Sudan University of Science and Technology College of Graduate Studies Charge Carriers (Electrons and Holes) in Semiconductors ﺣﺎﻣﻼﺕ ﺍﻟﺸﺤﻨﺔ (ﺍﻹﻟﻜﱰﻭﻧﺎﺕ ﻭﺍﻟﻔﺠﻮﺍﺕ) ﰲ ﺃﺷﺒﺎﻩ ﺍﳌﻮﺻﻼﺕ A thesis submitted for partial fulfillments of the requirement of the degree of science master in physics Submitted by Nada Hamad AdamAbdelrahman Supervisor Dr: RawiaAbdelganiElobaid Mohammed May 2017 اﻵﯾــــــــــــﺔ ﻗﺎل ﺗﻌﺎﻟﻰ:( وَأَﻣﱠﺎ ﺑِﻨِﻌْﻤَﺔِ رَﺑﱢﻚَ ﻓَﺤَﺪﱢثْ)(11) ﺻﺪق اﷲ اﻟﻌﻈﯿﻢ {ﺳﻮرة اﻟﻀﺤﻰ} I Acknowledgement Thank god, the lord of the worlds, and blessings and peace be upon the prophet Mohammed and his family and companions and after: I cannot thank almighty Allah after completing this research because I give thanks to the virtuous worker Dr. rawia abdelgani .for advice and ongoing guidance value for the success of this research, I call her health .finally, I thank everyone who has helped me. II DEDICATION The source of my power and inspiration….my husband To ask of Allah because of their satisfaction ….my parents. The flower of life, Mohammed and yousuf To my brothers and sisters To both lows for second Both told me if the word III ABSTRACT Had been calculate the charge carriers concentration(ni) and energy gap (Eg), by indication of change temperature(T) ,know resistance(R0),unknow resistance(Rt)and lengths(L1,L2),where it was found that whenever increase temperature decreased concentration and energy gap. IV اﻟﻤﺴﺘﺨﻠﺺ ﺗﻢ ﺣﺴﺎب ﺗﺮﻛﯿﺰ ﺣﺎﻣﻼت اﻟﺸﺤﻨﺔ (ni)وﻃﺎﻗﺔ اﻟﺤﺎﺟﺰ (Eg) وذﻟﻚ ﺑﺪﻻﻟﺔ اﻟﺘﻐﯿﯿﺮ ﻓﻲ درﺟﺎت اﻟﺤﺮارة (T) اﻟﻤﻘﺎوﻣﺔ اﻟﻤﻌﻠﻮﻣﺔ(R0) ،اﻟﻤﻘﺎوﻣﺔ اﻟﻤﺠﮭﻮﻟﺔ(RT) و اﻷﻃﻮال( L1,L2)،ﺣﯿﺚ وﺟﺪ أن ﻛﻠﻤﺎ زادت درﺟﺔ اﻟﺤﺮارة ﯾﻨﺨﻔﺾ اﻟﺘﺮﻛﯿﺰ وﻃﺎﻗﺔ اﻟﺤﺎﺟﺰ. V Table of content Subject Page No No I اﻵﯾﺔ 1 2 Acknowledgement II 3 DEDICATION III 4 Abstract IV V ﻣﺴﺘﺨﻠﺺ اﻟﺒﺤﺚ 5 6 Table of content VI 7 List of tables VIII Chapter one 8 (1-1) Introduction 1 9 (1-2) Objective 2 10 (1-3) Problem 2 11 (1-4) Previous studies 2 12 (1-5) Thesis lay out 3 Chapter two 13 (2-1)Introduction 4 14 (2-2)Conduction semiconductors 5 15 (2-3)Intrinsic semiconductors 8 16 (2-4)Conductivity of charge carriers 11 VI 17 (2-5)Carrier concentration in intrinsic semiconductors 14 18 (2-6)Extrinsic semiconductors 20 19 (2-6-1)N-type semiconductor 23 20 (2-6-2)P-type semiconductors 27 21 (2-7)Charge carrier density in extrinsic semiconductors 30 22 (2-8)Motion of carriers in electric and magnetic fields 32 23 (2-9)Carrier diffusion 39 24 (2-10)Semiconductor devices 42 25 (2-11)The p-n junction 42 26 (2-12)Current-voltage characteristics of p-n junction 45 27 (2-13)The transistor 47 28 (2-14)Bimodal(bipolar)junction transition(BJT) 47 29 (2-15)Field effect transistor(FET) 49 Chapter Three (3-1)Introduction 54 30 (3-1)Equilibrium of distribution of electron and hole 54 31 (3-2)The n0and p0 equation 57 32 (3-3)The intrinsic carrier concentration 62 33 (3-4) The intrinsic Fermi –level position 65 34 (3-5)Dopant atoms and energy level 66 35 (3-5-1)Qualitative description 67 36 (3-6)The extrinsic semiconductor 71 37 (3-6-1)Equilibrium distribution of electrons and holes 72 38 (3-6-2)The n0 p0 product 75 39 (3-6-3)Degenerate and no degenerate semiconductor 76 VII 40 (3-7)Statistics of donors and acceptors 78 41 (3-7-1)probability function 78 42 (3-7-2)Complete ionization and freeze –out 80 43 (3-8)Charge neutrality 82 44 (3-8-1)Compensated semiconductors 83 45 (3-8-2)Equilibrium electron and hole concentration 83 46 (3-9)Position of the Fermi energy level 88 47 (3-9-1)Mathematical derivation 88 (3-9-2)Variation of Ef with doping concentration and 90 48 temperature 49 (3-9-3)Relevance of the Fermi energy 92 Chapter four 50 (4-1)Introduction 93 51 (4-2)Aim of experiment 93 52 (4-3)The theory 93 53 (4-4)The apparatus 94 54 (4-5)Results 98 55 (4-6)Calculation 99 56 (4-7)Conclusion 100 57 (4-8)Recommendation 101 58 References VIII List of figure No Subject Page No 1 Figure(2-1)The conductivity of a few selected solid at 5 temperature 2 Figure(2-2)(a)Energy level occupation in case of an inslated 6 carbon atom (b)the energy band in diamond crystal 3 Figure(2-3)Energy level separation plot for group of n 6 carbon atoms 4 Figure(2-4)Band structure of semiconductors 7 5 Figure (2-5)A silicon crystal two dimensional representation 9 6 Figure(2-6)Motion of the electron-hole pair from location x 9 and y 7 Figure(2-7)a-two dimensional representation of germanium 10 crystal at T=0K(b)a vacancy created corresponds to an in compelet band 8 Figure(2-8)(a)a plot of resistivity versus temperature(1/T) 13 (b)conductivity versus(1/T) 9 Figure(2-9)The Fermi distribution function f(E)versus(E-Ef) 16 at various temperature 10 Figure(2-10)(a)Band diagram for intrinsic 17 semiconductor,(b)the density of state (c)distribution function ,(d)carrier concentration for an intrinsic semiconductor 11 Figure(2-11)Depicting conduction band energy structure of 17 semiconductor IX 12 Figure(2-12)Electron energy state 22 13 Figure(2-13)Acceptor impurity level for hole 22 14 Figure(2-14)A donor impurity (phosphours )in (si) crystal 24 15 Figure(2-15)(a)Electronic arrangement (b)a collection of 14 24 electron as a single positive charge 16 Figure(2-16)A pictorial representation of energy band 25 17 Figure(2-17)Variation of Fermi energy with temperature 27 18 Figure(2-18)Germanium atom getting displaced due to the 28 insertion of impurity 19 Figure(2-19)The acceptor stats energy 29 20 Figure(2-20)Temperature dependence of conductivity of 35 three samples 21 Figure(2-21)Experiment set up for the Hall effect 37 22 Figure(2-22)Electron concentration versus distance 39 23 Figure(2-23)Two isolated metal x and y 42 24 Figure(2-24)P and n type semiconductor 43 25 Figure (2-25)Depletion layer caused by the diffusion 43 26 Figure(2-26)The distribution of charge at p-n junction 44 27 Figure(2-27)Current-voltage characteristics of the p-n 46 junction diode 28 Figure(2-28)Representation of p-n junction 46 29 Figure(2-29)A bimodal junction transistor 47 30 Figure(2-30)(a)Energy band structure an n-p-n 48 bipolar(b)when the voltage us applied the emitter is made negative with respect to the collector X 31 Figure(2-31)Schematic presentation of current symbols(a)p- 49 n- p and n-p-n transistor 32 Figure (2-32)The basic structure of an n channel JFET 51 33 Figure(2-33)Current-voltage (Id-Vds)characteristics 51 34 Figure(2-34)(a)The structure of n- channel MOSFET 52 (b)when positive voltage is applied to the gate 35 Figure(2-34 c)When the gate voltage exceeds the threshold 52 value 36 Figure(2-35)The energy band structure at the m-o-s 52 interface in MOSFET 37 Figure(3-1)(a)Density of states function ,Fermi probability 56 function and areas representing electron and hole concentration(b)expanded view near conduction band energy (c)expanded view near valence band energy 38 Figure(3-2)The intrinsic carrier concentration as a function 65 of temperature 39 Figure(3-3)Two dimensional representation the intrinsic 67 silicon lattice 40 Figure(3-4)Two dimensional representation the intrinsic 68 doped with phosphours atom 41 Figure(3-5)The energy band diagram(a)the discrete donor 69 energy states (b)the effect of donor states being ionized 42 Figure(3-6)Two dimensional representation of silicon 70 lattice(a)doped with a boron atom(b)showing the ionization of the boron atom result in a hole XI 43 Figure(3-7)The energy band diagram showing (a)the 71 discrete acceptor energy states(b)the effect or an acceptor state being ionized 44 Figure (3-8)Density of state function ,Fermi probability and 72 areas representing electron and hole concentration for the case when Efi is above the intrinsic Fermi energy 45 Figure(3-9)Density of state function , Fermi probability and 73 areas representing electron and hole concentration for the case when Efi is a below the intrinsic Fermi energy 46 Figure(3-10)Simplified energy band diagram for 77 degenerately doped (a)n-type (b) p- type semiconductor 47 Figure(3-11)Energy band diagram showing complete 81 ionization (a)donor(b)acceptor states 48 Figure(3-12)Energy band diagram at T=0K for(a)n-type 82 (b)p –type semiconductor 49 Figure(3-13)Energy band diagram a compensated 84 semiconductor a showing ionized and un-ionized donor and acceptor 50 Figure(3-14)Energy band diagram a showing the 86 redistribution of electron 51 Figure(3-15)Electron concentration versus temperature 87 showing the three regions partial ionization ,extrinsic and intrinsic XII 52 Figure(3-16)Position of Fermi level for an (n- type Nd>Na) 90 and p- type (Na>Nd) semiconductor 53 Figure(3-17)Position of Fermi level as a function of donor 91 concentration (n- type) and acceptor concentration(p- type) 54 Figure (3-18)Position of Fermi level as a function of 91 temperature for various doping concentration 55 Figure(3-19)The Fermi energy(a) material in thermal 92 equilibrium (b)material B is in thermal equilibrium (c)A and B at the instant they are placed in contact (d) A and B is contact at thermal equilibrium 56 Figure(4-1)The sample 96 57 Figure(4-2)The bridge 97 58 Figure(4-3)The oven 97 59 Figure(4-4)Relation between concentration and temperature 99 XIII List of Table No Subject Page No 1 (2-1)Mobilities for various semiconductor at room 34 temperature 2 (3-1) Effective density of state function and effective mass 62 value 3 (3-2)Commonly accepted value ni at T=300K 64 XIV Chapter One 1-1 Introduction: In physics,a charge carrier is particle free to move, carrying on electric charge, especially the particles that carry electric charges in electrical conductors.