Jumping into a VLSI based career?
VLSI is a composed of multiple disciplines each of which are highly sought. Making it simpler though, it has three categories,
Front end(RTL Design,microarchitecture,Functional Verification,Synthesis, etc)
Back end(Floorplanning ,Placement and Routing, Timing and Clock Tree Synthesis, etc)
Silicon Validation and testing SW and HW framework and test generation for silicon testing in lab
Some of the important field the companies look for expertise in are
Digital Electronics/Digital Logic/Computer Architecture: Combinational/Sequential circuits, logic design using Gates, State machines, etc.
Programming Basics/HDL:From basic concepts to programming questions or design implementation, verification methodologies, and scripting languages like Perl/Python, etc.
MOS Transistors/Circuits/Clock Tree: MOS transistor theory, process technologies, cross talk and transmission line effects, Clock Tree, and Power distribution mechanisms, Timing analysis, buffer modeling, etc.
These are some of the VLSI giants in the industry
Intel
Nvidia
Qualcomm
Broadcom
Samsung
Texas Instruments (TI)
AMD
ARM
Analog devices Inc
ST Microelectronics
MediaTek
Nxp Semiconductor
Some EDA companies related to VLSI — Tools as well as IP designs
Cadence
Mentor Graphics
Synopsis