Calibration of GaAlAs Semiconductor Diode

doi:10.4236/jmp.2012.310184

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Journal of Modern Physics, 2012, 3, 1490-1493

http://dx.doi.org/10.4236/jmp.2012.310184 Published Online October 2012 (http://www.SciRP.org/journal/jmp)

Calibration of GaAlAs Semiconductor Diode

S. B. Ota1, Smita Ota1,2

1Institute of Physics, Bhubaneswar, India

2DST Project, DST, New Delhi, India

Email: [email protected]

Received July 29, 2012; revised September 1, 2012; accepted September 11, 2012

ABSTRACT

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.

Keywords: Semiconductor; Temperature Sensors; GaAlAs

1. 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 [1-5]. The behavior of the

diode has been understood in terms of conduction pri-

marily 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 [7-9]. 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 [10-16]. 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 cer-

tain possible applications of semiconductor diodes for

temperature measurement, a high precision in the meas-

urement of temperature is needed. Such situations in-

clude, 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 pa-

per concludes with the conclusions in Section 4.

2. 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 configu-

ration is epoxied into a flat cylindrical disk and the sen-

sor 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 an-

chored at the sample space to minimize any thermoelec-

tromotive force developed. The temperature of the sam-

ple 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 tem-

perature 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 cur-

rent source. The forward voltage was measured using a

Keithley model 182 sensitive digital voltmeter.

S. B. OTA, S. OTA 1491

3. Least Squares Fitting and Discussions

The forward current If is related to the forward voltage Vf

in a GaAs p-n junction, as follows:



IexpqVkT





iT;n14

(1)

where q is the electronic charge, k is the Boltzmann con-

stant, T is the temperature, and η is the ideality factor

[19,20]. Depending on the value of η, four operating re-

gions have been defined: recombination, diffusion, high

injection and series resistance regions. The Equation (1)

gives rise to a linear temperature dependence of Vf, for a

fixed value of current. However, for extended tempera-

ture range (~100 K), there is significant deviation of li-

nearity. Therefore, the semiconductor diode are generally

calibrated with respect to standard and interpolation data

is made. However, in some situations a lower order po-

lynomial 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 po-

lynomials:



 (2)

For the 1st order least squares fitting, there are two

coefficients, which are given in Table 1, for various val-

ues of current. The coefficient a0 and a1 are found to be

positive and negative, respectively. The R2 of the least

squares fitting was nearly 1.00. There is high temperature

root T0, 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 T0 is 454.100 K

and 949.350 K 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 a1, represents

the average sensitivity of the diode, which is found to

decrease with increase in current. a1 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 a0 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 coef-

ficient a0 is found to be positive, whereas, the coeffi-

cients a1 and a2 are found to be negative. The R2 of the

least squares fitting was nearly 1.00. It is seen from Ta-

ble 2 that there is high temperature root T0 for all values

of current. The T0 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

Table 1. The 1st order least squares fitting of GaAlAs diode.

Current a0 a1 R2 T0 (K)

10 nA 1.61769 −3.56241 × 10−3 1.00 454.100

30 nA 1.62027 −3.56578 × 10−3 1.00 481.395

100 nA 1.62279 −3.15623 × 10−3 0.99 514.155

300 nA 1.62340 −2.96112 × 10−3 0.99 548.239

1 μA 1.62220 −2.74034 × 10−3 0.99 591.970

3 μA 1.61955 −2.53210 × 10−3 0.99 639.607

10 μA 1.61480 −2.29636 × 10−3 0.99 703.200

30 μA 1.60964 −2.08137 × 10−3 0.99 773.356

100 μA 1.60706 −1.87127 × 10−3 0.99 858.807

300 μA 1.61385 −1.73685 × 10−3 0.99 929.182

450 μA 1.61999 −1.70642 × 10−3 0.99 949.350

the fitted polynomials are of similar character. The coef-

ficient a0 varies more compared to the 1st order least-

squares fitting for different values of current. The coeffi-

cient a0 is nearly 1.5 V, which lower compared to that in

the case of 1st order. The minimum of the coefficient a1

occurs for a current value of 30 µA. Here, the coefficient

a2 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 de-

viation. Moreover, the I-V characteristic changes sig-

nificantly below 50 K.

In case of 3rd and 4th order least-squares fitting (Ta-

bles 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.

4. 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 func-

tion 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 crrent dependent. u

S. B. OTA, S. OTA

1492

Table 2. The 2st order least squares fitting of GaAlAs diode.

Current a0 a1 a2 R2 T0 (K)

10 nA 1.54101 −2.49623 × 10−3 −3.03030 × 10−6 1.00 411.637

30 nA 1.54291 −2.29010 × 10−3 −3.05732 × 10−6 1.00 428.549

100 nA 1.54063 −2.01391 × 10−3 −3.24671 × 10−6 1.00 445.308

300 nA 1.53514 −1.73395 × 10−3 −3.48788 × 10−6 1.00 459.896

1 μA 1.52699 −1.41643 × 10−3 −3.76282 × 10−6 1.00 476.041

3 μA 1.51931 −1.13836 × 10−3 −3.96129 × 10−6 1.00 492.070

10 μA 1.51420 −8.97665 × 10−4 −3.97539 × 10−6 1.00 514.505

30 μA 1.51854 −8.14531 × 10−4 −3.60063 × 10−6 1.00 546.084

100 μA 1.54048 −9.45485 × 10−4 −2.63127 × 10−6 1.00 606.295

300 μA 1.58091 −1.27878 × 10−3 −1.30194 × 10−6 0.99 715.318

450 μA 1.60155 −1.44998 × 10−3 −7.28841 × 10−7 0.99 790.460

Table 3. The 3rd order least squares fitting of GaAlAs diode.

Current a0 a1 a2 a3 R2 T0 (K)

10 nA 1.49824 −1.52918 × 10−3 −9.20392 × 10−6 1.17004 × 10−8 1.00 454.69

30 nA 1.48601 −1.00362 × 10−3 −1.12708 × 10−5 1.55664 × 10−8 1.00 428.55

100 nA 1.47027 −4.22960 × 10−4 −1.34033 × 10−5 1.92490 × 10−8 1.00 -

300 nA 1.45653 4.36255 × 10−5 −1.48359 × 10−5 2.15070 × 10−8 1.00 -

1 μA 1.44679 3.97017 × 10−4 −1.53398 × 10−5 2.19409 × 10−8 1.00 -

3 μA 1.44864 4.59626 × 10−4 −1.41628 × 10−5 1.93341 × 10−8 1.00 -

10 μA 1.46903 1.23853 × 10−4 −1.04967 × 10−5 1.23594 × 10−8 1.00 -

30 μA 1.50732 −5.60957 × 10−4 −5.21944 × 10−6 3.06799 × 10−9 1.00 587.04

100 μA 1.57098 −1.63505 × 10−3 1.77085 × 10−6 −8.34299 × 10−9 1.00 524.02

300 μA 1.65570 −2.96994 × 10−3 9.49439 × 10−6 −2.04614 × 10−8 1.00 498.49

450 μA 1.69658 −3.59868 × 10−3 1.29884 × 10−5 −2.59971 × 10−8 0.99 489.30

Table 4. The 4th order least squares fitting of GaAlAs diode.

Current a0 a1 a2 a3 a4 R2 T0 (K)

10 nA 1.42610 7.24218 × 10−4 −3.23316 × 10−5 1.06777 × 10−7 −1.35152 × 10−10 1.00 389.77

30 nA 1.40344 1.57558 × 10−3 −3.77412 × 10−5 1.24385 × 10−7 −1.54686 × 10−10 1.00 -

100 nA 1.38432 2.26200 × 10−3 −4.09602 × 10−5 1.32534 × 10−7 −1.61035 × 10−10 1.00 411.15

300 nA 1.38030 2.42464 × 10−3 −3.92733 × 10−5 1.21968 × 10−7 −1.42805 × 10−10 1.00 427.38

1 μA 1.39792 1.92366 × 10−3 −3.10084 × 10−5 8.63539 × 10−8 −9.15631 × 10−11 1.00 463.60

3 μA 1.43889 7.64118 × 10−4 −1.72879 × 10−5 3.21814 × 10−8 −1.82625 × 10−11 1.00 792.82

10 μA 1.50556 −1.01745 × 10−3 1.21696 × 10−6 −3.57950 × 10−8 6.84515 × 10−11 1.00 -

30 μA 1.57724 −2.74504 × 10−3 1.71968 × 10−5 −8.90838 × 10−8 1.30994 × 10−10 1.00 -

100 μA 1.67849 −4.99342 × 10−3 3.62394 × 10−5 −1.50041 × 10−7 2.01425 × 10−10 1.00 -

300 μA 1.82753 −8.33737 × 10−3 6.45827 × 10−5 −2.46927 × 10−7 3.21921 × 10−10 1.00 -

450 μA 1.90347 −1.00615 × 10−2 7.93194 × 10−5 −2.98681 × 10−7 3.87620 × 10−10 1.00 -

S. B. OTA, S. OTA 1493

5. Acknowledgements

The author is benefited from his visit to Europe in

1988-1992 for HTSC research, Xiamen, China during

1995 for statistical physics conference and New Orleans,

USA during 2008 for APS March meeting. We ac-

knowledge Dr. C. Iannicello and others of American In-

stitute of Physics for providing access to the URL of AIP

UniPHY.

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