Physical View of a PN Junction - courses.edx.org
Transcript of Physical View of a PN Junction - courses.edx.org
p
metal
n+ orp+p
metal
n+ p+
p+
p
oxiden
p
metaln
PN junction on a wafer• Actual PN junction is 2-D and 3-D
• Integrated diodes usually have top contacts to both terminals
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
Physical View of a PN Junction
• The + after n/p means heavy doping
2-D 3-D
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
When P- and N- Types Meet [1]From your previous notes
P Si Si+
-Si Si B
• when a electron made available from a group V element moves to a location with a hole made available from a group III element, the electron may take it place by recombination
• at the site of the group V element becomes slightly positive and at the location of the group III element becomes slightly negative
• No special effects if it is distributed over the entire system• What happens if the group V elements and group III elements
are separated into different locations?
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
When P- and N- Types Meet [2]
Si Si Si Si Si B Si P P Si Si P
Si B Si Si B Si P Si Si P P Si
B Si Si B Si Si Si P Si P Si P
Si Si B Si Si B Si Si P Si Si Si
Si B Si Si Si Si P P Si Si P Si
Atomic view right after PN junction formation• Right after putting the P and N together, the excess carriers
stay with the parent atoms and the whole system is neutral
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
Formation of depletion region
Si Si Si Si Si B Si P P Si Si P
Si B Si Si B Si P Si Si P P Si
B Si Si B Si Si Si P Si P Si P
Si Si B Si Si B Si Si P Si Si Si
Si B Si Si Si Si P P Si Si P Si
++
+++
++
--
-----
When P- and N- Types Meet [3]
• Carriers near the junction recombines and removed (depleted) forming a region with charges but no (very few) carriers
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
Properties of the PN junction regions
Si Si Si Si Si B Si P P Si Si P
Si B Si Si B Si P Si Si P P Si
B Si Si B Si Si Si P Si P Si P
Si Si B Si Si B Si Si P Si Si Si
Si B Si Si Si Si P P Si Si P
++
+++
++
--
-----
When P- and N- Types Meet [4]
Si
negative charge• neutral region • with carrierpositive charge
depletion region (no carrier)• neutral region • with carrier
P-type N-type
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
Abrupt junction approximationApproximations used
+-
---
--++
+++
xnxp
• There is a clear boundary between the n-type and p-type silicon• In really, there is a transition region where both donors and
acceptors co-exist
Depletion approximation• There is a clear boundary between the depletion region and
the neutral region• All carriers in the depletion region are depleted
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
PN Junction at Thermal Equilibrium [1]Band diagram representation• PN junction are formed by injecting dopants to different
locations of a piece of silicon• Starts from the band diagram of an intrinsic silicon at thermal
equilibrium• Gradually dope one side to P-type and the other to N-type
Intrinsic silicon N-doping P-doping
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
PN Junction at Thermal Equilibrium [2]Band Diagram Representation• the Fermi level (represent external
forces or voltages) of the system align at thermal equilibrium (or there will be continuous current flow)
EC
EV
EF
p
n Ei
VBi
Quantity of interest• How high is the energy barrier for electron from the n-region to
the p-region• How wide is the depletion region
Ø Noted that energy is proportional to voltage like mechanical potential energy is proportional to height
Ø We have E = qV where q is the electron charge =1.6x10-19C
• The band diagram defines the static landscape (or voltage) of the system sense by the carriers
VBi the built-in potential of a PN junction
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
PN Junction at Thermal Equilibrium [3]Determining the built-in potential• As the band bending for the
conduction band is the same as the band bending of Ei, we have
EC
EV
EF
p
n Ei
VBiVP
VN
VBi = VP + VN
• Recall that for P-silicon, we have
qVN = EF −EiN = kT lnND
ni
⎛
⎝⎜
⎞
⎠⎟• For N-silicon, we have
qVP = EiP −EF = kT lnNA
ni
⎛
⎝⎜
⎞
⎠⎟
• Adding together, we have
!"# = !% + !' = ()* ln
'-./
+ ()* ln
'0./
= ()* ln
'0'-./1
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
PN Junction at Thermal Equilibrium [3]Determining the depletion region width
• For charge neutrality, the charge at p-side depletion region has to be balanced by the charge at the n-side
• We have
• From this point onward, we’ll normalize with respect to the area to simplify the calculations
+-
---
--++
+++
xnxp
• Want to find xp and xn in the given figure
NDxn=NAxp
• Still two unknown and we have to find another relationship to solve for both xp and xn
NDxnA=NAxpA or
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
PN Junction at Thermal Equilibrium [4]
erf -=Ñ2
er
-=2
2
dxVd
er
=dxEd!
The Poisson’s Equation
• Interpretation of the Poisson’s equation
• A very important equation relating voltage, electric field and charge density
dVdx
= −!E
+--
++
--
+++-
-+-
V = −!Edx∫
!E = 1
ερ dx∫
where
f : the spatial potential (or voltage)r : the charge densitye : dielectric constant of the material
(8.85x10-14F/cm for free space (e0) and 11.9e0 for silicon and 3.9e0 for SiO2 )
• In 1-D, it becomes
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
PN Junction at Thermal Equilibrium [5]Apply to PN Junction• Solving the Poisson’s
equation graphically
ionized dopant
NA
ND
-+xpxn
Q=qNDxnQ=qNAxp
xp xn
Si
pAxqNe Si
nD xqNe
or
xp xn
VSi
pA
Si
nDbi
xqNxqNV
ee 22
22
+=
E!
integrate
integrate
+-
---
--++
+++
xnxp
Charge distribution
Electric field
Voltage• The voltage at the two end
of the PN junction is known to be Vbi
Solution
21
)(2
÷÷ø
öççè
æ+
=DAD
AbiSin NNN
NqV
xe 2
1
)(2
÷÷ø
öççè
æ+
=DAA
DbiSip NNN
NqV
xe
21
112úû
ùêë
é÷÷ø
öççè
æ+=+=
DA
biSipnd NNq
Vxxx
e
Si
pA
Si
nDbi
xqNxqNV
ee 22
22
+=• solving NDxn=NAxpand
• result
• where ÷÷ø
öççè
æ= 2ln
i
ADbi n
NNqkTV
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
PN Junction at Thermal Equilibrium [6]
• Now we have two equations to solve for the two unknown
• very often we have N+/P or P+/N junction- note that: ni/pi ~ 1010cm-3
ND+/NA
+ ~1018cm-3
ND/NA ~1015cm-3
• e.g. for P+/N, only xn has to be considered
21
12÷÷ø
öççè
æ=
D
biSin Nq
Vx
e
NA
ND
-
+xn
xp ~ 0
- ND above is only about 0.1% of ND+
- note: depletion region have carriers ~ ni
Asymmetric Junctions
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
PN Junction at Thermal Equilibrium [7]
r
ansunMansunMHong Kong University of Science & Technology, Department of Electrical & Electronic Engineering
What have we learned up to this point• the property of the PN junction is mostly controlled by
the lighter doped side
xp xnP+ N0
EC
EV
EFp+ n Ei
VBi
D
biSinnp Nq
Vxxx
12e=»+ ÷÷
ø
öççè
æ= 2ln
i
ADbi n
NNqkTVand
PN Junction at Thermal Equilibrium [8]
ansunMansunMHong Kong University of Science & Technology, Department of Electrical & Electronic Engineering
Contact PotentialCan built-in potential be measured?• For any two materials in contact, there exist a contact potential
p n
V
m1 m2
BA
( ) ( ) ( ) 2121 mmmnnppmAB VVVVVVVVV -=-+-+-=
• Can the voltage be measured by the voltmeter?• The answer is no, because contact potential is also developed
between at the leads voltmeter made up of the same material• No matter how many different materials you connected, it will
end up with a close loop without any measurable voltage• So, even there is a build-in potential in a PN junction, no
voltage can be measured• Metal semiconductor contact will be covered later
m3