Antenna diode leakage

WHAT YOU ARE LOOKING AT

An antenna diode is there to protect a gate during manufacturing. Plasma steps — etch, deposition, implant — charge up whatever metal is connected to that gate, and without somewhere for the charge to go the gate oxide takes it. The diode is that somewhere: reverse biased in normal operation, so it does nothing except leak, and forward biased or in breakdown when the antenna charges up, so it clamps.

So there are two questions, and they pull in opposite directions. Does it leak enough to matter when the chip is running? And does it conduct enough to matter during the plasma step, which happens at a few hundred degrees Celsius? The plot answers both by sweeping the reverse leakage from 200 K to 1000 K.

The leakage has two parts. Minority carriers diffusing in from the neutral regions give the Shockley saturation current, which goes as n_i². Carriers generated inside the depletion region give the Sah-Noyce-Shockley generation current, which goes as n_i — one power, not two. At low temperature generation wins because n_i is tiny and n_i² is tinier. At high temperature diffusion catches up and takes over. The crossover readout tells you where.

THINGS WORTH TRYING

Look at the two shaded bands. The leakage during a plasma etch is not much different from room temperature; during plasma deposition at 200-400 °C it is orders of magnitude higher, which is the whole point — a diode that leaks nothing when cold conducts usefully when the wafer is hot.
Move the marker to 300 K and read the leakage per µm². Then look at the last readout: how long a 1 fF node takes to droop 100 mV through that leakage. At room temperature the answer is comfortable. Move the marker to 400 °C and it is not, which is why an antenna diode on a high-impedance analog node is a real design decision and not a formality.
Raise the reverse bias. The diffusion current does not care — it saturates, which is what “saturation current” means. The generation current does, because the depletion region gets wider and there is more volume generating carriers. That is why reverse leakage in a real junction is not quite flat with voltage.
Drop N_A towards 10¹⁵, i.e. put the diode in the substrate instead of the well. The depletion region widens by more than an order of magnitude, the generation current follows, and the diffusion current rises too. The junction sees the well doping, not the substrate, so getting this right matters.
Untick D and τ vary with T to get the fixed-coefficient model of ex/vd.py back. Over 800 K the difference is visible but small compared to the exponential: the bandgap dominates everything.

THE PYTHON

# Shockley diffusion saturation current
I_s = q*A*ni**2 * (1/NA*np.sqrt(Dn/tau_n) + 1/ND*np.sqrt(Dp/tau_p))

# Depletion width of a one-sided n+/p junction (NA << ND)
V_bi = (k*T/q) * np.log(NA*ND/(ni**2))
W = np.sqrt(2*eps_si*(V_bi + V_R)/(q*NA))

# Sah-Noyce-Shockley depletion-region generation current
tau_g = 2*tau_n
I_gen = q*A*ni*W/tau_g

I_leak = I_s + I_gen

Source: ex/antenna_diode_leakage.py, which reuses the n_i(T) derivation from ex/vd.py. The script normalises to 1 µm²; leakage scales linearly with area, so the area slider just multiplies.