The word 'semiconductor industry' does not hold a definite meaning today. In a vague sense it has to do something with semiconductor to be a semiconductor industry. Thus google, youtube, facebook are also semiconductor industry, although more precisely they can be regarded as software industry.
I'm just assuming here that you are actually interested in hardware industry. Then you should look for companies like intel, IBM, AMD, HP, Tektronics, Analog Devices, Texas Instruments, Freescale Semi, On Semi, NXP Semi, Cadance, Synopsys, TSMC, UMC and numerous others. Some of them design and manufacture hardwares, some of them provides foundry services and others make EDA tools.
If I am not much wrong most of the companies have their base in San Jose and a few towns around the Silicon Valley. Others have bases in Germany, China, Taiwan or Japan.