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I know MOSFETs are much more efficient than BJTs in that they don't consume as much power when on whereas a BJT consumes base current the whole time it is on. I also know that MOSFETs tend to fail shorted. I can't find any information on BJT failure modes though/do they usually fail open or closed. Does anyone know about this?

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    \$\begingroup\$ "bad current" did you mean base current? \$\endgroup\$ – Brian Drummond Mar 15 '14 at 13:12
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In my experience, all semiconductors tend to fail shorted unless you put enough current through them to physically blow them apart or fuse the bonding wires. Physically broken packages (eg. diodes) can also result in an open.

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To address the first part of your question: It isn't true that MOSFETs are always more efficient than BJTs.

In high-current applications, the I2R losses in a MOSFET can far exceed the ICVCE(SAT) losses in a BJT. This is why IGBTs are often preferred in high-power equipment.

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    \$\begingroup\$ .. in high frequency switching, the gate drive power requirements of a MOSFET can be higher than an equivalent BJT. \$\endgroup\$ – Spehro Pefhany Mar 15 '14 at 1:27

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