Calibration of GaAlAs Semiconductor Diode

The forward voltage of GaAlAs semiconductor diode has been measured in the temperature range 50 K 300 K and for current values between 10 nA and 450 μA. The forward voltage as a function of temperature is least-squares fitted and the coefficients are given. The 1st and 2nd order least-squares fitting has high temperature root between 400 K and 950 K. The presence of the high temperature root indicates that the fitted polynomials are of similar character. The high temperature root is found to increase for the least squares fitted polynomials corresponding to higher current values.


Introduction
GaAlAs semiconductor diodes have been used in the measurement of low temperatures in the presence of magnetic field.The measurement of low temperature using GaAlAs diodes is based on the usual observation that the voltage across the forward-biased diode increases with decrease in temperature [1][2][3][4][5].The behavior of the diode has been understood in terms of conduction primarily by recombination-generation currents given by the theory of Shockley and coworkers [6].Below about 50 K, the forward voltage increases more rapidly as the temperature is reduced, which gives rise to a bend in the temperature dependence of forward voltage [7][8][9].The diodes are generally calibrated with 10 µA of forward current.The factors among others which decide the use of GaAlAs semiconductor diodes for the measurement of low temperature are sensitivity, linearity, stability, power dissipation and noise [10][11][12][13][14][15][16].The GaAlAs diodes can possibly be used in the ultra low temperature range (0.05 -1 K) by reducing the forward current to ~10 nA.In certain possible applications of semiconductor diodes for temperature measurement, a high precision in the measurement of temperature is needed.Such situations include, the measurement of temperature drift curve in low temperature heat pulse calorimetry [17].In this article we have studied the calibration of GaAlAs diode and report the coefficients for five decades of current values, 10 nA to 450 μA and in the temperature range 50 K -300 K.
In this paper, we give the temperature dependence of forward voltage of GaAlAs diode for various current values between 10 nA and 450 µA and in the temperature range 50 K to 300 K.The paper is organized as follows.
In the following Section 2, the experimental details are given.Section 3 gives the least-squares fittings.The paper concludes with the conclusions in Section 4.

Experimental Details
The measurements were carried out using a computer controlled four-probe setup built around a closed cycle refrigerator [18].The diode in the CU package configuration is epoxied into a flat cylindrical disk and the sensor leads are thermally anchored to the same disk.The metal encapsulation of the diode was fixed to the sample space of the closed cycle helium refrigerator with 0.2 mm thick indium foil and a thin layer of Apiezon-N grease by clamping with an aluminum disk with screws using moderate pressure.The leads were further anchored at the sample space to minimize any thermoelectromotive force developed.The temperature of the sample site was controlled using a calibrated type-D silicon diode thermometer in conjunction with a Leybold model LTC60 temperature controller (Leybold AG, Germany).The setup is automated using GPIB-IEEE-488 interface and the control program is written in MSDOS GWBAS-IC.Measurements were carried out between 50 K -300 K, for forward current from 10 nA to 450 μA.The temperature increment was 10 K and the current increment was in 11 equal logarithm interval.Each data point was obtained by averaging 50 reading.A constant current was provided to the GaAlAs diode from a Keithley (Keithley Instruments, USA) model 224/2243 programmable current source.The forward voltage was measured using a Keithley model 182 sensitive digital voltmeter.

Least Squares Fitting and Discussions
The forward current I f is related to the forward voltage V f in a GaAs p-n junction, as follows: where q is the electronic charge, k is the Boltzmann constant, T is the temperature, and η is the ideality factor [19,20].Depending on the value of η, four operating regions have been defined: recombination, diffusion, high injection and series resistance regions.The Equation ( 1) gives rise to a linear temperature dependence of V f , for a fixed value of current.However, for extended temperature range (~100 K), there is significant deviation of linearity.Therefore, the semiconductor diode are generally calibrated with respect to standard and interpolation data is made.However, in some situations a lower order polynomial covering a large temperature range is needed.The least-squares fitting provides such a polynomial.First the temperature is determined using the calibrated voltage value of the GaAlAs diode for 10 μA of current, which was provided by the manufacturer.The measured voltage as a function of temperature, for various current values, was then least-squares fitted to the following polynomials: For the 1st order least squares fitting, there are two coefficients, which are given in Table 1, for various values of current.The coefficient a 0 and a 1 are found to be positive and negative, respectively.The R 2 of the least squares fitting was nearly 1.00.There is high temperature root T 0 , for the least squares fitting, which is found to increase as the corresponding values of the current is increased from 10 nA to 450 μA.The T 0 is 454.100K and 949.350K for 10 nA and 450 μA, respectively.The presence of the high temperature root indicates that the fitted polynomials are of similar character.In case of 1st order least squares fitting the coefficient a 1 , represents the average sensitivity of the diode, which is found to decrease with increase in current.a 1 varies from −3.562 × 10 −3 to −1.706 × 10 −3 V/K as the current is increased from 10 nA to 450 μA.The coefficients a 0 represent the extrapolated voltage at zero temperature, which was nearly constant and have a value of 1.6 V.
In case of the 2nd order least squares fitting, there are three coefficients, which are given in Table 2.The coefficient a 0 is found to be positive, whereas, the coefficients a 1 and a 2 are found to be negative.The R 2 of the least squares fitting was nearly 1.00.It is seen from Table 2 that there is high temperature root T 0 for all values of current.The T 0 increased from 411.637 K to 790.460 K as the current is increased from 10 nA to 450 μA.The presence of the high temperature root indicates that the fitted polynomials are of similar character.The coefficient a 0 varies more compared to the 1st order leastsquares fitting for different values of current.The coefficient a 0 is nearly 1.5 V, which lower compared to that in the case of 1st order.The minimum of the coefficient a 1 occurs for a current value of 30 µA.Here, the coefficient a 2 represents the deviation from linearity.It is seen from Table 2 that, there is maximum deviation from linearity, for current of 10 μA.The reason for choosing the 50 -300 K range is that for low currents (~10 nA) the least squares fitting extends to ~50 K without systematic deviation.Moreover, the I-V characteristic changes significantly below 50 K.
In case of 3rd and 4th order least-squares fitting (Tables 3 and 4) there were no high temperature roots for all current values.Therefore, we conclude that the fitted polynomials for different values of current are not of similar nature.

Conclusions
The forward voltage of GaAlAs semiconductor diode is measured at low temperatures.The data is obtained for current values between 10 nA and 450 μA and in the temperature range 50 K to 300 K.The voltage as a function of temperature is least-squares fitted to polynomials.From the second order fitting it is found that there is maximum deviation from linearity, for current of 10 μA.There are high temperature roots for all current values, in case of 1st and 2nd order least-squares fittings.
There were no high temperature roots for all current values for 3rd and 4th order fitted polynomials.
Further study is being carried out on the 1/f noise which has been found to be c rrent dependent.u