pn junction & schottky diode
TRANSCRIPT
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PN Junction& Schottky
Diode
Cathode Anode
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Reverse-Bias PN Junction Charge Density
Electric Field
Potential2lni
DATbi n
NNV=φ
mVqkTVT 26≅=
26≅=qkTVT mV at 300oK
ni is the intrinsic carrier concentration approximates 1.5e-10 cm-3 at 300oKK is Boltzsmann Constant
Reverse-biasis similaras 0 biascondition
Built-In Potential (0 Bias)
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* Built-In Potential oppose the diffusion of mobile holes and electrons across the junction.
Demand overall charge neutrality.*
ερ
−=∂∂
2
2
xV* Apply Poisson’s equation to solve for V
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* Maximum field increase as the doping density increase.
* Increase reverse bias voltage will increase maximum field.* Junction breakdowns when bias exceeds VBREAKDOWN voltage
I
VBREAKDOWN
V
$ Higher doing will causehigher or lowerVBREAKDOWN?
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21
1
)0()(
Φ
−
==
∂∂
=
bi
j
V
VCVQVC
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1
)0()(
Φ
−
==
∂∂
=
bi
j
V
VCVQVC
Graded doping
Junction Capacitance
for uniform doping in bothp,n region
* Apply
for graded doping in bothp,n region
*
V is the reverse bias voltage
$ Higher doping will causehigher or lowercapacitance?
** C-V for forward bias?C-V curve for uniform doping
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I-V CharacteristicsForwardBias
Impedance of diode vary with bias point and RF swing level
(Curve of exponential)
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Forward Bias (used to approximate reverse bias too)
)1( −= nkTqV
S eIIideality factor
reverse saturation current
Boltzmann constant
absolute temperature
bias voltage::::
:
VTkIn
S
CMOS
PN junction is everywhere
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Review:
•Junction capacitance resulted from reverse bias and vary withvoltage
•Breakdown voltage inversely proportional with doping•Diffusion capacitance resulted from forward bias (hard tomeasure C-V curve, more later)
•One thing not mentioned is the leakage current through the the surrounding edge of diode structure for both forwardand reverse bias. It’s a OMIC phenomena.•Breakdown phenomena is not modeled in:
)1( −= nkTqV
S eII
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VII
KTqN
∂∂
≈
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11N
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Straight linein logarithm scalefor large V
=
SII
qkTV log
For large V
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Series Resistance(parasitic component)
• Accounts forOhmic drop, neglected so far
Current (I) appearsin both side of equations
+=
Ss I
IqkTIRV log
For large V
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SIIlogUse here
+=
Ss I
IqkTIRV log
For large V
SIIlogIf =6, IS=1.6e-6 A, and V=0.71V
then what is the value of Rs at 300oK? 0.346 OHM
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Fabricate PN junction diode in CMOS
Substrate usually is groundedThis P layer substrate provides isolation
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CMOS
NPN structure is vertical instead of horizontal(meaning of plug)
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* pn junction is one kind of diode
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In Practical!
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Vj can not change abruptly, need to get rid of minoritycarrier
Current Spike
trr is the time requiredto neutralize minoritycarrier
The mass ofP is more heavierthan N
No trr forschottky diode
Cd(V) then Cj(V)?
Cj(V) then Cd(V)
! Initial large or small Cd(V)?
$ Initial large orsmall Cd(V)?
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---+ ++Forward-bias
P
+
- ----
++
++
P
Reverse-bias
- --
+++
Cd(V)Cj(V)
It takes time
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Majority electron
+
- ----
++
++
+
-Vf Vr
P+
- ----
++
++
P Instant switchedto reverse biasForward bias
Act like voltage source, sothe resultant voltage sorce is Vf+Vr-(If*Rs)Majority electron
Generate current spike
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Switch offTransient
Vr >> VfandRs is very small
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Schottky Diode
• Metal-Semiconductor junction.• Lower forward turn-on voltage.
• Steeper I-V curve• Majority-carrier (Electron) device. Not like p-n diode usingminority-carrier charge-storage effects.
• Higher cutoff frequency, reproducibility and ease of fabrication.• Exitaxial and ion-implantation.• Rectifying or non-rectifying (ohmic-contact)
No minoritycarrier storage!ID
VD
Schottky
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Gx : Gx1 // Gx2
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I-V characteristics
• Based on •
)1( −= nkTqV
S eII
::
::::
:
S
x
S
IRVG
VTkIn ideality factor
reverse saturation current
Boltzmann constant
absolute temperature
bias voltage
edge leakage current
voltage drop due to ohmic contact and bulk resistance of semiconductor channel. (ohmic contact is a metal-semiconductor contact that has a linear I-V and non-rectifying characteristics. )
VGeII xnkT
RIVq
SD
sD
+−=
−
)1()(
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C-V characteristics
• Semi-empirical equation•
• approximated by•
:
:
::
0
C
j
j
F
C
Vm
C
n
j
jD
VVC
VC)1(
)( 0
−=
VIG D
D ∂∂
=
grating coefficient
built-in potential of the barrier height of junction
zero-bias junction capacitance.
depletion capacitance coefficient.
m
j
j
VVC
)1(0
−=)(VCD
))1(1()1( 1
0
jCm
j
j
VmvmF
VVC
++−− +
for
for
jCVFV <
jCVFV >
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Diode modeling
• DC I-V measurement
• When IDRs << Bias voltage and ignore Is and GxV as compared with
Total diode current ID approximated by
nkTSeIqV
nkTqV
SD eII =
)log()log()log( nkTqV
SD eII += )log()log( SIenkTqV
+=
VIkTeqn∆∆
=/)log(/)log(
By taking the derivation with respect to V
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• Is can be calculated from the curve.• knowing n and Is. Gx can be found by curve fitting at low current region• At high current region, ignore GxV and Is as compared with
−
nkTRIVq
S
SD
eI)(
−
= nkTRIVq
SD
SD
eII)(
)log()()log()log( enkTRIVqII SD
SD−+=
)log()()log( enkTVVqIS
∆−+=
SDRIV =∆
For Rs is a weak function of bias voltage V and increase with it
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Small signal model
or simplified as
• measure S-parameter at particular bias voltage and curve fitting.• measure S-parameter at various bias V and curve fitting to findC-V relation data. One can use the C-V data and curve fitting to find C-V semi-empirical equation.
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Large Signal Model
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• : cutoff frequency
(bias and RF power dependent)
• Noise: shot noise and thermal noise are two major source
Shot noise (mean square value)
Thermal noise (mean square value)
: bandwidth q : charge of electronn : ideality factorT : absolute temperatureK : Boltzmann constant
• these two noise sources are statistically uncorrelated.
Tf
DsT CRf
π21
=
fIInqi sDs ∆+=>< )2(22
2>< si
2>< Tif
RkTis
T ∆=><42
f∆
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In addition Flicker noise
• A random fashion of generation-recombination effect in the depletion layer.
• Energy concentrated at low frequency.
• ID : the diode current.f : center frequency
: bandwidth, a, b : constant
(device dependent, a in the range of 0.5-2, and b is close to 1)
• flicker noise is in the shunt with shot noise, and is uncorrelated to thermal noise.
2>< fi
ffIki b
aD
ff ∆=>< 2
f∆fk
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Noise model
• model parameters can be estimated from the measurementof the diode noise.
cathode anode
Cp2
Lp2
Rs
CD
ID
2>< fi
2>< siCp1
2>< Ti
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Schottky diode as level shift
ID
V
ID
SffDropD
S
Df
fSD
RIVVII
qKTV
KTqV
II
+=
=
−≅
,
)ln(
)1(exp
• Both Vf and Rs are function of temperature but temperature coefficientof Vf dominates.
• Temperature coefficient of VD drop typically ranges from -1 to –2 mV/oC• Low diode forward current have temperature coefficient close to –2 mV/oC• High diode forward current have temperature coefficient close to –1 mV/oC
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Diode• multiplier• Detector• Mixer• Varactor• Switch• Limiter• Level-Shifting Device
Cathode Anode
Small signal model