Chapter 1 Introduction
1.2 Thesis Organization
The major objective of this thesis is the development of small signal equivalent circuit models for 4-port RF MOSFET and new cascode structure with different configurations to facilitate RF CMOS circuit simulation and design.
First, chapter 2 addresses the fundamental theory of scattering matrix and parameters and RF amplifier consideration. The former one will cover both 2-port and 4-port networks. The latter one includes impedance matching, gain, noise, linearity, and stability.
In chapter 3, a new body network model is developed for 4-port RF MOSFET fabricated with UN65 process in which the p-well body and deep n-well tied together to one port for body terminal. A complete model parameters extraction flow will be provided with details of the extraction formulas. The proposed body network model and can be easily integrated with intrinsic MOSFET to build a small signal equivalent circuit model. The simulation accuracy will be verified by an extensive comparison with measured 4-port S-parameters up to 40GHz and under different operation conditions, such as off-state, linear region, and saturation. Also, a comparison with simulation by BSIM-4 using default body network has been carried out to explore the problem and solution.
In chapter 4, a small signal equivalent circuit is developed for new cascode structure based on a dual gate MOSFET with merged source/drain diffusion region. A modified body network model is created to match different configurations in deep n-well and p-well body.
4-port S-parameters can facilitate the extraction of complicated model parameters in the dual gate MOSFET, such as in-stage capacitances, inter-stage capacitances, and cross-stage capacitances. The small signal equivalent circuit model built with core model for dual gate MOSFET and modified body network model demonstrates acceptable simulation accuracy at off state and saturation region. BSIM-4 is utilized to approach new cascode structure by incorporating parasitic elements such as inter-stage resistance and capacitances into conventional cascode with two single MOSFETs and enable both small signal and large signal
4
simulations.
Finally, chapter 5 concludes with a summary and plan for future work.
5
Chapter 2 Fundamental theory
2.1 Scattering Matrix and Parameters
At microwave frequency the Z, Y and H parameters are very difficult to measure, the reason is that short and open circuits to ac signals are difficult to implement at microwave frequencies, so that, the scattering matrix are used usually in the analysis of two port networks usually.
2.1.1 Two–port network and scattering parameters
Considering the two-port network with incident wave a1 and reflected wave b1 at port1, and incident wave a2 and reflected wave b2 at port 2, the S parameters can be written in matrix form as:
1 1 1 1 2 1
2 2 1 2 2 2
b S S a
b S S a
(2.1)2.1.2 Four –port scattering matrix and parameters
The extension of the formulation to four-port network is simple, the transmission lines are assumed to be lossless with characteristic impedance Z0, and then, we can write the scattering parameters of the four-port in matrix form.
11 12 13 14
1 1
21 22 23 24
2 2
31 32 33 34
3 3
41 42 43 44
4 4
S S S S
b a
S S S S
b a
S S S S
b a
S S S S
b a
;
b S a
(2.2) Note that the value of S11 in (2.2) will be different from the value of S11 in a two-port common source configuration. For example, S11 can be arranged form the S matrix in (2.2) as6 the ratio b1/a1 is obtained. In a two-port common source configuration, S11 is measured with reference resistance 50Ω at port 2 and source/body grounding. Similarly, the parameters S12, S21, and S22 in four-port S matrix will be different form the parameters in two-port matrix.
2.1.3 Port reduction method
Considering a 4-port networks system, the I-V relationship of the extrinsic and intrinsic parameters can be written as a 4X4 Y matrix.
configuration of the MOSFET, therefore, the 4 x 4 matrix of the 4-port networks can be reduced to 3-port or 2-port Y matrix. For example, the common source(CS) configuration is source (port3) and body (port4) grounding, the CS 2-port Y matrix can be obtained by setting the Vs=Vb=0V in the 4-port measurement, in this case, the term of source and body in (2.4) is negligible, the reduced Y matrix can be written as
2.2 RF Amplifier Design Consideration
In this section, we introduce the consideration in RF amplifier. It include impedance
7
matching , gain,noise Inter modulation and linearity.
2.2.1 Impedance matching
Low noise amplifier is the first stage in the receiver front-end circuits and is used to amplify the received weak RF signal with the minimum noise figure. As it is well recognized that impedance matching is the fundamental requirement in LNA designs for achieving the target performance of both gain and noise. There are four basic 50-Ω input matching architectures that have been explored in the traditional transistor-amplifier shown in Fig. 2.1 In this section, we will have a review and discussion on the mentioned matching circuit architectures that can be used in LNA design. [1, 2]
Zin
Zin
Zin
Zin
(1) Resistive termination (2) Inductive degeneration (3) Shunt-series feedback (4) 1/gm termination
Fig. 2.1 Traditional transistor-amplifier of input matching
2.2.2 Power gain and voltage gain
Consider an arbitrary two-port network connected to source and load impedances Zs and ZL, respectively, the reflection coefficient seen looking toward the load is
0
0 L L
L
Z Z Z Z
(2.6)
0
0 S S
S
Z Z Z Z
(2.7) Consider Network analyzer Agilent 8510C in measurement, It‘s internal impedance is set 50Ω,so S and L are too small to ignore. By the way , the process which Network analyzer is set 50Ω is called calibration. We define expression for power gain in terms of the S parameters of the two-port network and the reflection coefficients, Γs and Γl, of the source and
8
Power dissipated in the load power Gain :G=
Power delivered to the input (1 ) 1
L Consider the same s parameter ,we can convert from s parameter to ABCD parameter.ABCD parameter define as follow
A is the reciprocal of voltage gain.voltage gain can expressive by Y parameter as follow, 22 Rds.we can check Rds and voltage gain has same trend.
9
450 90nm nMOS L90709 4-GSG
WF=2m, NF=16 Vg=1V Vds=1.2V
Fig. 2.2 (a) MOSFET‘s power gain comparisons between simulation and measurement (b) MOSFET‘s voltage gain comparisons between simulation and measurement
(c) MOSFET‘s Rds comparisons between simulation and measurement
2.2.3 Noise [1]
Noise Factor
Noise factor (F) is defined as the signal-to-noise power ratio at the input to the signal-to-noise power ratio at the output. Considering a network with gain G and noise Na, noise factor then can be express as (2.14)
Generally we use this measure in the unit of dB, namely noise figure (NF) written in (2.15) 10log
NF F (2.15)
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A useful measure of the noise performance of a system is the noise factor, denoted as F and given in (2.14). To define it and understand why it is useful, consider a noisy (but linear) two-port network driven by a source that has an impedance Z and an equivalent series noise s
voltage e , illustrated in Fig. 2.3. s2
If we are concerned only with overall input-output behavior, it is an unnecessary complication to keep track of all of internal noise source. Fortunately, the net effect of all of those sources can be represented by just one pair of external sources like a noise voltage en2
and a noise current i as shown in Fig. 2.4. This simplification allows a rapid evaluation of n2 how the source impedance affects the overall noise performance. As a consequence, we can identify the criteria, which one must satisfy for optimum noise performance.
Fig. 2.3. Noisy two-port driven by noisy source
Fig. 2.4. Equivalent circuit for two-port noise model
Carrying out the calculations based on the equivalent circuit of noisy two-port illustrated in Fig.
2.4, the noise factor is written as
11
In order to accommodate the possibility of correlations between en and in, express en as the sum of two components in (2.17) in which enc, represents the term correlated with in, and enu, the un-correlated term.
n nc nu
e e e (2.17) Since en is correlated with in, it may be treated as proportional to in through a constant namely ZC whose dimensions are those of impedance:
nc c n
e Z i (2.18) Combining (2.16),(2.17),(2.18) and, the noise factor becomes
2 2 treated as thermal noise produced by an equivalent resistance or conductance:
2 2 2 Using these equivalences, the expression for noise factor can be written purely in terms of impedances and admittances:
Linearity is one of the key requirements in LNA design to maintain linear operation in the presence of a large interfering signal and when the input is driven by a large signal. Any nonlinear transfer function can be mathematically written as a series expansion of power-law
12
terms unless the system contains memory. The input V and output i V of a two-port network o can be related by a power series. For simplicity, we make an approximation to the third order term:
2 3
1 2 3
o i i i
V V V V (2.22)
where 1,2,3 are constants.
If a sinusoidal waveform is applied to a nonlinear system, the output generally exhibits frequency dependent components that are integer multiples of the input frequency. In (2-22), setting V ti( )Acos(t), the
2 2 3 3
1 2 3
( ) cos( ) cos cos
V to A t A t A t (2.23)
3 2
3 2
1 cos( ) [1 cos(2 )] [3cos( ) cos(3 )]
2 4
A A
A t t t t
(2.24)
3 3
2 2
3 3
2 2
1
( 3 ) cos( ) cos(2 ) cos(3 )
2 4 2 4
A A
A A
A t t t
(2.25)
In (2.23), the term with the input frequency is called the ―fundamental‖ and the higher-order terms the ―harmonics‖. The first term in (2.23) is the linear term and is the ideal output if the two-port network is completely linear. Other terms in (2.23) are responsible for nonlinearity, and they cause a DC shift as well as distortion at frequencies 2, 3, and higher harmonics derived in (2.24) and(2.25), which result in either gain compression or gain expansion. It can be observed from (2.25) that distortion is present in any signal level.
In most circuits of interest, the output is a ―compressive‖ or ―saturating‖ function of the input; that is, the gain approaches zero for sufficiently high input levels. In (2.25) this occurs if
3 0
. Written as
3 3 1
3 4 A A
, 1A represents the fundamental amplitude and the gain is
therefore a decreasing function of the third-order harmonic proportional to 3A3. In RF circuits, this effect is quantified by the ―1-dB compression point‖, defined as the input signal level that causes the small-signal gain to drop by 1 dB. As shown in Fig. 2.5, which is plotted on a log-log
13
scale as a function of the input level, the output level falls below its ideal value by 1 dB at the 1-dB compression point [3].
Fig. 2.5 Definition of the 1-dB compression point
To calculate the 1-dB compression point, we can write from (2.25)
2
1 3 1 1
20 log 3 20 log 1
4 A dB dB
(2.26) That is,
1 1
3
0.145
A dB
(2.27)
2.2.5 Intermodulation [3]
Harmonic distortion that was introduced previously is the result of nonlinearity due to a single sinusoidal input. When two signals with different frequencies are applied to a nonlinear system, the output in general exhibits some components that are not harmonics of the input frequencies. Called intermodulation (IM), this phenomenon arises from ―mixing‖
(multiplication) of the two signals when their sum is raised to a power greater than unity. To investigate the effects of both harmonic distortion and intermodulation, we assume that the input signal is composed of two different frequencies 1 and 2 given in (2.28)
1 1 2 2
( ) cos( ) cos( )
V ti A t A t (2.28) (2.28) can be substituted into (2.22) Thus, the output can be expressed as
14 intermodulation products expressed in (2.30) and (2.31) for the second order and (2.32) for the third order IM products, namely IM2 and IM3.
1 2: 2A A1 2cos[( 1 2) ]t 2A A1 2cos[( 1 2) ]t
and the fundamental components written in (2.33)
3 2 Fig. 2.6 in which the input RF signals are two-tone with two different frequencies such as 1 and 2
Fig. 2.6 Intermodulation in a nonlinear system where it is assumed that A1 A2 A.
From Fig. 2.7(a), it is apparent that the third-order intermodulation distortion IM3 signals are close to the signals of interest F, which makes the filtering out of IM3 signals difficult when recovering the signals of interest. Therefore minimizing intermodulation distortion is a key
15
objective in many RF circuit design.
Third-Order Intercept Point (IIP3) [3]
From(2.30)~(2.33) and let A1 A2 A, we can drive the expression
2 2
1 3 1 1 3 2
3 3
3 1 2 3 2 1
9 9
( ) ( ) cos( ) ( ) cos( )
4 4
3 3
cos[(2 ) ] cos[(2 ) ]
4 4
V to A A t A A t
A t A t
(2.34)
We note that as the input amplitude A is small to keep 1 9 3 2
| |
4 A , the fundamentals increase proportional to A , whereas if the input level A increases to the intercept point so that
2
1 3
9| |
4 A is no longer valid, the gain will drop and the third-order IM products in proportion to A3 will take over the fundamentals, as shown in Fig. 2.7(a). Plotted on a logarithmic scale in Fig. 2.7 (b), the magnitude of the IM products grows at three times the rate at which the main components increase. The third-order intercept point, namely IP3 is defined to be at the intersection of the two lines. The horizontal coordinate of this point is called the input IP3 (IIP3), and the vertical coordinate is called the output IP3 (OIP3).
(a) (b)
Fig. 2.7 (a) The linear gain and the nonlinear component (b) The IIP3 and OIP3
If 1 9| 3| 2
4 A , the input level for which the output components at 1 and 2 have the same amplitude as those at 2 1 2 and 2 2 1 is given by
16
3
1 3 3 3
3
IP 4 IP
A A
(2.35) Thus, the input IP3 is
1 3
3
4
IP 3
A
(2.36)
2.2.6 Stability [4]
One more important consideration for an amplifier design is the assurance of stability. For example, LNAs in the form of a two-port network, the requirement for ensuring stability is that it must not produce an output with oscillatory behavior. The stability of a two-port network can be determined from the S-parameters, the matching networks, and the terminations. Simpler tests can be used to determine unconditional stability [4]. One of these is the K-△ test, where it can be shown that a device will be unconditionally stable if Rollet‘s condition, defined as
2 2 2
11 22
12 21
1 1
2
S S
K S S
(2.37)
along with the auxiliary condition that
11 22 12 21 1
S S S S
(2.38) are simultaneously satisfied. These two conditions are necessary and sufficient for unconditional stability.
If the transistor, as unconditionally stable, so that K > l, the maximum transducer power gain can be reduced as follows:
m a x
21 2
12
( 1)
T
G S K K
S
(2.39) The maximum transducer power gain is also sometimes referred to as the matched gain. The maximum gain does not provide a meaningful result if the device is only conditionally stable, since simultaneous conjugate matching of the source and load is not possible if K < 1 . In this case a useful figure of merit is the maximum stable gain, defined as the maximum transducer
17
power gain of with K=1. Thus.
21
12 msg
G S
S
(2.40)
The maximum stable gain is easy to compute, and offers a convenient way to compare the gain of various devices under stable operating conditions.
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Chapter 3 Four-port RF MOSFET Modeling for Simulation with
DBB ( UN65 CMOS Technology)
In this chapter, four-port (4-port) RF MOSFET model development will be carried out based on experimental data from UN65 RF n-MOSFET. At first, 4-port RF MOSFET layout design, measurement and deembedding methods will be described in sec. 3.1 to address layout effects on high frequency characteristics and equivalent circuit model for simulation. In sec. 3.2, a new body network model will be introduced and proven for 4-port RF MOSFET with deep n-well and different layouts in the connections of p-well body, deep n-well, and p-substrate. In sec. 3.3, small signal equivalent circuit models will be developed for 4-port RF MOSFET in different operation regions, such as off state, linear region, and saturation region.
The new body network model can be easily adopted into the small signal equivalent circuits to enable accurate simulation of 4-port S- and Y-parameters. In sec. 3.4, BSIM-4 calibration will be performed on both I-V and C-V models to improve simulation accuracy for 4-port RF MOSFET under dynamic body biases (DBB). The comparison of measurement and simulation by using BSIM-4 and small signal equivalent circuit models will be presented in sec. 3.3.
3.1 Four-port RF MOSFET Layout and Measurement
In this thesis, there are totally three kinds of 4T RF MOSFET layouts and 4-port test structures implemented in different CMOS processes, such as UN90 (L90709), UN65 (L65003), and TN90RF (100A). 4-port RF MOSFET layout analysis for parasitic RLC extraction is introduced in sec. 3.1.2. 4-port RF MOSFET measurement and deembedding method are addressed in sec. 3.13. Finally, the parasitic resistance extraction from 4T RF MOSFET in 4-port test structure and the impact on electrical performance, such I-V and gm
19
are presented in sec. 3.1.4. with a comparison with 3T RF MOSFET in 2-port test structure.
3.1.1 4T MOSFET Layout Analysis for Body Network Model Development
The circuit architectures of body network model and small signal equivalent circuits are critically determined by the layouts of RF MOSFETs, particularly for those built in 4-port test structures. Fig. 3.1(a)~(c) illustrate 3 different layouts of 4-port RF MOSFETs, which were implemented by UN65, UN90, and TN90RF processes, with test chip names given as L65003, L90709, and 100A, respectively.
Table 3.1 (a) summarizes 3 items of layout features in 4-port RF MOSFETs, which are identified as the major differences between the mentioned 3 test chips. For body contacts layout, L65003 adopts two rows of contacts in parallel with the gate finger, namely parallel body contacts. As for L90709 and TN90RF-100A, ring type body contacts enclosing the multi-finger MOSFET is employed to reduce body resistance. All of the 3 test chips were fabricated with deep n-well but different layouts in the connection to deep n-well and p-well body. For L65003, the deep n-well is tied together with p-well body and connected to port-4.
For L90709, deep n-well is connected to ground and p-well body is individually connected to port-4. As for TN90RF-100A, deep n-well is floating, i.e. without any connection to the external node. In this chapter, we will focus on the characterization, analysis, and modeling on L65003 and also the differences between L65003 and L90709. The study on TN90RF-100A will be presented in chapter 5.
In our previous work (YH Tsai in Prof. Guo group), a simple body network model as shown in Fig. 3.2 was developed for 4-port RF MOSFET in L90709. This body network model incorporates Cjs and Cjd for junction capacitances from source and drain to body, and Cdnw for junction capacitance between deep n-well and p-well body. Rbb represents p-well body resistance and Rdnw is deep n-well resistance. According to L90709 layout feature, i.e.
body to port-4 and deep n-well to ground, this simple body network model is built with simple series RdnwCdnw from port-4 to ground (Fig. 3.2). Thus, the model parameters can be
20
extracted from 4-port Y-parameters, based on equivalent circuit analysis on the proposed body network model as follows. First, Cjs and Cjd are extracted from Im(Y42) and Im(Y43) at very low frequency, given by (3.3) and (3.4). Then, the body resistance Rbb can be extracted from Re(Y42) or Re(Y43) with pre-extracted Cjs and Cjd at very low frequency, denoted as Rbb(LF) given by (3.5) or (3.6). Also, Rbb can be determined from Re(Y42) or Re(Y43) at very high frequency, according to (3.9) or (3.10) and denoted as Rbb(HF). Note that it is considered that the Y-parameters under cold device condition (Vg=Vd=Vs=Vb=0) follow symmetric rule At very low frequency C C R
42( )
21
[ ]
[ ] 43( )
[ ] [ ]
Re( )
( )
jd LF
bb HF HF
jd LF js LF
R Y C
C C
(3.10)
Theoretically, all of the RLC elements in the equivalent circuit should be constant independent of frequency. It is expected that Rbb(LF) extracted at very low frequency is equal to Rbb(HF) extracted at very high frequency. Table 3.2(b) summarizes Rbb extracted from L90709 and L65003 to verify 4-port RF MOSFET layout effects and frequency dependence.
The results from L90709 indicate very minor difference between Rbb(LF) and Rbb(HF) and prove that Rbb extracted from the equivalent circuit model is a simple resistance in dependent of frequency. Furthermore, the larger finger number can help reduce Rbb. However, Rbb extracted from L65003 reveal dramatic difference between Rbb(LF) and Rbb(HF). The extraordinary frequency dependence suggests that the body network model proposed for L90709 cannot be applied to L65003, due to fundamental differences in the 4-port RF MOSFET layout summarized in Table 3.2(a). As for L90709, the body network model is proven by a good match between the measured and simulated Re(Y43) using (3.2), as shown in Fig. 3.3. Note that Re(Y43) tends to saturate to a constant at very high frequency, which is predicted by (3.10). The saturation of Re(Y42) or Re(Y43) at high frequency suggests the saturation of substrate loss when the frequency increases beyond the attenuation frequency of the series RC in the body network model. However, the comparison of measured Re(Y42) or Re(Y43) between L90709 and L65003 shown in Fig. 3.4 indicates that both Re(Y42) and Re(Y43) reveal a fall off without any saturation when increasing frequency. Again, the results suggest that the simple body network model derived for L90709 is no longer valid for L65003. Potentially, a simple series RC for deep n-well cannot be applied to L65003 and a new body network model will be presented in sec. 3.2. Besides Re(Y42) and Re(Y43) for Rbb, Cdnw is one more important parameter to verify the difference between L90709 and L65003 with different layouts in deep n-well and p-well body. Considering that all of the capacitances related to body, i.e. port-4 have to follow charge conservation law, Cdnw can be extracted from 4 components of Im(Y4i)
22
(i=1,2,3,4) at very low frequency given by (3.11).
44 43 42 41
01 Im( ) Im( ) Im( ) Im( ) |
Cdnw Y Y Y Y
(3.11)
Fig. 3.5 (a) and (b) present Cdnw extracted from L90709 and L65003, respectively. Note that
Fig. 3.5 (a) and (b) present Cdnw extracted from L90709 and L65003, respectively. Note that