Transmission rates through tunnel diode potential barriers

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PsychonautQQ
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Can somebody help me understand why it is possible to have a 100% transmission rate through both potential boundaries created by a tunnel diode, while the transmission rate through only one of the walls can be very small??
 

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The fact there are two barriers in the second example and only one in the first is what makes the difference - the wavefunctions do not interact with one barrier and then the other one - but the two barriers together make an entire system that informs the whole wavefunction in one go.

The peicewise analysis you may have met is just a mathematical convenience.