As the rest of the country fights stubbornly high unemployment, the shortage of qualified engineers has grown acute in the last six months, tech executives and recruiters say, as the flow of personal or venture capital investing has picked up. In Silicon Valley, along the southern portion of the San Francisco Bay in California, and other tech hubs like New York, Seattle and Austin, Tex., start-ups are sprouting by the dozen, competing with well-established companies for the best engineers, programmers and designers. At the same time, all the companies are seeking ever more specialized skills.

And there has been a psychological shift; many of the most talented engineers want to be the next Mark Zuckerberg, not work for him.

Shannon Callahan, who recruits engineers for the venture capital firm Andreessen Horowitz’s portfolio of companies, said a third of the engineers she called ask for financing to start their own companies instead.

“They have that entrepreneurial spirit and you want to talk to them because you know they’d do great in a small environment working a million hours a week, but those folks are saying, ‘Actually, I think I want to do my own thing,’ ” she said.

In an only-in-Silicon-Valley twist, start-ups are acknowledging this phenomenon by recruiting ambitious engineers with promises to help them to leave someday to start their own, potentially competitive companies.

“It’s less about us competing against start-ups and more against the person who wants to start their own thing,” said Dave Morin, co-founder and chief executive of Path. Mr. Morin, an early Facebook employee, knows the type because he was one of them. He tells recruits that he will help them start their own companies down the road, by advising or investing in them.