The full requirements can be found here: https://www.sbir.gov/sites/default/files/elig_size_compliance_guide.pdf
SBIR/STTR program eligibility requirements are in place to ensure that the funds go only to small, independent US businesses. The regulations include restrictions about:
The type of firm
Its ownership structure
The firm’s size in terms of the number of employees.
Type of Firm:
Essentially, the type of firms that qualify are for profit small businesses:
Note: Non‐profit entities are not eligible (except as research institutions under the STTR Program).
If you read the full requirements text you may see the term "business concern", see here for more info on what that means: https://www.law.cornell.edu/cfr/text/13/121.105
Ownership and Control
The SBIR requirements explains this fairly clearly so the following is an excerpt. A majority (more than 50%) of your firms’ equity (e.g., stock) must be directly owned and controlled by one of the following:
One or more individuals who are citizens or permanent resident aliens of the US,
Other for‐profit small business concerns (each of which is directly owned and controlled by individuals who are citizens or permanent resident aliens of the US).
A combination of (1) and (2) above.
Multiple venture capital operating companies, hedge funds, private equity firms, or any combination of these, so long as no one such firm owns or controls more than 50% of the equity.
Note: This option is allowed only for SBIR awards from agencies that are using the authority provided in § 5107 of the SBIR/STTR Reauthorization Act (majority‐VC‐owned authority)
Number of employees in a firm
The size requirement: An SBIR/STTR awardee, together with its affiliates, must not have more than 500 employees.
Again, the full requirements can be found here: https://www.sbir.gov/sites/default/files/elig_size_compliance_guide.pdf