Yes it can be done.
Usually, this type of diode is called zener shunt voltage regulator or shunt references; it can be a 2 or 3-terminal device.
Two terminal devices rely only on the zener b2b tunneling quantum breakdown effect for generating a fixed voltage drop.
Three terminal devices work in closed loop: you put a voltage divider at the output and feed the divided voltage to the additional "control terminal", so that a closed loop is used to compensate temperature and load variations. You can check LM4041 datasheet as an example.
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