Determining the thermal response time of temperature sensors embedded in semiconductor wafers

Abstract

We present a non-contact method for the determination of the thermal response time of temperature sensors embedded in wafers. In this method, a flash lamp illuminates a spot on the wafer in periodic pulses; the spot is on the opposite side from the sensor under test. The thermal time constant of the sensor is then obtained from measurement of its temporal response, together with a theoretical model of heat flows both into the sensor and laterally within the wafer. Experimental data on both platinum resistance thermometers (PRTs) and on thermocouples embedded in silicon wafers show good agreement with the heat transfer models. Values of the thermal response time for a wide range of experimental parameters agree to within standard deviations of 8% (PRTs) and 20% (thermocouples), demonstrating the self-consistency of our results. The method is directly applicable to determining the thermal properties of sensors used in instrumented silicon wafers. We anticipate that the method will have use in development of new sensor attachment methods, in verifying the proper attachment of sensors during production, and in confirming that the thermal attachment has not degraded with age or thermal cycling. To simplify the application of the method, we have produced a table of calculated relevant quantities to be used in relating the measured signal to the thermal response time.

Dynamic Characterisation of Fibre-Optic Temperature Sensors for Physiological Monitoring

“…The experiments found that the time constants of the sensors were in the range 2.55 ms to 6.24 ms in air, 1.24 ms to 2.37 ms in still water and 1.20 ms to 1.83 ms in stirred water. These results compare favourably with response times measured in FBG based sensors [ 17 , 18 , 35 , 36 ], and to electrical temperature sensors that have been characterized using optical heating methods [ 71 , 73 ]; faster response times have been measured with fibre optic temperature sensors based on silicon FP cavities [ 50 ] and thin-film thermocouples [ 72 ]. The sensor responses to optical heating were also highly repeatable within each sensor, showing impulse response curves having a consistent form and magnitude across multiple laser pulses, and reproducible, with similar measured impulse response curves and time constants across all sensors tested.…”

“…A ramped temperature input can also be used for measuring the dynamic temperature response [ 37 , 68 , 70 ]; however, the minimum measurable time constant is limited by the gradient of the ramp [ 68 ]. Other approaches include heat-transfer modelling [ 35 ], and optical heating methods: several investigators have studied the dynamic responses of thermocouples and resistance thermometers using pulsed or modulated light to induce rapid temperature cycles [ 71 , 72 , 73 , 74 , 75 ].…”

Measurements of instantaneous heat transfer in a two-dimensional T-junction using a multi-thermocouple probe

“…Results are first shown for the streamwise evolution of the mean and RMS values of the wall heat flux. This is portrayed in figure 6, where the error bars indicate the uncertainties obtained from (19). Close to the secondary flow slot (x 3D), the mean heat flux is negative, which indicates that the wall is heating the fluid in this region, i.e.…”

“…The uncertainty in the measurement of the heat fluxes u( w ) was estimated by following the basic principles of uncertainty propagation [19]. After the mathematical manipulation of expressions ( 6), ( 15) and ( 16) in terms of the spatial uncertainty u( y) and the uncertainty in temperature differences u( T), one obtains…”

Heterodyne lock-in thermal coupling measurements in integrated circuits: Applications to test and characterization

“…Practical applications consist of extracting the information from one of these entities when the other ones are already known. [1][2][3] The use of lock-in amplifiers allows measuring the amplitude and phase of one spectral component of the sensed temperature 4,5 when the dissipating device operates in a modulated regime. Being very sensitive to small temperature increases and robust to noise, this sensing strategy is suitable for temperature measurements in low-power circuits.…”