If you finish the course in VLSI then there are number of opportunities available for you. Some of these career options are from the companies such as :
3. Texas Instruments
4. Alliance Semiconductor
and many other companies out there. Mostly packages start from 20L onwards if recruited by these companies for R&D purpose.
The most common jobs in this field are some of these :
1. ASIC frontend designer
2. FPGA frontend designer
3. ASIC physical design engineer
4. AMS (Analog Mixed Signal) designer
5. IP design engineer Verification Engineers
6. Front-end verification engineer
And most of the other jobs depending on the specific set of skill. I think every engineer starts with the knowledge required for the basic skills and then grows on for the higher job.
Considering the growth of the digital signal processors and the high performance computing, in future there is a lot of demand. So it is one of the financially lucrative and challenging field for those who wish to get a better career.