It's anecdotal, but this is exactly what I've experienced. I'm a Caltech EE (~5 years in industry), and have about a dozen friends here in the valley. The ones that went to Google/Facebook/Amazon have had significantly higher starting salaries (about 2x, though as time has passed the gap is closing) than what I started with at a chipmaker company. I do think there is a wage problem. We've all heard that the only way to get meaningful pay increases is to switch companies every few years. Rents are ridiculous, and graduating students just don't have the money to live where they work, making a high starting salary extremely attractive. Some companies, like the one I used to work at, are also moving jobs offshore because it's significantly cheaper, and when you hear that kind of story, you wonder if it won't be your job next. Verification is almost entirely gone overseas at my previous company, and they had begun moving design teams when I left. Given the choice of lower starting pay, having to change jobs every few years, and a feeling of job insecurity, is it really any wonder that most talented students choose to go to Google or Facebook? Further making things worse from a talent-recruitment standpoint, most non-Googles/Facebooks just don't offer the same kind of job amenities and tend to suffer due to their more corporate image. Google and Facebook have made huge pushes to show off how "fun" it is to work for them, and made their campuses more like universities, offering lots of open green space, and areas for hobby work (like woodshops, metalshops, full kitchens, etc). They all offer amazing quality and variety of on-campus food options, and have various on-campus services like child care, laundry service, bus shuttles, etc. Most hardware companies I interviewed at were fairly plain office complexes with not much in the way of non-work amenities. An onsite cafeteria serving burgers and fries was touted as a big plus at my previous employer. Even if the pay were the same, all the other little things add up. It's not just about "awareness". Would it be better to get more graduates to know your company exists? Absolutely, but then the offer you present has to be competitive with what Google can offer.
A couple of questions: What type of EE talent are they missing? PhD Level? BS Level? Entry level? Mid-career clevel? Do these chip vendors make extensive use of ATS systems, which are a headache for job applicants and often filter out well-qualified candidates? Are they really missing talent, or are they missing talent that they can pay at a sub-standard level?
Without a relationship with consumers, without marketing budgets, scale and transparency, how can anyone expect awareness. People don't even know what's inside their phones and info is scarce even if someone is interested. Maybe a platform like WikiChip could be turned into a real thing and include info that consumers might care more about - price, die shot and so on. The fact that major conferences (like IEDM, ISSCC or Hot Chips) are not live streamed, even today, is just silly and a bit ironic as nowadays even toasters are online. You can't do without both transparency and marketing $$$.
Events in schools are as archaic as using pigeons to deliver mail. Use the internet, that's why it exists.
Anyway, awareness will decline further as software and services grow much faster in terms of revenue and are in direct contact with consumers.
Companies which a) use Taleo, and b) post on Taleo sleep-inducing job ads shouldn't be described exactly as 'rallying".
Who needs Ambien when you can read https://appliedmat.taleo.net/careersection/10020/jobsearch.ftl ?