DETERMINATION OF CARRIER TEMPERATURE FROM JUNCTION I(V) MEASUREMENTS

Transcription

1 Journal of Eletron Devies, Vol. 15, 2012, pp JED [ISS: ] DETERMIATIO OF CARRIER TEMPERATURE FROM JUCTIO I(V) MEASUREMETS 1 Mohamed H. Boukhatem, 2 Mario El Tahhi, 3 Pierre Mialhe 1 Département de physique, Collège de l'outaouais, Gatineau (QC), Canada 2 LPA, Department of Physis, Lebanese University-Faulty of Sienes 2, PO Box Jdeidet, Lebanon 3 PROMES et Laboratoire Euro-méditerranéen Sienes et Tehnologies, Université de Perpignan Via Domitia, 52 Avenue Paul Alduy, Perpignan edex, Frane ABSTRACT The arrier temperature differs from the lattie temperature in operating silion juntions. This paper desribes a pratial experiment that an be performed by undergraduate students to introdue and understand the onept of the arrier temperature or the Kineti temperature. An appliation is proposed, for the determination of the semiondutor energy gap at T=0 K, E g (0), from the analysis of the pn juntion urrentvoltage harateristi. Keywords: semiondutor, silion, energy gap, arriers temperature, juntion, thermal potential I. ITRODUCTIO Ideal pn silion juntion I(V) harateristis are often desribed in low injetion onditions by a one exponential model [1-4]: exp V I I 0 (1) VT where I is the load urrent, V is the juntion voltage. In Eq. (1), the thermal potential VT kt e introdues the arrier temperature T and I 0 is the reverse diode saturation urrent. Ideal juntion signifies that the series resistane R s is low, thus the ohmi potential drop in the neutral regions is negligible ompared to the applied voltage ( Rs I V ), and that spae harge reombination urrents are negligible ompared to the arrier diffusion urrents. An expression of I 0 for the low injetion behavior may be written in the form [1, 2]: 2 I 0 I 0 L n i, (2) where I 0L is determined from the desription of the arrier diffusion proesses. The intrinsi arrier onentration n i is dependant on both the energy gap E g and the arrier temperature: 12 E g ni v exp (3) 2kT A reent work [5] has also derived Eq. (1) from the desription of arrier distributions at low and high injetion onditions. The urrent appeared as the sum of the ontribution of eah part of the pn juntion, the p region, the n region and the spae harge region. Eah region was desribed by its own behavior, either low or high injetion, thus the total ontribution orresponds to a ombination of behavior and harateristis. We present here an experimental method based on urrent-voltage, I(V), measurements at various lattie temperature values, T, varying from 92 K to 422 K. The desription of I(V) urves by Eq. (1) leads to determine arrier temperature values, T, different from T values. In addition, measurements of the juntion voltage needed to obtain the same low injetion level urrent, at eah temperature, are shown to enable the determination of the silion energy gap value. II. EXPERIMETAL PROCEDURE AD RESULTS The experimental study was realized with the measuring setup shown in Fig. 1-a. The silion pn juntion is the emitter-base juntion of the P 22222A transistor. The transistor metal pakage (TO-18) should be ut open to enable even heat flow around the transistor hip. Enapsulating a transistor holder and a thermoouple with the orresponding wiring in a plaster body makes a heat/old resistant holder, whih is shown in Fig. 1-b. The tip of the thermoouple (or the sensing end) is plaed lose to the transistor. The urrent-voltage measurements were made in two different ways. A ontrolled oven is used to heat the sample from room temperature to the desired higher temperature (from 300 K to 422 K). For dereasing the transistor temperature

2 from room temperature, liquid nitrogen is used and the distane of the transistor from the surfae of the liquid nitrogen determines the desired temperature (from 300K to 92K). The sample temperature is monitored on the temperature ontrol unit display (REX CB100 equipped with a thermoouple of type K whih an hold until 1150 C and having a 0.3 % of preision.), and the I(V) measurements are aquired one the temperature is stable at the desired temperature, in heating oil or liquid nitrogen. The I(V) harateristis are measured at different temperature values using a Keithley Model 2400 General-Purpose SoureMeter. The LabTraer software was used to aquire all I(V) data. hip Thermoouple (K type) box holder Computer GPIB Plaster enapsulation Temperature ontrol unit (TCU) Oven or Dewar vessel Keithley 2400 (a) Fig. 1: The measuring ell. To TCU (b) To Keithley The I(V) harateristis, measured at eight temperature values as shown in Table 1, are reported in the semi logarithmi plots of Fig. 2. Fig. 2: Current-voltage harateristis in semi logarithmi plot for eight different temperature values as reported in Table 1. Using Eq. (1) and the plot of Log(I) versus the applied voltage V it is easy to obtain the values of the thermal potential [4] V T from the slope of the most linear part of the plot. The experimental reverse saturation urrent I 0 is determined from the intersetion with Log(I) axis. The extration software is the graphial interfae Miroal origin 5.0 using defined fitting proedure. Results are displayed in Table

3 Table 1. Experimental results for the reverse saturation urrent I 0, the thermal potential V T and the omputed values of the arrier temperature T. T (K) I 0 (A) V T (x10-3 V) T (K) The last olumn in Table 1 gives omputed values of the arrier temperature using T evt k. Table 1 points out that the arrier temperature T is different from the experimentally imposed lattie temperature T. Further more, Table 1 shows that T =T for a temperature value lose to 230 K. This result may be related to the temperature dependent arrier-lattie interation [6], and have a relation with Debye temperature. These results are displayed in Fig. 3; at low temperature the behavior is quadrati, ompared to the quasi-linear variation at higher temperature. Fig. 3: The arrier temperature in low injetion versus the lattie temperature. The dotted urve is the experimental data, and the dashed urve is T T. These results may be applied to desribe the temperature dependene of the juntion I(V) harateristi. It an be done with an additional experiment that onsiders measurements, at different temperatures, of the voltage values applied to the juntion in order to obtain a steady urrent. From the same measurement displayed in Fig. 2, the student ould use horizontal lines to determine the variation of the juntion voltage at onstant urrent. Using Eqs. (1), (2) and (3), the applied juntion voltage V, for a steady value I=I st, may be obtained in the form: ln I E st g V VT 0 I L v e. (4) The temperature dependene of voltage V is related [2] to the variations with temperature of the energy gap E g whih is given by Varshni s equation [7]: 2 T E g T E g 0. (5) T where E g (0) is the energy gap limit at 0 K, and α and β are related to the semiondutor properties. 1271

4 Our results are based on the observation from Eqs. (4) and (5) that as temperature dereases towards the absolute zero, the voltage goes towards the value [1, 8] E g (0)/e at 0 K. Fig. 4: Dependene of the values of the voltage aross the juntion on the lattie temperature T. The data indiated by squares, up triangles and down triangles orrespond respetively to urrent at A, A and A. The solid straight lines result from least-square fitting proedure applied to the separated data sets. Figures 4 and 5 represent the values of the measured applied voltage aross the juntion as a funtion of temperature, respetively T and T, for steady values I=I st of the injeted urrent in low injetion onditions. The lines in both figures represent a omputed fit. All the lines in Fig. 5 interept the T =0 K voltage axis at the same point V(0) = 1.2 V. This result is in agreement with the above observation sine the value of voltage V at 0 K orresponds to the value of the energy gap at 0 K, E g (0). This value ould be ompared with the literature [7, 2] determinations (E g (0) = 1.17 ev). It is not the ase in Fig. 4 where the lines do not interept at 0 K and more deliate extrapolation is needed. Fig. 5: Dependene of the values of the voltage aross the juntion, on the arrier temperature T. The data indiated by squares, up triangles and down triangles orrespond respetively at A, A and A. The solid straight lines result from least-square fitting proedure applied to the separated data sets. This additional experiment points out the differene between the arrier temperature and the lattie temperature. 1272

5 III. DISCUSSIO AD COCLUSIO Experimental values in Fig. 3 (square symbols) show two types of variations of the arrier temperature in silion, linear at temperature higher than 200 K and a quadrati approah for temperature lower than 200K; these observations were made by Varshni [7] for the forbidden energy gap, who introdued Eq. (5) to fit these results. The introdution of the arrier temperature results in a new desription, whih is of importane for the understanding of optial properties of semiondutor devies, but a disussion of this point is not the aim of this work. The use of the arrier temperature gives rise to orret preditions of e/k in Inman work. Experiments have been desribed whih lead students to introdue the onept of arrier temperature whih is related to the exitation of arriers sine thermal agitation indues a dominant proess of arrier generation. The onept is applied to the desription of I(V) measurements. Furthermore, the desribed method is of simple use and introdues a pratial way to experiment on temperature dependene of semiondutor properties. Referenes [1] S. M. Sze, Physis of Semiondutor Devies (Wiley-Intersiene, ew York, 1981). [2] A. Sonza, G. Torzo and G. Viola, Experiment on the physis of the P juntion, Am. J. Phys. 62, (1994). [3] M.H. Boukhatem, M. El Tahhi, G.W. El Haj Moussa, M. Ajaka, A. Khoury, P. Mialhe, "Carrier temperature for an operating silion p-n juntion" Miroeletronis Journal 38, (2007). [4] F. Inman, A simple laboratory experiment to measure e/k, The Physis Teaher 43, (2005). [5] M. El Tahhi,. Toufik, F. Pelanhon, M. Ajaka, A. Khoury, and P. Mialhe, ew modelling method for forward juntion I V analysis, J. Phys. D.: Appl. Phys. 35, (2002). [6] C. D. Thurmond, The standard thermodynami funtions for the formation of eletrons and holes In Ge, Si, GaAs, and GaP, J. Eletrohem. So. 122, (1975). [7] Y. P. Varshni, Temperature dependene of the energy gap in semiondutors, Physia (Amsterdam) 34, (1967). [8] A. S. Grove, Physis and Tehnology of Semiondutor Devies (Wiley, ew York, 1967). 1273