System and method for determining the temperature of a semiconductor wafer
View Patent ↗A system and method for determining the temperature of a semiconductor wafer at the time of thermal contact of the semiconductor wafer with a temperature sensing element. According to the invention, a temperature profile of the temperature sensing element is recorded from the time of thermal contact up to the time of thermal equilibrium between the semiconductor wafer and the temperature sensing element and the temperature of the semiconductor wafer at the time of thermal contact is determined on the basis of a time period between the time of thermal contact and the time of thermal equilibrium and the temperature T G of the semiconductor wafer reached at the time t G of thermal equilibrium is determined by back calculation with the aid of an equation derived from Newton's law of cooling.
1. A temperature determining device for a receiving device for receiving a semiconductor wafer, with a temperature sensing element, which records a temperature profile for a time period from a first point of time of thermal contact of the semiconductor wafer with the temperature sensing element up to a second time of thermal equilibrium between the semiconductor wafer and the temperature sensing element, and with an evaluation device which determines back at the second point of time the temperature of the semiconductor wafer at the first point of time of thermal contact of the semiconductor wafer with the temperature sensing element based on the time period between the first point of time of thermal contact and the second point of time of thermal equilibrium of the semiconductor wafer and the temperature sensing element and based on a temperature of the semiconductor wafer reached at the second point of time of thermal equilibrium of the semiconductor wafer and the temperature sensing element with use of an equation T 0 =T G *e kΔt +T U *(1−e kΔt ), where T U is an ambient temperature and k is a time constant, the time constant k being determined by an equation k=(α*A)/(c*m), where α corresponds to a heat transfer coefficient of the semiconductor wafer in still air, A corresponds to an area of an entire surface of the semiconductor wafer, c corresponds to a specific heat capacity and m corresponds to a mass of the semiconductor wafer, and
a display element, which is designed to display the temperature of the semiconductor wafer at the time of thermal contact between the semiconductor wafer and the temperature sensing element.
2. A temperature determining device for a receiving device for receiving a semiconductor wafer, with a temperature sensing element, which is designed to record a temperature profile from a time of thermal contact of the semiconductor wafer with the temperature sensing element up to a time of thermal equilibrium between the semiconductor wafer and the temperature sensing element, and with an evaluation device which is designed to determine the temperature of the semiconductor wafer at the time of thermal contact of the semiconductor wafer with the temperature sensing element based on a time period between the time of thermal contact and the time of thermal equilibrium of the semiconductor wafer and the temperature sensing element and based on a temperature of the semiconductor wafer reached at the time of thermal equilibrium of the semiconductor wafer and the temperature sensing element with use of an equation T 0 =T G *e kΔt +T u *(1−e kΔt ), where T u is an ambient temperature and k is a time constant, the time constant k being determined by an equation k=(α*A)/(c*m), where a corresponds to a heat transfer coefficient of the semiconductor wafer in still air, A corresponds to an area of an entire surface of the semiconductor wafer, c corresponds to a specific heat capacity and m corresponds to a mass of the semiconductor wafer; and
a display element, which is designed to display the temperature of the semiconductor wafer at the time of thermal contact between the semiconductor wafer and the temperature sensing element.
3. A receiving device for a semiconductor wafer with a temperature determining device, comprising a temperature sensing element, which is designed to record a temperature profile from a time of thermal contact of the semiconductor wafer with the temperature sensing element up to a time of thermal equilibrium between the semiconductor wafer and the temperature sensing element, and with an evaluation device which is designed to determine the temperature of the semiconductor wafer at the time of thermal contact of the semiconductor wafer with the temperature sensing element based on a time period between the time of thermal contact and the time of thermal equilibrium of the semiconductor wafer and the temperature sensing element and based on a temperature of the semiconductor wafer reached at the time of thermal equilibrium of the semiconductor wafer and the temperature sensing element with use of an equation T 0 =T G *e kΔt +T U *(1−e kΔt ), where T u is an ambient temperature and k is a time constant, the time constant k being determined by an equation k=(α*A)/(c*m), where a corresponds to a heat transfer coefficient of the semiconductor wafer in still air, A corresponds to an area of an entire surface of the semiconductor wafer, c corresponds to a specific heat capacity and m corresponds to a mass of the semiconductor wafer, the temperature sensing element being arranged on a supporting surface of the receiving device that is designed for bearing the semiconductor wafer; and
a display element, which is designed to display the temperature of the semiconductor wafer at the time of thermal contact between the semiconductor wafer and the temperature sensing element.