Lec 5 The pn Junction (II)

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2 Νοε 2013 (πριν από 3 χρόνια και 7 μήνες)

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Lec

5 The
pn

Junction (II)


Contents:

1.
pn

junction under bias

2. I
-
V characteristics

1

Key questions


Why does the
pn

junction diode exhibit current
rectification (
整流
)
?



Why does the junction current in forward bias
increase



What are the leading dependences of the
saturation current (the factor in front of the
exponential)?



2

1. PN junction under bias

Upon application of voltage:


electrostatics upset:
depletion region widens or
shrinks


current flows (with rectifying
behavior)


carrier charge storage


3

IV Characteristics

4

I
D
=0

I
D
>0

V
D
>0.7 V

I
D
<0

V
D
<V
BD

5

To model IV characteristics we need 2 concepts


• The Law of the Junction


• Steady State Diffusion

Carrier profiles in thermal
equilibrium:

Inside SCR in thermal
equilibrium:

dynamic balance between

drift and diffusion
for
electrons and holes
.

6

Carrier concentrations in
pn

junction under bias:

7

8

Current balance in SCR broken:

Net drift current in SCR

=> minority carrier extraction from
QNR’s


deficit of minority carrier
concentrations in QNR’s


Few minority carriers in QNR’s

=>current small.

9

What happens if minority carrier concentrations in QNR change
from equilibrium?

=>Balance between generation and recombination broken

• In thermal equilibrium: rate of break up of Si
-
Si bonds
balanced by rate of formation of bonds

• If minority carrier injection:

=> carrier concentration above equilibrium

=> recombination prevails

• If minority carrier extraction:

=> carrier concentrations below equilibrium

=> generation prevails

10

Where does generation and recombination take place?

1. Semiconductor bulk

2. Semiconductor surfaces & contacts


In modern devices, recombination and generation mainly takes
place at surfaces:

• perfect crystalline periodicity broken at a surface

=>lots of broken bonds: generation and recombination

centers

• modern devices are very small


high area to volume ratio.


High generation and recombination activity at surfaces

=> carrier concentrations cannot deviate much from equilibrium

values:

11

Complete physical picture for
pn

diode under bias:

• Forward bias: injected minority carriers diffuse through

QNR => recombine at semiconductor surface

At semiconductor surface:
carrier concentration
unchanged from
equilibrium.

12

• Reverse bias: minority carriers extracted by SCR

=> generated at surface and diffuse through QNR

At semiconductor surface:
carrier concentration
unchanged from
equilibrium.

13

14

The current view:

• Forward bias:

15

• Reverse bias:

16

What limits the magnitude of the diode current?

• not generation or recombination rate at surfaces

• not injection or extraction rates through SCR

• diffusion rate through QNR’s

17

Development of analytical current model:

1. Calculate concentration of minority carriers at edges

of SCR,
p(
x
n
) and n(−
x
p
)

2. calculate minority carrier diffusion current in each

QNR,
I
n

and
I
p

3. sum electron and hole diffusion currents,
I = I
n

+
I
p

2. I
-
V characteristics


Step 1: computation of minority carrier boundary conditions
at edges of SCR


In thermal equilibrium in SCR,



18


Define


Recall


Rewrite

19

• Solving for the equilibrium minority carrier concentrations
in terms of the built in potential,

Special case of
Boltzman

statics.

V

20

Under bias in SCR,

but if difference small with respect to absolute values of
current: This is called
quasi
-
equilibrium
.


• The new potential
barrier
φ
j

= (
φ
B
-

V
D
)

is substituted for the
thermal equilibrium barrier
to find the new minority
carrier concentrations at
the SCR edges.

IN quasi
-
equilibrium

21

At edges of SCR, then:

This is
the low
-
level injection approximation

Charge neutral at each side:

Since


Law of the Junction


22

23


The minority carrier concentration at the SCR is an
exponential function of applied bias. It changes one
decade for every 60mV change in V
D
.


Law of the Junction is valid if minority carrier concentration
is less than equilibrium majority concentration. This
condition is called
Low Level Injection
.

24

Voltage dependence:

• Equilibrium (
V = 0):

• Forward (
V >0):

Lots of carriers available for injection:

=>
V
increasing, concentration of injected carriers increases

=> forward current can be high and increases with
V
.

25

• Reverse (
V <0):

Few carriers available for extraction:

=> reverse current is small.

Minority carrier concentration becomes vanishingly small:

=> reverse current saturates.

Rectification property of
pn

diode arises from minority carrier

boundary conditions at edges of SCR.

26

Step 2: Diffusion current in QNR:

Diffusion equation (for electrons in p
-
QNR):

Inside p
-
QNR, electrons diffuse to reach and recombine

at contact =>
J
n

constant in p
-
QNR => n(x) linear.

Boundary conditions:

Electron profile:

27

Similarly

Since QNR region remains charge neutral,

The majority carrier concentration
must increase by the same
amount as the injected minority
carrier concentration

28

Electron current density:

Similarly for hole flow in n
-
QNR:


Since the current is
continuous, the total current
density J cannot vary with
position.


In depletion region, drift
current and diffusion current
nearly cancel.


=> The total current density is
the sum of the minority carrier
diffusion current density at the
edge of the depletion region.


29

Step 3: sum both current components:

often written as:

with

equation valid in forward and reverse bias.

30

Since the total current density are constant,

1)
The holes diffusion across n bulk region are supplied from the
majority holes at the p
-
side of the junction.

2)
Similarly, there must be a majority electron current flowing from
n
-
type to supply the injection of electrons in p
-
side.

pn

junction current under reverse bias

31

32

The total current density:

The total current

Analyze current components in reverse bias:


The minority diffusion currents are extracted and
become the majority carrier current on the other side
of the junction.

Key conclusions

• Application of voltage to
pn

junction results in
disruption of balance between drift and diffusion in
SCR:




in forward bias, minority carriers are
injected into
quasi
-
neutral regions




in reverse bias, minority carriers are
extracted
from quasi
-
neutral regions


In forward bias, injected minority carriers
recombine at surface.


In reverse bias, extracted minority carriers are
generated at surface.



33


Computation of boundary conditions across SCR
exploits
quasi
-
equilibrium:
balance between
diffusion and drift in SCR disturbed very little.


Rate limiting step to current flow: diffusion through
quasi
-
neutral regions.


I
-
V characteristics of p
-
n diode:



34

Example


Given a diode with the p
-
region doped with
N
a
=10
18
cm
-
3

and the n
-
region doped with
N
d
=10
16
cm
-
3
,calculate the minority carrier
concentrations at the edge of the depletion region
as the function of the applied voltage V
D
=0.6V and
V
D
=
-
0.6V respectively.

35

36

Solution:


we begin by finding the minority carrier concentrations in
thermal equilibrium:



According to the law of the junction

Homework


An IC diode is designed to have a room
-
temperature
saturation current of I
0
=5*10
-
17
A for a particular application.
The fabrication process results in the device dimensions
and physical parameters listed below.

37

Dimensions

Doping

Diffusion coefficient

Wp
=0.5 um

Na=2.5X10
17
cm
-
3

Dn
=14cm
2
s
-
1

Wn
=1.0um

Nd
=4.0X10
16
cm
-
3

Dp
=10cm
2
s
-
1

a)
What diode area A is required for I
0
?

b)
Find the current and minority carrier concentrations at the edges of the
depletion region for a forward bias V
D
=720 mV.

c)
Plot the carrier concentration distribution along the diode.