Learn English – Commas before and after therefore

The rule you were taught is an over-generalization. The sentence written above is correct with no commas at all. The "rule" about especially only applies to the case when especially is being used as a parenthetical phrase, usually at the end of a sentence.

We really like ice cream, especially chocolate ice cream.

This rule is not unique to the word especially, but is used for all sorts of sentence-final parentheticals:

The "rule" about especially only applies to the case when especially is being used as a parenthetical phrase, usually at the end of a sentence.

Since your sentence is not using especially to begin a parenthetical statement, it does not require a comma. It is, however, stylistically awkward, and I would recommend the following revision:

Secondary electron emission from metallic surfaces, especially dielectric surfaces, is a fundamental process of great technological significance

Both are perfectly correct. If you have a style guide, you may wish to consult its preference on this subject.

For what it's worth, the Elements of Style (a popular-but-controversial American style guide) endorses the latter:

If a dependent clause, or an introductory phrase requiring to be set off by a comma, precedes the second independent clause, no comma is needed after the conjunction.

The situation is perilous, but if we are prepared to act promptly, there is still one chance of escape.