Without doubt, VLSI is top branch of ECE which fascinates many graduates and also a hot cake, henceforth making it a very competitive branch to get into even in your Mtech.
Roughly one can divide VLSI into 3 specializations:
Analog VLSI
Digital VLSI
Device Electronics
Analog VLSI --- is something that really fascinates many VLSI students but often, doesn't become a career option for many of those bright students. It is much more than the coding stuff. Analog needs your thinking cap to be on always. It needs understanding of device physics too to a reasonable extent.
Any chip that gets taped out has all blocks of analog, digital. Band gap ckts, Reference current sources, IO components, PLLs, Amplifiers, filters, transmitters, receivers and many blocks are all analog in nature.
Most of the digital stuff are coded and even the interface circuits that is A/D convertors, sensors, and D/A convertors are all analog blocks !!!
The real world is analog in nature and any advancements we talk about DSP, can be appreciated only if u have proper interface circuits to convert the analog signal to digital and do DSP and convert it back to analog again.