Reliability of MOS Devices and Circuits

Transcription

1 Reliability of MOS Devices and Circuits Gilson Wirth UFRGS - Porto Alegre, Brazil MOS-AK Workshop Berkeley, CA, December 2014

2 Variability in Nano-Scale Technologies Electrical Behavior / Parameter Variation Time Zero Time Dependent Random: RDF, LER, etc Systematic: Process Gradients, etc Aging: NBTI, HCI, Electrom., etc Transient: SET/SEU, Noise, etc There are also environmental sources of variation: Voltage, Temperature, etc. 2 Gilson Wirth

3 Issues in Nano-Scale Technologies Performance Average Speed Minimum Acceptable Performance Transient Error Permanent Failure Time 3 Gilson Wirth

4 Issues in Nano-Scale Technologies Speed Variability Minimum Acceptable Speed Transient Error Permanent Failure Time 4 Gilson Wirth

5 Issues in Nano-Scale Technologies - V DD saturating at 1V due to non-scaling of sub-threshold slope. - Increased Electric Field in Gate Dielectric and Semiconductor. - Increased power density: Increased Temperature. 5 Gilson Wirth

6 Discrete Charges and Traps Source: Hans Reisinger 6 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

7 Charge Trapping Our Modeling Approach for Charge Trapping Low-Frequency Noise: Frequency Domain Models (DC and AC Large Signal) Time Domain Analysis and Simulation NBTI: Charge Trapping Component Amplitude of the V T Induced by a Trap Conclusion 7 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

8 BTI x RTS V G V G Gate Contact Dielectric Gate Contact Dielectric Semiconductor Semiconductor current V G Positive: PBTI V G Negative: NBTI current time time 8 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

9 Low-Frequency Noise E F E F Traps within a few kt from the Fermi Level contribute to noise 9 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

10 Charge Trapping Component of BTI Transistor Off Transistor On E F After a Long Time E F Traps Mostly Empty Traps Mostly Occupied 10 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

11 BTI x RTS Traps that contribute to noise are the ones with C E i.e., traps that keep switching state Traps that contribute to NBTI are the ones with C < E i.e, traps that become occupied 11 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

12 Modeling Approach Based on Microscopic (Random) Quantities, instead of distributed (homogeneous) quantities. 1. Charge trapping and de-trapping are stochastic events governed by characteristic time constants, which are uniformly distributed on a log scale. 2. Number of traps is assumed to be Poisson distributed. 3. Amplitude of the fluctuation induced by a single trap is a random variable, studied by atomistic simulations. 4. Trap energy distribution is assumed to be U shaped (key to explain the AC behavior). 12 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

13 Some Advantages of our Approach 1. Can be Applied to both DC and AC Large Signal Excitation. 2. Can be Applied also for Transient Simulation. 3. Random Variables Lead to Statistical Model (Today Variability is a Major Issue). 4. Can be Applied to Different Phenomena where Charge Trapping Plays a Role, such as Noise and NBTI. 13 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

14 Low-Frequency Noise Frequency Domain Modeling (DC) Noise due to a Single Trap Noise due to the Ensemble of Traps AC Large Signal Excitation Time Domain (Transient) Analysis and Simulation 14 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

15 Evaluating the Noise Power due to One Trap Poisson Process 15 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

16 Evaluating the Noise Power due to One Trap The autocorrelation is given by And the power spectrum density (Fourier Transform) is a Lorentzian + Singular term It is not important 16 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

17 RTS: Random Telegraph Signal S(log) Current c d e Time f(log) 17 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

18 Evaluating the Noise Power due to Many Traps S(f) N tr S(f) = A i i=1 f i 1+ f 2 f i f(hz) 18 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

19 Evaluating the Noise Power due to Many Traps Superposition of Lorentzians Averaging on many variability sources 19 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

20 Evaluating the Noise Power due to Many Traps Average Value <A 2 > N dec WL < S (f) > = f π 2 Standard Deviation σ S(f) < S (f) > = 2 π N dec WL <A 4 > <A 2 > 2 G Wirth et al. IEEE Trans Electron Dev, Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

21 Average Value and Variability Gate referred voltage noise [VHz -1/2 ] 10-3 n-mos, W / L = 25µm / 0.25µm V d = 1.0V, V g,eff = 0.5V Frequency [Hz] R Brederlow iedm Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

22 Average Value and Variability Gate referred voltage noise [VHz -1/2 ] 10-3 n-mos, W / L = 2.5µm / 0.25µm V d = 1.0V, V g,eff = 0.5V Frequency [Hz] R Brederlow iedm Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

23 Average Value and Variability Gate referred voltage noise [VHz -1/2 ] 10-3 n-mos, W / L = 0.25µm / 0.25µm V d = 1.0V, V g,eff = 0.5V Frequency [Hz] R Brederlow iedm Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

24 Variability: Dependency on Frequency Sf / <S f > Frequency [Hz] G Wirth et al. IEEE Trans Electron Dev, Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

25 Variability Scaling 4 np /<np BW > Triangles: Measurement Dots: Monte Carlo Simulation Line: Model (N dec W L) -0.5 G Wirth et al. IEEE Trans Electron Dev, Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

26 Low-Frequency Noise Frequency Domain Modeling (DC) Noise due to a Single Trap Noise due to the Ensemble of Traps AC Large Signal Excitation Time Domain (Transient) Analysis and Simulation 26 Gilson Wirth

27 Switched Bias: Modulaton Theory Klumperink et al., IEEE J. SOLID-STATE CIRC, VOL. 35, NO. 7, Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

28 Noise Spectra for a Single Trap under Square Wave Excitation <1/ c > = ( / c,on + (1- ) / c,off ) <1/ e >=( / e,on + (1- ) / e,off ) eq ( E, E, ) on off e 2E t / k B T ( E, on E off, ) e e E on E on / / k T B k T B (1 ) e (1 ) e E off E off / / k T B k T B G Wirth et al. iedm 2009

29 Noise Reduction under Cyclo-Operation WL S ID [ m 2 A 2 / Hz] V DS = V L = L nom = 0.04 m 1/f fit V GS,OFF = 0 = 1 V GS,ON = V T f [ Hz] CONST BIAS FREQ = 10 khz FREQ = 100 khz FREQ = 100 khz SIM_CONST BIAS SIM_FREQ_10kHz Modulation theory predicts four times noise reduction for CS operation Noise reduction is larger and in good agreement to the proposed model. G Wirth et al. iedm 2009

30 Normalized Variability of Noise Behavior WL S ID [ A 2 m 2 /Hz] SAMPLE SIZE = 40 CYCLO_FREQ = 1 KHz DC CYCLO DC Variability is seen to increase under Cyclo-Stationary Operation. CYCLO L = 0.04 m L = 1 m CHANNEL LENGTH G Wirth et al. iedm 2009

31 Low-Frequency Noise Frequency Domain Modeling (DC) Noise due to a Single Trap Noise due to the Ensemble of Traps AC Large Signal Excitation Time Domain (Transient) Analysis and Simulation 31 Gilson Wirth

32 RTS and Time Domain V T Fluctuations 32 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

33 Possible Simulation Methodologies Static Dynamic V T V T Change dvt at instantiation Verilog-A wrapper to Trans. model Ids = + f(delvto(t)) Change transistor Model equations 33

34 RTS: Transient Simulation (1) Charge trapping and de-trapping are stochastic events, governed by capture and emission time constants, c and e, which are uniformly distributed on a log-scale; the number of traps (N tr ) is assumed to be Poisson distributed, and the average number of traps (parameter of the Poisson) is assumed to be proportional to the channel area; trap energy distribution, g(e T ), is assumed to be U-shaped; the amplitude of the V T fluctuation induced by a single trap, is a random variable given by atomistic device simulations. 34 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

35 RTS: Transient Simulation (2) At each simulation time step, it is checked if a trap changes state. Trap switching probability is evaluated based on the device bias point at each transient simulation step. If one or more trap change state, transistor threshold voltage is changed accordingly. Simulators do not support this kind of simulation: ngspice and BSIM4 code modified. 35 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

36 V T Fluctuates Over Time V T (t) V T Fluctuation (V) x x x10-7 Time (s) 36 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

37 Transient Simulation of a Ring Oscillator 37 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

38 Period Jitter Period Jitter Period Jitter is the difference between a clock period andtheidealclockperiod(itcanoccurafteror before the ideal transition). 38 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

39 Transient Simulation of a Ring Oscillator 1200 Stationary No FBB Non-Stationary No FBB 2000 Non-Stationary With FBB 1000 Counts Counts Counts E E E E E-011 Period E E E E E-011 Period E E E E E E-011 (a) (b) (c) Period Histogram of oscillation period: (a) stationary DC noise analysis, (b) and (c) non-stationary simulation methodology here proposed. Case (c) is for the oscillator under forward body biasing (FBB). Stationary noise analysis predicts a jitter (σ T ) of 2.2ps, non stationary analysis predicts a 1.3ps jitter. FBB decreases σ T to 0.8ps. 39 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

40 Pros Comments Properly implements the physical-based equations into a circuit simulator Computationally efficient (minor impact on the run time of the transient simulation) Easy to use: Transparent for the circuit designer (no change needed in the netlist). Monte Carlo by its nature. Cons Changes made on simulator source code: time intensive work, and restriction to access proprietary code (HSpice, Spectre, etc.) 40

41 Outline Our Modeling Approach for Charge Trapping Low-Frequency Noise: Frequency Domain Models (DC and AC Large Signal) Time Domain Analysis and Simulation NBTI: Charge Trapping Component Amplitude of the V T Induced by a Trap Conclusion 41 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

42 NBTI: Charge Trapping Component Huard et al., IRPS Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

43 Modeling Approach V G Gate Contact Dielectric Semiconductor V G Positive: PBTI V G Negative: NBTI current time

44 Motivation To propose a Unified Model for DC and AC Bias Temperature Instability. The model should be based on first principles able to model both short term (cycle-to-cycle or ripple) and long term ( permanent ) components of AC BTI. Model equations should be simple and ease to implement in simulation tools.

45 Fast and Slow Traps 0,08 0,06 V T,Total (a.u) 0,04 0,02 V T,Fast V T,Slow 0, Time (a.u.) V T,Total = V T,Slow + V T,Fast

46 Fast Traps Transistor Off Transistor On E F At the End of Stress Semi-Cycle E F Fast Traps Mostly Empty Fast Traps Mostly Occupied Relevant Trap Time Constant: τ C,On

47 Fast Traps Transistor On Transistor Off E F At the End of Recovery Semi-Cycle E F Fast Traps Mostly Occupied Fast Traps Mostly Empty Relevant Trap Time Constant: τ e,off

48 Slow Traps Off On Off On Off On E F E F E F E F E F E F Traps are too slow to follow bias point change. Equivalent Time Constants <1/ c >=( / c,stress +(1- )/ c,recovery ) <1/ e >=( / e,stress +(1- )/ e,recorery )

49 Fast and Slow Traps V T [a.u.] Time [a.u.] Stress Receovery Stress followed by Recovery. Stress of 500 time units, followed by 500 time units of Recovery. Please note that Recovery is shifted by 500 time units in the Time axis, so that start of both Stress and Recovery correspond to time equal to zero.

50 Slow Traps V T,Slow (a.u) Time (a.u) V T,Slow k S. [log(α+ k A )-log(1-α+ k A )].log(t)

51 Slow Traps 0,08 V T,Slow (V) 0,06 0,04 0,02 0,00 0,0 0,2 0,4 0,6 0,8 1,0 Duty Cycle V T,Slow k S. [log(α+ k A )-log(1-α+ k A )].log(t)

52 Fast Traps Figure from J. Martin Martinez et al., IRPS 2011 V T,Fast = [k C +k F log(t S )] *[ (log(α+k A )+log(1-α+k A )]

53 Fast Traps Figure from D S Ang et al IEEE TDMR pp.19, March 2011 V T,Fast = [k C +k F log(t S )] *[ (log(α+k A )+log(1-α+k A )]

54 Fast Traps 2,5 2,0 V T,Fast (a.u) 1,5 1,0 0,5 0,0 0,0 0,2 0,4 0,6 0,8 1,0 Duty Cycle V T,Fast = [k C +k F log(t S )] *[ (log(α+k A )+log(1-α+k A )]

55 ΔV T Total V T,Total (a.u) Time (a.u.) x 10 4 Monte Carlo Simulation

56 NBTI: Temperature Dependence 0.02 (V G -V t0 ) I D /I D0 [V] C / C / C / C / C / C / C / C / Stress Time [seconds] 56 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

57 Model for the Charge Trapping Component G Wirth et al, IEEE TED Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

58 Normalized standard deviation of the BTI induced V T shift : Model : MC Simulation G Wirth et al, IEEE TED Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

59 Circuit Activity (Duty Cycle) Dependence V T [a.u.] : Measurement : Model : MC Simulation Duty Cycle G Wirth et al, IEEE TED Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

60 Simulation of Both RTN and BTI 60 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

61 Simulation of Both RTN and BTI 61 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

62 Simulation of Both RTN and BTI Vmin on some SRAM arrays varied from one measurement to the next (90nm node). Source: M Agostinelli et al. (Intel), IEDM Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

63 Outline Our Modeling Approach for Charge Trapping Low-Frequency Noise: Frequency Domain Models (DC and AC Large Signal) Time Domain Analysis and Simulation NBTI: Charge Trapping Component Amplitude of the V T Induced by a Trap Conclusion 63 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

64 RDF: Random Dopant Fluctuations In the past all transistors were similar because of self averaging Today, Each Transistor is Different Slide Courtesy Prof Dragica Vasileska, ASU 64 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

65 Threshold Voltage Values For Different RDF Configurations Vt(threshold voltage) data from EMC simulation Vt(threshold voltage) data from analytical model Vt(threshold voltage) data from percolation theory model Threshold voltage (V) Random dopant configuration (integer) N Ashraf et al, IEEE EDL Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

66 Dependence of V T Fluctuations on Trap Position Along the Channel Threshold voltage fluctuation ( V ) Threshold voltage deviation (analytical model 1) Threshold voltage deviation (EMC simulation(with short range e-e and e-i force)) Threshold voltage deviation (EMC simulation(without short range e-e and e-i force)) Trap position along the interface (nm) N Ashraf et al, IEEE EDL Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

67 Conclusion A microscopic, statistical modeling approach for charge trapping is presented. It is applied to study the role of charge trapping and de-trapping in Noise and BTI. Mutual relation between different reliability phenomena (LF noise, BTI and RDF) is discussed. The modeling approach may be applied for time domain (transient) or frequency domain analysis. 67 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization

68 Work here presented is due to People at UFRGS, Brazil: Roberto da Silva, Lucas Brusamarello, Vinicius Camargo, Mauricio Silva, Gilson Wirth, and many others People at ASU, USA: Dragica Vasileska, Nabil Ashraf, Yu Cao, Jyothi B Velamala, Ketul B Sutaria. People at Texas Instruments: Ralf Brederlow and P Srinivasan (SP). People at IMEC, Belgium: Ben Kaczer, Philippe Roussel, Guido Groeseneken, Maria Toledano- Luque, Jacopo Franco,... and many others 68 Gilson Wirth. IEEE/ACM Workshop on Variability Modeling and Characterization