Materials Science and Engineering - Electronic and Mechanical Properties of Materials Part 6 pps

3.225 7 Use of Minority Carrier Diffusion Equations • Example: Light shining on a surface of a semiconductor hν G at x=0 (assume infinite absorption coefficient to simplify example) G p x p D t p h h + ∆ − ∂ ∆∂ = ∂ ∆∂ τ 2 2 n-type ∆p(x)? 0 Steady state solution =0 in bulk x hh hh axax axax axax hh D a D BeAe BeaAea BeAep D p x p τ τ τ 1 22 2 2 = + =+ +=∆ ∆ = ∂ ∆∂ − − − try Now use boundary conditions of the problem: hh D x Bep A px τ − =∆ = ∴ =∆∞= 0 0,@ Units of length: minority carrier diffusion length, L h h L x h h h eGp GB Gpx − =∆ = ∴ =∆= τ τ τ ,0@ ∆p x Gτ h x p eDJ hh ∂ ∆∂ = © E. Fitzgerald-1999 3.225 8 Semiconductor Electronics • Single crystalline - largely Si some III - V compounds • Dominated by many nearly identical, highly engineered junctions • DRAMS (today) ≈ 10 9 transistors • Microprocessors (2002) ≈ 10 8 transistors •Total ≈ 10 18 yr ≈ 10 6 /person/day © H.L. Tuller, 2001 4 3.225 9 Junction Fabrication Processes © H.L. Tuller, 2001 3.225 10 CMOS Devices © H.L. Tuller, 2001 5 3.225 11 The p-n Junction (The Diode) • Note that dopants move the fermi energy from mid-gap towards either the valence band edge (p-type) or the conduction band edge (n-type). p-type material in equilibrium n-type material in equilibrium p~N a n~N d n~n i 2 /N a p~n i 2 /N d         += C d bgF N N TkEE ln         −= V a bF N N TkE ln E c E c E F E v E F E v What happens when you join these together? © E. Fitzgerald-1999 3.225 12 - - + + + + Holes diffuse Electrons diffuse + + + + - - - - + + + + - - + + + + An electric field forms due to the fixed nuclei in the lattice from the dopants Therefore, a steady-state balance is achieved where diffusive flux of the carriers is balanced by the drift flux E Drift and Diffusion © E. Fitzgerald-1999 6 7 3.225 13 Joining p and n E c E F E v p n Carriers flow under driving force of diffusion until E F is flat - - + + + + Holes diffuse Electrons diffuse © E. Fitzgerald-1999 3.225 14 - - + + + + - - + + + + W: depletion or space charge width Metallurgical junction ρ E V V bi dx x E ∫ = ε ρ )( dxxEV ∫ = )( pand xNxN = x p x n )( 2 ada dbior p NNN N e V x + = εε )( 2 add abior n NNN N e V x + = εε ad dabior NN NN e V W + = εε2 Space Charge, Electric Field and Potential © E. Fitzgerald-1999 1 What is the built-in voltage V bi ? E c E F E v p n eV bi =E Fn -E Fp         −=         −= dV i b V n bFn NN n Tk N p TkE 2 lnln         −=         −= V a b V bFp N N Tk N p TkE lnln         = ∴ 2 ln i dab bi n NN e Tk V We can also re-write these to show that eV bi is the barrier to minority carrier injection: Tk eV np b bi enn − = Tk eV pn b bi epp − = n n n p p n p p eV bi eV bi © E. Fitzgerald-1999 Qualitative Effect of Bias • Applying a potential to the ends of a diode does NOT increase current through drift • The applied voltage upsets the steady-state balance between drift and diffusion, which can unleash the flow of diffusion current • “Minority carrier device” E c E F E v n n n p p n p p eV bi eV bi Tk VVe np b abi enn )( −− = Tk VVe pn b abi epp )( −− = +eV a -eV a © E. Fitzgerald-1999 2 Current Flow - Recombination, Generation © H.L. Tuller, 2001 • Forward bias (+ to p, - to n) decreases depletion region, increases diffusion current exponentially • Reverse bias (- to p, + to n) increases depletion region, and no current flows ideally E c E F E v n n n p p n p p eV bi -e|V a | Qualitative Effect of Bias E c E F E v n n n p p n p p eV bi +e|V a | eV bi -e|V a | eV bi +e|V a | Forward Bias Reverse Bias + - V a         −=         −         += 11 22 Tk qV o Tk qV d i h h a i e e b a b a eJe N n L D N n L D qJ q TkD b i i = iii DL τ = V I Linear, Ohmic Rectification, Non-linear, Non-Ohmic V=IR V=f(I) Solve minority carrier diffusion equations on each side and determine J at depletion edge © E. Fitzgerald-1999 Devices Solar Cell/Detector Reverse Bias/Zero Bias J edrift E c E F J hdrift E v LED/Laser J ediff E c Laser E F •population inversion E v •reflectors for cavity J hdiff © E. Fitzgerald-1999 Potential Wells - Heterojunction Lasers Energy bands of a light-emitting diode under forward bias for a double heterojunction AlGaAs-GaAs-AlGaAs structure. © H.L. Tuller, 2001 3 4 Transistors Bipolar (npn) E c E F E v emitter base collector J diff J drift Barrier, controlled by V EB V EB V BC base emitter collector © E. Fitzgerald-1999 Field Effect © H.L. Tuller, 2001 Transistors FET source gate drain n p x n x=metal is a MESFET x=metal/poly Si/oxide is a MOSFET CMOS © E. Fitzgerald-1999 Polycrystalline Solar Cells • Local field enhances minority carrier capture → reduced minority carrier lifetime • majority carriers experience potential barrier → increased resistivity; reduced effective mobility • boundaries intersecting p-n junction provide shorting paths → increase I o , decrease V oc . © H.L. Tuller, 2001 5 6 Effect of Traps (Defects) on Bands • Trapping (Fermi level in defect) creates depleted regions around defect         += C d bgF N N TkEE ln •E F position in semiconductor away from traps in n-type material •E F pulled to mid-gap in defect/trap area E c E F E v E F pulled to trap level in defect E trap Depleted regions; internal electric field E donor © E. Fitzgerald-1999 Other Means to Create Internal Potentials: • Different semiconductor materials have different band gaps and electron affinity/work functions • Internal fields from doping p-n must be superimposed on these effects: Poisson Solver (dE/dx=V=ρ/ε) E F Vacuum level ϕ 1 ϕ 2 E g1 E g2 Thin films Substrate Potential barriers for holes and electrons can be created inside the material Heterojunctions © E. Fitzgerald-1999 . when you join these together? © E. Fitzgerald-1999 3.225 12 - - + + + + Holes diffuse Electrons diffuse + + + + - - - - + + + + - - + + + + An electric field forms due to. n E c E F E v p n Carriers flow under driving force of diffusion until E F is flat - - + + + + Holes diffuse Electrons diffuse © E. Fitzgerald-1999 3.225 14 - - + + + + - - + + + + W: depletion or space charge. dopants move the fermi energy from mid-gap towards either the valence band edge (p-type) or the conduction band edge (n-type). p-type material in equilibrium n-type material in equilibrium p~N a