how to upgrade production PostgreSQL from 9.4 to 11.3

We have 2 TB of data on our production server, we want to use 11.3 or latest stable version of PostgreSQL as our DB server on aws EC2 instance.

I have tried couple of way to upgrade but they are not production friendly:

I have tried pg_upgrade but as it require to stop the server we can't do it.

I have tried with --link option too but it also take time.

I have created replication and I tried to take pg_basebackup using 11.3 version but the backup was created with 9.4 version.

I have also tried to do the same with pglogical but it is showing pglogical schema not found.

please tell me the proper way to upgrade our 2TB of production database.

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