What half-bandgap voltage reference is?
A bandgap voltage reference is a circuit that is relatively easily made on an integrated circuit. The basic premise is that it uses two different sized NPN transistors driven at the same current, and the sum of these two voltages can be an accurate reference voltage near the bandgap voltage of silicon at 0K, which is 1.25eV. There are many descriptions of the circuit, which began as the Brokaw cell, then the Widlar bandgap, and then the many variations you can see today. The Wikipedia page is a decent brief read. 

It has several benefits: 


It gives roughly the same result regardless of power supply (PSRR)
It can be temperature-compensated to give a very flat response over temperature
It derives its accuracy from the ratio of transistors instead of the absolute value of components, which is a major benefit for integrated circuits.


The traditional method for generating the reference voltage is to add the voltages at the two paths, which will give the typical bandgap voltage of 1.25V, or two forward diode drops. As supply voltages have dropped, there has been a push for lower output voltages. They typically use more current mirroring to derive an output voltage that is closer to a single diode drop. 

While I have never seen the term "half-bandgap" while doing research on low-voltage reference circuits, there are plenty of bandgap reference based circuits with an output voltage of 0.5 - 0.7V.