Ch1 4 PN IV Characteristics

8/11/2019 Ch1 4 PN IV Characteristics

http://slidepdf.com/reader/full/ch1-4-pn-iv-characteristics 1/18

Current-Voltage Characteristics

Qualitative Analysis: Thermal Equilibrium

Diffusion

- electron diffusion from n-side to p-side

- most will be reflected- few electrons will have enough energy

and overcome the barrier height

Drift

- Electron drift from p-side to n-side

- few electrons will be drifted (e- isminority carriers in p-side)

- at thermal equilibrium, diffusion and

drift are balanced

Net electron current = 0

Similar, net hole current=0

Thus, the total current=0

Electrons




Qualitative Analysis: Forward Bias (V A

>0)

More electron diffusion from n-side to p-side

due to lowering of barrier height

Electrons drift from p-side to n-side remains

same (minority concentration unchanged)

Electron diffusion dominates

Diffusion current increases exponentiallywith V A

potential barrier (Vbi-V A) linearly

decrease with V A,

plus electron concentration (in n-side,majority carrier) above the barrier

height increases exponentially when

the energy level moves upward

Electrons




Qualitative Analysis: Forward Bias (V A>0)

Similar analysis applied to holes

The total current is dominated by both

electron and hole diffusion and given

as

JF=JN, F+JP, F

Forward current increasesexponentially with V A

Particle Flow

Hole diffusion

Current

Hole drift

electron

diffusion

electron drift

Will V A be larger than Vbi?




Qualitative Analysis: Reverse Bias (V A<0)

- Very few electron diffusion from n-side to

p-side due to increased barrier height

- Electrons drift from p-side to n-side

remains same (minority concentration

unchanged)

- Electron current is dominated by drift- Thus electron current is very small

Similar analysis applied to holes

So, the total reverse current dominated byboth electron and hole drift currents

Reverse currents are very small and nearly

independent with V A value

Electrons




Qualitative Analysis: I-V Characteristics




Quantitative Analysis: I-V Characteristics

Assumptions

(1) The diode is being operated under steady state conditions

(2) A non-degenerately doped step junction models the doping profile(3) The diode is one dimensional

(4) Low level injection prevails in the quasineutral regions

(5) There are no processes other than drift, diffusion, and thermal R-G (with

negligible) taking place inside the diode.

Thus, the current can be calculated as




Quanti tative Analysis: I-V Characteristics

Quasi-neutral regions

- The minority carrier diffusion equations are

E0E0

-x p xn

Depletion

region

Quasi-neutral

regions

P-region N-region

E≠0

n

p

nnP

p

n

p p

N

x x p

dx

pd D

x xn

dx

nd D

2

2

2

2

0

0

From the above two equations (plus boundary

condition, will be discussed later),

both and

can be obtained

pn n p





Quasi-neutral regions

- Since low level injection (E≈0) and 000

dx

dp

dx

dn

Thus, current density in these two quasi-neutral region

can be calculated as

dxnd qD x J

p

N N )(

dx

pd qD x J n

PP

)(

For x ≤ -xp

For x ≥ xn

Recall:

pqD pE q J J J p pdiff pdrift p p ,,

nqDnE q J J J nndiff ndrift nn ,,

Thus, we are able to calculate the current density (diffusion current)

at quasi-neutral regions!!!

Since low-level injection,

the majority carrier

concentration remains

same within quasi-neutral

regions, thus the E-field isalmost zero





Depletion region

E0E0

-x p xn

Depletionregion

Quasi-neutral

regions

P-region N-region

E≠0G R

P

G R N

t

p

dx

dJ

q

t

n

dx

dJ

q

|1

0

|1

0- Recall

- From assumption (5), we have

0|

0|

G R

G R

t

p

t

n

- Then, we have0

dx

dJ N

0dx

dJ P

- Which mean that JN and JP are constant within depletion region

)()(

)()(

nPn pP

p N n p N

x J x x x J

x J x x x J





Depletion region

E0E0

-x p xn

Depletionregion

Quasi-neutral

regions

P-region N-region

E≠0

- Since JN and JP are constant within depletion

region

)()(

)()(

nPn pP

p N n p N

x J x x x J

x J x x x J

- The total current density can be given asbelow

)()()()( nP p N P N x J x J x J x J J

Thus, the total current density can be calculated as the sum of

diffusion currents at both depletion edges JN(-xp) and JP(xn)!!!




Quanti tative Analysis: I-V Characteristics

Boundary Conditions

At the Obmic contacts

- Consider long “wide” base diode, which

means the diode has contacts which are

larger than the minority carrier diffusion

lengths, the contacts can be viewed at

- So, the boundary conditions are

x

0)(

0)(

xn

p

x pn





Boundary Conditions

At Depletion Region Edges

- Introducing “quasi-Fermi level” FN and FP

(FN-FP=V A), inside depletion region, we have

- So, the boundary conditions are

kT E F

ii N enn

/)(

kT F E

iPien p /)(

recall

kT qV

i Aennp

/2

kT qV

A

i p p

Ae N

n xn

/2

)( A p p N x p )(

)1()( /2

kT qV

A

i

p p

Ae N

n xn

at x = -xp

Dnn N xn )( kT qV

D

inn

Ae N

n x p

/2

)(

)1()( /2

kT qV

D

i

nn Ae

N

n x p

at x = xn





Calculation of Current JP(xn)

xn-x p

x

x’0

(1) Shift the origin of coordinates to xn

(2) the equation and boundary conditions are

(3) Solving the above equations, we have

Lp xkT qV

D p

pn pP ee

N L

n Dq

dx pd qD x J Ai /'/

2

)1('

)'(

(4) So, JP(xn) can be given as

)1()0'()( /

2

kT qV

D p

p

PnP Ai e

N L

n Dq x J x x J





Calculation of Current

(1) Similarly, JN(-x

p) can be obtained as follow

)1()( /

2

kT qV

An

n

p N Ai e

N L

n Dq x x J

(3) A useful and important equation

)1)(( /22

kT qV

A N

n

DP

p Aii e

N L

n D

N L

n DqA AJ I

(2) So, the total current

)(

)1(22

0

/0

A N

n

DP

p

kT qV

N L

n D

N L

n DqA I

e I I

ii

A




Some Useful Discussions

IV Characteristics (Ideal)

(i) For reverse biases greater than a few

kT/q,

(ii) For forward biasing larger than a few

kT/q,

(iii) In forward bias conditions, I-V alwaysplotted as semilog scale since

(iv) Saturation current

- depends on intrinsic concentration

- depends on doping concentration

0 I I

)/exp(0 kT qV I I A

AV kT

q I I )ln()ln( 0

)(22

0

A N

n

DP

p

N L

n D

N L

n DqA I ii





Carrier Current Components

Think Again: How we calculate the current?





Carrier Concentrations (Forward bias)

- Carriers are injected into other side by

diffusion and become minority

carriers.

- The excess minority carriers are

eliminated by recombination during

diffusion deeper into the regions

- Thus, there is a build-up of minority

carrier in the quasinetural regionsimmediately adjacent to the edges of

the depletion regions.





Carrier Concentrations (Reverse bias)

- The depletion region acts like a “sink”for minority carriers, draining the carriers

from the adjacent quasineutral region.

- A reverse bias of a few kT/q effectively

reduces the minority carrier concentrations

to zero at the edges of the depletion

region.

- Larger reverse biases have little effecton the carrier concentration (consistent

with the saturation current in reverse

bias).

Ch1 4 PN IV Characteristics

Documents