Using multiple "by"s in a compound sentence
Solution 1:
To avoid confusion and ambiguity I would keep the "by".
How can the avalanche be triggered? There are three possibilities:
by photogenerated carriers;
by carriers thermally generated;
by trapping levels in the semiconductor.
If "by" is omitted, we might understand a fourth and erroneous possibility:
by carriers thermally generated or trapping levels in the semiconductor. (The non-technical reader may wrongly imagine carriers that are either thermally generated in the semiconductor or are somehow "trapping levels" in it.)