EEPC13 Electron Devices Lecture Notes PDF

# EEPC13 ELECTRON DEVICES **Lecture Note-Dr Shelas Sathyan** ## Reference Text books 1. Electronic Devices and Circuits-David A Bell, PHI 2. Electronic Devices and Circuits - Milman and Halkias MCGraw-Hill 3. Electronic Devices and ckt theory-Boylestad 4. Fundamentals of Microelectronics - Behzad...

# EEPC13 ELECTRON DEVICES **Lecture Note-Dr Shelas Sathyan** ## Reference Text books 1. Electronic Devices and Circuits-David A Bell, PHI 2. Electronic Devices and Circuits - Milman and Halkias MCGraw-Hill 3. Electronic Devices and ckt theory-Boylestad 4. Fundamentals of Microelectronics - Behzad Razavi ## Basic Concepts of semiconductors: Semiconductors are a special class of elements having conductivity between that of a good conductor and that of an insulator. - **Semi Conductors**: - **Single Crystal (Ge, Si)**: Have repetitive crystal structure - **Compound**: - GaAs (Galium Arsenide) - CdS (Cadmium sulfide) - GaN (Galium Nitride) - GaAsP (Galium Arsenide Phosphate) **Lecture Notes by Dr. Shelas Sathyan, AP/EEE/NITT** ## All matter is composed of atoms. All atoms consist of electron, proton and neutrons except normal hydrogen which does not have a neutron. - **Niels Bohr Model**: - **Model of atom**: - Quantum model (More accurate and difficult to visualize) According to Bohr model, atoms have nucleus (e, Proton and uncharged neutrons) - **Atomic Number**: In periodic tables of elements, elements are arranged in the order of atomic number - **Atomic Number = Number of Protons in the nucleus** Maximum number of electrons in each shell: maximum no of electrons (Ne) that can exist in each shell of an atom is given by: $Ne = an^2; n = shell number$ A given atom has a fixed number of shells. The shell numbers are designated as 1, 2, 3... ## Outermost shell is known as "Valance shell" and electrons in that shell is known as "Valance electron". Outermost shell of an atom can not accomodate more than 8 electrons. - **Valance shell have highest energy level** - **Energy level increases from first shell to Valance shell** **eg**: * **Neon's outermost shell is full (8 electrons). Hence no tendency for chemical reaction.** * **Sodium have one valance electron → Very reactive** * **Chloride have 7 valance electrons → Very reactive** * **Best conductors (silver, copper, gold) → 1 valance electron** * **Best insulators have 8 valance electrons** ## Solids - **Insulator** ins = 0 - **Semi Conduttor** - **Conductor** Cond = ∞ **At absolute zero temperature, semiconductor is equal to an insulator.** ## In metals atoms are closly packed/periodic Arrangement, Lattice Structure. **Lecture note by Dr. Shelas Sathyan** + + + + + + + + + + - + **free electron** ## At absolute zero temperature, resistivity = 0. As temp ↑ Kinetic energy ↑. So the ions Vibrate. Electrons collide with the vibrating ions. So electron loss energy. These Vibration are random. ## Energy Level → with in each energy level we have sublevels s, p, d, f | n | Sublevels inside | Number of sublevels in an energy level is equal to number of energy level | |:---:|:---:|:---:| | 1 | S | | | 2 | S,P | | | 3 | S,P,d | | | 4 | S, P,d,f | | **eg- n=1, 1 Sublevel (S); n=2, 2 Sublevels (S,P) etc** **with each sublevel, there are orbitals. A maximum of 2 electrons can occupy an orbital.** ## Sublevel | Sublevel | No of orbitsals in the sublevel | |:---:|:---:| | S | 1 → 2 electron | | P | 3 → 6 electrons | | d | 5 → 10 electrons | | f | 7 → 14 electrons | ## Diagonal Rule of dectron filling: 1S 2S 2P 3S 3P 4s 3d 4p *1S 2S 2P 3S 3P 3d 4S 4P 5S 5P 6S 6P 7S * **Diagonal rule of electron filling** **eg: Silicon = 14 electron, 1S² 2S² 2P^6 3S² 3P²** **Energy level** - 3P - 3S - 2P - 2S - 1S **Single Si atom** ## 2 silicon atoms form a moleculas orbitals - 3P 3P molealas orbital - 35 - 2P - 2P - 2S - 2S - 1S 1S moleules orbital. - 1S } 3p energy band. } 3S } 2P } 2S } 1S **N atoms. forms energy band.** ## Spacing between two nearby atoms is called lattice constant. A silicon atom in isolation contain 4 Valence electron. Hence need 4 more electrons to complete its outermost shell. Hence we can make a silicon Crystal where each si atoms us - surrounded by exactly 4 others. As a result each atom share one valance electron with its neighbours and completing its own shell. The bond thus formed is called "covalent bond". ## At temperature near absolute zero CT= ok), valance electrons are confined to their respective covalent bonds, refusing to move freely ie, Si crystal behave as an insulator for T= ok. ## At higher temperature, electrons gain thermal energy occasionally breaking away from the bonds and acting as free carriers. - **Si** - **Si** - **Si** - **Si** - **Si** - **Si** - **Si** - **Si** - **Si** **Covalent bond** **Final Crystal structure is a tetrahedral. Si** **Silicon Crystal** ## When free from a covalent bond, an electron leaves a "Void" bond is now incomplete. This void is called "hole" **This hole can absorbe a free electron if one become avilable electron-hde pair.** ## When an dectron is freed, an "electron-hole" pair is formed. When an electron falls into a hde electron-hole recombination occurs | IN | IV | V | Section of periodic table conteuning number of 3 to 5 valeme e electron. | |:---:|:---:|:---:|:---:| | Boron (B) | Carbon (C) | Phosphorus (P) | | | Aluninum (A1) | Silicon (Si) | | | | Galium (Ga) | Germanium (Ge) | Arsenic (As) | | ## Bandgap Energy **A minimum energy is required to dislodge an dectron from a covalent bond. And this is called Band energy (Eg) for Silicon Eg= 1.12ev, Eg = 0.67ev for Ge** **Electron volt - Energy necessary to move one dectron across potential difference of IV. lev = 1.6x10^-19 J lev = 1.6x10^-19 J NT.** - **lev** **Insulator have higher Eg= 2.5ev ( for diamond** **Semiconductor have Eg= 1 lev to 1.5ev** **Eg = 1.12ev for Si; 0.67ev for Ge; 1.43ev for GaAs** ## Semiconductors whose conductivity can be tailored Hunned for a metal and insulator can not change the concluctivity as easliy at room temperature **Semi Conductor can be used as** - Switch - Amplifier - logic devices - memary devices - LED - Solar pv - Photo detector ete **1948 transistor@Bell lab → 2021** ## IC - ㅁㅁㅁ - ㅁㅁ **Moore's Law- Number of transistors in an Ic Ichip doubles about every two years.** - ↓ - → **Small size, complexity and functionality increas energy.** **Eneray band.** - } mostly empty. - } fully filled with electron. - distance **Let us convide Si atoms. Atomic No: 14 1s², 2s² 2p^6, 3s² 3p²** **outer most shell** - 3P - 3S - 2P - 2S - 1S **Outermost shell have 4 Valance electron.** **A Silicon crystal will have large number of atoms and equally spaced** Spacing between two nearly atoms is called "lattice constant" and at room temp. it is a fixed number for each material. ## Lets bring each si atoms have their own shell. When bringing them close, atoms will intract each other. le, discreter enersy level (1S,2S etc) will interact each other Cach discrete energy level then star to Spliting into band. **One Si atom** **One Si atom** **discrete lever.** **eneray level.** - } continum of levels appears as a band **al T ok** - **CB** * **Ec** * **Eg= Ec-Ev.** * **Ev** * **VB.** **CB** **CB** - **Gev** - **^lev** - **VB** - **VB** **///////// Ge= Eg= 0.78sev** - **Se=121ev od ok** **lev=1.6x10^19 J** **Insulator'** **Semi Cond** **metal** ## Si ## Si ## Si ## Si ## Si Si ## Si ## Si ## Si ## Si Si ## Si ## δι ## Si ## Si ## Si ## Si **Can Conduet at rom temperative** **Concept of band gap eneray** **denrity↑** **free electrons in si** - **Ge** - **Si** **OK** **T** ## Density of electron Ni (No of electrons / cm³) **intrinsic.** **Ni = 5.2x10^15 3/2T^-Eg/2KT electrons/cm³** **K=Boltzman's constant = 1.38x10^23J/K** **Eg ≈ 112 ev Si; 0.67 ev (Ge), 2.Sev for diamond.** ## Q) at T= 300k, ni = ? for silicon- **1cm³ of Silicon- 10 ni = 10 dectron/cm³ - 1.5x10^10 exact Value** **10 free electron** ## how many atomy of Silicon Icm³ = 5x10^22 atoms/cm³ So compared to the number of actual atoms, very low number of free electrons are thermally generated at room temperature. ## Pure Silicon/intrinsic Silicon. ## Concept of holes **hole due to void of electron. So we associate the charge to hole.** **hole Si** **t=0** **Si =Si = Si = si** **Si** **Si** **Si** **Si =Si = Si = si** **Si** **Si** **t:0** **Si** **Si =Si Si = si** **Si** **Si** **t:1** **Si** **Si =Si St Si osi** **Si** **Si** **t: 2** **hdes moves from left to right = the Current** ## why holes slower than electron? **hole movement is based on the redase and trap mechanism. So their movement is slower than electron.** ## Density of holes = Density of free electrons for purre Si **P = n = Ni** **Pin = n²** **→for intrinsic Semiconductor** ## EC **Ev = maximum energy of the Valance energy band** **forbiden band gap Eg** **Ec = Minimum energy level of the conduction band.** **Ev** **Eg=Ec-Ev** ## Materials with very large band gap energy (3 to 6ev) are insulators. In a semiconductor the band gap energy is in the order of lev. ## The net charge in a semiconductor is Zero. That is a Semiconductor is neutral. ## The concentration of the electrons / holes are important in a semiconductor material. In a purel intrinsic semiconductor the density of the electrons and holes are equal. So we use notation "ni" as the intrinsic carried concentration for the concentration of the free electrons as well as that of the holes. **Ni = BT^3/2 e^-Eg/2KT** **B=Coefficient related to a specific semiconductor material** **Eg = Band gap energy** **T = Temp. in kelvin** **K = Boltzman's constant (1.38×10^23J/K) (60) (86x10 ev/12** **for Si B=5.2X10^15, Ge B=1.66x10^15** ## Q) Calulate the intrinsic Carried concentration (ne) in GaAs (gallium Arsenide and germanium at T= 300k, Eg of GaAs = 1.4eV and B= 2.10x10^14 ## It is possible to modify the resistivity of silicon by replacing some of the atoms in the crystal cwith atoms of another material. **Let us consider phosphorus (P) which have 5 Valence election. Once a 'P'atom introdied in a Silicon Crystal, each P atoms share 4 electrons with neighbouring 'se atoms. The 5th electron is unattached and free to move. If N Phosphorus atoms are uniformily introduced in each Cubic centrimeter of a Si Crystal, the density of the free electrons rises by the same amount.** - **Si** - **Si** - **Si =** - **Si = P = SI =** - **Si =** **✓ free electron.** ## The controlled addition of an impurity to an intrinsic Semiconductor is called **Doping**. In above example 'P' is the dopant. The doped Silicon Crystal is now called as **Extrinsic Semiconductor**. More specifically **n-type** ## n-type semiconductors are formed when pentavalent material is added to tetravalent element. **Pentavalent elements includes Antimony (SD), Posphorus (P) Arsenic (As).** ## The free electrons thus formed is not completly free. It is still have some influence of nucleus. Hence they form another discrete energy level just below the Conduction band ## CB ## ↓ ## 0.05ev for Si ## 0.01 ev for Ge ## →lonization energy level. ## V-B ## ↑ED free dectron energy level ## *In ambient Iroom temperature all these free electrons are avilable in CB **Since the pentavalent impurities are donate excess election, therefore referred to as donor OD n-type impurities** ## P-type Semiconductor **Here trivalent impurities like Boron (B), Galium**(Ga), **indium (Id) etc are introduced to the lattice of tetravalend element.** - **Si** - **Si = B = St** - **St** **Void/hole is formed due to the absence of electron** ## P-type impurities forms "holes". These holes can accept external/ free electrons. Hence these impurities are called Acceptor or P-type impurities. - **CB** - **V.B** **0.05ev for si** **0.01 ev for Ge** **↓ holes energy level** **↑** **here a very small amount of energy is required for an electron to leave the valance band and occupy the acceptor energy level. Thus holes are generated in the Valance band.** ## In n-type semiconductor → Majority carmer = electron ## → Minority camier = hole ## In P-type semiconductor Majority cormer = hole ## → Minority carrier = electron ## The Mass-Action Law **For an intrinsic Semiconductor we have n = P= ni or n.p=ni²** - **Let we adde ND donor atoms to an intrinsic Si. Now the density of free electrons increases to Notn for an n type semiconductor** **ND+n = nn (density of free electrons/cm³ in an n-type semiconductor).** **The density of the hole: Pn** **Now (ND+n) Pn = ni² [since ND>n]** **:: ND. Pn = ni² Pn = n²/ND** - **as No increases no of free electrons, more hole-electron recombination occurs in n-type semiconductor so that ND. Pp = ni².** **eg- in intrinsic Let n=P=1.5×10^10. Let due to doping nn = 1.5X10³. Then Pn = 1.5x10^7 so that nn. Pn = Constant** **Similary for a P-type semiconductor, NA ~ Pp NA np=ni; np= n²/NA** ## Q)A Piece of Crystaline si is doped uniformily with Phosphorus atoms. The doping density is 10^16 tomo/cm³. Determine the electrons and hole density in this material at room temperature. **sd - Addition of 10^16 Patoms = 10^16 free electrons/cm3. so n = ND = 10^16** **No. pn = ne²: P= n²/Np = (1.5x10^10)^2/10^6** ## Q) What will be the value of Pat T= 600k? ## Transport of carriers - **→Drift** - **→Diffusion** **We have studied charge carries and the concept of doping. Let us examine the movement of charge commer in semiconductor. le, mechanisms leading to the flow of Current. Drift: Material can conduet current in response to a Potential difference and hence an electric field. The field accelerates the charge carriers in the material, forcing some to flow from one end to the other end. Movement of charge carries due to an electric field is called Drift.** **Note - Potential (voltage) difference, Vis equal to the negative integral of the electric field E with respect to distance.** **b** **Vab = -SEdx** **E** **a** **-** **+** ## In semiconductor, charge carriers are accelerated by the field and accidentally collide with the atoms in the Crystal, eventually reaching the other end and flowing into the battery.** **Acceleration due to the field and the collision with the Crystal counteract, leading to a constant Velocity for the carmers. (This phenomenon is analogous to the terminal velocity' that a sky diver with parachute experience). we expect this constant velocity 'v' es proportional to the electric field strength E.** **να Ε** **V=ME; M = Mobility in cm²/v.s** **In silicon, mobility of dedron Mn = 1350cm²/Vs and mobility of hole Mp=480cm²/v.s.** ## Since electrons moves in a direction opposito to the electric field, we must express the velocity vector as **vë = -MnẺ** **And for holes.** **V Tỉn = MpẺ** **Due to the electric field, charge carrier experience a force and accelerates. when electron accelerate, it hit with atoms and lose velocity. Finaly reach a steady velocity.** - **W** - **L** - **h** **Ymetry** **Let v be the velocity of the carmer. we need to find the current Current. B** **Electoncheld F = VB. And E is constant. The current is given by the charge that passes through the crossectional area in one second. Velocity of the charge carries is V. All the charges in the volume passes the crossectional area in one second le, the current ← free electrons Icm³** **:: Total charge = (W. w.h) n.q = I=MnVB. w.h.n.g** **R= L Mn whng A** **R= ㅗ | R= L Ang A A** **I un. a** **Current density is given by Jn = Mn Ven. q = MnEngel electron. hole. Total Current density J=(unng+Mp.P.PDE J=qCMn.n +Mp.PDE** **.. Total Drift Current density is given by J = q (Mn-n+Mp.DE = FE onductorty.** **Velocity Saturation. We have V = ME. Velocity rise linearly with E. But in reality, If E increases, I no longer follous E linearly. Because Carmes collide with the lattice so frequently and the time between the collision is so shoot that they can not accelerate much. Hence at high E, ✓ varmies "Sublinearly" and eventually reaching a saturation level Vsat = Velouty saturation.** **Velocity↑** **Vsatt** **←** **E**