Eece 352notes
EECE 352: 352 PN Junctions
Peyman Servati y
Outline
• • • • Diffusion and drift currents Current continuity PN Junctions Diodes, photodetectors, solar cells
Diffusion of Electrons
Movement of electrons and holes (charge carriers) results in ( g ) conduction in materials. Electrons and holes in solids move based on Brownian motion (random walk). In this random movement, electrons effectively move from a movement location where the concentration is higher to where the concentration is lower.
1D random walk
2D random walk
Δx
x − Δx x + Δx
x
x
Diffusion Current
The current carried due to the diffusion of electrons is proportional to the gradient of electron density:
dn( x ) dn( x ) J n ( x ) = qDn dx dx The coefficient Dn is the diffusion constant for electrons with a unit of cm2/Vs.
J n ( x) ∝
Since electron charge is negative the sign for current is positive.
The current carried due to the diffusion of holes is proportional to the gradient of hole density:
n(x) p(x) ( )
J p ( x ) = − qD p
The coefficient D p is the diffusion constant for holes with a unit of cm2/Vs.
x
dp ( x ) dx
Total Current
The total current carried in a semiconductor is the sum of diffusion and drift currents for both electrons and holes:
J ( x) = J n ( x) + J p ( x) dn ( x ) dx drift diffusion dp ( x ) J p ( x ) = qμ p p ( x )E ( x ) − q p qD dx d J n ( x ) = q μ n n ( x ) E ( x ) + qD n D
The diffusion constant and drift mobility are related.
n(x) p(x) ( )
Δx 2 Dn = 2τ
The kinetic energy of electron is given by:
K .E . =
* mn vavg g
2
2
= kT
Dn Dp 2/s) (cm2/s) (cm
Ge Si GaAs 100 35 220 50 12.5 10
Einstein relation
μn
(cm2/Vs)
3900 1350 8500
(cm2/Vs)
1900 480 400
Dn
kT = = Vth q μn
Dp
kT = μp q
x
μp
Examples
1. 1 An intrinsic Si is doped with donor atoms with a density of (a) In equilibrium J(x) = 0 what is electric field E(x)? (b) Sketch a band diagram.
N D (x)
Peyman Servati y
Outline
• • • • Diffusion and drift currents Current continuity PN Junctions Diodes, photodetectors, solar cells
Diffusion of Electrons
Movement of electrons and holes (charge carriers) results in ( g ) conduction in materials. Electrons and holes in solids move based on Brownian motion (random walk). In this random movement, electrons effectively move from a movement location where the concentration is higher to where the concentration is lower.
1D random walk
2D random walk
Δx
x − Δx x + Δx
x
x
Diffusion Current
The current carried due to the diffusion of electrons is proportional to the gradient of electron density:
dn( x ) dn( x ) J n ( x ) = qDn dx dx The coefficient Dn is the diffusion constant for electrons with a unit of cm2/Vs.
J n ( x) ∝
Since electron charge is negative the sign for current is positive.
The current carried due to the diffusion of holes is proportional to the gradient of hole density:
n(x) p(x) ( )
J p ( x ) = − qD p
The coefficient D p is the diffusion constant for holes with a unit of cm2/Vs.
x
dp ( x ) dx
Total Current
The total current carried in a semiconductor is the sum of diffusion and drift currents for both electrons and holes:
J ( x) = J n ( x) + J p ( x) dn ( x ) dx drift diffusion dp ( x ) J p ( x ) = qμ p p ( x )E ( x ) − q p qD dx d J n ( x ) = q μ n n ( x ) E ( x ) + qD n D
The diffusion constant and drift mobility are related.
n(x) p(x) ( )
Δx 2 Dn = 2τ
The kinetic energy of electron is given by:
K .E . =
* mn vavg g
2
2
= kT
Dn Dp 2/s) (cm2/s) (cm
Ge Si GaAs 100 35 220 50 12.5 10
Einstein relation
μn
(cm2/Vs)
3900 1350 8500
(cm2/Vs)
1900 480 400
Dn
kT = = Vth q μn
Dp
kT = μp q
x
μp
Examples
1. 1 An intrinsic Si is doped with donor atoms with a density of (a) In equilibrium J(x) = 0 what is electric field E(x)? (b) Sketch a band diagram.
N D (x)