The correct thing to do if you want your phone not to be searched is to shut it off. The tools used to search phones generally work with unpatched vulnerabilities and you don’t want to do anything that looks like tampering with evidence.
When off the encryption of the device will be most effective and resilient to attack because nothing will be unencrypted until you enter your passcode at boot.
If you haven't altered, destroyed, or concealed the physical phone in any way, then why would turning it off be considered tampering with evidence? Also, I believe there would be a burden to prove that some material stored on the phone would constitute "evidence." Pretty hard for the cops to do that if they can't get into the phone.
When off the encryption of the device will be most effective and resilient to attack because nothing will be unencrypted until you enter your passcode at boot.