Slide 1: Semiconductor Fundamentals & PN Junction Device Physics
Semiconductor Fundamentals & PN Junction Device Physics Reviewed 2025 © 2022-2025 Micron Technology, Inc. All rights reserved. Information, products, and/or specifications are subject to change without notice. All information is provided on an “AS IS” basis without warranties of any kind. Statements
Slide 2: Copyright guidelines
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Slide 4: Table of contents
Table of contents Semiconductor Fundamentals & PN Junction Device Physics 1 Goals, objectives and target audience 2 Energy band formation 3 Intrinsic vs extrinsic semiconductor 4 Fermi-Dirac distribution 5 Transport properties 6 PN junction 7 Glossary 8 References 4
Slide 5: Semiconductor Fundamentals – goal and objectives
Semiconductor Fundamentals – goal and objectives Goal Objectives • Participants will have foundational understanding • Cite basic knowledge of atomic theory and band of semiconductors, PN diode device physics, and formation, semiconductor carrier concentration, how it relates to electrical character
Slide 6: Target Audience
Target Audience • Interns, NCGs (new college grads) and new employees in some technical roles need to understand these concepts Pro tip • Examples of critical target audience roles at Micron that utilize Everyone interviewing at Micron these concepts can use this presentation to – Device Engineer –
Slide 7: Potential Energy
E - Potential energy V - Electric potential Potential Energy ξ - Electric field Analogy between gravitational & electrical energy Gravitational Potential Energy, U = Work done to move an Electric Potential Energy, E = Work done to move a test object, with mass m against gravitational field (g) over
Slide 8: Potential
E - Potential energy V - Electric potential Potential ξ - Electric field Normalized quantity, energy per unit mass or charge Gravitational potential is the amount of gravitational Electric potential is the amount of electric potential energy potential energy per unit mass at a specific point in a pe
Slide 9: Potential vs Energy
E - Potential energy V - Electric potential Potential vs Energy ξ - Electric field • Unit of potential is Volt (V) and the unit of energy is Electron-Volt (eV) Potential Energy, E = q ξ d We know potential V = ξ d, then Potential Energy, E = q V For electron energy, E = -e V • 1 electric charge x 1
Slide 10: Electric Field
Electric Field V1 V2 V1 V2 + - + - + - + - 𝒅𝑽 + - + - ξ=− + - + - 𝒅𝒙 + - + - + - + - ∆𝑽 ∆𝑽 𝒅 𝟐𝒅 Electric field strength V1 V1 reduces by half V2 V2 Electric field also can be denoted by # flux lines/area 10
Slide 11: Charge, Potential, Energy and Electric Field
Charge, Potential, Energy and Electric Field +Q -Q + - + - + - + - + - + - Gauss’s Law 𝝆𝒗 𝒙 𝝆𝒗 𝒙 Charge Density, 𝝆𝒗 𝒙 ξ=න 𝒅𝒙 x 𝜺 𝜀 ∶ 𝑝𝑒𝑟𝑚𝑖𝑡𝑖𝑣𝑖𝑡𝑦 𝒅𝑽 ξ Electric Field, ξ=− 𝒅𝒙 V1 Potential, V, 𝝍 𝑽 = − න ξ 𝒅𝒙 V2 Energy (electron), E E = -e.V 11
Slide 12: Silicon
Silicon Silicon is the most used semiconductor element in electronics world 14 Si Silicon 28.0855 Neutral Si atom has 14 electrons [2, 8, 4] Si Electronic Configuration: 1S2 2S2 2P6 3S2 3P2 Si has 4 valence electrons © American Chemical Society - Used with Permission. 12
Slide 13: Energy Level
Energy Level Energy levels of electrons are quantized (discrete) Increasing Electron Potential Energy Si : 1S2 2S2 2P6 3S2 3P2 E0, Vacuum level n=3 Total of 8 valence states, 3p orbital (2/6) 4 of them are filled 3s orbital (2/2) 14 2p orbital (6/6) Nucleus is positively charged; inner electrons are
Slide 14: Energy Level
Energy Level • Silicon is tetrahedrally bonded, each Si atom bonded 4 nearest neighbors to neighboring 4 Si atoms • Lattice structure is like that of diamond • Silicon has N ~ 5 x 1022 atoms per cm3 • 8 valence states give rise to 8N states per cm3 5.43 Å N ~ 5 x 1022 cm-3 14
Slide 15: Energy Bands
Si : 1S2 2S2 2P6 3S2 3P2 Energy Bands N isolated non-interacting atoms, they don’t feel the presence of other atoms. Isolated atoms have discrete energy level Energy of electron 3p 2N electrons/6N states 3s 2N electrons/2N states 2p 6N electrons/6N states 2s 2N electrons/2N states 1s 2N electrons/2N
Slide 16: Energy Bands
Si : 1S2 2S2 2P6 3S2 3P2 Energy Bands If the interatomic distance are reduced slightly, still each atom do not feel the presence of other atoms (non-interacting system) Energy of electron 3p 2N electrons/6N states 3s 2N electrons/2N states 2p 6N electrons/6N states 2s 2N electrons/2N states 1s 2N el
Slide 17: Energy Bands
Si : 1S2 2S2 2P6 3S2 3P2 Energy Bands When atomic spacing reduced, each atom starts to feel the presence of other atom (interacting system) ➔3p & 3s split as per Pauli Exclusion principle. It will Energy of electron take a range of energy levels 2N electrons/6N states 3p 2N electrons/6N states 3s 2N
Slide 18: Interacting system
Interacting system No two electrons with same state 1. PAULI’S exclusion principle states that no two electrons which interact with each other can have the same quantum state 2. When interatomic distance is very large the electrons in orbital will not influenced/disturbed by neighboring atom. The en
Slide 19: Energy Bands
Si : 1S2 2S2 2P6 3S2 3P2 Energy Bands When atomic spacing further reduced, bands originating from different discrete levels lose their identities and merge together Energy of electron 2N electrons/6N states 3p 2N electrons/6N states 3s 2N electrons/2N states 2N electrons/2N states 4N electrons/8N st
Slide 20: Energy Bands
Si : 1S2 2S2 2P6 3S2 3P2 Energy Bands Bands will split again into two different bands Energy of electron 2N electrons/6N states 3p 2N electrons/6N states 3s 2N electrons/2N states 2N electrons/2N states 4N electrons/8N states 2p 6N electrons/6N states 2s 2N electrons/2N states 1s 2N electrons/2N sta
Slide 21: Energy Bands
Si : 1S2 2S2 2P6 3S2 3P2 Energy Bands Energy of electron 0 electron/4N states 2N electrons/6N states Band Gap 3p 2N electrons/6N states 3s 2N electrons/2N states 2N electrons/2N states 4N electrons/8N states 4N electrons/4N states 2p 6N electrons/6N states 2s 2N electrons/2N states 1s 2N electrons/2
Slide 22: Energy Bands
Si : 1S2 2S2 2P6 3S2 3P2 Energy Bands Energy of electron 0 electron/4N states Conduction band EC 2N electrons/6N states Band Gap 3p 2N electrons/6N states EV 3s 2N electrons/2N states Valence band 2N electrons/2N states 4N electrons/8N states 4N electrons/4N states 2p 6N electrons/6N states 2s 2N el
Slide 23: Energy Bands
Si : 1S2 2S2 2P6 3S2 3P2 Energy Bands As temperature increases, the interatomic distance increases (material expands) and hence bandgap reduces Group 14 6 Energy of electron C EG T=0K T=300K Carbon 12.011 Si 1.21eV 1.12eV 14 Ge 0.74eV 0.66eV Si Silicon 28.085 32 Band Gap 3p 2N electrons/6N states Ge
Slide 24: Energy Bands
Energy Bands Energy band diagram is drawn Simplified View of Band Model with respect to electron energy Increasing electron energy EC Eg Eg = EC - EV EV Increasing hole energy Si 24
Slide 25: Intrinsic Semiconductor
Intrinsic Semiconductor Intrinsic: no foreign atoms/undoped, pure crystal T=0K Si Si Si EC Si Si Si Eg EV Si Si Si Increasing hole energy Si At T=0K , no electrical conduction will take place (no electrons in CB & no space for electrons to move in VB) 25
Slide 26: Intrinsic Semiconductor
Intrinsic Semiconductor Intrinsic: no foreign atoms/undoped, pure crystal Higher T Increasing electron energy Si Si Si EC Si Si Si Eg EV Si Si Si Vacant state in VB = Hole Increasing hole energy As T ↑, atoms vibrates which potentially break Si-Si bond and create a free electron and simultaneously S
Slide 27: Extrinsic Semiconductor
Extrinsic Semiconductor Doping with Group 5 elements (Pentavalent/Donors) Group 5 elements have one extra electron which is weakly bounded to nucleus and at room Si Si Si temperature is readily freed (“donated”) to wander around the lattice and hence become a carrier When the Si is doped with donor
Slide 28: Extrinsic Semiconductor
Extrinsic Semiconductor Doping with Group 3 elements (Trivalent/Acceptors) Group 3 elements have 3 valence electrons and cannot complete semiconductor bonds when substituted for Si Si Si Si atoms, however it readily “accepts” an electron from nearby Si-Si bond When the Si is doped with acceptors (NA
Slide 29: Fermi-Dirac Distribution
Fermi-Dirac Distribution 𝒇(𝑬) gives probability of electron filling an energy level 1 𝑬𝒇 = Fermi Level 1-𝒇(𝑬) gives probability of hole filling 𝑓 𝐸 = (𝐸−𝐸𝑓 ) an energy level 1 + 𝑒 𝑘𝑇 𝐸 0 ≤ 𝑓 𝐸 ≤1 0𝐾 𝑇 =0𝐾 1 𝐸 > 𝐸𝑓 𝑓 𝐸 = (+𝑣𝑒) = 0 Ef 1+𝑒 0 1 𝐸 < 𝐸𝑓 𝑓 𝐸 = (−𝑣𝑒) =1…
Slide 30: Fermi-Dirac Distribution
Fermi-Dirac Distribution 𝒇(𝑬) gives probability of electron filling an energy level 1 𝑓 𝐸 = (𝐸−𝐸𝑓 ) 1 + 𝑒 𝑘𝑇 • As T increases, Si bond will break and 0 ≤ 𝑓 𝐸 ≤1 𝐸 there will be more electrons in higher 0 𝐾 < 300 𝐾 energy levels (i.e: conduction band) • Hence, the probability of…
Slide 31: Fermi-Dirac Distribution
Fermi-Dirac Distribution Definition of Fermi Level 1 𝑓 𝐸 = (𝐸−𝐸𝑓 ) 1 + 𝑒 𝑘𝑇 • As T increases, Si bond will break and 0 ≤ 𝑓 𝐸 ≤1 𝐸 there will be more electrons in higher 𝟎 𝑲 < 𝟑𝟎𝟎 𝑲 < 𝑻𝟏 𝑲 energy levels (i.e: conduction band) • Hence, the probability of finding an electron 𝑭𝒐𝒓…
Slide 32: Density of States (DOS)
Density of States (DOS) Energy DOS: Number of electron (hole) states DOS, g(E) per unit energy per unit volume Derived from solution of Schrödinger equation (gives EC dispersion relation) and Heisenberg’s uncertainty principle (defines volume element) EV 32
Slide 33: Carrier Concentration
Carrier Concentration DOS : How energy states are distributed Fermi-Dirac : How carriers are distributed within the energy DOS x Fermi Dirac : Distributions of carriers with respect to energy 33
Slide 34: Carrier Concentration
∞ Carrier Concentration Area under the curve ➔ 𝑛 = න 𝑔 𝐸 𝑓 𝐸 𝑑𝐸 𝐸𝐶 Scenario 1, n=p DOS, 𝒈 𝑬 Fermi function Carrier Distribution Energy 𝒇 𝑬 1-𝒇 𝑬 Exponential tail of electron concentration n = Electron Distribution Fermi Level Midgap X Ef = Ef p = Hole Distribution Exponential tail of…
Slide 35: Carrier Concentration
∞ Carrier Concentration Area under the curve ➔ 𝑛 = න 𝑔 𝐸 𝑓 𝐸 𝑑𝐸 𝐸𝐶 Scenario 2, n>p DOS, 𝒈 𝑬 Fermi function Carrier Distribution Energy 𝒇 𝑬 1-𝒇 𝑬 n = Electron Distribution Fermi Level Midgap X Ef = Ef p = Hole Distribution Electron Distribution = DOS x Probability of finding an…
Slide 36: Carrier Concentration
∞ Carrier Concentration Area under the curve ➔ 𝑛 = න 𝑔 𝐸 𝑓 𝐸 𝑑𝐸 𝐸𝐶 Scenario 3, n<p DOS, 𝒈 𝑬 Fermi function Carrier Distribution Energy 𝒇 𝑬 1-𝒇 𝑬 n = Electron Distribution Fermi Level Midgap X = Ef Ef p = Hole Distribution Electron Distribution = DOS x Probability of finding an…
Slide 37: Energy Bands
Energy Bands Ef Ei = Fermi level = Intrinsic Fermi level Basics EC = Conduction band edge EV = Valence band edge Eg = Band gap EC EC EC Ef q Фb Ef/Ei Ei Ei Eg=1.12eV qФb Ef EV EV EV Undoped Si N-Type Si P-Type Si n=p=ni n >> p n << p | Ef – Ei | = q Фb is known as Fermi potential (bulk potential), m
Slide 38: Energy Bands
• E0, Vacuum energy level is a common reference level which is defined as the energy Energy Bands • level at which the electron is free, i.e: no longer bonded to the lattice qФM /Si, Energy difference between vacuum level and Fermi level, Ef (workfunction) • qχSiO2/Si, Energy difference between vacu
Slide 39: Drift Current
ξ=𝟎 ξ≠𝟎 Drift Current Electric current due to presence of electric field Jn,Drift Random thermal motion Net displacement - ve + ve Jp,Drift ξ, Electric Field 𝐽𝑛,𝐷𝑟𝑖𝑓𝑡 ∝ 𝑒𝑛𝑣 𝑣 = 𝜇𝑒 𝜉 𝑣 : velocity 𝜇𝑒 : mobility 𝑞𝜏 𝑚𝑒∗ : effective mass of electron 𝐽𝑛,𝐷𝑟𝑖𝑓𝑡 = 𝑒𝑛𝜇𝑒 𝜉…
Slide 40: Diffusion Current
Diffusion Current Electric current due to concentration gradients of carriers n A Diffusion of electrons Diffusion current B Higher Lower concentration Diffusion of concentration x region electrons region N type 𝑑𝑛 𝐽𝑛,𝐷𝑖𝑓𝑓 ∝ 𝑑𝑥 𝑑𝑛 𝐽𝑛,𝐷𝑖𝑓𝑓 = 𝑒𝐷𝑛 𝐷𝑛 : Diffusion coefficient 𝑑𝑥…
Slide 41: PN Junction
PN Junction E0, Vacuum level E0, Vacuum level Фbi, built-in potential EC EC Ef Ei Ei Ef EV EV N+ P N+ P Thermal Equilibrium • No external bias/excitations • Reaches steady state/invariant of time • No net current flow • Fermi level needs to be constant/aligned 41
Slide 42: PN Junction
PN Junction Summary of equilibrium process 1. Large concentration gradient of electrons and holes at the junction causes diffusion current 2. Recombination of electron and holes will take place, exposing ionized donors and acceptors Фbi, built-in potential 3. Depletion region causes electric field a
Slide 43: PN Junction
PN Junction Diode ➔ Current flows in one direction only PN Junction Equilibrium Forward Bias Reverse Bias E0 E0 E0 Net current flow VB = Фbi + VR Фbi VB = Фbi -VF EC EC EC EV EV EV WD WD WD ξ bi ξ bi ξ bi ++++ +++ ----- +++++ -------- ------ +++++ -------- N+ ++++ ++++ ------ ------ P N+ +++ +++ ---
Slide 44: PN Junction
N+ P PN Junction ρv qND Equilibrium x -qNA ξ 𝝆𝒗 𝒙 ξ=න 𝒅𝒙 𝜺𝒐 x V 𝒅𝑽 Фbi, built-in ξ=− energy 𝒅𝒙 x 𝑽 = − න ξ 𝒅𝒙 EC qФbi, EF 𝑬 = −𝒆. 𝑽 EV 44
Slide 45: PN Junction
-Ve N+ P +Ve PN Junction ρv qND Forward Bias x -qNA ξ 𝝆𝒗 𝒙 ξ=න 𝒅𝒙 𝜺𝒐 x V 𝒅𝑽 ξ=− VB 𝒅𝒙 x 𝑽 = − න ξ 𝒅𝒙 EC qФbi, EF 𝑬 = −𝒆. 𝑽 EV 45
Slide 46: PN Junction
+Ve N+ P -Ve PN Junction ρv qND Reverse Bias x -qNA ξ 𝝆𝒗 𝒙 ξ=න 𝒅𝒙 𝜺𝒐 x V VB 𝒅𝑽 ξ=− 𝒅𝒙 x 𝑽 = − න ξ 𝒅𝒙 EC qФbi, 𝑬 = −𝒆. 𝑽 EF EV 46
Slide 47: Glossary
Glossary Term or acronym Definition/description Bandgap The energy difference between the conduction band edge (EC) and the valence band edge (EV) in a material. It determines the electrical conductivity of a material as it represents the minimum energy required to excite an electron up to a state i
Slide 48: Glossary
Glossary Term or acronym Definition/description Fermi-Dirac Distribution A statistical distribution that describes the probability of an electron occupying a specific energy level at a given temperature. Forward Bias A condition in which the positive terminal of a power supply is connected to the p-
Slide 49: References
References 1. Fundamental of Modern VLSI Devices, Yuan Taur and Tak H. Ning 2. Modern Semiconductor Devices for Integrated Circuits, Chenming Hu 3. Semiconductor Fundamentals, Robert F. Pierret 4. Semiconductor Physics and Devices, Donald Neamen 5. Physics of Semiconductor Devices, Simon Sze 49
Slide 50: © 2022-2025 Micron Technology, Inc. All rights reserved. Information, products, and/or specifications are subject
© 2022-2025 Micron Technology, Inc. All rights reserved. Information, products, and/or specifications are subject to change without notice. All information is provided on an “AS IS” basis without warranties of any kind. Statements regarding products, including statements regarding product features,