I'm new in NFC thing, so I tested several phones with calling getTagId() method in HCE mode, and this is the result:
device | UID
LG G2 | random
LG G3 | static
S4 | random
HTC One Mini | static
Xiaomi mi3 | static
My questions:
Any documents that can explain/support the answer?
Why do some phones have static UID and some do not? Is this chipset related?
That depends on the chipset and the implementation of the NFC stack. As far as I'm aware of, there are three different scenarios used by various Android NFC devices:
Is it possible to get a fixed UID?
Typically, you can't influence this. Specifically without modifying the Android device firmware (changes to the NFC stack) it's definitely not possible. See this answer for a method to set the UID value on Broadcom chipsets through modifying the libnfc-nci library.
I need it to authenticate the device.
Don't do this! See this answer for more information on that.