Snubberless TRIAC not turning on in negative cycle

Are you sure whatever is driving the MOC3010 can sink 15 mA? The MOC3010 is only guaranteed to switch at 15 mA forward current through the LED. The optriac may switch at lower forward currents, but the apparently Motorola bins those parts by forward current sensitivity, and the 3010 is the lowest sensitivity.

_{IFT = LED Trigger Current, Current Required to Latch Output}

With a footnote:

All devices are guaranteed to trigger at an I_F value less than or equal to max I_FT. Therefore, recommended operating IFlies between max 3.IFT(15 mA for MOC3010, 10 mA for MOC3011, 5 mA for MOC3012) and absolute max I_F(60 mA).

What is driving the LED? Can you measure the voltage on the IO line going to the optocoupler?

It's also worth noting that even with the microcontroller completely out of the picture, you'll only get 10 mA forward current with a 330Ω resistor (\$5V - 1.5V_{F} = 3.5V\$ across the resistor. \$\frac{3.5V}{330} = ~10.6 mA\$).

From the graphs we see that gate leakage currents of all transistors decrease with increasing \$T_{OX}\$. This means that the increase in total leakage current must be attributed to subthreshold conduction.

Why would subthreshold current increase? The following equation for subthreshold curent appears in BSIMv4.7 User's Manual:

While there are many parameters involved, the main suspect is the treshold voltage, \$V_{th}\$, which is known to be sensitive to gate oxide thickness (as well as almost any other transistor's parameter).

In order to verify this I built the following circuit:

Sweeping \$T_{OX}\$ and measuring \$V_{th}\$ resulted in:

This linear decrease in threshold voltage explains an exponential increase in subthreshold leakage (based on the above equation).

The natural continuation of the answer would be to explain why \$V_{th}\$ decreases with \$T_{OX}\$. The equation used to calculate the threshold voltage for BSIMv4.7 model in Spice is:

\$T_{OX}\$ dependence appears in the above equation both explicitly (TOXE) and implicitly (through other parameters which depend on \$T_{OX}\$). It is beyond my expertise and knowledge to perform this task and map various numerical parameters into physical effects taking place in the actual transistor.

In summary:

The reduction in threshold voltage due to thicker oxide leads to higher subtreshold leakage current. The exact effects which cause the reduction are very complex.