Global TCAD Solutions

Predictions based on Physics

Reliability / BTI

One of the most critical degradation mechanisms in p-channel CMOS technologies is the negative bias temperature instability (NBTI). This non-ideal behavior of metal–oxide–semiconductor field effect transistors (MOSFETs) is essentially determined by defects at the semiconductor–insulator interface as well as inside the insulating oxide [Grasser09].

Non-Radiative Multiphonon Model - State diagram
Fig.1: State diagram of the NMP model
Pre-cursor for trap generation
Fig.2: Trap generation precursor
Charge state of traps at the beginning of the stress cycle
Fig.3a: Trap charge state at the beginning of the stress cycle
Charge state of traps at the end of the stress cycle
Fig.3b: Trap charge state at the end of the stress cycle
Stress - relaxation ΔVth curves at T=50°C and 150°C
Fig.4: ΔVth measurements vs. simulation (left - stress, right - relaxation)
Fig.5: Inverse modeling. Left: Score function, trap parameters. Right: Measurements to be fitted, actual implementations during process.

Nonradiative Multiphonon (NMP) Model

For accurate modeling of NBTI, GTS Framework R.2013 offers a reliability module which comes with an implementation of the latest non-radiative multiphonon (NMP) model [Grasser12].

Trap States and Transition Rates

The model assumes four trap states as shown in Fig.1. It assumes two different types of transitions between its states 1, 1', 2, and 2'.

The transition rates of the relaxation processes (k1'1 , k11', k2'2 and k22') are bias-independent:
Transition rates for the relaxation process - bias-independent

The barriers ε1'1 and ε2'2 are defined trap parameters, ν is the attempt frequency and β = 1 / (kB*T).

The transition rates where charge exchanges are involved (k12' , k2'1, k1'2 and k21') are bias-dependent and take NMP processes and tunneling into account:
Transition rates for the NMP process - bias-dependent

Here, σ is the effective trap capture cross section and vth is the thermal velocity. For the full set of rate-equations of the model, please check Tibor Grasser's publications on BTI (available at IμE) or consult the Minimos-NT user manual.

Trap Generation, Charge

Traps can be generated randomly from  a continuum distribution using the Grid option (see Fig.2) or loaded from file using the ReadIn option. The physical trap parameters can be either specified directly or given by a Gaussian distribution with mean value and standard deviation.

Depending on simulation setup, the equilibrium solution or the transient progress of the occupation will be calculated self-consistently. The charge of a trap, which affects the behavior of a device, depends on the occupation probabilities of the states 2 and 2'.

Stress and Relaxation Cycles

The typical stress and relaxation cycles used in BTI measurements can be simulated using a transient simulation setup. The trap-state occupation over time is given by the initial trap-state and the transition rates which are bias-dependent and follow self-consistently from device simulation [Bina12].

Fig.3a and Fig.3b show the charge of each trap at the beginning and at the end of the stress cycle. This yields the threshold voltage shift ΔVth during the BTI stress. Fig.4 shows ΔVth for a period of stress at the left followed by relaxation at the right, both at temperatures of 50°C and 150°C, with VG of -1.0V and -2.0V respectively.

Inverse Modeling

The NMP model can be applied for inverse modeling of statistical parameters like trap density and distribution. Fig.5 illustrates a single trap optimization: Based on an initial guess, the capture and emission time constants of a non-radiative multiphonon trap are optimized to match measurement data. At the left, Fig.5 shows the score function and trap parameters. At the right, the measurements to be fitted and the actual implementations during the process can be seen.


Profound understanding of degradation physics is key for optimizing device reliability in your technology. With the latest implementation of the nonradiative multiphonon (NMP) model, Minimos-NT allows accurate simulation of BTI phenomena.

Key Features

  • Statistical reliability modeling
  • Simulation of NBTI and PBTI degradation
  • Discrete oxide and interface traps
  • Can be combined with RDD
  • Integrated post-processing
  • Automatic job distribution on cluster

Applications and Benefits

  • Planar and FinFET transistors
  • Reliability on device and circuit level
  • Automatic simulation work flow
  • Fully integrated in GTS Framework R.2013
  • Efficient yet very affordable solution

Download Application Flyer: Variability & Reliability

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GTS Framework Application Flyer: Reliability (web version)

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[Grasser09]: T. Grasser, B. Kaczer, W. Gös, T. Aichinger, Ph. Hehenberger, M. Nelhiebel: "A Two-Stage Model for Negative Bias Temperature Instability"; "2009 IEEE International Reliability Physics Symposium Proceedings", (2009), 33 - 44.

[Grasser12]: T. Grasser:"Stochastic Charge Trapping in Oxides: From Random Telegraph Noise to Bias Temperature Instabilities"; Microelectronics Reliability (invited), 52 (2012), 1; 39 - 70.

[Bina12]: M. Bina, O. Triebl, Bened. Schwarz, M. Karner, B. Kaczer, T. Grasser: "Simulation of Reliability on Nanoscale Devices"; "Proceedings of the 17th International Conference on Simulation of Semiconductor Processes and Devices", (2012), ISBN: 978-0-615-71756-2; 109 - 112.