What is the use of "w" as Semi-vowel?

Alphabets which sounds like vowels (phonetically) but functions like consonants are called "Semi-vowels".

Eg. A sound that has the quality of one of the high vowels, as (ē) or (o͞o), and that functions as a consonant before or after vowels such as 'y' and 'w' in Yell and Well.

Source:http://www.thefreedictionary.com/semivowel

I expect the inclusion of "w" as a semi-vowel probably dates from an earlier century, and I'm not certain there is any basis for calling it one. The function of the 'y' and 'w' in Yell and Well are not in any material sense different to the leading consonants in Tell, Sell, and Fell.

The inclusion of 'y' as a semi-vowel in "cry" or "rhythm" is of course not controversial, but I think it's quite a stretch to go much further than that, when both letters are used as regular consonants.

I can't even think of an English word where 'w' is used anything like a vowel (or semi-vowel).

TL;DR: When it is at the start of a syllable, not when it is at the end of a syllable.

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First, do not confuse letters with sounds. It is pointless to talk about letters.

Semivowels are glides like /w/ and /j/ that act as part of a diphthong, so in conjunction with a vowel sound. In practice, only those semivowels that precede the vowel count as a consonant, not those that follow it where they count as a vowel.

So the words wet and yet are pronounced with a consonant glide at their fronts, and this is referred to as a semivowel because they start with a consonant sound. Contrast this with cow and coy where there is no consonant property involved, so those are purely vocalic: they end in a vowel sound, not in a consonant sound.

Spelling may or may not reflect this, though, because English spelling derives at best from the sounds of English that was spoken five to nine centuries ago, not from the sounds of English today. That’s why it’s pointless to talk about letters.

You have a false premise here: there is no semivowel in the word cry, only a purely vocalic, garden variety diphthong. The y in cry /kraɪ/ represents a falling diphthong /aɪ/, whereas the one is in yes /jɛs/ is the semi-vocalic glide /j/ you’re looking for, being the first element of a rising diphthong /jɛ/. Similarly in few /fju/.

Semi-vowels are things like /w/ and /j/, and they are frequently talked about only in rising diphthongs in English where they take on a consonant character. So cow has /kaʊ/ while coward has /ˈkaʊɚd/, which can also be written /ˈkawɚd/.

Similarly the noun toe and verb tow have /tou/, which can also be written /tow/. In concrete phonetics, you may see narrow transcriptions like [tʰo̞ʊ̯].

A semivowel at the start of the rising diphthong does not usually count as part of the syllable’s rime¹ so yet /jɛt/ rhymes with bet /bɛt/. Similarly the glide in queen /kwin/, [kʰwi:n] doesn’t count for rhyming, allowing it to rhyme with seen /sin/ and machine /məˈʃin/.

However with the /ju/ diphthong, some poets prefer to include the leading semivowel, preferring to rhyme cute /kjut/ with dispute /dɪˈspjut/ instead of with words lacking that /j/ component like shoot /ʃut/. So for them the vowel is the entire diphthong /ju/ including its leading semi-vowel and not just /u/, since they’re trying to rhyme with /jut/ not just with /ut/.

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1. rime: (linguistics) The second part of a syllable, from the vowel on, as opposed to the onset. ^[Wiktionary]

In short, wye is not a semivowel in cry. It represents the /ɪ/ part of the diphthong /äɪ/, in this case.

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According to the official chart (PDF) distributed by the International Phonetic Association, /j/ and /w/ (i.e. the sounds usually associated with wye and double-u, respectively) are approximant consonants. That is they have more constriction than vowels but less than fricatives, so they cannot form diphthongs but can be syllabic, as they are sonorants.

A dispute arises when one uses the term semivowel, a class of approximants which are articulated at the same place as and sound similar to a corresponding vowel but have more constriction. Some prefer to analyze semivowels as approximants with vowel-like qualities (including diphthongization) or even nonsyllabic vowels because of the audible similarities.

In English, our semivowels (/w/ and /j/) can only occur in the syllable onset, and when they appear to be in the coda from the orthography, they usually represent [ɪ̯] and [ʊ̯].