need help to build a 220v - 110v AC converter?

While linear CMOS devices do exist, CMOS ICs are primarily digital logic and have nothing to do with electrical power except possibly to make decisions that control other devices that do handle electrical power. Any kind of electrical power circuit will have to use some kind of inductor or capacitor, most likely a transformer of some kind. A TRIAC can chop up an AC voltage but the result still has high voltage peaks; it is not a 110V sine wave. I don't think there is any point discussing switch mode power conversion so the answer is you need a transformer.

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No electronic designer used this dumb idea CMOS IC to make this device. To avoid using transformer, TRIAC can do this simple job. This device was existed in market 30 years ago.

Buy one this small unit online with less than $10 and good up to 600W. To make a same one, parts cost more than that.

you need a step down transformer.