As far as I know (please correct me if I missed something) you can only search for the entire matrix by matrixField:value
and not certain fields within your matrix since the table searchindexes
only contains the id of the matrix field itself, not the id of the field inside the matrix.
However: you could create a Query
from your ElementCriteriaModel
in PHP via
$command = craft()->elements->buildElementsQuery($criteria);
Join your matrixblock table as well as your matrixblock content table
$command->join("your matrixTable", "matrixTable.ownerId = elements.id");
$command->join("your matrixContentTable", "matrixContentTable.elementId = matrixTable.id");
And search for your field with a where
$command->andWhere('MyAwesomeField LIKE %whatever%');