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Study on RF Characteristics and Modeling of Scaled MOSFET Study on RF Characteristics and Modeling of Scaled MOSFET Presented by: 05M36370 Masayuki Nakagawa Supervisor: Professor Hiroshi Iwai Department of Electronics and Applied Physics Interdisciplinary of Graduate School of Science and Engineering Tokyo Institute of Technology 2007, January Contents Chapter 1 Introduction ---------------------------------------------------- 1 1.1 RF CMOS Technology ---------------------------------------------------------- 1 1.1.1 RF CMOS Applications ------------------------------------------------ 2 1.2 The Indicators of RF Device --------------------------------------------------- 3 1.2.1 The Cut-off Frequency ------------------------------------------------- 4 1.2.2 The Maximum Frequency --------------------------------------------- 4 1.2.3 The Noise Figure -------------------------------------------------------- 5 1.3 Requirements of RF Characteristics ---------------------------------------- 6 1.4 High-k Gate Materials ---------------------------------------------------------- 6 1.4.1 Dielectric Dissipation --------------------------------------------------- 8 1.5 Purpose of This Study --------------------------------------------------------- 10 Chapter 2 Methodology of RF Measurement ---------------- 11 2.1 RF Measurement --------------------------------------------------------------- 11 2.1.1 de-embedding ----------------------------------------------------------- 12 2.2 Noise Figure Measurement -------------------------------------------------- 13 2.3 Modeling of DC Model -------------------------------------------------------- 16 2.3.1 Threshold Voltage Model --------------------------------------------- 16 2.3.2 Essential Equation for I-V Characteristics ----------------------- 17 2.3.3 Channel Charge Density Model ------------------------------------ 19 2.3.4 Mobility Model --------------------------------------------------------- 21 2.3.5 I-V Model in the Strong Inversion Region------------------------ 23 2.3.6 Subthreshold I-V Model ---------------------------------------------- 26 i 2.3.7 Other Important Parameters --------------------------------------- 28 2.3.8 Source/Drain Series Resistance ------------------------------------- 29 2.4 Modeling of the Extrinsic MOSFET --------------------------------------- 34 2.4.1 Gate Resistance Model ----------------------------------------------- 35 Chapter 3 RF characteristics of High-k MOSFET --------39 3.1 device structure ---------------------------------------------------------------- 39 3.2 DC characteristics ------------------------------------------------------------- 42 3.3 RF characteristics ------------------------------------------------------------- 45 3.3.1 Cut-off Frequency and Maximum Oscillation Frequency ----45 3.4 Parameter Extraction -------------------------------------------------------- 52 3.4.1 Extraction of DC parameter ---------------------------------------- 52 3.4.2 Extraction of Extrinsic Components by Using Equivalent Circuit ------------------------------------------------------------------- 54 3.4.3 Influence of Gate Leakage Current to Gate Resistance ------- 56 3.4.4 fT and fmax in conjunction with Rg ------------------------------- 61 3.4.5 Analysis of Gate capacitance ---------------------------------------- 62 Chapter 4 Exploration for Optimum Device Structutre --- 66 4.1 Device Structure ---------------------------------------------------------------- 66 4.2 DC Characteristics ------------------------------------------------------------ 67 4.3 RF Characteristics ------------------------------------------------------------- 73 4.3.1 Finger Length Dependency of fT and fmax ---------------- 73 4.3.2 Noise Characteristics ---------------------------------------- 74 Chapter 5 Conclusions and Future Issue ---------------------- 76 ii Reference ------------------------------------------------------------------------ 78 Acknowledgements -------------------------------------------------------- 81 iii Chapter 1 Introduction 1.1 RF CMOS Technology With recent fast growth in the RF(Radio-Frequency) wireless communications market, the demand for high performance but low cost RF solutions is rising. And with the rapid growth of CMOS (Complementary Metal Oxide Semiconductor) technology due to its scaling, it comes to be considered as the mainstream of RF technology due to its low cost, low power and high integration. This advanced performance of CMOS is attractive for RF circuit design in view of a system-on-chip realization, where digital, mixed-signal baseband, and RF transceiver blocks would be integrated on a single chip. RF CMOS application is discussed in section 1.1.1. However, with extreme scaling down of CMOS, several serious issues, e.g. short-channel and narrow width effects, impact ionization and gate leakage current, etc. have come out. Especially, gate leakage current is the most serious issue, because it makes difficult to realize Low Stand-by Power (LSTP) of CMOS devices. To improve this issue, high dielectric constant materials, so-called High-k, for gate oxide as replacement for conventional SiO2 have attracted attention. High-k technology is discussed in section 1.1.2. 1 1.1.1 RF CMOS Applications Figure 1.1 Application spectrum, ITRS2005 Recently, with the development of a highly-information-oriented society, the RF (Radio-Frequency) wireless communications market dramatically grows up. In the future, the demands of RF wireless technology will continue to increase all the more in various areas, e.g. our daily life, industrials and medicals. These demands are realized by the development of semiconductor products. Beforetime, the compound semiconductors composed of elements from group and in the periodic table such as SiGe, GaAs and InP had been mainly dominant for high-speed communications and RF applications as shown in Figure 1 [1]. However, RF CMOS application has been researched and developed by Universities in Europe and the United States cheifly [2][3], and then RF CMOS technology gets to be considered as the mainstream due to its low cost, low power, high integration and easy access to the technology, even though the compound semiconductors still dominate out of 5GHz as shown in Figure 1 [4]. Since RF characteristics, such as the cut-off frequency (fT) and the maximum oscillation frequency (fmax), of Si ULSI come to advance up to several dozen GHz (see 2 Tabel 1), available bandwidth increases and the signal frequency transmitted to interconnection of LSI comes to over GHz. Thus, CMOS technology comes to be important for both the RF technology of wireless applications and digital LSI applications. The feature that CMOS circuit configuration and multi-layer interconnections are available for RF applications are also attractive. However, there are some challenges for RF CMOS applications in the following: 1. The necessity of optimization at semi-restricted process conditions. 2. The difficulty of adopting high resistive substrate. The solution of these challenges is necessary for RF CMOS applications. Table 1.1 The roadmap of RF CMOS characteristics [5] Year 1995 1997 1999 2001 2003 2005 2007 2009 Gate length [nm] 250 180 140 120 100 70 50 35 Gate width [um] 200 150 110 100 80 80 50 35 fT[GHz] 39 50 65 80 105 145 205 420 fmax[GHz] 39 42 46 50 60 62 68 85 NFmin@2GHz 0.3 0.26 0.22 0.17 0.14 0.13 0.1 0.08 1.2 The Indicators of RF Device In evaluating device RF performance, some indicators are employed as the cut-off frequency fT, the maximum oscillation frequency fmax, the minimum Noise Figure NFmin (and sometimes 1/f noise). In this section this three indicators are discussed especially. 3 1.2.1 The Cut-off Frequency fT fT is defined as the transition frequency which small-signal current gain drops to unity. It is a measure of the maximum useful frequency of a transistor when it is used as an amplifier. fT can be easily obtained by converting measured S21 parameter to H21 parameter. gm fT = (1.1) 2πCgs 1.2.2 The Maximum Oscillation Frequency fmax fT is surely a good indicator of the low-current forward transit time. However, as a performance indicator, it does not include the effects of gate resistance Rg, which are very important in determining the transient response of a transistor. So a indicator including Rg effects have been proposed, fmax. fmax is the frequency at which the unilateral power gain becoms unity. 2 1 S 21 −1 2 S UnilateralGain = 12 ; K=Kfactor (1.2) S 21 ⎛ S 21 ⎞ K − Re⎜ ⎟ S12 ⎝ S12 ⎠ fT fmax = (1.3) 2 gds (Rg + Rs) + 2πfT RgCgd 4 1.2.3 The Noise Figure NFmin The RF noise Figure is an important parameter. Due to the low effective gate resistance Rgate and the high fT the minimum noise Figure is extremely small at frequencies of few GHz, and the measurements have to be accurately de-embedded and extended to get a proper picture. Noise can be defined as any interference unrelated to the signal of interest. The most commonly accepted definition for NF is given by Eq. (1.4), where SNRin and SNRout are the signal-to-noise ratios measured at the input and output, respectively. SNR NF = in (1.4) SNR out T =300K NF is a measure of the degradation of the SNR as the signal passes through a system. For a noiseless circuit SNRin = SNRout . Therefore, regardless of the gain, NF equals to the unity. However in real systems the inner noise degrades the SNR, yielding NF>1. NF for circuits working in voltage-mode becomes 2 Vn,out NF = 2 (1.5) Av N RS For current-mode circuits NF becomes: 2 I n,out NF = 2 (1.6) Ai N RS 2 2 Where Vn,out =voltage of the total output-noise, I n,out = current
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