respect to its layout structure. Physical geometry equations are proposed to represent these parasitic components, and by implementing them into the RF model, a scalable RFCMOS model, that is, valid up to 49.85 GHz is demonstrated. A new verification technique is proposed to verify the quality of the developed scalable RFCMOS model. The proposed technique can shorten the verification time of the scalable RFCMOS model and ensure that the coded scalable model file is error-free and thus more reliable to use.


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## Body

## 1. Introduction

The relentless scaling down of CMOS technologies has greatly improved the RF performance of MOSFET. It has been reported that for a technology node of 90 nm, highft of 209 GHz and fmax of 248 GHz are achieved [1]. Furthermore, the scaling down of the transistor has brought about lower NFmin, and it is now comparable to the reported SiGe BJT process [1, 2]. The improved RFCMOS performance coupled with its lower cost has motivated circuit designers to integrate digital, mixed-signal, and RF transceiver blocks into a single chip [3–7]. However, for these RF chips to operate at higher-frequency region, the circuit design specifications will become more stringent, and this will require accurate and scalable RFCMOS models that can be simulated accurately at high-frequency region. Furthermore, by employing scalable RF CMOS model into the process design kit (PDK), the circuit design environment is improved, and this can help circuit designers in their circuit optimization and shorten the design cycle and time to market of these RF chips.Most of the RF models developed today are based on the macromodelling approach. In this approach, subcircuit components are added to the transistor’s core model to model the RF parasitic of MOSFET structure [8, 9], and the core model used is usually the commercially available models such as BSIM3v3 [10] and BSIM4 [11]. The subcircuit components are extracted from the measured S-parameters of the transistor, but the extracted values of these RF components can differ when different extraction technique is used. All the existing RF parameter extraction technique is based on the transistor’s small-signal equivalent circuit analysis. Therefore, to characterize an RF MOSFET, all its RF parasitic elements must be included into the small-signal equivalent circuit. Although it has been demonstrated that including the subcircuit components into the core model can accurately simulate for the transistor’s RF characteristics, such developed model is normal for discrete transistor sizes. In order to generate a geometry-scalable RFCMOS model, the extracted subcircuit component values must be studied for its geometry dependency and by formulating equations to capture their physical effects at high-frequency region, and a physical scalable RFCMOS model can be generated. Presently, some publications are reported for the scalable RF MOSFET modelling [12–14], but these publications [12, 14] do not show all the geometry-scalable equations of the subcircuit components. In [13], the formulated equations for the subcircuit components were empirical and have no physical meaning, and furthermore, only one device size of ft and fmax plot is presented.In this paper, the geometry dependencies of the RF subcircuit components were studied, and the formulation of these RF components was done based on their physical effects and the geometry of the layout structure. The scalable transistor’s RF characteristics with respect to the layout geometry, biasing, and frequency will be demonstrated with good accuracy between the measured and simulated results. Presently, there is no standard technique proposed for quantifying the quality of a developed scalable RF model. Hence, a new technique is proposed in this paper to help modelling engineers to verify and check the developed scalable RF model for their scalability and accuracy. By utilizing this proposed technique, the model geometry scalability with respect to the transistor’s unit width (Wf) and finger number (Nf) is monitored to ensure that the formulated geometry equations are correct. Furthermore, by plotting the proposed accuracy plots, the error population of the developed model is monitored and ensured that they are below the error’s specification of the developed model. The scalable RF model was developed for 90 nm process with channel length of 70 nm for a frequency range of 50 MHz to 49.85 GHz. The devices under test (DUT) are NMOS transistors with Nf of 4, 8, 16, 24, 32, 48, and 64 and Wf of 1, 2.5, and 5 μm. By studying the geometry dependence of the RF subcircuit components for the above DUT, the physical geometry equations with fabrication process parameters are formulated, and from the comparison between the extracted and calculated component values, excellent agreement for all the above combinations of Nf and Wf is shown.Section2 shows the transistor’s equivalent subcircuit model and the layout of the DUT used. The detailed explanation on the formulation of the equation for the subcircuit components is then shown, and the plots to compare between the calculated and extracted component values are presented. In Section 3, the good fitting between the measured and simulated DC and RF results for the various geometry combinations is shown, and the further verification with the proposed technique for the generated scalable RFCMOS model is presented. The conclusion follows in Section 4.


## 2. Scalable RF MOSFET Modelling

Figure1 shows the proposed RF equivalent subcircuit model. All the subcircuit components are physical and can be used for transistor that has the source and body terminal tied together and grounded.Figure 1
RF equivalent subcircuit model.The resistanceRgate represents the effective lumped gate resistance that consists of both the electrode resistance and the distributed channel resistance [15]. The resistances Rs and Rd represent the effective source and drain resistance that consist of the metal line, via, and contact resistances.The capacitancesCgs_ext and Cgd_ext represent the effective gate-to-source and gate-to-drain capacitances and consist of both the overlap and fringing capacitances between the terminals. Cds represents the drain-to-source fringing capacitance between the metal lines that connect to the source and drain diffusions. As the internal junction capacitances of the core model are turned off, the external diodes Djdb, Djdb_perim, Djsb, and Djsb_perim are added as the junction capacitances to connect the substrate resistance network. Djdb stands for the area intensive diode, while the Djdb_perim stands for the perimeter intensive diode, and the definition is the same for the source-to-body junction diodes. The parameters Rsub1, Rsub2,and Rsub3 represent the substrate network resistances. Finally, Csubg and Rsubg are defined as the gate-to-substrate capacitance and resistance over the shallow trench isolation (STI) region.Figure2 shows the simplified layout of the RF NMOS transistor. The transistor has a multifinger configuration with double-contacted gate polystructure. Dummy gate poly is added to improve the gate structure formation. The metal 1 and metal 2 are used for the connection of the gate terminal. The source diffusions are connected using the metal 1 and shortened to the body terminal or P-well, while the drain diffusions are pulled out using the metal 3.Figure 2
Simplified RF NMOS layout.In order to extract physical subcircuit components in the macromodel, all the physical layers and their geometry that are used to form the structure of the transistor must be known. The extraction technique used to extract the subcircuit components values is as shown in [16].


### 2.1. Gate Resistance Modelling

Figure3 shows the simplified polysilicon gate structure and its distributed parasitic resistances. At RF frequency region, Rgate is influenced by three physical effects. The three effects are the distributed gate electrode resistanceRg,poly_Wf, the non-quasi-static (NQS) effect in the channel Rg,ch [15, 17], and the polysilicon gate extension out of the active region Rg,poly_Wext follows:(1)Rgate=Rg,poly_Wf+Rg,ch+Rg,poly_Wext.
In [18], the distributed effect of the gate electrode has been studied and the following equations have been derived to calculate the distributed gate electrode resistance.(2)Rg,poly_Wf=ρpoly⋅Wf/Lg3⋅Nf,Single-contacted gate,(3)Rg,poly_Wf=ρpoly⋅Wf/Lg12⋅Nf,Double-contactedgate.
In (2) and (3), the variable Nf is the number of fingers, ρpoly is the gate sheet resistance, and Lg and Wfs are the channel length and unit width of a single finger. The factors of 1/3 and 1/12 are used in (2) and (3) to account for the distributed gate resistance effect and the different gate connection configuration at the ends of the gate structure.Figure 3
Simplified polysilicon gate structure and its distributed parasitic resistances.The polysilicon gate extensionWext as shown in Figure 1 contributes to the total gate resistance as follows:(4)Rg,poly_Wext=ρpoly⋅(Wext/2)Nf⋅Lg.
At RF frequency region, the channel will become like a distributed RC network as shown in Figure 1. The distributed channel resistance will reflect to the gate through the capacitance network and increase the total gate resistance. Note that this NQS channel resistance is bias and geometry dependent. However, it is reported that a simple gate resistance can model the distributed gate resistance effect, and it is accurate up to ft/2 for an MOSFET without any significant NQS effects [19]. Hence, only a geometry-dependent NQS channel resistance is assumed to contribute to the total gate resistance as follows:(5)Rg,ch=x1⋅(Lg)Nf⋅Wf.
Note that the variable x1 is defined as a factor of the channel sheet resistance that is reflected back to the gate structure.Figure4 shows the comparison between the extracted and calculated Rgate versus Nf and Wf plots. It is observed that Rgate is inversely proportional to Nf, and there exists a minimum Rgate at the Wf of 2.5 μm. The Nf,and Wf dependence of Rgate can be explained by considering (1)–(5). From (2)–(5), the three physical effects on the gate resistance are inversely proportional to Nf, and this explains the trend of Rgate versus Nf. As shown in (3), the resistance Rg,poly_Wf is directly proportional to Wf, but in (5), the resistance Rg,ch is inversely proportional to Wf. The Wf effect on the resistanceRg,poly_Wf and Rg,ch will compete with each other and cause Rgate to have a minimum point as shown in Figure 4. Therefore, based on the proposed physical geometry equation, the calculated and extracted Rgate resistance matches well with the change in Nf and Wf of the transistor.Extracted and calculatedRgate versus (a) Nf and (b) Wf.
(a)(b)


### 2.2. Source and Drain Resistance Modelling

The resistancesRs and Rd shown in Figure 1 are defined as the effective resistances that consist of the metal line, via, and contact resistances as shown in the layout of Figure 5. It is assumed that the source and drain resistance model in the BSIM3v3 model only models the active region of the parasitic resistances. Based on the above layout, the following equations can be derived to represent Rs and Rd:(6)Rs=(ρm1⋅l1)/x1+(Rcon/ncon)ndiff,source,Rd=(ρm3⋅l2)/x2+(Rcon+Rvia1+Rvia2)/nconndiff,drain.
The variables ρm1 and ρm3 represent the sheet resistance for metal 1 and metal 3, and the variables Rcon, Rvia1, and Rvia2 represent the contact, via1, and via2 resistances and the ncon, ndiff,source, and ndiff,drain are the numbers of contacts and source and drain diffusions in the transistor.Figure 5
Source and drain metal structure.Figure6 shows the comparison between the extracted and calculated Rs and Rd versus Nf plots. It is observed that both resistances are inversely proportional to Nf, and there exists a minimum point of resistance value at the Wf of 2.5 μm. From (6), the ndiff,source and ndiff,drain are the number of source and drain diffusions, and they are proportional to Nf. Hence, the Rs and Rd resistances show the inverse proportionality with Nf. From Figure 5, the variables l1, l2 and ncon are proportional to the Wf of the transistor, and when they are applied to (6), the Wf effect on both l1 and l2 will compete with ncon and cause a minimum resistance level to occur at Wf of 2.5 μm.Extracted and calculated (a)Rs and (b) Rd versus Nf.
(a)(b)


### 2.3. Gate-to-Substrate Capacitance and Resistance Modelling

The componentsCsubg and Rsubgthat are shown in Figure 1 are defined as the gate-to-substrate capacitance and resistance over the STI region, and they are shown in the cross-sectional structure in Figure 7. The dotted enclosed region in Figure 7 is the gate area that is on top of the STI region generating the parasitic components Csubg and Rsubg, and based on the above layout geometry, the following equations are formulated:(7)Csubg=CM1,STI⋅aM1+CM2,STI⋅aM2.
The variables CM1,STI and CM2,STI are the parasitic capacitances per unit area of metal 1 and metal 2 over the STI region, while the variables aM1 and aM2 are the area of the dotted enclosed region of metal 1 and metal 2 as shown in Figure 7.(8)Rsubg=Rsubstrate,STINf.
From (7), it is shown that Csubg is mainly contributed by the parasitic capacitances due to the layers of gate metal 1 and metal 2 over the STI region. The extracted variables CM1,STI and CM2,STI in (7) represent the capacitance per unit area (fF/μm2) of the enclosed metal 1 and metal 2 regions as shown in Figure 7. As the dielectric thickness between metal 2 and the substrate is higher than that of metal 1, it is expected that the extracted CM1,STI is higher than CM2,STI. Since there is some area under the enclosed metal 1 and metal 2 regions that is overlapped with the polysilicon gate, the proposed equation (7) may overestimate Csubg slightly, and a small capacitance may be required to be subtracted from the above equation.Figure 7
Gate-to-substrate capacitance and resistance structure.Csubg and Rsubg are extracted using Seneca and Substrate storms [20] that simulate the layout structure as shown in Figure 7. Based on the extracted results of Rsubg, it is found that it is only dependent on Nf,  and it is formulated as shown in (8). Note that the extracted Rsubstrate,STI is defined as the substrate parasitic resistance under the STI region.Figure8 shows the comparison between the extracted and calculated Csubg and Rsubg versus Nf plots. It is observed that Csubg is proportional to Nf while Rsubg is inversely proportional to Nf. In (7), Csubg is dependent on aM1 andaM2, and when Nf increases, the two areas will increase and cause Csubg to increase.Extracted and calculated (a)Csubg and (b) Rsubg versus Nf.
(a)(b)Based on the layout structure in Figure7, it is observed that the length of lx is proportional to Nf. By using the simple resistance equation that uses the sheet resistance multiply with the number of squares, it is obvious that the number of squares in the signal flow path of Rsubg is inversely proportional to the length of  lx. Hence, Rsubg will decrease with increasing Nf.


### 2.4. Gate-to-Source and Gate-to-Drain Capacitances Modelling

The capacitanceCgs_ext and Cgd_ext in Figure 1 represent the overlap and fringing capacitances between the gate-to-source and gate-to-drain terminals as shown in Figure 9. Based on the above layout structure, it is obvious that the amount of overlap capacitance is dependent on the number of source and drain metal lines that overlap the gate metal, while the fringing capacitances will be dependent on the separation distance between the source/drain metal lines to gate polysilicon structure and the Wf of the transistor. Since the separation distance between the source/drain metal lines and the gate polysilicon structure is fixed, therefore the fringing capacitance is only dependent on transistor’s Wf. Based on the above analysis, the following equations are formulated:(9)Cgs_ext=CM2-M1,gs_overlap⋅ndiff,source+CM1-Poly,gs_fringing⋅Nf⋅Wf.
Note that CM2-M1,gs_overlap is the overlap capacitance between the gate (metal 2) and source (metal 1) metal lines, and CM1-Poly,gs_fringing is the fringing capacitance between the gate structure (polysilicon) and the source (metal 1) metal lines.(10)Cgd_ext=CM3-M1,gd_overlap⋅ndiff,drain+CM1-Poly,gd_fringing⋅Nf⋅Wf.
Here CM3-M1,gd_overlap is the overlap capacitance between the gate (metal 1) and drain (metal 3) metal lines and CM1-Poly,gd_fringing is the fringing capacitance between the gate structure (polysilicon) and the drain (metal 1) metal lines. It is assumed that the fringing capacitances from the metal 2 and metal 3 lines of the drain metal structure to the polysilicon gate are small and negligible when compared to the metal 1 and to the polysilicon gate fringing capacitance.Figure 9
Gate-to-source and gate-to-drain capacitance structures.As the dielectric separation distance between the metal 3 (drain) and metal 1 (gate) is larger than the case of metal 2 (gate) and metal 1 (source), it is expected thatCM2-M1,gs_overlap will be larger than CM3-M1,gd_overlap. Furthermore, the extracted CM1-Poly,gs_fringing must be close to the extracted CM1-Poly,gd_fringing or slightly smaller.Figure10 shows the comparison between the extracted and calculated Cgs_ext and Cgd_ext versus Nf plots. It is observed that both capacitances are proportional to Nf and Wf, and the extracted Cgs_ext capacitance is slightly larger than Cgd_ext. In (9) and (10), the Nf dependence in both of the capacitances is due to the variables ndiff,sourceand ndiff,drain, and since ndiff,source has one more diffusion than the ndiff,drain, the extracted Cgs_ext capacitance is slightly larger than Cgd_ext. The Wf dependence as shown in Figure 10 is mainly due to the fringing capacitance effect in (9) and (10).Extracted and calculated (a)Cgs_ext and (b) Cgd_ext versus Nf.
(a)(b)


### 2.5. Drain-to-Source Capacitance Modelling

Cds is defined as the fringing capacitance between the metal lines that connect the source and drain diffusions. The location of the fringing capacitance is indicated in Figure 11(a) that uses the cross-section view of A-A′ in Figure 9. Based on the layout structure, it is predicted that the fringing capacitance is proportional to Nf and Wf of the transistor. Hence, the following equation is formulated for Cds:(11)Cds=Cds_fringing⋅Nf⋅Wf.
Note that Cds_fringing is the fringing capacitance per unit width between the metal lines of the source and drain metal structures.Drain-to-Source capacitance structure (a) and extracted and calculatedCds versus Nf (b).
(a)(b)In Figure11(b), the comparison between the extracted and calculated Cds shows that the proposed formulated equation can accurately predict the change in Nf and Wf.


### 2.6. Substrate Resistances Modelling

By using the cross-section view of A-A′ in Figure9, the substrate resistances network is added into the structure to indicate the location of the parasitic as shown in Figure 12. Cjsb and Cjdb are junction capacitances that are replaced by the junction diodes as shown in Figure 1. Rsub2 and Rsub3 represent the substrate resistances under the channel, while Rsub1 connects the intrinsic bulk node to the body terminal. Based on the layout structure, it is predicted that Rsub2 and Rsub3 are proportional to Lg/(Nf·Wf), while Rsub1 is inversely proportional Nf·Wf. Hence, the following equations are formulated for the substrate resistances:(12)Rsub1=ρsubstrateNf⋅(Wf+2⋅XJ),Rsub2=Rsub3=ρsubstrate,sheet⋅Lg2⋅Nf⋅(Wf+2⋅XJ).
In (12), the variable ρsubstrate is the substrate resistivity and has the unit of Ω μm, and ρsubstrate,sheet is the substrate sheet resistance under the active region and has the unit of Ω/number of square. The parameter XJ represents the source and drain junction depth, and its value can be found in the BSIM3v3 model parameters.Figure 12
Substrate resistances network.In Figure13, the comparison between the extracted and calculated substrate resistances shows that the proposed formulated (12) can accurately predict the change in Nf and Wf.Extracted and calculated (a)Rsub1 and (b) Rsub2 and Rsub3 versus Nf.
(a)(b)


## 2.1. Gate Resistance Modelling

Figure3 shows the simplified polysilicon gate structure and its distributed parasitic resistances. At RF frequency region, Rgate is influenced by three physical effects. The three effects are the distributed gate electrode resistanceRg,poly_Wf, the non-quasi-static (NQS) effect in the channel Rg,ch [15, 17], and the polysilicon gate extension out of the active region Rg,poly_Wext follows:(1)Rgate=Rg,poly_Wf+Rg,ch+Rg,poly_Wext.
In [18], the distributed effect of the gate electrode has been studied and the following equations have been derived to calculate the distributed gate electrode resistance.(2)Rg,poly_Wf=ρpoly⋅Wf/Lg3⋅Nf,Single-contacted gate,(3)Rg,poly_Wf=ρpoly⋅Wf/Lg12⋅Nf,Double-contactedgate.
In (2) and (3), the variable Nf is the number of fingers, ρpoly is the gate sheet resistance, and Lg and Wfs are the channel length and unit width of a single finger. The factors of 1/3 and 1/12 are used in (2) and (3) to account for the distributed gate resistance effect and the different gate connection configuration at the ends of the gate structure.Figure 3
Simplified polysilicon gate structure and its distributed parasitic resistances.The polysilicon gate extensionWext as shown in Figure 1 contributes to the total gate resistance as follows:(4)Rg,poly_Wext=ρpoly⋅(Wext/2)Nf⋅Lg.
At RF frequency region, the channel will become like a distributed RC network as shown in Figure 1. The distributed channel resistance will reflect to the gate through the capacitance network and increase the total gate resistance. Note that this NQS channel resistance is bias and geometry dependent. However, it is reported that a simple gate resistance can model the distributed gate resistance effect, and it is accurate up to ft/2 for an MOSFET without any significant NQS effects [19]. Hence, only a geometry-dependent NQS channel resistance is assumed to contribute to the total gate resistance as follows:(5)Rg,ch=x1⋅(Lg)Nf⋅Wf.
Note that the variable x1 is defined as a factor of the channel sheet resistance that is reflected back to the gate structure.Figure4 shows the comparison between the extracted and calculated Rgate versus Nf and Wf plots. It is observed that Rgate is inversely proportional to Nf, and there exists a minimum Rgate at the Wf of 2.5 μm. The Nf,and Wf dependence of Rgate can be explained by considering (1)–(5). From (2)–(5), the three physical effects on the gate resistance are inversely proportional to Nf, and this explains the trend of Rgate versus Nf. As shown in (3), the resistance Rg,poly_Wf is directly proportional to Wf, but in (5), the resistance Rg,ch is inversely proportional to Wf. The Wf effect on the resistanceRg,poly_Wf and Rg,ch will compete with each other and cause Rgate to have a minimum point as shown in Figure 4. Therefore, based on the proposed physical geometry equation, the calculated and extracted Rgate resistance matches well with the change in Nf and Wf of the transistor.Extracted and calculatedRgate versus (a) Nf and (b) Wf.
(a)(b)


## 2.2. Source and Drain Resistance Modelling

The resistancesRs and Rd shown in Figure 1 are defined as the effective resistances that consist of the metal line, via, and contact resistances as shown in the layout of Figure 5. It is assumed that the source and drain resistance model in the BSIM3v3 model only models the active region of the parasitic resistances. Based on the above layout, the following equations can be derived to represent Rs and Rd:(6)Rs=(ρm1⋅l1)/x1+(Rcon/ncon)ndiff,source,Rd=(ρm3⋅l2)/x2+(Rcon+Rvia1+Rvia2)/nconndiff,drain.
The variables ρm1 and ρm3 represent the sheet resistance for metal 1 and metal 3, and the variables Rcon, Rvia1, and Rvia2 represent the contact, via1, and via2 resistances and the ncon, ndiff,source, and ndiff,drain are the numbers of contacts and source and drain diffusions in the transistor.Figure 5
Source and drain metal structure.Figure6 shows the comparison between the extracted and calculated Rs and Rd versus Nf plots. It is observed that both resistances are inversely proportional to Nf, and there exists a minimum point of resistance value at the Wf of 2.5 μm. From (6), the ndiff,source and ndiff,drain are the number of source and drain diffusions, and they are proportional to Nf. Hence, the Rs and Rd resistances show the inverse proportionality with Nf. From Figure 5, the variables l1, l2 and ncon are proportional to the Wf of the transistor, and when they are applied to (6), the Wf effect on both l1 and l2 will compete with ncon and cause a minimum resistance level to occur at Wf of 2.5 μm.Extracted and calculated (a)Rs and (b) Rd versus Nf.
(a)(b)


## 2.3. Gate-to-Substrate Capacitance and Resistance Modelling

The componentsCsubg and Rsubgthat are shown in Figure 1 are defined as the gate-to-substrate capacitance and resistance over the STI region, and they are shown in the cross-sectional structure in Figure 7. The dotted enclosed region in Figure 7 is the gate area that is on top of the STI region generating the parasitic components Csubg and Rsubg, and based on the above layout geometry, the following equations are formulated:(7)Csubg=CM1,STI⋅aM1+CM2,STI⋅aM2.
The variables CM1,STI and CM2,STI are the parasitic capacitances per unit area of metal 1 and metal 2 over the STI region, while the variables aM1 and aM2 are the area of the dotted enclosed region of metal 1 and metal 2 as shown in Figure 7.(8)Rsubg=Rsubstrate,STINf.
From (7), it is shown that Csubg is mainly contributed by the parasitic capacitances due to the layers of gate metal 1 and metal 2 over the STI region. The extracted variables CM1,STI and CM2,STI in (7) represent the capacitance per unit area (fF/μm2) of the enclosed metal 1 and metal 2 regions as shown in Figure 7. As the dielectric thickness between metal 2 and the substrate is higher than that of metal 1, it is expected that the extracted CM1,STI is higher than CM2,STI. Since there is some area under the enclosed metal 1 and metal 2 regions that is overlapped with the polysilicon gate, the proposed equation (7) may overestimate Csubg slightly, and a small capacitance may be required to be subtracted from the above equation.Figure 7
Gate-to-substrate capacitance and resistance structure.Csubg and Rsubg are extracted using Seneca and Substrate storms [20] that simulate the layout structure as shown in Figure 7. Based on the extracted results of Rsubg, it is found that it is only dependent on Nf,  and it is formulated as shown in (8). Note that the extracted Rsubstrate,STI is defined as the substrate parasitic resistance under the STI region.Figure8 shows the comparison between the extracted and calculated Csubg and Rsubg versus Nf plots. It is observed that Csubg is proportional to Nf while Rsubg is inversely proportional to Nf. In (7), Csubg is dependent on aM1 andaM2, and when Nf increases, the two areas will increase and cause Csubg to increase.Extracted and calculated (a)Csubg and (b) Rsubg versus Nf.
(a)(b)Based on the layout structure in Figure7, it is observed that the length of lx is proportional to Nf. By using the simple resistance equation that uses the sheet resistance multiply with the number of squares, it is obvious that the number of squares in the signal flow path of Rsubg is inversely proportional to the length of  lx. Hence, Rsubg will decrease with increasing Nf.


## 2.4. Gate-to-Source and Gate-to-Drain Capacitances Modelling

The capacitanceCgs_ext and Cgd_ext in Figure 1 represent the overlap and fringing capacitances between the gate-to-source and gate-to-drain terminals as shown in Figure 9. Based on the above layout structure, it is obvious that the amount of overlap capacitance is dependent on the number of source and drain metal lines that overlap the gate metal, while the fringing capacitances will be dependent on the separation distance between the source/drain metal lines to gate polysilicon structure and the Wf of the transistor. Since the separation distance between the source/drain metal lines and the gate polysilicon structure is fixed, therefore the fringing capacitance is only dependent on transistor’s Wf. Based on the above analysis, the following equations are formulated:(9)Cgs_ext=CM2-M1,gs_overlap⋅ndiff,source+CM1-Poly,gs_fringing⋅Nf⋅Wf.
Note that CM2-M1,gs_overlap is the overlap capacitance between the gate (metal 2) and source (metal 1) metal lines, and CM1-Poly,gs_fringing is the fringing capacitance between the gate structure (polysilicon) and the source (metal 1) metal lines.(10)Cgd_ext=CM3-M1,gd_overlap⋅ndiff,drain+CM1-Poly,gd_fringing⋅Nf⋅Wf.
Here CM3-M1,gd_overlap is the overlap capacitance between the gate (metal 1) and drain (metal 3) metal lines and CM1-Poly,gd_fringing is the fringing capacitance between the gate structure (polysilicon) and the drain (metal 1) metal lines. It is assumed that the fringing capacitances from the metal 2 and metal 3 lines of the drain metal structure to the polysilicon gate are small and negligible when compared to the metal 1 and to the polysilicon gate fringing capacitance.Figure 9
Gate-to-source and gate-to-drain capacitance structures.As the dielectric separation distance between the metal 3 (drain) and metal 1 (gate) is larger than the case of metal 2 (gate) and metal 1 (source), it is expected thatCM2-M1,gs_overlap will be larger than CM3-M1,gd_overlap. Furthermore, the extracted CM1-Poly,gs_fringing must be close to the extracted CM1-Poly,gd_fringing or slightly smaller.Figure10 shows the comparison between the extracted and calculated Cgs_ext and Cgd_ext versus Nf plots. It is observed that both capacitances are proportional to Nf and Wf, and the extracted Cgs_ext capacitance is slightly larger than Cgd_ext. In (9) and (10), the Nf dependence in both of the capacitances is due to the variables ndiff,sourceand ndiff,drain, and since ndiff,source has one more diffusion than the ndiff,drain, the extracted Cgs_ext capacitance is slightly larger than Cgd_ext. The Wf dependence as shown in Figure 10 is mainly due to the fringing capacitance effect in (9) and (10).Extracted and calculated (a)Cgs_ext and (b) Cgd_ext versus Nf.
(a)(b)


## 2.5. Drain-to-Source Capacitance Modelling

Cds is defined as the fringing capacitance between the metal lines that connect the source and drain diffusions. The location of the fringing capacitance is indicated in Figure 11(a) that uses the cross-section view of A-A′ in Figure 9. Based on the layout structure, it is predicted that the fringing capacitance is proportional to Nf and Wf of the transistor. Hence, the following equation is formulated for Cds:(11)Cds=Cds_fringing⋅Nf⋅Wf.
Note that Cds_fringing is the fringing capacitance per unit width between the metal lines of the source and drain metal structures.Drain-to-Source capacitance structure (a) and extracted and calculatedCds versus Nf (b).
(a)(b)In Figure11(b), the comparison between the extracted and calculated Cds shows that the proposed formulated equation can accurately predict the change in Nf and Wf.


## 2.6. Substrate Resistances Modelling

By using the cross-section view of A-A′ in Figure9, the substrate resistances network is added into the structure to indicate the location of the parasitic as shown in Figure 12. Cjsb and Cjdb are junction capacitances that are replaced by the junction diodes as shown in Figure 1. Rsub2 and Rsub3 represent the substrate resistances under the channel, while Rsub1 connects the intrinsic bulk node to the body terminal. Based on the layout structure, it is predicted that Rsub2 and Rsub3 are proportional to Lg/(Nf·Wf), while Rsub1 is inversely proportional Nf·Wf. Hence, the following equations are formulated for the substrate resistances:(12)Rsub1=ρsubstrateNf⋅(Wf+2⋅XJ),Rsub2=Rsub3=ρsubstrate,sheet⋅Lg2⋅Nf⋅(Wf+2⋅XJ).
In (12), the variable ρsubstrate is the substrate resistivity and has the unit of Ω μm, and ρsubstrate,sheet is the substrate sheet resistance under the active region and has the unit of Ω/number of square. The parameter XJ represents the source and drain junction depth, and its value can be found in the BSIM3v3 model parameters.Figure 12
Substrate resistances network.In Figure13, the comparison between the extracted and calculated substrate resistances shows that the proposed formulated (12) can accurately predict the change in Nf and Wf.Extracted and calculated (a)Rsub1 and (b) Rsub2 and Rsub3 versus Nf.
(a)(b)


## 3. Measurement Results and Discussion

### 3.1. Modelling Results

The devices under test (DUT) are thin gate NMOSs with fixedLgof 70 nm, Wf of 1, 2.5, and 5 μm, and Nf of 4, 8, 16, 24, 32, 48, and 64. The S-parameters were measured using the HP8510 network analyzer with GSG RF probes for a frequency range from 50 MHz to 49.85 GHz at the various bias combinations of the gate-to-source Vgs and drain-to-source Vds potentials. After the system calibration was performed using LRRM technique, the RF transistor and its deembedding structures were measured. In this measurement, the standard open and short deembedding structures were used to remove the pad and interconnects parasitic [21].In order to demonstrate the scalability of the RF model, measured and simulated DC, Y-parameters, andft plots are presented in this section. Figures 14–16 show the measured and simulated results for fixed Wf of 1 μm with varying Nf of 8, 24, and 64 at the biasing combination of Vgs and Vds ranging from 0.3 to 1.2 V. From the comparison between the measured and simulated results, it is observed that the RF model can accurately predict the measured results as Nf varies. The Wf scalability of the RF model is demonstrated in Figures 15, 17, and 18 for fixed Nf of 24 with varying Wf of 1, 2.5, and 5 μm. Hence, from Figures 14–18, the proposed RF model is shown to be geometry scalable for Nf and Wf for the frequency range from 50 MHz to 49.85 GHz.Measured and simulated results for NMOS transistor withNf of 8, Wf of 1 μm, and Lg of 70 nm.
(a)(b)(c)(d)(e)(f)Measured and simulated results for NMOS transistor withNf of 24, Wf of 1 μm, and Lg of 70 nm.
(a)(b)(c)(d)(e)(f)Measured and simulated results for NMOS transistor withNf of 64, Wf of 1 μm, and Lg of 70 nm.
(a)(b)(c)(d)(e)(f)Measured and simulated results for NMOS transistor withNf of 24, Wf of 2.5 μm, and Lg of 70 nm.
(a)(b)(c)(d)(e)(f)Measured and simulated results for NMOS transistor withNf of 24, Wf of 5 μm, and Lg of 70 nm.
(a)(b)(c)(d)(e)(f)


### 3.2. Further Verification with Proposed Technique for the Scalable Model

In a scalable RFCMOS model, there are many different variables that determined the scalability of the RF model. It becomes very tedious to verify and monitor the model accuracy further so that the developed model, file has to be scalable for a certain range of geometry, biasing and frequency variables. Hence, a new verification technique is proposed in this paper. This proposed verification technique is crucial to both the modelling engineers and the model file end users as it helps them to monitor the quality of the developed model and at the same time, the model file can be checked for any errors in the coded geometry equations of the parasitic subcircuit components. Furthermore, by using this proposed technique, the amount of verification time required to check the developed model file is reduced, and thus reducing the overall model development time.Figure19 shows the model accuracy plots for NMOS transistors with different Nf of 4, 8, 16, 24, 32, 48, and 64 and Wf of 1, 2.5, and 5 μm extracted at Vgs=0.95 V and Vds=0.8 V. From the box plots, it is observed that 10 to 90% of the error population from the DC, S-parameters, and Ft are within ±10%. In the three plots, the model accuracy for all the fabricated devices is monitored at DC, 2.45, 5.45, and 10.25 GHz. Therefore, by generating such model accuracy plots, the quality of the developed RF model in terms of its accuracy is monitored for all the fabricated device sizes and at the different frequency points. Furthermore, by plotting at the other biasing points, the model accuracy of the RF model can be checked for those important biasing regions.Model accuracy for NMOSFETs with differentNf and Wf of 1 μm at Vgs=0.95 V and Vds=0.8 V (a), with different Nf and Wf of 2.5 μm at Vgs=0.95 V and Vds=0.8 V (b), and with different Nf and Wf of 5 μm at Vgs=0.95 V and Vds=0.8 V (c).
(a)(b)(c)Figure20 shows the model continuity plots for the parameters Gm and Y21 versus different Nf and Wf of 1, 2.5, and 5 μm extracted at Vgs=0.95 V and Vds=0.8 V. From the three plots, it is observed that the simulated Gm (blue line) and Y21 (red line) overlap each other, and this observation implies that the RF model is continuous from DC to RF region. Furthermore, the simulated transistor’s gain (red and blue lines) can accurately predict the measured data (red and blue symbols) as the Nf and Wf changes and their calculated absolute errors are within the error specification of ±10%. It is also observed that the simulated Gm and Y21 scale linearly with Nf for all the three Wf. By plotting such model continuity plots at other biasing points, the Nf, Wf, and biasing effect on the RF model are monitored at both the DC and low-frequency region. In the case when the coded equations of the subcircuit components in the model file are incorrect, the model accuracy and continuity plots will immediately reflect the incorrect effects of the wrong equations, and this will alert the modelling engineer to check the coded model file again.Model continuity forGm and Y21 for NMOSFETs with different Nf and Wf of 1 μm at Vgs=0.95 V and Vds=0.8 V (a), with different Nf and Wf of 2.5 μm at Vgs=0.95 V and Vds=0.8 V (b), and with different Nf and Wf of 5 μm at Vgs=0.95 V and Vds=0.8 V (c).
(a)(b)(c)In this proposed technique, the model accuracy and continuity plots are generated to monitor the device geometry, biasing, and frequency variables of the RF model. From these two types of plots, the quality of the developed model and the coded model file will be inspected, and the final verified model file will be error-free and reliable to use.The proposed model accuracy and continuity plots can also be used as one of the model acceptance criteria, whereby its accuracy and continuity can be checked before accepting and using the developed RF model file.


## 3.1. Modelling Results

The devices under test (DUT) are thin gate NMOSs with fixedLgof 70 nm, Wf of 1, 2.5, and 5 μm, and Nf of 4, 8, 16, 24, 32, 48, and 64. The S-parameters were measured using the HP8510 network analyzer with GSG RF probes for a frequency range from 50 MHz to 49.85 GHz at the various bias combinations of the gate-to-source Vgs and drain-to-source Vds potentials. After the system calibration was performed using LRRM technique, the RF transistor and its deembedding structures were measured. In this measurement, the standard open and short deembedding structures were used to remove the pad and interconnects parasitic [21].In order to demonstrate the scalability of the RF model, measured and simulated DC, Y-parameters, andft plots are presented in this section. Figures 14–16 show the measured and simulated results for fixed Wf of 1 μm with varying Nf of 8, 24, and 64 at the biasing combination of Vgs and Vds ranging from 0.3 to 1.2 V. From the comparison between the measured and simulated results, it is observed that the RF model can accurately predict the measured results as Nf varies. The Wf scalability of the RF model is demonstrated in Figures 15, 17, and 18 for fixed Nf of 24 with varying Wf of 1, 2.5, and 5 μm. Hence, from Figures 14–18, the proposed RF model is shown to be geometry scalable for Nf and Wf for the frequency range from 50 MHz to 49.85 GHz.Measured and simulated results for NMOS transistor withNf of 8, Wf of 1 μm, and Lg of 70 nm.
(a)(b)(c)(d)(e)(f)Measured and simulated results for NMOS transistor withNf of 24, Wf of 1 μm, and Lg of 70 nm.
(a)(b)(c)(d)(e)(f)Measured and simulated results for NMOS transistor withNf of 64, Wf of 1 μm, and Lg of 70 nm.
(a)(b)(c)(d)(e)(f)Measured and simulated results for NMOS transistor withNf of 24, Wf of 2.5 μm, and Lg of 70 nm.
(a)(b)(c)(d)(e)(f)Measured and simulated results for NMOS transistor withNf of 24, Wf of 5 μm, and Lg of 70 nm.
(a)(b)(c)(d)(e)(f)


## 3.2. Further Verification with Proposed Technique for the Scalable Model

In a scalable RFCMOS model, there are many different variables that determined the scalability of the RF model. It becomes very tedious to verify and monitor the model accuracy further so that the developed model, file has to be scalable for a certain range of geometry, biasing and frequency variables. Hence, a new verification technique is proposed in this paper. This proposed verification technique is crucial to both the modelling engineers and the model file end users as it helps them to monitor the quality of the developed model and at the same time, the model file can be checked for any errors in the coded geometry equations of the parasitic subcircuit components. Furthermore, by using this proposed technique, the amount of verification time required to check the developed model file is reduced, and thus reducing the overall model development time.Figure19 shows the model accuracy plots for NMOS transistors with different Nf of 4, 8, 16, 24, 32, 48, and 64 and Wf of 1, 2.5, and 5 μm extracted at Vgs=0.95 V and Vds=0.8 V. From the box plots, it is observed that 10 to 90% of the error population from the DC, S-parameters, and Ft are within ±10%. In the three plots, the model accuracy for all the fabricated devices is monitored at DC, 2.45, 5.45, and 10.25 GHz. Therefore, by generating such model accuracy plots, the quality of the developed RF model in terms of its accuracy is monitored for all the fabricated device sizes and at the different frequency points. Furthermore, by plotting at the other biasing points, the model accuracy of the RF model can be checked for those important biasing regions.Model accuracy for NMOSFETs with differentNf and Wf of 1 μm at Vgs=0.95 V and Vds=0.8 V (a), with different Nf and Wf of 2.5 μm at Vgs=0.95 V and Vds=0.8 V (b), and with different Nf and Wf of 5 μm at Vgs=0.95 V and Vds=0.8 V (c).
(a)(b)(c)Figure20 shows the model continuity plots for the parameters Gm and Y21 versus different Nf and Wf of 1, 2.5, and 5 μm extracted at Vgs=0.95 V and Vds=0.8 V. From the three plots, it is observed that the simulated Gm (blue line) and Y21 (red line) overlap each other, and this observation implies that the RF model is continuous from DC to RF region. Furthermore, the simulated transistor’s gain (red and blue lines) can accurately predict the measured data (red and blue symbols) as the Nf and Wf changes and their calculated absolute errors are within the error specification of ±10%. It is also observed that the simulated Gm and Y21 scale linearly with Nf for all the three Wf. By plotting such model continuity plots at other biasing points, the Nf, Wf, and biasing effect on the RF model are monitored at both the DC and low-frequency region. In the case when the coded equations of the subcircuit components in the model file are incorrect, the model accuracy and continuity plots will immediately reflect the incorrect effects of the wrong equations, and this will alert the modelling engineer to check the coded model file again.Model continuity forGm and Y21 for NMOSFETs with different Nf and Wf of 1 μm at Vgs=0.95 V and Vds=0.8 V (a), with different Nf and Wf of 2.5 μm at Vgs=0.95 V and Vds=0.8 V (b), and with different Nf and Wf of 5 μm at Vgs=0.95 V and Vds=0.8 V (c).
(a)(b)(c)In this proposed technique, the model accuracy and continuity plots are generated to monitor the device geometry, biasing, and frequency variables of the RF model. From these two types of plots, the quality of the developed model and the coded model file will be inspected, and the final verified model file will be error-free and reliable to use.The proposed model accuracy and continuity plots can also be used as one of the model acceptance criteria, whereby its accuracy and continuity can be checked before accepting and using the developed RF model file.


## 4. Conclusion

In this paper, the physical formation of the subcircuit parasitic is discussed with respect to its layout structure. The scaling effect of the device geometry is accounted for in the proposed scalable equations for each of the parasitic components. By implementing the proposed scalable equations for the parasitic components into the conventional subcircuit RF model, a scalable RFCMOS subcircuit model can be generated and shown to be valid up to 49.85 GHz. By using the proposed verification technique, the time required to verify a scalable RFCMOS model can be reduced greatly, and the verification step can also ensure that the developed model is error-free, and therefore, it is more robust and reliable to use. Although the scalable RFCMOS model can accurately predict the DC and RF characteristics of the transistor it will still require being able to predict its high-frequency noise. Hence, the scalable RFCMOS model will form the base of the RF transistor modelling so that the study of the scalable high-frequency noise modelling can be embarked on to achieve a fully scalable RFCMOS model.



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*Source: 452348-2011-12-21.xml*