MIT6_012F09_lec02

MIT6_012F09_lec02 - Clif Fonstad, 9/15/09 Lecture 2 - Slide...

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Unformatted text preview: Clif Fonstad, 9/15/09 Lecture 2 - Slide 1 6.012 - Electronic Devices and Circuits Lecture 2 - Uniform Excitation; Non-uniform conditions Announcements Review Carrier concentrations in TE given the doping level What happens above and below room temperature? Drift and mobility - The full story. Uniform excitation: optical generation Generation/recombination in TE Uniform optical generation - external excitation Population excesses, p' and n', and their transients Low level injection; minority carrier lifetime Uniform excitation: applied field and optical generation Photoconductivity, photoconductors Non-uniform doping/excitation: diffusion, continuity Fick's 1st law; diffusion Diffusion current; total current ( drift plus diffusion ) Fick's 2nd law; carrier continuity Clif Fonstad, 9/15/09 Lecture 2 - Slide 2 Extrinsic Silicon, cont.: solutions in Cases I and II Case I - n-type : N d > N a :, (N d- N a ) >> n i "n-type Si" Define the net donor concentration, N D : N D " ( N d # N a ) n o " N D , p o = n i 2 ( T )/ n o " n i 2 ( T )/ N D We find: In Case I the concentration of electrons is much greater than that of holes. Silicon with net donors is called "n-type" . n o >> n i >> p o Case II - p-type : N a > N d :, (N a- N d ) >> n i "p-type Si" Define the net acceptor concentration, N A : N A " ( N a # N d ) p o " N A , n o = n i 2 ( T )/ p o " n i 2 ( T )/ N A We find: In Case II the concentration of holes is much greater than that of electrons. Silicon with net acceptors is called "p-type" . p o >> n i >> n o Clif Fonstad, 9/15/09 Lecture 2 - Slide 3 Variation of carrier concentration with temperature (Note: for convenience we assume an n-type sample) Around R.T. Full ionization Extrinsic doping N d + " N d , N a # " N a N d + # N a # ( ) >> n i n o " N d # N a ( ) , p o = n i 2 n o At very high T Full ionization Intrinsic behavior N d + " N d , N a # " N a n i >> N d + # N a # n o " p o " n i At very low T Incomplete ionization Extrinsic doping, but with carrier freeze-out N d + << N d assuming n " type ( ) N d + " N a " >> n i n o # N d + " N a " ( ) << N d " N a ( ) , p o = n i 2 n o Clif Fonstad, 9/15/09 Lecture 2 - Slide 4 Uniform material with uniform excitations (pushing semiconductors out of thermal equilibrium) A. Uniform Electric Field, E x , cont. Drift motion : Holes and electrons acquire a constant net velocity, s x , proportional to the electric field: At low and moderate |E|, the mobility, , is constant. At high |E| the velocity saturates and deceases. Drift currents : Net velocities imply net charge flows, which imply currents: Note: Even though the semiconductor is no longer in thermal equilibrium the hole and electron populations still have their thermal equilibrium values....
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MIT6_012F09_lec02 - Clif Fonstad, 9/15/09 Lecture 2 - Slide...

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