Overview of Silicon Device Physics Dr. David W. Graham West - PowerPoint PPT Presentation

Overview of Silicon Device Physics Dr. David W. Graham West Virginia University Lane Department of Computer Science and Electrical Engineering 1

������� Silicon is the primary semiconductor used in VLSI systems Si has 14 Electrons Energy Bands (Shells) Valence Band Nucleus At T=0K, the highest energy band occupied by an electron is Silicon has 4 outer shell / called the valence valence electrons band. 2

������������ • Electrons try to occupy the lowest Disallowed energy band possible } Energy • Not every energy States level is a legal state Increasing for an electron to Electron occupy Allowed Energy • These legal states } Energy tend to arrange States themselves in bands Energy Bands 3

������������ E C Conduction Band First unfilled energy band at T=0K Energy E g Bandgap E V Valence Band Last filled energy band at T=0K 4

������������� Increasing electron energy E C E g E V Increasing voltage Band Diagram Representation Energy plotted as a function of position � Conduction band E C � Lowest energy state for a free electron � Valence band E V � Highest energy state for filled outer shells � Band gap E G � Difference in energy levels between E C and E V � No electrons (e - ) in the bandgap (only above E C or below E V ) � E G = 1.12eV in Silicon 5

����������������������� Silicon has 4 outer shell / valence electrons Forms into a lattice structure to share electrons 6

����������������� The valence band is full, and no electrons are free to move about E C E V However, at temperatures above T=0K, thermal energy shakes an electron free 7

������������������������ For T > 0K • Generation – Creation of an electron (e - ) Electron shaken free and can cause current to flow and hole (h + ) pair • h + is simply a missing electron, which leaves an excess positive charge (due to an extra proton) • Recombination – if an e - and an h + come in contact, they annihilate each other • Electrons and holes are called “carriers” h + e – because they are charged particles – when they move, they carry current • Therefore, semiconductors can conduct electricity for T > 0K … but not much current (at room temperature (300K), pure silicon has only 1 free electron per 3 trillion atoms) 8

������ • Doping – Adding impurities to the silicon crystal lattice to increase the number of carriers • Add a small number of atoms to increase either the number of electrons or holes 9

�������������� Column 3 Column 4 Elements have 3 Elements have 4 electrons in the electrons in the Valence Shell Valence Shell Column 5 Elements have 5 electrons in the Valence Shell 10

���������������������� Donors • Add atoms with 5 valence-band electrons • ex. Phosphorous (P) • “Dontates an extra e - that can freely travel around • Leaves behind a positively charged nucleus (cannot move) • Overall, the crystal is still electrically + neutral • Called “n-type” material (added negative carriers) • N D = the concentration of donor atoms [atoms/cm 3 or cm -3 ] ~10 15 -10 20 cm -3 • e - is free to move about the crystal (Mobility µ n ≈ 1350cm 2 /V) 11

���������������������� Donors n-Type Material • Add atoms with 5 valence-band electrons – – – – + + – + + + + • ex. Phosphorous (P) • “Donates” an extra e - that can freely – – + + – – + + – + + + travel around – – – + – • Leaves behind a positively charged + + + + + – – – nucleus (cannot move) • Overall, the crystal is still electrically neutral Shorthand Notation + • Called “n-type” material (added Positively charged ion; immobile negative carriers) – Negatively charged e-; mobile; • N D = the concentration of donor Called “majority carrier” atoms [atoms/cm 3 or cm -3 ] + Positively charged h+; mobile; ~10 15 -10 20 cm -3 Called “minority carrier” • e - is free to move about the crystal (Mobility µ n ≈ 1350cm 2 /V) 12

������������������������������ Acceptors • Add atoms with only 3 valence- band electrons • ex. Boron (B) • “Accepts” e – and provides extra h + to freely travel around • Leaves behind a negatively h + charged nucleus (cannot move) • Overall, the crystal is still – – electrically neutral • Called “p-type” silicon (added positive carriers) • N A = the concentration of acceptor atoms [atoms/cm 3 or cm -3 ] • Movement of the hole requires breaking of a bond! (This is hard, so mobility is low, � p ≈ 500cm 2 /V) 13

������������������������������ p-Type Material Acceptors • Add atoms with only 3 valence- + + + band electrons + – – + – – – – • ex. Boron (B) + + – – • “Accepts” e – and provides extra h + + + – – + – – – + to freely travel around + + – + – – – – • Leaves behind a negatively – + + + charged nucleus (cannot move) • Overall, the crystal is still Shorthand Notation electrically neutral – Negatively charged ion; immobile • Called “p-type” silicon (added + Positively charged h+; mobile; positive carriers) Called “majority carrier” • N A = the concentration of acceptor – Negatively charged e-; mobile; atoms [atoms/cm 3 or cm -3 ] Called “minority carrier” • Movement of the hole requires breaking of a bond! (This is hard, so mobility is low, � p ≈ 500cm 2 /V) 14

������������������ The Fermi Function • Probability distribution function (PDF) • The probability that an available state at f(E) an energy E will be occupied by an e - 1 1 ( ) = f E ( ) kT − 1 + E E e f 0.5 � Energy level of interest E E f � Fermi level E f E � Halfway point � Where f(E) = 0.5 � Boltzmann constant k 1.38×10 -23 J/K = 8.617×10 -5 eV/K = � Absolute temperature (in Kelvins) T 15

���� ����������������� − f >> If E E kT f(E) Then 1 ( ) kT ( ) − − ≈ E E f E e f 0.5 Boltzmann Distribution •Describes exponential decrease in the density of particles in thermal equilibrium E f E with a potential gradient •Applies to all physical systems • Atmosphere � Exponential distribution of gas molecules ~Ef - 4kT ~Ef + 4kT • Electronics � Exponential distribution of electrons • Biology � Exponential distribution of ions 16

��������������!"�#������$ E E C E g E f E V 0.5 1 f(E) Band Diagram Representation Energy plotted as a function of position � Conduction band E C � Lowest energy state for a free electron � Electrons in the conduction band means current can flow • Virtually all of the � Valence band E V � Highest energy state for filled outer shells valence-band energy � Holes in the valence band means current can flow levels are filled with e - • Virtually no e - in the � Fermi Level E f � Shows the likely distribution of electrons conduction band � Band gap E G � Difference in energy levels between E C and E V � No electrons (e - ) in the bandgap (only above E C or below E V ) � E G = 1.12eV in Silicon 17

�%%�����%�����������������&�#�� E f is a function of the impurity-doping level n-Type Material E E C E f E V 0.5 1 f(E) • High probability of a free e - in the conduction band • Moving E f closer to E C (higher doping) increases the number of available majority carriers 18

�%%�����%�����������������&�#�� E f is a function of the impurity-doping level p-Type Material ( ) 1 − f E E E E C E f E V 0.5 0.5 1 1 f(E) f(E) • Low probability of a free e - in the conduction band • High probability of h + in the valence band • Moving E f closer to E V (higher doping) increases the number of available majority carriers 19

����������������%�'���������������� • Applies to both electronic systems and biological systems • Look at drift and diffusion in silicon • Assume 1-D motion 20

���%� Drift → Movement of charged particles in response to an external field (typically an electric field) E-field applies force F = qE which accelerates the charged particle. However, the particle does not accelerate indefinitely because of collisions with the lattice (velocity saturation) Average velocity <v x > ≈ -µ n E x electrons < v x > ≈ µ p E x holes µ n → electron mobility → empirical proportionality constant between E and velocity µ p → hole mobility E µ n ≈ 3µ p 21