aging_examples

Device aging (reliability degradation flow) — Enhancement-157

aging <t_target> ages every aging-capable device in the loaded circuit to a target operating lifetime and re-stamps the circuit, so any analysis run afterwards sees the degraded devices. It is the industry "stress → degrade → re-simulate (fresh vs aged)" reliability flow (HCI / NBTI / TDDB), built on top of the Verilog-A / OSDI device layer.

aging <t_target> [rate <opvar>] [param <ageparam>] [dynamic <tstop> [tstep]] [verbose]

How a model opts in

The command is model-agnostic: a device participates by exposing two things in its Verilog-A source (see agemos.va, a square-law NMOS with an NBTI-style threshold shift):

• a degradation-rate operating-point variable — default name agerate — the instantaneous stress rate at the present bias, in dose units per second (here, gate overdrive above the fresh threshold):

  (* desc="NBTI aging rate", units="V/s" *) real agerate;
  ...
  agerate = (V(g,s) > vth0) ? (V(g,s) - vth0) : 0.0;

• a per-instance age parameter — default name age — the accumulated stress dose, written back by the command; the model owns the physics mapping age to a parameter shift:

  (* type="instance" *) parameter real age = 0.0 from [0:inf);
  ...
  dvth   = dvth_ref * pow(age/age_ref, nnbti);   // sublinear NBTI power law
  vtheff = vth0 + dvth;

The engine only integrates the rate into a dose and feeds it back; all the degradation physics lives in the model. Devices without both names (ordinary resistors, sources, …) are skipped, so probing never errors.

Two modes

• static (default) — read the rate at the DC operating point and multiply by the lifetime: age = agerate(op) · t_target. For a device held at a fixed stress bias.

• dynamic (dynamic <tstop> [tstep]) — run a transient over one representative window, integrate the rate over time, and extrapolate: age = (∫ agerate dt / tstop) · t_target. This captures duty cycle: a gate biased on only part of the time ages by its time-averaged stress.

Run it

openvaf-r agemos.va -o agemos.osdi
ngspice -b aging_demo.cir          # static: fresh vs aged operating point

aging_demo.cir reads the fresh drain current, ages the device to ~10 years at its stress bias, and reads the degraded current and shifted threshold. The aging line prints a per-device report:

aging: 1 device aged to t = 3.15e+08 s (9.98 years), static stress [rate 'agerate' -> param 'age']
  device                       rate       age (dose)
  n1                            1.3        4.095e+08

Verify + figure

python3 verify_aging.py     # 6 checks, under BOTH the Sparse and KLU solvers
python3 make_aging_fig.py   # -> aging_iv.png

• A. Transfer curves Id(Vg) fresh and after 10 / 20 / 40 years of NBTI stress at Vg = 1.8 V: the threshold shift pulls the curve down and right.
• B. The extracted threshold shift ΔVth vs stress time follows the sublinear ΔVth ∝ t^0.25 power law the model implements.

Why the results are physically correct

• Dose ∝ stress × time. The reported age is exactly rate · t_target (static) or mean-rate · t_target (dynamic); a device biased below threshold accrues zero dose and does not age.
• Sublinear in time. ΔVth ∝ age^0.25 reproduces the classic NBTI/HCI power-law: ten times the stress time is only ~1.8× the shift.
• Near-threshold sensitivity. A device biased close to threshold loses a larger fraction of its current for the same ΔVth — the well-known reason analog/low-overdrive stages are the reliability bottleneck. In st.cir the hard-driven N1 (Vgs = 1.8) loses 8% while the near-threshold N2 (Vgs = 0.9) loses 22%, even though N1 accumulates the larger dose.
• Duty cycle. In dynamic mode a gate pulsed at 30% duty ages at 0.30× the rate of an identically-biased DC device — the time-weighted average of the stress waveform.

Notes

• The command runs the fresh operating point / transient first, leaving it as the current plot — a convenient "fresh" baseline to compare against.
• age is a per-instance parameter ((*type="instance"*)), so devices at different bias in the same .model age independently.
• Aging is solver-independent (it drives op/tran and reads opvars); results are identical under Sparse 1.3 and KLU.

See Enhancement-157 for the full write-up.