Chip Antennas on Substrate

Hi,
I am interested in learning more about Chip antennas on Silicon Substrates. I understand that they tend to be lossy due to the Silicon underneath.

All the papers I have read till now mention this issue in a qualitative sense and show measurement results.

I am looking for literature where someone had theoretically shown the effect of Substrate losses for any antenna. Even hertzian dipole will be fine. Some of the questions I am interested are in

- What are the loss components
- How do they change with distance to semiconductor and resistivity of semiconductor

Is there any publication that can help me with these questions. I have access to IEEE Xplore and Web of Science so I can dig up papers.

Thank you