Investigating the Absorption of Radiation in Matter using G-M Counter

 Abstract

In this experiment, we shall measure the ratio of the electronic charge (e) to the Boltzmann's constant, k_B, from the current-voltage characteristics of a bipolar junction transistor (BJT).

investigate the effect of temperature on the current-voltage characteristics of such a transistor.

Introduction

Semiconductors and Band theory of solids

We know that when we talk about the structure of an atom, we mention that it is consist of a nucleus and electrons rotate about it in a specified shells with specific energy. But when we take about a material it is pointless to talk about shells since the number of atoms is so large. So, we use another method to express this subject which is band theory. In this case we are interested in the valence electrons (the electrons in the outer shell). When the electrons in the material are found in the ground state, we say that they are in the Valence Band. And when the electrons of a material are found in an excitation state, we say that they are in the Conduction Band. And between them there is a Gap  which is forbidden for electron to exist.

Now this gap differs from material to other, in the insulators the gap will be so large in which does not allow the electron to transmit to the conduction band. In the conductor it will be so small in which the electron transmits easily to the conduction band. In semiconductor the gap will be in between.

  The energy levels of a semiconductor can be modified so that a material that is normally an insulator will conduct electricity. In semiconductors there is a small enough gap between the valence and conduction bands such that thermal or other excitations can bridge this gap.

Types of Semiconductors

The p-type semiconductor is formed when the Trivalent impurity is added to the pure semiconductor. Similarly, when a Pentavalent impurity is added to the pure semiconductor n-type semiconductor is obtained.

The impurity added in p-type semiconductor provides extra holes known as Acceptor atom, whereas in n-type semiconductor impurity provides extra electrons and termed as Donor atom. In a p-type semiconductor, the majority carriers are holes, and minority carriers are electrons. In the n-type semiconductor, electrons are majority carriers, and holes are minority carriers.

Doping

Doping is a process where impurities are incorporated to a semiconductor to lower its resistivity or equivalently to increase its conductivity. Increasing the conductivity (σ= e n μ) requires the increase of the concentration of mobile charge carriers (n). e is the electron charge and μ is the charge carrier mobility.

Diodes

When we put an n-type and p-type materials together the electron from n-type material (which has high electron concentration) began to diffuse toward the p-type material. Similarly, holes flow by diffusion from the p-type side to the n-type side. The P-side is called anode, and the N-side is called cathode. Diode acts as a one-way gate for electron flow, which means that it allows current to pass only in one direction and blocks its flow in the opposite direction.

Transistor

The transistor is a three terminal solid state electronic device which transfers a weak signal from low resistance circuit to high resistance circuit. Transistor contains two PN-junctions connected back to back. It has three terminals namely emitter (which is heavily dopped), base ( which is slightly dopped) and collector ( which is moderately dopped) . A transistor is a miniature electronic component that can do two different jobs. It can work either as an amplifier or a switch.

The transistor contains three layers separated by two PN-junctions. If the collector and emitter are n-type and the base is p-type we call it ( npn-transistor). And if the collector and emitter are p-type and the base is n-type we call it ( pnp-transistor).

The I-V Characteristic curve

An I-V curve is a graphical representation of the relationship between the voltage applied across an electrical device and the current flowing through it. It is one of the most common methods of determining how an electrical device functions in a circuit.

Formalism

I = I0exp(eV/KBT)    equ. (1)

The characteristic equation for any p-n junction

Ic= I0exp(eV_BE/K_BT)     equ (2)

The characteristic equation for translator, Ic is the collector current, VBE is the voltage between the base and emitter

Δe/KB=e/KB*[(Δslope/slope)² + (ΔT/T)²]^^1/2   equ (3) 

Methodology

In order to avoid an eventual overheating of the semi-conductor, the power dissipated within the transistor should not exceed 1mW. Thus the largest current should not exceed 2.5 to 3 mA.

1. At room temperature, measure the current IC for various values of the voltage VBE (from 0.1 to 0.6) by steps of 0.05,

2. Turn on the electrical oven fixing the thermostat at 40 ⁰C. Put the transistor in the oven and repeat step 1 for the same values of V_BE.

3. Repeat step 2 but this time set the temperature at 70 C.

4. Thus, at the end, you normally have three tables for the three temperatures.

Data Analysis

T = 295K

(y-a-bx)^2	x*y	x^2	V(BE) volt=x	Ln(I)=y	I(c) micro A
4.8527656	-5.812540061	0.149769	0.387	-15.01948336	0.3
2.171022704	-5.582269301	0.160801	0.401	-13.92087107	0.9
1.94815238	-5.583896273	0.169744	0.412	-13.55314629	1.3
1.442037533	-5.519762145	0.175561	0.419	-13.17365667	1.9
1.736926826	-5.588605822	0.184041	0.429	-13.0270532	2.2
1.225051501	-5.504903066	0.188356	0.434	-12.68410845	3.1
1.362575294	-5.542267632	0.198025	0.445	-12.454534	3.9
1.262502472	-5.526276459	0.204304	0.452	-12.22627535	4.9
1.02016017	-5.475293135	0.207936	0.456	-12.00722179	6.1
0.782502606	-5.417925009	0.208849	0.457	-11.85541577	7.1
0.689829579	-5.39262934	0.210681	0.459	-11.7486478	7.9
0.631421174	-5.374150335	0.214369	0.463	-11.60723614	9.1
0.602521622	-5.362732231	0.218089	0.467	-11.48336666	10.3
0.52924054	-5.338109788	0.219961	0.469	-11.3818972	11.4
0.456363378	-5.30790638	0.224676	0.474	-11.19811473	13.7
0.416233888	-5.292146907	0.225625	0.475	-11.14136191	14.5
0.331780518	-5.24408769	0.234256	0.484	-10.83489192	19.7
0.283073263	-5.218764373	0.236196	0.486	-10.7381983	21.7
0.364076457	-5.249320101	0.238144	0.488	-10.75680349	21.3
0.229693257	-5.181805445	0.241081	0.491	-10.55357524	26.1
0.206672598	-5.16476097	0.243049	0.493	-10.47618858	28.2
0.205215096	-5.161418076	0.244036	0.494	-10.44821473	29
0.106380948	-5.065817067	0.255025	0.505	-10.03132092	44
0.088962991	-5.030906727	0.261121	0.511	-9.845218644	53
0.059417531	-4.995580208	0.263169	0.513	-9.737973114	59
0.066184679	-4.990945929	0.266256	0.516	-9.672375832	63
0.052534675	-4.960199108	0.2704	0.52	-9.538844439	72
0.051926203	-4.951053708	0.272484	0.522	-9.484777218	76

Slope = e/ kT = 36.504

Y-intercept = ln(I.) =-27.179

e/k = slope * T = 11900

theoretical value of e/KB = 1.15 *10^4 C K/J   P.E= 3.48%

s= 2.103291431

a=y-intercept = -27.17878351

b= slope = 36.5037931

δa= 4.939581841

I. = 1.75* 10^-12 Amp

δb = 11.16543679

Δe/KB = δb *T = 3630

T=325K

(y-a-bx)^2	x*y	x^2	V(BE) volt=x	Ln(I)=y	I(c) micro A
9.655787956	-5.049033739	0.135424	0.368	-13.72020038	1.1
8.361360228	-5.071857819	0.148225	0.385	-13.17365667	1.9
7.579323467	-5.06683965	0.155236	0.394	-12.85999911	2.6
7.087094525	-5.060943899	0.16	0.4	-12.65235975	3.2
6.382823446	-5.038833395	0.165649	0.407	-12.38042603	4.2
6.12249331	-5.02638679	0.167281	0.409	-12.28945425	4.6
5.640349314	-5.006396	0.171396	0.414	-12.09274396	5.6
5.237080793	-4.9860883	0.174724	0.418	-11.92844091	6.6
4.810915896	-4.964357194	0.178929	0.423	-11.73606902	8
4.35859222	-4.936178858	0.183184	0.428	-11.53312817	9.8
3.930246411	-4.906151492	0.187489	0.433	-11.33060391	12
3.70981779	-4.887352772	0.189225	0.435	-11.23529373	13.2
3.633454441	-4.884110061	0.190969	0.437	-11.17645323	14
3.13853042	-4.839836488	0.196249	0.443	-10.9251388	18
2.873930609	-4.81463169	0.199809	0.447	-10.77098812	21
2.61856714	-4.789678899	0.204304	0.452	-10.59663473	25
1.463369241	-4.627275014	0.226576	0.476	-9.721165996	60
1.506135202	-4.636884777	0.229441	0.479	-9.680344001	62.5
1.341206452	-4.604464388	0.232324	0.482	-9.552830681	71
0.985457642	-4.521054975	0.246016	0.496	-9.115030192	110
0.903885617	-4.497614496	0.25	0.5	-8.995228992	124
0.813834699	-4.470793207	0.253009	0.503	-8.888256873	138
0.746274897	-4.448564799	0.256036	0.506	-8.791630037	152

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Slope = e/ kT = 36.504

Y-intercept = ln(I.) =-27.179

e/k = slope * T = 11900

theoretical value of e/KB = 1.15 *10^4C K/J   P.E= 3.48%

s= 2.103291431

a=y-intercept = -27.17878351

b= slope = 36.5037931

δa= 4.939581841

I. = 1.75* 10^-12 Amp

δb = 11.16543679

Δe/KB = δb *T = 3630

T =343K

(y-a-bx)^2	x*y	x^2	V(BE) volt=x	Ln(I)=y	I(c) micro A
1.320330144	-3.89034467	0.097969	0.313	-12.4292162	4
1.049501762	-3.893392618	0.1024	0.32	-12.16685193	5.2
0.8843354	-3.883671602	0.104329	0.323	-12.02375109	6
0.688616196	-3.896374913	0.110224	0.332	-11.73606902	8
0.588228974	-3.900707893	0.113569	0.337	-11.57480087	9.4
0.479053907	-3.90399074	0.117649	0.343	-11.3818972	11.4
0.398683316	-3.892225742	0.119025	0.345	-11.28181374	12.6
0.346406849	-3.903430065	0.123201	0.351	-11.12088338	14.8
0.180810589	-3.873480626	0.128164	0.358	-10.81977828	20
0.151280628	-3.871532986	0.130321	0.361	-10.7244681	22
0.084705104	-3.863105801	0.136161	0.369	-10.46912141	28.4
0.019694892	-3.838736627	0.1444	0.38	-10.10193849	41
0.003596107	-3.822746195	0.148996	0.386	-9.903487553	50
0.001288958	-3.805883904	0.156816	0.396	-9.610817939	67
0.018094575	-3.773393569	0.16	0.4	-9.433483923	80
0.032316727	-3.770653443	0.169744	0.412	-9.152071464	106
0.04091335	-3.766802617	0.174724	0.418	-9.011489513	122
0.055694348	-3.756505804	0.179776	0.424	-8.8596835	142
0.068719904	-3.748410651	0.191844	0.438	-8.558015186	192
0.089926208	-3.730894174	0.196249	0.443	-8.421883012	220
0.092951232	-3.722228034	0.207025	0.455	-8.180720955	280
0.038375846	-3.724442205	0.2401	0.49	-7.60090246	500
0.011145443	-3.740000175	0.253009	0.503	-7.435388021	590
0.004750295	-3.794685869	0.266256	0.516	-7.354042382	640
0.109556135	-3.809037816	0.305809	0.553	-6.887952652	1020
0.332070057	-3.843336531	0.332929	0.577	-6.660895201	1280
1.083942223	-3.983020898	0.364816	0.604	-6.59440546	1368
0.965086377	-3.936762708	0.367236	0.606	-6.496308099	1509

Slope = e/ kT = 20.583

Y-intercept = ln(I.) =-18.139

e/k = slope * T = 7060k/v

theoretical value of e/KB = 1.15 * 10^4C K/J   P.E= 38.6%

s= 0.59290924

a=y-intercept =-18.1393

b= slope =20.58264 

δa= 0.555262353

I. = 1.33 *10^-8 Amp

δb =1.295626788

Δe/K_B = δb *T = 444

Conclusion 

  Transistors are the heart of modern electronics (they replaced vacuum tubes). Their main use, as said earlier, is in1-  voltage and current amplifier circuits.

  The transistor can be used as a switch and as an amplifier.

 When we want to use an electrical device the most important thing that we should know it is the IV-curve of that device.

 We can notice that the relationship between Ln[I] and VBE is linear, all line have almost the same slope so we got close values of e/KB at different temperatures.

References

t  PRACTICAL PHYSICS 5 Physics (0342411).

t  Electronic devices lectures by Dr.Bashar Lahlouh, Department of Physics, University of Jordan.