Why study SOI MOSFETs nonlinearities ?

2. Why study SOI MOSFETs nonlinearities ? MOSFET SOI f f • Simplified process • Low parasitic capacitances • Low leakage current • Low Vth • => promising for RF ICs Distortion Silicon-on-Insulator (SOI) • Non-idealities of “linear circuits” • Amplifiers • Active filters • Used in some applications • Mixers • Oscillators • Frequency multipliers • Inherent to the physics of semiconductors

3. G G S/D S/D S/D S/D Burried Ox Burried Ox body FD vs PD SOI MOSFETs ID [mA] - : Fully Depleted (FD) --: Partially Depleted (PD) with floating body VD [V] DuTs: FD and PD SOI MOSFETs, 12x6.6 µm/0.25 µm (0.25 µm LETI technology)

4. + + + + + + + Impact Ionization current High E field near the drain: => impact ionization => creates e--h+pairs => injection of holes inside the body => body potential increase up to Vtsb => Parallel path for Id and Id increase => Vt lowering and Id increase What happens inside?- gd kink - n ++ p n ++ Body region SiO2 Depletion region

5. Linearity of SOI MOSFETs using Integral Function Method and Volterra modeling Outline • DC based characterization methods • Taylor series • Integral Function Method (IFM) • Comparison with Large-Signal Network Analyzer (LSNA) • measurements • HF MOSFETmodel based on Volterra series • Frequency limitation of DC based methods • Third order intermodulation • Conclusions • Devices performances => Does the kink influence the linearity ? => Which methods to characterize the linearity of MOSFETs ?? The simplest is the best

6. Method : Taylor analysis f VG(t) ID(t) ID t f VG t If the circuit is excited by a sine wave, Consider the memoryless nonlinear system: Taylor series:

7. t Methods: quid for large amplitude? ID VG Taylor: add terms => too complicated ! IFM: good approximation of HD at LF further advantage: less sensitive too measurement noise [CerdeiraSSE02, CerdeiraSSE04, CerdeiraICSICT04]

8. IFM: How does it work ? 2. Observe that Area1-Area2 is proportionnal to the THD 3. Define theD function Area1 Area2 Out 1. Normalize the characteristics In HD3is obtained by computing the D function of Ir = I(V)-I(-V) => even harmonics eliminated ! HD of order higher than 3 are neglected [CerdeiraSSE02, CerdeiraICSICT04]

9. IFM takes the influence of the amplitude of the applied signal into account HD3 [dB] VG [V] Not by a scale factor as from Taylor approach, cfr.

10. Comparison with LSNA measurements full-wave (magnitude and phase) RF (900 MHz) characterization (V,I fundamental and harmonics at input and output) in single take => Real RF nonlinear behavior LSNA = [VerspechtMTTS95] 900 MHz, 50 Ω, A = 0.2 V • Good agreement before the minimum • Minimum located at : • - IFM : max. of gm • - LSNA : max. of power gain • Nonlinearity of gm and gd LSNA HD2 [dB] gm and gd gm only VG [V]

11. Harmonic distortion af HF Cgd RG Gm Gd Cds => Answer this question with the help of a Volterra series based model: YL Vin Cgs Gm=gm1+gm2VG+gm3VG² Gd=gd1+gd2VD+gd3VD² DC method vs 900 MHz measurements in agreements => Which frequency limit ??

12. HD from Nonlinear current method HD2 fp fz freq [ParvaisGAAS04]

13. Poles of HD2 and HD3 as a function of ZL Pole Voltage Gain Av 26 GHz 9 GHz 5 GHz Pole HD2 Pole HD3

14. Characterization methods • Good agreements between results calculated using IFM and using Fourier coefficients. • IFM: advantages = amplitude dependent, no derivatives. • Frequencyvalidity range cfr. Volterra model (several GHz).

15. HD: PD ~ FD transistors

16. frequency limitation caused by RC body impedance Vb Rb and Cb= body resistance and capacitance iii Cb Rb Frequency analysis of the kink effect [SinitskyIEDL97] • As Vd  Rb  => fc 

17. Kink effect ! Third order intermodulation Volterra model: ZL↑

18. PD SOI: Floating body or not ? PD, from ST Microelectronics 60x 1µm/0.12 µm, f=2 GHz FB: higher fT, fmax than BC and isoc. BC/Isoc.: parasitic C, gm degradation

19. Conclusions • At 900 MHz, when the polarization voltage is varied, HD is dominated by the DC I-V characteristics. • Frequency validity range of DC methods provided by a Volterra model. • PD versus FD: • HD ---> idem (gm dominates) • IMD ---> depends on the tone separation • cfr. Kink effect • Thanks to • FRIA for financial support