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SDN0013.06 – Temperature Calibration

  

1. Introduction

 The purpose of this design note is to summarize the calibration of the temperature sensors that will be used in the testing of the GNIRS mechanisms and within the instrument itself.

 The temperature sensors used in cryogenic instruments are usually diodes, for which the forward bias voltage is a function of temperature.  This voltage is a very weak function of bias current, but a value of 10 mA is typically used to minimize the ohmic heating in the sensor and voltage drops in the leads, which are typically small gauge of low thermal conductivity materials such as manganin.  With this bias current, the effective sensor resistance is ~ 100 KW and is much greater than the lead resistance, making a 4-lead arrangement unnecessary.

 2.      Sensors

 Temperature sensors may be purchased commercially from vendors such as Lakeshore Cryotronics.  Those which are useful in the temperature range of interest to us are based on the DT-470 diode and are individually certified and calibrated over the temperature range 10 – 340 K.  Although reliable and accurate, there is a cost associated with their certification, and they are sufficiently expensive to have been used historically at NOAO only for applications where a precision temperature measurement (e.g., an IR array) is warranted.

 General-purpose temperature sensors are made from 1N914 diodes, which are purchased in bulk and tested by immersion in LN₂ to cull those that fail to survive cryogenic temperatures.  The diodes themselves, approximately 1 mm diameter and 2 mm long, are epoxied into copper blocks (5 X 5 X 12 mm, with a 4-40 clearance hole) for mounting at strategic points within instrumentation.

 3.      Calibration Curve

 Both Lakeshore DT-470 and 1N914 diodes show a similar behavior of forward bias voltage with temperature, although the actual curves are quite distinct (Fig. 1).  The voltage/temperature relation is almost linear over a wide range with an approximate slope of –2.5 mV/K.   There is a sharp “knee” at about 30 K for DT-470 diodes (~40K for 1N914 diodes), below which the slope increases sharply.  This behavior results from carrier freezeout, so there is greater variation in the calibration of individual sensors in this low temperature regime.

 Large complex instruments such as Phoenix and GNIRS have a large number of temperature sensors installed at critical points to monitor temperature during cooldown and steady-state operation.  This is particularly important during the initial testing phases of the instrument.   Since all points within these instruments, except for the second stage of the cryocooler and the detector mount, are within the linear range of the 1N914 diodes, these relatively inexpensive sensors are used. 

We have calibrated a number of 1N914 diodes against two calibrated Lakeshore DT-470 diodes to produce a generalized calibration curve for the 1N914 over the range 40 – 340 K.  Although the 1N914 sensors are often considered less accurate than the Lakeshore sensors, this may be a result of the latter sensors being individually selected and calibrated.  Our initial tests suggest that the 1N914 sensors may be accurate to at least 1 K after applying a zero-point correction based on individual calibration at LN₂ temperature.

 The calibrations for both diodes are in the file "Temp9911.xls".  For automatically logging the temperatures during testing and operation of the instruments, we have generated polynomial fits to the calibration curves.

 T = a + b*v + c*v² + d*v³ + e*v⁴ + f*v⁵

The calibration curve in the region of the knee (24 - 32K) is sufficiently sharp that it cannot be fit well with a polynomial of low order.  One may use the m=5 polynomial coefficients if one is working at T > 32 K or T < 24 K.  If one wishes to cover the entire calibration range, one may use the lookup table "Temp9911.xls", or the polynomial coefficients for T > 32 K and the lookup table for T < 32 K (the lookup table uses the polynomial fit for T > 32 K and is generated in voltage increments of 1 mv).  The polynomial coefficients for the 1N914 are sufficient for T > 42 K. 

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