Iddah

In Islam, iddah or iddat (Arabic: العدة‎; period of waiting) is the period a woman must observe after the death of her husband or after a divorce, during which she may not marry another man. Its purpose is to ensure that the male parent of any offspring produced after the cessation of a nikah (marriage) would be known. The length of iddah varies according to a number of circumstances.

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Sayyed Muhammad Husaini Ragheb, Sayyed Muhammad Husaini Ragheb has a BA in Law from Guilan University, Iran and has also undertaken Hawzah studies in Qom. He used to be a Cultural Affairs director of Ethics Group of Al-Mustafa... Answer updated 7 years ago

Being sterilized or using any other means of contraception don't have anything to do with observing Iddah period.
In fact preventing Ikhtilate Miah* is one of the reasons of putting this law and not the entire reason.
It is said that the respect of the previous marriage is among the reasons.
Unless she has reached the age of menopause, so in this case there is no need for observing Iddah period.

*It means the mixture of semens and to avoid uncertainty in whose child the foetus will be, is intended by it.