Under the Constitutional Law 

Article III, Section 1 states that judges of Article III courts shall hold their offices "during good behavior." "The phrase "good behavior" has been interpreted by the courts to equate to the same level of seriousness 'high crimes and misdemeanors" encompasses.

In addition, any federal judge may prosecuted in the criminal courts for criminal activity. If found guilty of a crime in a federal district court, the justice would face the same type of sentencing any other criminal defendant would. The district court could not remove him/her from the Bench. However, any justice found guilty in the criminal courts of any felony would certainly be impeached and, if found guilty, removed from office.

In the United States, impeachment is most often used to remove corrupt lower-court federal judges from office, but it's not unusual to find disgruntled special interest groups circulating petitions on the internet calling for the impeachment of one or all members of the High Court. His un fit to hold the position as well wrong for the country