Small Signal Equivalent Circuit in Linear Region

In this section, small signal equivalent circuit will be derived for 4-port RF MOSFET in linear region. Note that the bias condition for linear region has to follow the criterion of |Vgs| >

|V_T| and |V_ds|<< |V_gs -V_T| to ensure strong inversion of the channel and linear velocity vs. field under sufficiently low Vds. In this study for UN65 nMOS with Vdd=1.0V, the bias condition is specified as V_gs=V_dd =1.0V and V_ds=0 for linear region. Considering the channel conduction driven by inversion carriers, the channel resistance between source and drain is represented by R_ch in the device cross section and equivalent circuit as shown in Fig. 3.42 and Fig. 3.43, respectively. Then Rch appears as one additional model parameter compared with those required for off state shown in Fig. 3.27and Fig. 3.28. According to a simple equivalent circuit analysis on Fig. 3.43, Rch can be extracted from 1/Re(Y32) at very low frequency when all of the capacitors become open circuit, given by (3.47)~(3.48).

At very low frequency,

2 2

2

32 1

( )

1

Re( ) | ( )

s d

ch d s

ch d s

L L

R R R

Y _ R R R

 

   

  (3.47)

2(L_s L_d)2 1

 

32 1 32 1

1 1

( )

Re( ) | R^ch R^d R^s R^ch Re( ) | R^d R^s

Y _ Y _

        (3.48)

The body network model previously derived for 4-port RF MOSFET at off state can be applied to linear region with an appropriate modification on C_gb2, due to formation of inversion channel.

Besides necessary change to Cgb2, Fig. 3.44 reveals significant increase of Cgs and Cgd caused by the raising V_gs to well above V_T (V_gs =1.0V >>V_T ) as compared to those at off state (V_gs=0) shown in Fig. 3.29.

Table 3.5 summarizes the small signal equivalent circuit model parameters for 4-port RF MOSFET in linear region. It appears that the increase of Vgs to strong inversion region leads to increase of C_gs and C_gd whereas decrease of C_gb2, due to shielding effect from inversion carriers.

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Cgs is larger than Cgd by around 5.7% and it can be explained by the difference of finger numbers for source and drain contact in the multi-finger MOSFET with even finger number (NF=evern : NF/2+1 for source contacts and NF/2 for drain contacts). The channel resistance Rch

is determined by (3.48) to be around 7.3 .

Source Gate Drain Body

Cgs

Rbb

STI STI

DNW

P-well

Deep N-Well Cdnw1

P-substrate

STI

P-sub

Cgd

P-sub DNW

Cjs Cjd

Rdnw

Cdnw2

Rbb2

Rbb3

Cgb2 Rgb

R_ch

Fig. 3.42 4-port MOSFET device cross section and the representation of RC elements for the small signal equivalent circuit in linear region, V_gs=1.0V, V_ds=V_bs =0

S (2)

D (3)

Rbb Body

(4)

Cjs Cgb2 Cgd

Cgs

G

(1) ^{Lg Rg}

Ls Rs Rd Ld

Cjd

Rgb

Cgb1

Cdnw1 Cg

Rdnw Rbb2 Cdnw2

Rbb3

P-sub

Cds

Rch

Fig. 3.43 Small signal equivalent circuit with new body network model for 4-port RF MOSFET in linear region, V_gs=1.0V, V_ds= V_bs=0. R_ch represents channel resistance of the inversion channel.

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0 5 10 15 20 25 30 35 40 20

40 60 80 100 120

-Im(Y₁₂)/ Im(Y₁₁)/ Im(Y

11)/=C

gg

-Im(Y

12)/=C

gs

-Im(Y₁₃)/=C

gd

Im(Y 11)/, -Im(Y 12)/, -Im(Y 13)/(fF)

-Im(Y₁₃)/ Freq (GHz)

Vgs=1V, Vds=Vbs=0

Fig. 3.44 Im(Y11)/, -Im(Y12)/, and -Im(Y13)/ vs. frequency measured from 4-port RF MOSFET under the biases in linear region V_gs=1.0V, V_ds=V_bs=0. C_gg, C_gs, and C_gd determined from Im(Y₁₁)/, -Im(Y12)/, and -Im(Y13)/ at very low frequency

Table 3.5 Small signal equivalent circuit model parameters of 4-port MOSFET in linear region (V_gs=1.0V, V_ds= V_bs=0)

According to the model parameters shown in table 3.5 for 4-port MOSFETs in linear region, S- and Y-parameters are simulated. Fig. 3.45 ~ Fig. 3.52 present the 4-port S-parameters from measurement and simulation for this 4-port MOSFET (W2N32) in linear region under Vgs=1.0V and Vds=Vbs=0. Note that the simulation by using the small signal equivalent circuit shown in Fig. 3.43 and model parameters in Table 3.5 was compared with

4-port MOSFET model parameters in linear region

Capacitances (fF) Resistances Ω Inductances pH

Cgs 31.18 Rg 7.2 Ls 70

Cgd 29.44 Rd 1 Ld 70

Cgb1 2 Rs 1 Lg 70

Cgb2 1.4 Rb 1 Lb 70

Cg 2.1 Rbb 958

Cds 3 Rbb2 664

Cjs 18.91 Rbb3 5484

Cjd 17.12 Rdnw 476

Cdnw1 18.91 Rgb 518500

Cdnw2 18.91 Rch 7.3

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those calculated by BSIM-4 default model. The results indicate that the small signal equivalent circuit can predict 4-port S-parameters with promisingly good accuracy whereas the simulation uding BSIM-4 default model reveals large deviation from the measurement, particularly for the components related to the body, i.e. port-4, e.g. Mag(S₄₄), Mag(S₄₁), Mag(S42), and Mag(S43) as shown in Fig. 3.45 and phase(S44), phase(S41), phase(S42), and phase(S₄₃) as shown in Fig. 3.49. Besides S-parameters, Re(Y₄₂), Re(Y₄₃), and Re(Y₃₃) are three more important parameters to verify the body network model. Fig. 3.49 indicates that the small signal equivalent circuit with new body network can improve simulation accuracy for Re(Y42) and Re(Y43) compared with those simulated by using default body network model.

Fig. 3.54 presents similar effect from body network model when applied to BSIM-4 for Re(Y42) and Re(Y43) simulation. Similar with the condition for off state, the impact from body network model on Re(Y₃₃), i.e. the key parameter responsible for output resistance, is relatively smaller, as shown in Fig. 3.55. Again, the new body network model can be applied to both small signal equivalent circuit and BSIM-4 for an accurate simulation in linear region.

The verification by extensive data suggests that body network model is the key to determine simulation accuracy for 4-port RF MOSFETs and proves that the new body network proposed for linear region (Fig. 3.43) can fix the problem with BSIM-4 for 4-port MOSFET simulation.

67

0.10 Small signal eq. ckt Cds=3fF

measured : circuit with new body network model. Dash lines : BSIM-4 with default body network model.

0 5 10 15 20 25 30 35 40 Small signal eq. ckt Cds=3fF

measured :

BSIM-4 default model (c) (d)

(b)

Fig. 3.46 The measured and simulated Mag(S) of 4-port MOSFET in linear region V_gs=1.0V, Vds=Vbs=0 (a) Mag(S11) (b) Mag(S12) (c) Mag(S13) (d) Mag(S14). Solid lines : small signal equivalent circuit with new body network model. Dash lines : BSIM-4 with default body network model

68

Small signal eq. ckt Cds=3fF measured :

BSIM-4 default model (c) (d)

(a) (b) circuit with new body network model. Dash lines : BSIM-4 with default body network model

0 5 10 15 20 25 30 35 40 0.00

0.05 0.10 0.15

0.20 measured : Small signal eq. ckt Cds=3fF

simulation

Fig. 3.48 The measured and simulated Mag(S) of 4-port MOSFET in linear region V_gs=1.0V, Vds=Vbs=0 (a) Mag(S33) (b) Mag(S31) (c) Mag(S32) (d) Mag(S34). Solid lines : small signal equivalent circuit with new body network model. Dash lines : BSIM-4 with default body network model

69

Small signal eq. ckt Cds=3fF

measured : Small signal eq. ckt Cds=3fF

measured :

70

Small signal eq. ckt Cds=3fF

measured :

71 Default body network

Re(Y 42)(10-3 ) default body network

(b)

Freq (GHz)

Fig. 3.53 Measured and simulated Re(Y42) and Re(Y43) for 4-port MOSFET in linear region Vgs=1.0V, Vds=Vbs=0 (a) Re(Y42) (b) Re(Y43). Simulation by small signal equivalent circuit model. Solid lines : new body network model. Dash lines : default body network model

0 5 10 15 20 25 30 35 40 Default body network

Re(Y42)(10-3 ) default body network

(b)

Freq (GHz)

Fig. 3.54 Measured and simulated Re(Y42) and Re(Y43) for 4-port MOSFET in linear region Vgs=1.0V, Vds=Vbs=0 (a) Re(Y42) (b) Re(Y43). Simulation by BSIM-4, solid lines : with new body network model. Dash lines : with default body network model

0 5 10 15 20 25 30 35 40 default body network UN65 nMOS W2N32 default body network UN65 nMOS W2N32 V_GS=1V, V_DS=V_BS=0

(b)

Freq (GHz)

Fig. 3.55 Measured and simulated Re(Y₃₃) for 4-port MOSFET in linear region V_gs=1.0V, Vds=Vbs=0 (a) simulation by small signal equivalent circuit (b) simulation by BSIM-4. Solid

72

lines : with new body network model. Dash lines : with default body network model

在文檔中 四埠射頻金氧半電晶體與共用源汲極主動區之新型串疊結構的小訊號等效電路模型 (頁 85-94)