Small Signal Equivalent Circuit at Off State

First, the small signal equivalent circuit at off state is developed for 4-port RF MOSFET under cold device condition with V_g=V_d=V_s=V_b=0. Fig. 3.27 illustrates the device cross section for 4T MOSFET denoted with the RC elements located at proper regions, e.g. Cgs/Cgd

for the gate capacitances between gate and source/drain, C_js/C_jd for the junction capacitances between source/drain and p-well body, and Cdnw1/Cdnw2 for the junction capacitances between deep n-well and p-well(body)/p-substrate. Based on the proposed RC elements configuration, the equivalent circuit can be established as shown in Fig. 3.28. Note that series RL was deployed at each terminal, i.e. gate, drain, source, and body to account for the parasitic resistance and inductance remained even after short deembedding (M3 instead of M1 for this study). At off state, the channel is turned off due to depletion of free carriers, then C_gs and C_gd are composed of gate to source/drain overlap capacitance and fringing capacitance. The physical definition and modeling for C_gs and C_gd will be addressed in sec. 3.4. Regarding C_gb1 and Cgb2 introduced in our new body network model, the frequency and layout dependence and the extraction method can be referred to sec. 3.2.2. Rgb in parallel with Cgb2 represents a

53

DC leakage path, which cannot be neglected for UN65 MOSFET with ultra-thin gate oxide to 1.6 nm. The RC parameters of the body network model have been determined in sec. 3.2.2 and the model parameters remained for the 4T MOSFET can be extracted from 4-port Y-parameters at very low frequency given by (3.36)~(3.39). Fig. 3.29 presents C_gg, C_gd, and C_gd extracted from (3.36)~(3.38). Note that all of the capacitances should be physical elements independent of frequency but the capacitances extracted from Im(Y_ij) even after an open deembedding reveal significant increase at higher frequency. This frequency dependence suggests the effect from parasitic inductances, which cannot be eliminated using short M3 deembedding used in this work.To overcome this problem, extraction at very low frequency to make the parasitic inductance negligible becomes a compromized solution.

11,int

1

Im(Y ) Cgg

 

 (3.36)

12,int

1

Im(Y ) Cgs

 

  (3.37)

13,int

1

Im(Y ) Cgd

 

  (3.38)

14,int

1

Im(Y ) Cgb

 

  (3.39)

1 : gate (g), 2: source (s), 3: drain (d), 4: body (b)

where, Y_ij,int represent the intrinsic Y-parameters achieved after an open deembedding, i.e.

,int , ,

ij ij mea ij open

Y Y Y (3.40) For 4-port MOSFET, there exist 16 components of transcapacitance in the form of a 4×4 matrix given by (3.41) ,

54

gg gs gd gb

sg ss sd sb

ij

dg ds dd db

bg bs bd bb

C C C C

C C C C

C C C C C

C C C C

 

 

 

  

   

 

 

 

(3.41)

For 4-port devices at off state, the conductance associated with each port becomes zero and the capacitances incorporated in the 4×4 matrix must follow the charge conservation law for the sum of all capacitance at each port, represented by each row or each column in the 4×4 matrix, e.g.

11,int 12,int 13,int 14,int

Im(Y ) Im(Y ) Im(Y ) Im(Y )0

11,int 12,int 13,int 14,int

Im(Y ) Im(Y ) Im(Y ) Im(Y )

 0

  

  (3.42)

From (3.42), the capacitances associated with port-1, i.e. gate have to follow the conservation law as follows

gg gs gd gb 0 gg gs gd gb

C C C C  C C C C (3.43) Note that is valid under ideal condition that all of the parasitic capacitances can be removed to be clean by using open deembedding. The desired perfect deembedding can be approached by open deembedding to the bottom metal, i.e. M1. However, it cannot be achieved in this study due to the test structure limited to open M3 deembedding. Due to the limitation, an additional capacitance, namely Cg is added to (3.44) and given by (3.44)~(3.45).

gg gs gd gb g

C C C C C (3.44)

1 2

gb gb gb

C C C

1 2

gg gs gd gb gb g

C C C C C C

      (3.45)

One more extrinsic parasitic capacitance, namely Cds, which is located between drain and source is deployed in the small signal equivalent circuit to get best fitting to the measured Im(Y32), phase(S₃₂), and phase(S₂₃). C_ds can be extracted from Im(Y₃₂) given by (3.46). This C_ds

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existing at off state is contributed from inter-metal coupling capacitance instead of coupling through the channel between source and drain. Ideally, this C_ds can be eliminated through an improved open deembedding, e.g. open M1 deembedding. Unfortunately, this work is limited to open M3 deembedding and an additional C_ds cannot be avoided from the equivalent circuit.

32,int

1

Im(Y ) Cds

 

  (3.46)

Fig. 3.30 makes a comparison of C_ds=-Im(Y₃₂)/ from measurement and simulation using BSIM-4 and our small signal equivalent circuit. Note that the small signal equivalent circuit without extrinsic C_ds leads to under-estimation of C_ds=-Im(Y₃₂)/ and the adoption of an appropriate C_ds can result in a good match with the measurement.

Table 3.4 summarizes the small signal equivalent circuit model parameters determined for the 4-port RF MOSFET at off state. Fig. 3.31~ Fig. 3.38 present the 4-port S-parameters from measurement and simulation for this 4-port MOSFET (W2N32) at off state. Note that the simulation by using the small signal equivalent circuit shown in Fig. 3.28 and model parameters in Table 3.4 was compared with 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 significant 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. 3.31 and phase(S₄₄), phase(S₄₁), phase(S₄₂), and phase(S₄₃) as shown in Fig. 3.35. Besides S-parameters, Re(Y42), Re(Y43), and Re(Y33) are three more important parameters to verify the body network model. Fig. 3.39 indicates that small signal equivalent circuit with new body network can accurately predict Re(Y42) and Re(Y43) but that with default body network model reveal large deviation. Fig. 3.40 presents similar effect from body network model when applied to BSIM-4 for Re(Y42) and Re(Y43) simulation. Interestingly, the impact from body network model on Re(Y₃₃), i.e. the key parameter responsible for output resistance, is relatively

56

smaller, as shown in Fig. 3.41. Again, the new body network model can be applied to both small signal equivalent circuit and BSIM-4 for an accurate simulation. The extensive verification 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 in this thesis (Fig. 3.28) is the solution to fix the problem with BSIM-4 for 4-port MOSFET simulation.

Source Gate Drain Body

C_gs

R_bb

STI STI

DNW

P-well

Deep N-Well C_dnw1

P-substrate

STI

P-sub

C_gd

P-sub DNW

C_js C_jd

Rdnw

C_dnw2

Rbb2

Rbb3

Cgb2 Rgb

Fig. 3.27 4-port MOSFET device cross section and the representation of RC elements for the equivalent circuit at off state Vgs=Vds=Vbs =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

Fig. 3.28 Small signal equivalent circuit with new body network model for 4-port RF MOSFET at off state V_gs=V_ds= V_bs=0

57 Small signal eq. circuit w/o Cds

Cds=-Im(Y32)/ (fF) Small signal eq. circuit Cds=3fF Cds=-Im(Y32)/ (fF)

Freq (GHz) UN65 nMOS W2N32 Off state : Vg=Vd=Vs=Vb=0

Fig. 3.30 Measured and simulated Cds=-Im(Y32)/ for 4-port RF MOSFET at off state Vgs=Vds= Vbs=0. Simulation using BSIM-4 and small signal equivalent circuit (a) without extrinsic Cds (b) with extrinsic Cds =3fF

Table 3.4 Small signal equivalent circuit model parameters of 4-port MOSFET at off state 4-port MOSFET model parameters at off state

Capacitances (fF) Resistances Ω Inductances pH

Cgs 17.12 Rg 7.2 Ls 70

58

0.10 Small signal eq. ckt Cds=3fF

measured :

1.0 Small signal eq. ckt Cds=3fF

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

59

1.00 Small signal eq. ckt Cds=3fF

measured :

Fig. 3.33 The measured and simulated Mag(S) of 4-port MOSFET at off state V_gs=V_ds= V_bs=0 (a) Mag(S22) (b) Mag(S21) (c) Mag(S23) (d) Mag(S24). Solid lines : small signal equivalent circuit with new body network model. Dash lines : BSIM-4 with default body network model

0 5 10 15 20 25 30 35 40

1.00 Small signal eq. ckt Cds=3fF

measured :

Small signal eq. ckt Cds=3fF

measured :

Fig. 3.34 The measured and simulated Mag(S) of 4-port MOSFET at off state Vgs=V_ds= V_bs=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

60

80 Small signal eq. ckt Cds=3fF

measured :

Fig. 3.35 The measured and simulated phase(S) of 4-port MOSFET at off state V_gs=V_ds= V_bs=0 (a) phase(S44) (b) phase(S41) (c) phase(S42) (d) phase(S43). Solid lines : small signal equivalent 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 Small signal eq. ckt Cds=3fF

measured :

90 Small signal eq. ckt Cds=3fF

measured : Fig. 3.36 The measured and simulated phase(S) of 4-port MOSFET at off state Vgs=Vds=

Vbs=0 (a) phase(S11) (b) phase(S12) (c) phase(S13) (d) phase(S14). Solid lines : small signal equivalent circuit with new body network model. Dash lines : BSIM-4 with default body network model.

61

0 Small signal eq. ckt Cds=3fF

m e a s u r e d :

160 Small signal eq. ckt Cds=3fF

m e a s ur e d :

Fig. 3.37 The measured and simulated phase(S) of 4-port MOSFET at off state Vgs=V_ds= V_bs=0 (a) phase(S22) (b) phase(S21) (c) phase(S23) (d) phase(S24). Solid lines : small signal equivalent 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 Small signal eq. ckt Cds=3fF

measured :

160 Small signal eq. ckt Cds=3fF

measured :

Fig. 3.38 The measured and simulated phase(S) of 4-port MOSFET at off state Vgs=V_ds= V_bs=0 (a) phase(S33) (b) phase(S31) (c) phaseS32) (d) phase(S34). Solid lines : small signal equivalent circuit with new body network model. Dash lines : BSIM-4 with default body network model

62 Default body network Re(Y42)(10-3 )

default body network (b)

Freq (GHz)

Fig. 3.39 Measured and simulated Re(Y42) and Re(Y₄₃) for 4-port MOSFET at off state Vgs=Vds= Vbs=0 (a) Re(Y42) (b) Re(Y43). Simulation by small signal equivalent circuit model.

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 Re(Y42)(10-3 )

default body network (b)

Freq (GHz)

Fig. 3.40 Measured and simulated Re(Y42) and Re(Y₄₃) for 4-port MOSFET at off state Vgs=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 off-state V_G=V_D=V_S=V_B=0

(b)

Freq (GHz)

Fig. 3.41 Measured and simulated Re(Y33) for 4-port MOSFET at off state V_gs=V_ds= V_bs=0 (a) simulation by small signal equivalent circuit (b) simulation by BSIM-4. Solid lines : with new body network model. Dash lines : with default body network model

63

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 74-85)