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Lecture7-Equations+of+State+-+Continuity+and+Minority+Carr

Lecture7-Equations+of+State+-+Continuity+and+Minority+Carr...

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Unformatted text preview: ECE 3040 - Dr. Ying Zhang Georgia Tech ECE 3040: Microelectronic Circuits Lecture 7 Reading: Pierret 3.3-3.4 ECE 3040 - Dr. Ying Zhang Georgia Tech Recapture Energy Band Bending under Application of an Electric Field ( ) reference fixed arbitrary c E E q V − − = 1 If an electric field exists in the material, the conduction, valence and intrinsic energies will vary with position! dx dE q dx dE q dx dE q Thus direction one in dx dV or V i v c 1 1 1 , = = = − = −∇ = ε ε ε ECE 3040 - Dr. Ying Zhang Georgia Tech Recapture Diffusion t coefficien diffusion the is D and ion concentrat the is where D F η η ∇ − = The diffusion current density for electrons and holes: n qD J or p qD J n Diffusion n p Diffusion p ∇ = ∇ − = | | ECE 3040 - Dr. Ying Zhang Georgia Tech Recapture Total Current Einstein Relationship: n p n n Diffusion n Drift n n p p Diffusion p Drift p p J J J and n qD nE q J J J and p qD pE q J J J Since + = ∇ + = + = ∇ − = + = μ μ | | | | ... q kT D holes for q kT D electrons for p p n n = = μ μ , , ECE 3040 - Dr. Ying Zhang Georgia Tech Recapture Recombination-Generation: ECE 3040 - Dr. Ying Zhang Georgia Tech ¡ Photogeneration ¡ Indirect Thermal Recombination-Generation ¡ Continuity Equations ¡ Minority Carrier Diffusion Equations ¡ Quasi-Fermi Levels Agenda ECE 3040 - Dr. Ying Zhang Georgia Tech Photogeneration ¡ Light with photon energy, h ν < Eg is not easily absorbed. ¡ Light with photon energy, h ν > Eg is absorbed, which create EHPs. ¡ Photogenerated EHPs are excess carriers ¾ No longer at thermal equilibrium ¾ The excess carriers recombine after some time. ¡ The “unabsorbed” light intensity as a function of depth into the semiconductor is I(x) = I o e- α x where Io is the initial light intensity, x is distance and α is the absorption coefficient [1/cm]. h ν < Eg h ν > Eg ECE 3040 - Dr. Ying Zhang Georgia Tech Photogeneration α , the absorption coefficient, is a material and wavelength-dependent constant. ECE 3040 - Dr. Ying Zhang Georgia Tech Photogeneration Each Photon with energy greater than Eg can result in one electron hole pair. Thus, we can say, ( ) Sec cm e G x G where x G t p t n x LO L L Light Light − = = ∂ ∂ = ∂ ∂ − 3 # ) , ( ) , ( α λ λ G L is the photogeneration rate. ¾ If α is small (near bandgap light), the generation profile can be approximately constant. The light is being uniformly absorbed....
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