# ESE 372 / Spring 2013 / Lecture 5 Metal Oxide Semiconductor Field Effect Transistor

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1 Metal Oxide Semiconductor Field Effect Transistor V G V G 1

2 Metal Oxide Semiconductor Field Effect Transistor We will need to understand how this current flows through Si What is electric current? 2

3 Back to atom E 3 E 2 E 1 P 3 P 2 P 1 Electron near nucleus in atom can have only certain set of shapes of probability density functions. Each of them corresponds to different bond energy. In order to release electron from ground state in atom one has to spend energy E 1. In hydrogen this energy is ~13.6 ev. 3

4 Two atoms together Simple model of crystal A lot of atoms together Bands of energy levels 4

5 Semiconductors Once temperature is increased above absolute zero the vibration of lattice can excite electrons from valence band into conduction band and two types of mobile charges would appear: 1. Electrons in conduction band; 2. Holes in valence band. These quasi particles can move and thus give rise to electric current. We will need to learn how to calculate the concentrations of free electrons and holes. 5

6 Concentration of electrons in conduction band Top of conduction band Top of conduction band Density of states - Number of allowed states per unit energy per unit volume Probability of having electron at state with energy E. Number of electrons in energy interval de near energy E in crystal of unit volume: 6

7 Probability of having electron at energy E. Boltzmann's constant Now let s take into account the fact that for transition to occur one has to have electron in original state. Probability that electron is at E 1. Probability that electron is at E 2. 7

8 Fermi Dirac distribution function In equilibrium: hence Fermi energy 8

9 Concentration of electrons in conduction band HERE THERE ARE ALLOWED STATES AND NONZERO PROBABILITY OF HAVING ELECTRONS Density of states - Number of allowed states per unit energy per unit volume??? Fermi-Dirac distribution function 9

10 Consider crystal of volume Density of states From uncertainty principle hence Volume in momentum space per state: Two electrons per state (Paoli s exclusion principle) Number of states with momentum : Kinetic energy of electron in conduction band Density of states number of states per unit energy per unit volume. Electron s effective mass 10

11 Electron and Hole concentrations 11

12 Boltzmann s approximation Can not be taken analytically Fortunately for for Effective density of states at band edge 12

13 Electron and hole concentrations. 13

14 Intrinsic semiconductors 14

15 Drift Current in intrinsic Si Average time between collisions Electron mobility 15

16 Doping Intrinsic N-type P-type P donor atom P has 5 electrons, four of them are used to complete chemical bonds and one remains loosely bound to P. B acceptor atom B has 3 electrons, can still one extra to complete chemical bonds. Concentration of donor atoms Concentration of acceptor atoms 16

17 Doped Semiconductors N-type P-type 17

18 Drift current in n type Positive voltage means increased potential energy of positively charged particle Potential energy of negatively charged particle, i.e. electron 18

19 Diffusion current Flux of electrons from left to right: Diffusion coefficient 19

20 N type in equilibrium Einstein relationship: Hence 20

21 Excess (nonequilibrium) charge carriers Equilibrium Shine light with photon energy > bandgap Nonequilibrium Quasi-Fermi levels Steady-state nonequilibrium carrier concentration will be determined by light intensity and carrier lifetime. 21

22 Excess (nonequilibrium) charge carriers Once excitation is removed the carrier concentrations will decay to their equilibrium values. carrier lifetime 22

23 Inject excess carriers Diffusion current density Assume no electric field and observe that carriers recombine as they move due to diffusion 23

24 Diffusion length Electron concentration can change in time only if or due to recombination. - Continuity equation In case of diffusion: In steady-state: Diffusion length 24

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