Noise and Random Telegraph Signals in Nanoelectronic Devices Zeynep Çelik-Butler Electrical Engineering Department University of Texas at Arlington Arlington, Texas,
Noise and Reliability Laboratories, Zeynep Celik-Butler, 2 Outline u Motivation: Problems Encountered as the Devices Shrink, Frequencies Increase, and Voltages Reduce u Improved Model for 1/f Noise in MOSFETs u Random Telegraph Signals in MOSFETs u Complex RTS u Extraction of trapping parameters using RTS
Noise and Reliability Laboratories, Zeynep Celik-Butler, 3 UTA - Noise Characterization Facilities 6' x 6' x 8' Shielded Room 3 Spectrum and Signal Analyzers, f=1 Hz - 20 GHz. 3 Cryostats, T= 2 K to 350 K. Various Lock-ins, Preamps, System Controllers, Battery Operated Sources etc. Optical Equipment Computer Software for Modeling
Noise and Reliability Laboratories, Zeynep Celik-Butler, 4 Problems Encountered as the Devices Shrink, Frequencies Increase, and Voltages Reduce u Signal-to-noise ratio decreases. u Noise models based on large number of electrons break down. u Quantum effects become dominant.
Noise and Reliability Laboratories, Zeynep Celik-Butler, 5 Signal to Noise Ratio Decreases u For a MOSFET Start from W=100 m, L=10 m, t ox =800Å, N SS =4x10 10 eV - 1 cm -2. u Assume scaling factor is K. u Assume trap and surface state densities remain the same. u Increase in noise level due to the K 1/2 law chosen for t ox. u Unpredictability of noise level for K>20. u N SS is actually a two dimensional Poisson variable.
Noise and Reliability Laboratories, Zeynep Celik-Butler, 6 Large Area Noise Models Break Down uSingle electron, single trap effects. N SS =4x10 10 eV -1 cm -2, W=1 m, L=0.1 m. ECEC EVEV EFEF SiO 2 Si kT=26 meV 1 trap per channel
Noise and Reliability Laboratories, Zeynep Celik-Butler, 7 Large Area Noise Models Break Down Break-down of large-area models for sub-micron channel length. A=N t (cm -3 eV -1 ) B= eff N t (cm -1 eV -1 ) C= 2 eff 2 N t (cm eV -1 ) A=B 2 /(4C) Independent parameters: and N t
Noise and Reliability Laboratories, Zeynep Celik-Butler, 8 Large Area Noise Models Break Down V gs -V T = -1 V V ds = -50 mV
Noise and Reliability Laboratories, Zeynep Celik-Butler, 9 Large Area Noise Models Break Down
Noise and Reliability Laboratories, Zeynep Celik-Butler, 10 Large Area Noise Models Break Down Modified 1/f noise model that takes into account threshold variation along the channel. For simplicity assume two regions: – V, L, V T2,, A 2, B 2, C 2 – V ds - V, L- L, V T1, A 1, B 1, C 1 – L<<L, V T V T1 – A 1 = A 2, since N t1 = N t2 – B 1 2 /C 1 = B 2 2 /C 2 = 4A – I 1 = I 2 = I d – eff1 = eff2, Independent parameters: N t, 1, 2, V T2, and V
Noise and Reliability Laboratories, Zeynep Celik-Butler, 11 Large Area Noise Models Break Down Modified 1/f noise model that takes into account threshold variation along the channel.
Noise and Reliability Laboratories, Zeynep Celik-Butler, 12 RTS in MOSFETs Random Telegraph Signals: single electron switching. 11 00 IdId
Noise and Reliability Laboratories, Zeynep Celik-Butler, 13 RTS in MOSFETs Random Telegraph Signals (RTS) with a Lorentzian on 1/f spectum. Time Scale seconds Time Scale milliseconds Frequency (f) PSD
Noise and Reliability Laboratories, Zeynep Celik-Butler, 14 2 RTS levels 1 RTS process
Noise and Reliability Laboratories, Zeynep Celik-Butler, 15 3 RTS levels 2 RTS processes
Noise and Reliability Laboratories, Zeynep Celik-Butler, 16 5 RTS levels 4 RTS processes
Noise and Reliability Laboratories, Zeynep Celik-Butler, 17 COMPLEX RTS Complex random telegraph signals due to multiple traps
Noise and Reliability Laboratories, Zeynep Celik-Butler, 18 RTS in MOSFETs RTS can be used to characterize trapping sites. RTS modeling.
Noise and Reliability Laboratories, Zeynep Celik-Butler, 19 RTS in MOSFETs RTS can be used to characterize trapping sites. Position of the trap along the channel, y T Position of the trap in the oxide, x T Trap energy, E Cox - E T Screened scattering coefficient,
Noise and Reliability Laboratories, Zeynep Celik-Butler, 20 Trapping Parameters Through RTS in MOSFETs x T =2.7 nm y T /L=0.6 E Cox -E T =3.04 eV
Noise and Reliability Laboratories, Zeynep Celik-Butler, 21 Trapping Parameters Through RTS in MOSFETs
Noise and Reliability Laboratories, Zeynep Celik-Butler, 22 Trapping Parameters Through RTS in MOSFETs
Noise and Reliability Laboratories, Zeynep Celik-Butler, 23 Effects of Quantization Increase in effective energy band-gap: change in e and c Shift in carrier distribution: change in C ox
Noise and Reliability Laboratories, Zeynep Celik-Butler, 24 3-D Treatment of RTS
Noise and Reliability Laboratories, Zeynep Celik-Butler, 25 2-D Treatment of RTS - c and e
Noise and Reliability Laboratories, Zeynep Celik-Butler, 26 2-D Treatment of RTS From Stern - Howard wave-function:
Noise and Reliability Laboratories, Zeynep Celik-Butler, 27 2-D Treatment of RTS Calculate the inversion carrier concentration assuming they are located primarily at E 0 :
Noise and Reliability Laboratories, Zeynep Celik-Butler, 28 2-D Treatment of RTS - c and e To first order, the ratio is not affected by quantization.
Noise and Reliability Laboratories, Zeynep Celik-Butler, 29 RTS Measurements MDD n-MOSFETs W eff L eff = 1.37 0.17 m 2 T ox = 4 nm V T = V for V SB = 0 V strong inversion, linear region V DS = 100 mV V SB = V, V GS = V
Noise and Reliability Laboratories, Zeynep Celik-Butler, 30 E Cox -E T and z T from c and e ln( c / e ) V SB =0 V
Noise and Reliability Laboratories, Zeynep Celik-Butler, 31 E Cox -E T and z T from c and e ln( c / e ) V SB =0.4 V
Noise and Reliability Laboratories, Zeynep Celik-Butler, 32 E Cox -E T and z T from c and e T ox =4 nm
Noise and Reliability Laboratories, Zeynep Celik-Butler, 33 Dependence of e on V SB e (s) V GS =0.75 V V GS =0.55 V
Noise and Reliability Laboratories, Zeynep Celik-Butler, 34 Dependence of c on V SB c (s) V GS =0.55 V V GS =0.75 V V GS =0.65 V
Noise and Reliability Laboratories, Zeynep Celik-Butler, 35 c n Extracted from c and e
Noise and Reliability Laboratories, Zeynep Celik-Butler, 36 2-D Treatment of RTS - Amplitude Question: How does quantization affect number and mobility fluctuations? –Number fluctuation through N –Mobility fluctuations through oxide charge scattering, t.
Noise and Reliability Laboratories, Zeynep Celik-Butler, 37 Extraction of Scattering Coefficient Mobility Fluctuations: –Using Surya’s 2D surface mobility fluctuations model,
Noise and Reliability Laboratories, Zeynep Celik-Butler, 38 Calculation of Scattering Coefficient Considering a single trap: N t (E,z) = N t (E-E T ) (z-z T )
Noise and Reliability Laboratories, Zeynep Celik-Butler, 39 RTS Amplitude
Noise and Reliability Laboratories, Zeynep Celik-Butler, 40 Extraction of Scattering Coefficient = 2.91x x ln(N) T ox =4 nm
Noise and Reliability Laboratories, Zeynep Celik-Butler, 41 Extraction of Scattering Coefficient W L = 1.2 0.35 m 2 z T =0.25 nm T ox =8.6 nm
Noise and Reliability Laboratories, Zeynep Celik-Butler, 42 Possible Reasons for Discrepancy Threshold non-uniformity along the channel is not taken into account. Location of the trap along the channel Variation of the channel voltage from source to drain is neglected. N/ N t 1 is not valid, even in strong inversion, for very thin oxides.
Noise and Reliability Laboratories, Zeynep Celik-Butler, 43 ACKNOWLEDGEMENTS This work has been supported by NSF, THECB-ATP, SRC, TI, Legerity, Motorola and ST-Microelectronics.