On re-reading, perhaps I was a bit confused: with ê, I meant not "ie" as a whole, but the second part of that diphthong.
Ê by itself, I think, occurs only as an interjection (where you often have - across all languages - sounds that don't otherwise occur in words; compare the "tsk tsk" sound in English, which doesn't otherwise have clicks), so it's pretty marginal as a phoneme.
As a sound, it really only occurs (I think) as the second part of the "ie" (ye) diphthong and as the second part of the "üe" (yue) diphthong (xue, yue, etc.).
Compare "zhe" with "jie/jue", "che" with "qie/que", "she" with "xie/xue"; not only the consonant is different, but also the quality of the final "e" (monophthong "uh" vs. diphthong ending in "eh").
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Ê by itself, I think, occurs only as an interjection (where you often have - across all languages - sounds that don't otherwise occur in words; compare the "tsk tsk" sound in English, which doesn't otherwise have clicks), so it's pretty marginal as a phoneme.
As a sound, it really only occurs (I think) as the second part of the "ie" (ye) diphthong and as the second part of the "üe" (yue) diphthong (xue, yue, etc.).
Compare "zhe" with "jie/jue", "che" with "qie/que", "she" with "xie/xue"; not only the consonant is different, but also the quality of the final "e" (monophthong "uh" vs. diphthong ending in "eh").