ethereum – How to connect ethers.js library with Rinkeby programmatically?

According to official docs of ethers.js, this should be the way how to connect to a specific network like Rinkeby-testnet with custom data:

 const provider = ethers.getDefaultProvider(network, {
    etherscan: ETHERSCAN_API_KEY,
    infura: INFURA_API_KEY,

Also, this would be the way to get a signer in order to sign transactions:

 const signer = provider.getSigner()

However, there is now method “getSigner” available on the default provider.

TypeError: provider.getSigner is not a function

How to achieve that using ethers.js?