Improved Body Network Model-Equivalent Circuit and Extraction Method

According to the comments made in 3.1.1, the simple body network model proposed for L90709 (Fig. 3.2) cannot be applied to L65003, owing to different layout in the interconnection to p-well body and deep n-well. Due to the fact, a new body network becomes indispensable for 4-port RF MOSFET in L65003. First, the device structure of the 4-port MOSFET designed in L65003 is illustrated in Fig. 3.27 to facilitate the body network model development. Herein, R_bb represents the body resistance associated with p-well, R_dnw is the series resistance going through the deep n-well, and Rbb2 as well as Rbb3 denote p-substrate resistance. Regarding the capacitive components, C_js and C_jd are well known as the source and drain to body junction capacitances. Cdnw1 and Cdnw2 define the junction capacitances from deep n-well to p-well and p-substrate, respectively. Based on the device structure and RC components allocation defined in Fig. 3.19, an equivalent circuit can be derived as shown in Fig. 3.20. Note that the RC network in the solid-line box is composed of Rbb3 in parallel with the series Rbb2Cdnw2 and the equivalent impedance is defined asZ_sub. As for the RC network in the dash-line box, it is consisted of R_bb in parallel with the series R_bbC_dnw1 and the equivalent impedance is defined as Z_bb'. The idea underlying the proposed RC network comes from the strong frequency dependence of Re(Z44)=Re(Zsub) as shown in Fig. 3.21, which was measured from port-4 (body) when all the other 3 ports (1 : G, 2 : D, 3 : S) are at open state. The fast fall off of Re(Z₄₄) when increasing frequency and saturation to a constant when beyond 5 GHz suggests a large resistance at very low frequency (due to low open circuit) but fast decay at higher frequency, due to parallel resistors effect from high pass circuit. The proposed mechanism can be simulated by the substrate RC network denoted by solid-line box in Fig.

3.20 and shown in Fig. 3.22 (a) in which Re(Z44) at very low frequency is equivalent to Rbb3

due to open circuit of series Rbb3Cdnw2 but Re(Z44) at very high frequency approach Rbb3//Rbb2

(R_bb3 and R_bb in parallel) due to high pass of C_dnw2. According to the proposed RC network,

44

Z44=Zsub can be derived as given by (3.19). Note that Zsub can be approximated by (3.20) when operating at very low frequency, i.e. ²C_dnw² ₂(R_bb2R_bb3)² 1 and then Rbb3 can be extracted from Re(Zsub(LF)) given by (3.21). As for very high frequency, Re(Zsub(HF)) is given by(3.22), which is equal to Rbb3//Rbb2. The experimental data of Re(Zsub(LF)) and Re(Zsub(HF)) can be determined from Fig. 3.21 and then the initial values of R_bb2 and R_bb3 can be extracted from (3.21) and(3.22).

At very low frequency

2 2 2 At very high frequency

2 2 2

45

frequency, according to (3.23)-(3.26).

2 2 At very low frequency,

2 2 with the measured data, as shown in Fig. 3.21.

Considering that the structure of p-well/deep n-well is similar to p-sub/deep n-well, the proposed RC network can be extended to p-well(body)/ deep n-well, by adding body RC network, as shown in Fig. 3.22(b). According to this body RC network defined by dash-line box in Fig. 3.20, the equivalent impedance Zbb‘ can be derived as given by (3.27). Similar with the analysis made on Z_sub, Z_bb‘(LF) representing Z_bb‘ at very low frequency can be

At very low frequency,

2 2 2

1( ) 1

dnw dnw bb

C R R

  and ²C_dnw² ₁R_dnw(R_dnw R_bb) 1

46

( ) 1

' (1 )

bb LF bb dnw bb

Z R  j C R (3.28)

( )

Re(Z_bb'_LF )R_bb (3.29) At very high frequency,

2 2 2

1( ) 1

dnw dnw bb

C R R

  and ²C_dnw² ₁R_dnw(R_dnw R_bb) 1

2

( )

1

' ( )

dnw bb bb

bb HF

dnw bb dnw dnw bb

R R j R

Z R R C R R

 

      (3.30)

( )

Re( ' )

( )

dnw bb bb HF

dnw bb

R R

Z  R R

 (3.31) Unfortunately, Z_bb‘ cannot be measured directly and the RC components associated with the body network cannot be extracted simply following (3.28)~(3.31). The solution to treat this problem is to extract the resistances from Re(Y₄₄) under very high frequency, as given by(3.32). Y44 is measured from port-4 (body) with all of the other 3 ports at short state. It can be understood that all of the capacitors become high pass circuits at very high frequency and Re(Y44) can be approximated as two groups of parallel resistors, such as Rbb3//Rbb2 for substrate network and R_bb//R_dnw for body network, as expressed by (3.32). Then, Rdnw can be determined by (3.33) with previously extracted Rbb2 and Rbb3 and Rbb from Re(Y42) or Re(Y43) at very low frequency, as given by (3.3) or (3.4).

Fig. 3.23 outlines the extraction flow for this new body network model. Table 3.3 (a) presents the initial and optimized values of Rbb2 and Rbb3. Table 3.3 (b) summarizes a complete set of the resistances extracted according to the flow in Fig. 3.23 and also the body bias dependence under ZBB, FBB, and RBB. Again, the accuracy of the proposed body network model and the extracted model parameters was verified by a comparison between the measured and simulated Re(Y44) as shown in Fig. 3.24. Note that the simulated results indicate a good match with measurement under various body biases, i.e. ZBB(Vbs=0), FBB (V_bs=0.6V), RBB (V_bs= -0.6V).

47

Fig. 3.19 The cross section of 4T MOSFET with deep n-well tied together with p-well body and connected with port-4.

S

Fig. 3.20 A new body network model proposed for UN65 4-port MOSFET (L65003) in which the deep n-well (DNW) and p-well body (B) are tied together to port-4, and P-sub is connected to ground

48

0 5 10 15 20 25 30 35 40 0

1x10³ 2x10³ 3x10³ 4x10³ 5x10³ 6x10³

L65003 W2N32 V_G=V_D=V_S=V_B=0

Freq (GHz)

measure.ZBB measure.FBB measure.RBB curve fitting.ZBB curve fitting.FBB curve fitting.RBB

Re(Z bb)()

Fig. 3.21 Re(Z44)=Re(Zsub) measured from port-4 (body) with all the other 3 ports (1 : G, 2 : D, 3 : S) at open state and under various body biases : ZBB (V_bs=0), FBB (V_bs=0.6V), and RBB(Vbs=-0.6V).

Body (4)

Rbb2

Cdnw2 Rbb3

P-sub

Intrinsic Body ^Body(4)

Rbb2

Cdnw2 Rbb3

P-sub

Intrinsic Body

Rbb

Cdnw1 Rdnw

(a) (b)

Body (4)

Rbb2

Cdnw2 Rbb3

P-sub

Intrinsic Body ^Rbb

Cdnw1 Rdnw

Source (2)

Drain (3)

Cgb1 Cgb2

Gate (3)

(c)

Fig. 3.22 Step by step synthesis of body network model (a) substrate network for deep

49

n-well/p-substrate (b) p-well body network for p-well/deep n-well and substrate for deep n-well/p-substrate (c) a complete body network model for L65003 4T RFMOSFET

Fig. 3.23 A new body network model parameters extraction flow for 4-port RF MOSFET with equivalent circuit shown in Fig. 3.20

Table 3.3 Resistance parameters extracted for the new body network model (a) initial and optimized Rbb2 and Rbb3

Zsub default optimization

Rbb2 384 664

Rbb3 6741.12 5484

(b) Rbb, Rdnw Rbb2 and Rbb3 after optimization

Optimized parameters ZBB (Vbs=0V) FBB (Vbs=0.6V) RBB(Vbs=-0.6V)

Rbb () 958 977 842

Rdnw ( 476 202 233

Rbb2 () 664 874 813

Rbb3 () 5484 7994 8192

50

0 5 10 15 20 25 30 35 40 0.0

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

5.5 UN65-L65003 4T MOSFET VG=V

D=V

S=0

Meas Model

FBB

RBB

ZBB

Re ( Y

44

) ( 10

-3

)

Freq (GHz)

Fig. 3.24 Comparison of measured and simulated Re(Y44) using the new body network model and extracted parameters under ZBB (V_bs=0), FBB (V_bs=0.6V), and RBB(V_bs=-0.6V).

The final step to complete the extraction flow is the extraction of gate to body capacitances, namely Cgb1 and Cgb2 as shown in Fig. 3.20. Then the step by step synthesis of the body network model is moved from Fig. 3.22(b) to Fig. 3.22(c). In general, gate to body capacitance can be extracted from -Im(Y14)/ as shown in Fig. 3.25. However, the strong frequency dependence revealed in Fig. 3.25 with a fast fall off in lower frequency region and then saturation to a constant at frequency beyond 25GHz suggests that the gate to body capacitance is composed frequency independent and frequency dependent components, denoted as C_gb1 and C_gb2, respectively. The origin responsible for C_gb1 and C_gb2 can be explained by RF MOSFET layout shown in Fig. 3.26. The frequency independent component (C_gb1) is contributed from gate contact/metal to body contact/metal coupling capacitance. The frequency dependent component (Cgb2) comes from gate to channel (body) coupling, which may reveal non-quasi-static effect. According to the measured -Im(Y14)/ shown in Fig. 3.25 and the analysis supported by Fig. 3.26 , Cgb1 and Cgb2 can be extracted as follows, given by (3.34) and(3.35).

51

14(HF) 25

1

Im(Y ) |_{f GHz} Cgb



 

 (3.34)

14(LF) 1

2 1

Im(Y ) |_{f GHz}

gb gb

C C



   (3.35)

0 5 10 15 20 25 30 35 40 2.0

2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

C

gb

=-Im(Y

14

)/



( fF )

(c)

Freq-dependent, C_gb2

Freq-independent Cgb1

Freq (GHz)

Cold device Vg=Vd=Vs=Vb=0 Cgb= -Im(Y

14)/

Fig. 3.25 The gate to body capacitances measured from 4-port Y-parameters after openM3 deembedding on 4-port RF MOSFET –Im(Y14)/=Cgb=Cgb1+Cgb2

B

G

Fig. 3.26 RF MOSFET layout remarked with poly gate fingers, gate contact and metal to contacts, body contacts and metal to contacts. The metals to gate contacts and body contacts will contribute inter-metal coupling capacitance.

52

3.3 Four-port RF MOSFET Small Signal Equivalent Circuit Development

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 65-74)