What materials would maximize semiconductor efficiency if cost wasn't a constraint?

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If cost wasn't an issue, what would semiconductors be made from to maximise their efficiency,useful lifetime etc?
 

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It really depends on the application. Silicon, for example, isn't just cheap: it also has a native oxide that can be easily grown without forming surface states. III-V compounds, while generally faster, don't have good native oxides, and make poor-quality FETs. On the other hand, III-Vs are great for HBTs.