Write a file replacement powershell or batch script to replace undesirable files with a boilerplate file

I need someone that can write a PowerShell script (or even a bat script would probably be fine) that will recursively search through a directory tree of documents looking for files of 0 byte (they are corrupt files) and replace them with a small text file. The replacement file needs to be assigned the name as the file that was found and it needs to kept in the same location. For example (as per the attached sketch), you start the search from c:\files which contains multiple subfolders one of which might be called August which also has multiple subfolders one of which might be called 3rd and within this subfolder there is a zero byte file called 034323.1, this file needs to be replaced with a predetermined text file that gets copied into the 3rd folder and given the same name of 034323.1. The script then moves on through the rest of the directory structure taking exactly the same approach with any other zero byte file encountered but ignoring/leaving every file that has a size greater than zero. The basic functionality would be: 1. specify the starting location 2. specify the file that will be the 'boiler plate file' 3. write a log that includes every file touched/replaced and where it was found 4. preferably have the ability to include a date element which provides a mechanism to say 'update all files that were created before <this date> and are zero bytes'.