Small Signal Equivalent Circuit in Saturation Region

Finally, the small signal equivalent circuit for 4-port RF MOSFET in saturation region will be developed in this section. Note that the current saturation in short channel devices is dominated by velocity saturation rather than pinch off. Thus, the bias condition responsible for saturation region can be defined by |Vgs| > |VT|, |Vgs- VT| >|Vds| >|Vdsat|, and Vdsat is the onset voltage for velocity saturation. In this study for UN65 nMOS with V_dd=1.0V, the bias condition is specified as Vgs=0.8V and Vds=Vdd=1.0V for saturation region. Considering the channel conduction is limited by velocity saturation, the channel resistance R_ch in linear region is replaced by transconductance gm and gmb corresponding to gate and body, and output resistance r_o. Fig. 3.56 illustrates the small signal equivalent circuit proposed for 4-port RF MOSFET in saturation region by adopting gm, gmb, and ro along the channel between source and drain. Note that the body network model validated for off state and linear region can be extended to the saturation region when a proper modification is made on some key parameters, e.g. Cgb1 and C_gb2. Again, C_gs and C_gd are two key parameters for high frequency simulation and can be extracted from measured -Im(Y₁₂)/ and -Im(Y13)/after an appropriate open deembedding, as shown in Fig. 3.57. The frequency dependence suggests the effect from parasitic inductances, which cannot be eliminated using short M3 deembedding. To overcome this problem, the gate capacitances, Cgg, Cgs, and Cgd are extracted from Im(Y11)/, -Im(Y12)/, and -Im(Y13)/at very low frequency.

73

Fig. 3.56 A small signal equivalent circuit for 4-port RF MOSFET in saturation region. gm, gmb, and r_o are deployed to simulate conduction channel under saturation condition.

0 5 10 15 20 25 30 35 40

The extraction flow can be expressed by the iteration flow chart as shown in Fig. 3.58. Note that the extraction flow is started with the initial values of gm and gmb assuming that Rs is negligible and then goes into the optimization flow with extracted r_o and R_s. As a result, the extraction flow is critically dependent on the mentioned four key parameters, such as gm, gmb, ro

74

and Rs.

Fig. 3.58 Iteration flow chart for the extraction of gm, gmb, ro, and Rs in 4T RF MOSFETs

Step 1 :

Assume (g_mg_mb)r_O 1and (g_mg_mb)R_s 1 ,

Then the initial value of gm is determined by g_mb Re(Y )₃₄ Step 2 :

The initial value of gm is determined by

 

 

³¹34

Re Y

m mb Re Y

g g

Step 3 :

The output resistance ro can be extracted from (3.107) with initial gm and measured Re(Y31) and Re(1/Y33).

 

31

33

1 1

Re Y Re

O Y

m

r g

 

   

  Step 4 :

75

The source resistance Rs can be extracted from (3.109) with known ro and measured Re(1/Y22) and Re(1/Y₃₃)

 

 

   

    

 

 

22

33

33

Re 1 1 Y

Re Y 1

Re Y

s O

R r

Step 5 :

The extrinsic gm associated with I-V can be calculated by intrinsic transcondutance g_m incorporating Rs and Rcable , referring to (3.110) given by

 

( )

( ) ( )

1

m m I V

m mb s

s s DUT s DC cable

g g

g g R

where

R R R

 

 

 

Principle of the iteration flow

( ) ( )

m I V m I V

if calculated g _ measured g _

It means that the initial values of gm and gmb are under-estimated then, to increase the initial values of gm and g_mb, and re-extract r_o and Rs.

Otherwise if



calculated g^{m I V(}_ ⁾measured g^{m I V(}_ ⁾



 min error^. It means that the initial values of gm and gmb are over-estimated.

Then, the next step is to decrease the initial values of g_m and g_mb, and re-extract r_o and Rs.

The iteration flow can be finished when the difference between the calculated and measured g_m(I-V) is less than the specified minimum error, expressed by



calculated g^{m I V(}_ ⁾measured g^{m I V(}_ ⁾



 min error^.

76

Table 3.6 Iteration flow for gm and gmb extraction and optimization

Iteration cycles

g_mb (A/V)

g_m

(A/V) ro () Rs,DUT() g_m(I-V)(A/V) Initial 0.0039 0.0702 99.61538462 -0.69941657 0.068749323 2 0.00395 0.0711 98.35443038 -0.536046905 0.068829516

3 0.004 0.072 97.125 -0.376761481 0.068907885

4 0.00405 0.0729 95.92592593 -0.221409031 0.06898449

5 0.0041 0.0738 94.75609756 -0.069845666 0.069059391

6 0.00415 0.0747 93.61445783 0.078065571 0.069132645

7 0.0042 0.0756 92.5 0.222455111 0.069204304

8 0.00425 0.0765 91.41176471 0.363447251 0.069274421

9 0.0043 0.0774 90.34883721 0.501160503 0.069343044

10 0.00435 0.0783 89.31034483 0.635707934 0.069410221

11 0.0044 0.0792 88.29545455 0.767197468 0.069475998

12 0.00445 0.0801 87.30337079 0.895732182 0.069540417

13 0.0045 0.081 86.33333333 1.021410568 0.06960352

14 0.00455 0.0819 85.38461538 1.144326792 0.069665346

15 0.0046 0.0828 84.45652174 1.264570925 0.069725936

16 0.00465 0.0837 83.5483871 1.382229162 0.069785324

17 0.0047 0.0846 82.65957447 1.497384032 0.069843547

18 0.00475 0.0855 81.78947368 1.610114589 0.069900638

19 0.0048 0.0864 80.9375 1.720496593 0.069956631

20 0.00485 0.0873 80.10309278 1.828602679 0.070011556

21 0.0049 0.0882 79.28571429 1.934502519 0.070065443

22 0.00495 0.0891 78.48484848 2.038262968 0.070118323

23 0.005 0.09 77.7 2.139948208 0.070170222

24 0.00505 0.0909 76.93069307 2.239619879 0.070221169

25 0.0051 0.0918 76.17647059 2.337337203 0.070271188

26 0.00515 0.0927 75.4368932 2.433157104 0.070320305

27 0.0052 0.0936 74.71153846 2.527134314 0.070368545

28 0.00525 0.0945 74 2.619321482 0.07041593

29 0.0053 0.0954 73.30188679 2.709769269 0.070462483

30 0.00535 0.0963 72.61682243 2.798526444 0.070508225

31 0.0054 0.0972 71.94444444 2.885639967 0.070553179

32 0.00545 0.0981 71.28440367 2.971155078 0.070597363

Table 3.6 illustrates an example of the extraction flow based on the data measured from L65003. In this study, the measured g_m(I-V) is 68.5 mA/V and it happens that the 13^th cycle with gm=81 mA/V and Rs=1.02 leads to calculated gm(I-V) =69.7 mA/V, which approached the measured g_m(I-V) with error 1.2 mA/V, i.e. relative error of 1.2%.

Furthermore, the proposed assumptions for this extraction/iteration flow are verified as follows

Step 1 assumption

(g_mg_mb)r_O 1 and (g_mg_mb)R_s 1

77

4.5 / , 81 / , 86.33 , 1.02

( ) 7.38 10

( ) 0.08721 1

mb m O s

m mb O

m mb s

g mA V g mA V r R

g g r may introduce certain error from the assumption

g g R valid assumption

     

   

  

Assumption to derive (A9)~(A12): r_O R _d 86.33 , 1.02

/ 1.02

84.64

O s

d s

O

O d

d

r R

S D layout symmetry R R

r r R valid assumption R

   

   

  

Table 3.7 summarizes the small signal equivalent circuit model parameters for 4-port RF MOSFET in saturation region. It appears that the increase of Vds to saturation region leads to decrease of C_gd whereas increase of C_gs, due to non-uniform distribution of inversion carriers at source and drain. Cgs is larger than Cgd by near 80% and it accounts for drain side carriers depletion effect. Note that three key parameters for saturation region, such as g_m, g_mb, and r_o are determined by aforementioned extraction flow and the values listed in Table 3.7 are optimized one for the best fitting to measured I-V and S-parameters.

Table 3.7 Small signal equivalent circuit model parameters of 4-port MOSFET in saturation region (Vgs=0.8V, Vds=1.0V, Vbs=0)

4-port MOSFET model parameters in saturation region

Capacitances (fF) Resistances Ω Inductances pH

Cgs 33.16 Rg 6.5 Ls 60

Cgd 18.48 Rd 1 Ld 60

Cgb1 2.5 Rs 1 Lg 70

Cgb2 3.5 Rb 1 Lb 70

Cg 2.1 Rbb 958 Transconductance mA/V

Cds 2 Rbb2 664 gm 81

Cjs 22.42 Rbb3 5484 gmb 4.5

Cjd 18.75 Rdnw 476 Output resistance Ω

Cdnw1 44.94 Rgb 518500 ro 86

Cdnw2 44.94 Rgb1 500

According to the model parameters shown in Table 3.7 for 4-port MOSFETs in

78

saturation region, S- and Y-parameters can be simulated. Fig. 3.59 ~ Fig. 3.66 present the 4-port S-parameters from measurement and simulation for this 4-port MOSFET (W2N32) in saturation region under the biases of Vgs=0.8V, Vds=1V, and Vbs=0. Note that the simulation by using the small signal equivalent circuit shown in Fig. 3.56 and model parameters in Table 3.7 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 except a few parameters, such as Mag(S21), Mag(S22), Mag(S31), Mag(S34), phase(S₄₁), and phase(S₂₄) with somewhat larger mismatch. However, the simulation using 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. 3.59 and phase(S44), phase(S41), phase(S42), and phase(S43) as shown in Fig.

3.63. Besides S-parameters, Re(Y₄₂), Re(Y₄₃), and Re(Y₃₃) are three more important parameters to verify the body network model. Fig. 3.67 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. 3.68 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. 3.69. 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 saturation region (Fig. 3.56) can improve the problem with BSIM-4 for 4-port MOSFET simulation.

79

0.10 Small signal eq. ckt Cds=3fF

measured :

Small signal eq. ckt Cds=3fF measured :

80

Small signal eq. ckt Cds=3fF measured : default body network model.

0 5 10 15 20 25 30 35 40

Small signal eq. ckt Cds=3fF measured :

Small signal eq. ckt Cds=3fF

measured : simulation

small signal eq. ckt

@new body network model

BSIM-4 default model (c) (d)

(b)

81

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

simulation

Fig. 3.63 The measured and simulated phase(S) of 4-port MOSFET in saturation region Vgs=0.8V, Vds=1V, Vbs=0 (a) phase(S44) (b) phase(S41) (c) phase(S42) (d) phase(S43). Solid lines : small signal

Small signal eq. ckt Cds=3fF measured : with default body network model.

82

Small signal eq. ckt Cds=3fF measured : with default body network model.

0 5 10 15 20 25 30 35 40 with default body network model.

83 Default body network

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

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

(b)

Freq (GHz)

Fig. 3.68 Measured and simulated Re(Y42) and Re(Y₄₃) for 4-port MOSFET in saturation region V_gs=0.8V, V_ds=1V, V_bs=0 (a) Re(Y₄₂) (b) Re(Y₄₃). Simulation by BSIM-4. Solid lines : new body network model. Dash lines : 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=0.8V, V_DS=1V, V_BS=0

(b)

Freq (GHz)

Fig. 3.69 Measured and simulated Re(Y33) for 4-port MOSFET in saturation region Vgs=0.8V, Vds=1V, Vbs=0 (a) simulation by small signal equivalent circuit (b) simulation by BSIM-4.

84

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

3.4 BSIM-4 with Improved Body Network Model for Four-port RF

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 94-106)