There are cables available that large if you do not have a strict 'conduit only' rule.

You can definitely buy 3/3 NMD 90 cable at any electrical supply. You can also run 3/3 TECK, but it's waterproofed and armoured, and may not be necessary. If you need to have conduit for protection only , you could always put the 3/3 NMD 90 in 3" PVC, as long as there are no sharp bends.

Great info. Thanks!

I went to Home Depot this aft, and the electrical guy there gave me the name of a local industrial supply house, which does counter sales, and has 3/3 copper and 2/3 aluminum. Awesome! My problem is solved. However, this now gives me a few more questions. 3/3 copper is $23 Can per metre. 2/3 Aluminum is $9 Can per metre. Guess which one I'm buying? :) I've got about a 90 ft. run. But I've never worked with aluminum wire before.

1. I'll double check to make sure my service panel and subpanel are aluminum compatible, but I assume so. The service panels are Siemens, 3 years old, and the sub is Cutler Hammer, bought last year.
2. I know I need to use dielectric grease, but can you explain how I need to use it? I'll feed the cable from a 100 amp breaker, screw the lugs of the breaker onto the hot conductors, etc. Do I coat both breaker lugs, the neutral bus bar connection, and the ground connection with the dielectric grease? I'll then need to coat the subpanel connections the same way?
3. The cable they sell they called AC, not NMD. It's got a pvc casing. It's not UF. The sales gent said this can be used without conduit protection, so I can run it directly into the subpanel. I'll be drilling a hole through the insulated wall of the house into the attached garage and running the cable up into the sub panel. What is the maximum bend radius 2/3 aluminum is allowed?
4. With what do I attach this pvc armoured cable to sheathing?
5. Any other gotcha's with this? I want to do everything properly, to code, but also "best practice" not just "good enough" so I really appreciate your folks help. Thanks!

Buy some Penetrox, No-Alox or other approved anti-oxidant for aluminum wire. Wire brush the ends of the cable and immediately apply antioxidant. Some engineers prefer to have the anti-oxidant applied before wire brushing. The aluminum oxide film that causes some of the problems with aluminum connections forms rapidly. Coat the wires themselves with the anti-oxidant, not the lugs. Use PVC conduit strapping for the cable to attach to the walls. I have no idea what the max bend radius of 2/3 Al cable is.
Make sure and periodically retighten all lugs, as they will loosen over time.

Just to make sure, I wire brush the cable ends, apply the Penetrox, THEN insert it into the lug and tighten? Does tightening cause the grease to be squeezed out at the contact point of the lug and the wire allowing a good electrical connection to occur?

"Just to make sure, I wire brush the cable ends, apply the Penetrox, THEN insert it into the lug and tighten?"

Yes, that's the procedure. The grease is a conductor that also prevents oxygen from the air coming into contact with the aluminum. All that's needed is a layer of Penetrox to be thick enough to just cover the aluminum. Anything more is a waste of Penetrox.

Great! One more question.

I'll be drilling through the attached garage/house wall and running the cable up to the subpanel. Even if this cable is a PVC type of AC I'd feel better with some extra physical protection. I thought of running the 2/3 in a large PVC conduit, or terminating it at an LB fitting and running individual conductors into the subpanel, but both would be a lot of work. Would it be acceptable to just build a plywood box attached to the wall covering the cable from the wall penetration up to the bottom of the subpanel?

"Would it be acceptable to just build a plywood box attached to the wall covering the cable from the wall penetration up to the bottom of the subpanel?"

Might not be aesthetically pleasing, but will do the job.
You're much better off just terminating the 2/3 directly into the subpanel and not bothering with any transition to THWN/THNN (RW90 Xlink in Canada).
A heads up before you go the supply house: You'll need 2 cable clamps to fasten the 2/3 to both the main and sub panels. Check where the large knockouts on both panels are and make sure you get the correct size clamps for the knockouts and the cables.

Points well taken. Thanks very much for all your help and advice!!

"Points well taken. Thanks very much for all your help and advice!!"

I'm glad I was of help. You're very welcome.