Lecture 11 P-N Junction Diodes: Part 1 How do ... - ECE Users Pages

Lecture 11

P-N Junction Diodes: Part 1 How do they work? (postponing the math)

Reading: (Cont’d) Notes and Anderson2 sections Part 2 preface and sections 5.0-5.3

Georgia Tech

ECE 3080 - Dr. Alan Doolittle

Our First Device: p-n Junction Diode

N-type material

N-type material

P-type material

P-type material

A p-n junction diode is made by forming a p-type region of material directly next to a n-type region.

Georgia Tech

ECE 3080 - Dr. Alan Doolittle

Our First Device: p-n Junction Diode ND-NA ND x -NA Junction In regions far away from the “junction” the band diagram looks like: Ec

Ec Ef

Ei

Ei

Ef Ev Georgia Tech

Ev ECE 3080 - Dr. Alan Doolittle

Our First Device: p-n Junction Diode But when the device has no external applied forces, no current can flow. Thus, the fermi-level must be flat! We can then fill in the junction region of the band diagram as:

Ec Ei

Ec Ef

Ef Ev

Ei

or… Georgia Tech

Ev

ECE 3080 - Dr. Alan Doolittle

Our First Device: p-n Junction Diode

Ec Ei Ef Ev

Georgia Tech

ECE 3080 - Dr. Alan Doolittle

Our First Device: p-n Junction Diode Ec

-qVBI

Ei Ef Ev

Electrostatic Potential, V = -(1/q)(Ec-Eref) VBI or the “built in potential”

X Georgia Tech

ECE 3080 - Dr. Alan Doolittle

Our First Device: p-n Junction Diode Electrostatic Potential, V=-(1/q)(Ec-Eref) VBI or the “built in potential”

Electric Field

X

E=-dV/dx

X

Georgia Tech

ECE 3080 - Dr. Alan Doolittle

Our First Device: p-n Junction Diode

Poisson’s Equation: Electric Field

Charge Density (NOT resistivity)

ρ ∇•E = K sε o

ρ dE = or in 1D, dx K sε o

Permittivity of free space Relative Permittivity of Semiconductor (previously referred to as εR)

ρ=q( p – n + ND – NA ) Georgia Tech

ECE 3080 - Dr. Alan Doolittle

Our First Device: p-n Junction Diode Electric Field, E=-dV/dx

X

dE ρ = K sε o dx

X Georgia Tech

ECE 3080 - Dr. Alan Doolittle

Our First Device: p-n Junction Diode Energy -1/q

Potential -dV/dx

Electric Field K sε o

dE dx

Charge Density Georgia Tech

ECE 3080 - Dr. Alan Doolittle

P-N Junction Diodes: Part 2 How do they work? (A little bit of math)

Georgia Tech

ECE 3080 - Dr. Alan Doolittle

Movement of electrons and holes when forming the junction Circles are charges free to move (electrons and holes) Squares are charges NOT free to move (ionized donor or acceptor atoms) High hole Concentration

Electron diffusion

Fig Pierret 5.5High electron Concentration Hole diffusion

Local region of negative charge due to imbalance in hole-acceptor concentrations

Local region of positive charge due to imbalance in electron-donor concentrations

Space Charge or Depletion Region Georgia Tech

ECE 3080 - Dr. Alan Doolittle

Movement of electrons and holes when forming the junction E= - dV/dx -Edx=dV xn

V ( xn )

−xp

V (− xp )

− ∫ Edx = ∫

= V ( xn ) − V ( − x p ) = Vbi

dV

but... dn J N = qµ n nE + qDN =0 dx dn dn D kT dx E = − N dx = − µn n q n

No net current flow in equilibrium

thus... kT Vbi = − ∫ Edx = −xp q xn

Georgia Tech

∫

n ( xn )

n(− xp )

dn dx dx = kT ln ⎡ n( xn ) ⎤ ⎥ ⎢ n q ⎢⎣ n( − x p ) ⎥⎦ ECE 3080 - Dr. Alan Doolittle

Movement of electrons and holes when forming the junction ⎡ ⎤ kT ⎡ n( x n ) ⎤ kT ⎢ N D ⎥ Vbi = ln ⎢ 2 ln ⎢ ⎥= ⎥ q ⎢⎣ n(− x p ) ⎥⎦ q ⎢ ni ⎥ ⎣ NA ⎦ kT ⎡ N A N D ⎤ Vbi = ln ⎢ ⎥ q ⎣ ni2 ⎦

For NA=ND=1015/cm-3 in silicon at room temperature, Vbi~0.6 V* For a non-degenerate semiconductor, |-qVbi|