(D) In counties having a population in excess of three hundred thousand as ascertained by the federal census, one or more psychiatrists, psychologists, or other examiners or investigators, who shall take an oath of office, hold their positions at the will of such judges, and receive compensation to be fixed by the judges appointing them, not exceeding in the aggregate such amount as is appropriated therefor by the board of county commissioners, which compensation shall be in place of all fees. Such compensation so fixed shall be payable monthly from the county treasury upon the warrant of the auditor. Such employees, whenever called upon by a judge of such court, in a criminal case, shall perform the duties which are prescribed by section 2947.06 of the Revised Code respectively for psychiatrists or psychologists appointed in the particular case, or for probation officers or departments.