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Transcript
e/k of a trans istor Experiment-419 S DETERMINATION OF RATIO OF ELECTRONIC CHARGE TO BOLTZMANN CONSTANT (e/k) USING A SILICON TRANSISTOR Jeethendra Kumar P K KamalJeeth Instrumentation & Service Unit, Tata Nagar, Bengaluru-560092, INDIA Email: [email protected] Abstract Using a silicon transistor (SL100) the collector current variation with emitter base voltage is studied at fixed temperature and ratio of e/k is calculated and compared with standard value. Introduction The transistor invented by Bardeen, Brattain and Shockley is one of revolutionary inventions in Physics. It is mainly responsible for ushering in the present day electronic revolution. The theoretical aspects of semiconductor physics offer a means to determine various universal constants in lab experiments. It provides a means to experimentally determine various physical constants in Physics. One such experiment is the determination of ratio of e/k using the transistor equation, as described below. Theory Neglecting the reverse current in the base region, which is very small in a silicon transistor compared to a germanium transistor, the collector current of a transistor is given by [1,2] IC = ICO (eηౡ − 1) …1 where IC is collector current, ICO is collector current with its base open which gives the reverse saturation current, 1 KAMALJEETH INSTRUMENTS e/k of a trans istor T is temperature of the device, e is electronic charge (1.6x10-19 Coulomb) k is Boltzmann constant (1.38x10 -23 m2 kg s-2 K-1), V is the voltage across the depletion region, and η is known as the ideality factor. B E C JE JC Depletion regions Figure-1: The two depletion regions in an npn silicon transistor In Equation-1 the collector current is an exponential function of ICO, which is in turn a function of temperature; the value of the current doubles for every ten degree increase in the temperature. Figure-1 shows an npn silicon transistor with two depletion regions. In the normal use of a transistor, the emitter-base junction (JE) is forward biased and collector- base (JC) junction is reverse biased. In this mode the transistor conducts and collector current flows through the transistor. The emitter –base junction (JE) is forward biased and as a result the depletion region becomes very thin. The voltage across JE is VBE, hence replacing ‘V’ in Equation-1 by VBE; the collector current can be written as ాు IC = ICO (e ηౡ -1) …2 Taking natural logarithmic of both the sides of Equation-2, we can write ాు ln (IC) = ln (ICO) + ln [e η୩ ] +ln (-1) ଵ ୣ log IC = log ICO + ଶ.ଷଷ η୩ VBE …3 …4 Equation-4 represents a straight line in log IC versus VBE graph such that Y = log IC X = VBE Y-intercept C = log ICO, and Slope = ଵ ୣ ଶ.ଷଷ η୩ 2 KAMALJEETH INSTRUMENTS e/k of a trans istor Hence from the slope of the straight line represented by log IC versus VBE, one can determine the value of e/k. ୣ ୩ = slope 2.303 ηT …5 Equation-5 shows that e/k is dependent on the temperature of the device. At different temperatures the slope of the straight line is different such that the value of e/k is constant. Ideality factor (η) The ideality factor (η) of a transistor is not constant but depends on the voltage across the depletion region and the current flowing through it. The value of η is given by ୣ ିభ మష ୍భ ) η = ୩ [୪୬ሺ୍మ …6 where V1, I1 and V2, I2 are voltages across the junctions, and currents passing through the junctions 1 and 2 at a given temperature. From Equation-6, η is seen to be inversely proportional to temperature. Hence as seen from Equation-5, when temperature T is varied, both slope and η vary. Hence to get accurate value for e/k, one should know the value of η at the given temperature [2]. Figure-2 shows the variation of η with temperature for the silicon transistor SL100. In the temperature range of 27-80°C, the variation is linear, as shown in Figure-2. At room temperature (27°C), the ideality factor is 1.7 which matches with the value calculated from Equation-6. Ideality factor (η) 2 1.5 1 0.5 0 0 10 20 30 40 50 60 70 80 90 Temperature (0C) Figure-2: Variation of ideality factor with temperature 3 KAMALJEETH INSTRUMENTS e/k of a trans istor Apparatus used The experimental set-up consists of: a regulated power supply (0-10V), digital DC milliammeter (0-200mA), and digital DC voltmeter (0-2V). Experimental procedure I I 0-10V V C V BE 330 Figure-3: Circuit connections for determination of e/k The transistor is connected to power supply and milli-ammeter as shown in Figure-3. In this mode, the emitter base junction is forward biased and collector base junction is reverse biased. 1. The room temperature is noted using a digital themometer T =27.1°C 2. The transistor SL100 is mounted on its socket and circuit connections are made as shown in Figure-3. 3. The emitter-base voltage (VBE) is varied by varying the power supply voltage control knob and the correponding collector current is noted VBE = 0.572V and IC =2.4 mA The readings obtained are tabulated in Table-1. 4. The experiment is repeated by varying the emitter-base voltage in suitable steps up to the maximum value of 0.65V and noting the correponding collector current. The corresponding collector base volatge is recorded in Table-1. Table-1: IC variation with VBE at 27°C VBE(V) IC(mA) Log (IC) -0.572 -2.4 -2.619 -0.582 -3.0 -2.522 -0.592 -3.8 -2.420 -0.602 -4.5 -2.346 4 KAMALJEETH INSTRUMENTS e/k of a trans istor -0.612 -0.622 -0.632 -0.642 -5.6 -7.5 -9.6 -11.5 -2.251 -2.124 -2.017 -1.939 5. A graph is drawn taking log IC along Y-axis and VEB along X-axis. The slope of the straight line and Y-intercept are noted by extrapolating the line to meet the Y-axis as shown in Figure-4. 0 Log IC -2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 -4 -6 -8 -10 VBE (V) Figure-4: Variation of log IC versus VBE at 27°C Slope =9.842 Y-intercept= -8.25 = log ICO IC0= 5.6x10 -9 =5.6nA ୣ = Slope 2.303 ηT = 9.842 x2.303x1.7x300= 11560 ୩ 6. The experiment is repeated on a sunny day with room temperature =31°C. The IC variation with VBE variation is tabulated in Table-2. From the graph in Figure2, the ideality factor at 31°C is found as η31 = 1.7= η27 Table-2: IC variation with VBE at 31°C VBE(V) IC(mA) Log (IC) -0.572 -2.4 -2.619 -0.582 -3.0 -2.522 -0.592 -3.8 -2.420 -0.602 -4.5 -2.346 -0.612 -5.6 -2.251 -0.622 -7.5 -2.124 -0.632 -9.6 -2.017 -0.642 -11.5 -1.939 5 KAMALJEETH INSTRUMENTS e/k of a trans istor 0 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 -2 Log IC -4 -6 -8 -10 VBE(V) Figure-5: Variation of log IC versus VBE at 31°C Slope =9.896 Y-intercept= -8.10 = log ICO IC0= 7.94x10-9 =7.94nA From Figure-2, the η value (1.7) for 27° and 31° temperatures are almost the same, hence the slope remained also most same at 31°C, hence e/k. ୣ ୩ = Slope 2.303 ηT = 9.896 x2.303x1.7x300= 11623 Results The average value of ୣ ୩ obtained 11591 is found to tally with the standard value of 11594. The reverse saturation current of SL100 = 5.6nA at 27°C and it increased to 7.94nA at 30°C. To observe the effect of η on e/k one can repeate the experiment at higher temperature using a digitally controlled oven. The transistor is now placed in side the oven and connected to the set-up. In this digitally controlled oven one can set the temperature from room temperature to 150°C and experiment can be repeated. The temperature controlled oven is shown in Figure-6. 6 KAMALJEETH INSTRUMENTS e/k of a trans istor Figure-6:Microcontroller based oven for temperature variation study of seminconductor devices Reference [1] John D Ryder, Electronic fundamenatls and applications, 5th Edition,PrenticeHall of India Private Ltd, Page-56, 1978 [2] S Sankararaman and Miss Jaiby Joseph, Variation of ideality factor, LE,Vol-4, No3, Sept.-2004, Page-174 7 KAMALJEETH INSTRUMENTS