Leakage at concept level

Leakage flows even when nothing toggles: gates leak a small current at the supply voltage. The EXAMPLE model is linear: P_leak = N x I_gate x V, with a stated EXAMPLE current per gate.

This model is a teaching stand-in, not a device model. Real leakage varies with process, voltage, and temperature, so every number here is labelled EXAMPLE.

Threshold voltage mixing

Low-Vt cells switch fast and leak most. High-Vt cells leak far less but switch slower.

Mixing uses each where it pays: low-Vt on timing-critical paths, high-Vt everywhere else. The mix keeps the clock while cutting the leak.

Leakage recovery

Recovery runs after timing closes: it swaps low-Vt cells on paths with spare slack for high-Vt ones. Each swap keeps slack non-negative and trims leakage.

The calc block works a 30/70 mix. Average current falls from 10 nA to 4.4 nA per gate, and leakage falls from 9 mW to 3.96 mW.

EXAMPLE concept model (not real figures): P_leak = N x I_gate x V
all low-Vt: N = 1000000, I = 10 nA, V = 0.9 V
P = 1e6 x 10e-9 x 0.9 = 1e6 x 9e-9 = 9e-3 W = 9 mW
mixed: 30% low-Vt at 10 nA, 70% high-Vt at 2 nA
average I = 0.3 x 10 + 0.7 x 2 = 3 + 1.4 = 4.4 nA
P = 1e6 x 4.4e-9 x 0.9 = 1e6 x 3.96e-9 = 3.96e-3 W = 3.96 mW
saving = 9 - 3.96 = 5.04 mW, 5.04 / 9 = 0.56 = 56%

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import sys

def leak(n, i_gate, v):
    return n * i_gate * v

all_low = leak(1000000, 10e-9, 0.9)
avg_i = 0.3 * 10e-9 + 0.7 * 2e-9
mixed = leak(1000000, avg_i, 0.9)
all_high = leak(1000000, 2e-9, 0.9)

checks = [
    (all_low, 0.009),
    (mixed, 0.00396),
    (all_high, 0.0018),
    ((all_low - mixed) / all_low, 0.56),
]

for i in range(len(checks)):
    got, want = checks[i]
    if abs(got - want) > 1e-9:
        print("FAIL: check " + str(i + 1) + " got " + str(got) + " want " + str(want))
        sys.exit(1)

print("PASS: leakage model agrees with hand arithmetic on 4 checks")

Common mistakes

Blanket high-Vt replacement breaks timing on critical paths. Recovery must recheck slack after every swap, since gains vary with available slack.

Related topics

• Next: Sizing and Duplication Cost

• See also: Cell Libraries and Liberty