p-n Junction I-V Characteristics
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Transcript of p-n Junction I-V Characteristics
P-N Junction Diodes Current Flowing through a Diode
I-V Characteristics
Quantitative Analysis
(Math, math and more math)
p-n Junction I-V Characteristics
In Equilibrium (no bias) Total current balances due to the sum of the individual components
Electron Drift Current
Electron DiffusionCurrent
Hole Drift CurrentHole Diffusion
Current
Diode under no Bias.mov
no net current!
EC
EV
EF
Ei
p-Type Material n-Type Material- qVBI
+ +++++ +++ ++ ++ ++++++
0 nDqnEqJJJ nnDiffusionnDriftnn
no net current!
p-n Junction I-V Characteristics
EC
EV
EF
Ei
n vs. E
p vs. E
In Equilibrium (no bias)Total current balances due to the sum of the individual components
0 pDqpEqJJJ ppDiffusionpDriftpp
p-n Junction I-V Characteristics
Forward Bias (VA > 0)
I
Hole Drift Current
Electron Drift Current
Electron DiffusionCurrent
Hole Diffusion Current IP
IN
Diode under Forward Bias.mov
Current flow is dominated by majority carriers flowing across the junction and becoming minority carriers
VA
Current flow is proportional to e(Va/Vref) due to the exponential decay of carriers into the majority carrier bands
Lowering of potential hill
by VA
surmount potential barrier
PN III
Hole Diffusion Current negligible due to large energy barrier
Hole Drift Current
Electron Drift Current
Electron Diffusion Current negligible due to large energy barrier
Reverse Bias (VA < 0)
Diode under Reverse Bias.mov
p-n Junction I-V Characteristics
Current flow is constant due to thermally generated carriers swept out by E fields in the depletion region
Current flow is dominated by minority carriers flowing across the junction and becoming majority carriers
Increase of potential hill b
y VA
Where does the Reverse Bias Current come from?
Generation near the depletion region edges “replenishes” the current source.
p-n Junction I-V Characteristics
Putting it all together
p-n Junction I-V Characteristics
for Ideal diodeVref = kT/q
-I0
10
kT
qVexpII
: Diode Ideality Factor
p-n Junction I-V Characteristics
Diode Equation
Quantitative p-n Diode Solution
Assumptions:1) Steady state conditions
2) Non- degenerate doping
3) One- dimensional analysis
4) Low- level injection
5) No light (GL = 0)
Current equations:
)x(J)x(JJ npp
dx
dpqDpEqJ ppp
dx
dnqDnEqJ nnn
Application of the Minority Carrier Diffusion Equation
Since electric fields exist in the
depletion region, the minority carrier diffusion equation
does not apply here.
Quisineutral Region Quisineutral Region
00 0 0
Quantitative p-n Diode Solution
minority carrier diffusion eq. minority carrier diffusion eq.
Quisineutral Region Quisineutral Region
Quantitative p-n Diode Solution
kT)FF(i
PNennp 2
quasi-Fermi levels formalism
kTEE
i
kTEE
i
fi
if
enp
enn
)(
0
)(
0
Equilibrium
kTFEi
kTEFi
Pi
iN
enp
enn
)(
)(
Non-Equilibrium
The Fermi level is meaningful only when the system is in thermal equilibrium.
The non-equilibrium carrier concentration can be expressed by defining Quasi-Fermi levels Fn and Fp .
Equilibrium Non-Equilibrium
Quasi - Fermi Levels
Quisineutral Region Quisineutral Region
Quantitative p-n Diode Solution
kT)FF(i
PNennp 2
quasi-Fermi levels formalism
?
Quisineutral Region Quisineutral Region
Quantitative p-n Diode Solution
dx
dnDnEqJ nnn
dx
nndqD
p
n
0
dx
ndqD
p
n
dx
dpDpEqJ ppp
dx
ppdqD n
p
0
dx
pdqD n
p
0 0
Approach:
Solve minority carrier diffusion equation in quasineutral regions.
Determine minority carrier currents from continuity equation.
Evaluate currents at the depletion region edges.
Add these together and multiply by area to determine the total current through the device.
Use translated axes, x x’ and -x x’’ in our solution.
Quisineutral Region Quisineutral Region
x”=0 x’=0
Quantitative p-n Diode Solution
Quisineutral Region Quisineutral Region
x”=0 x’=0
Quantitative p-n Diode Solution
Holes on the n-side
Quantitative p-n Diode Solution
Quisineutral Region Quisineutral Region
x”=0 x’=0 Holes on the n-side
Quantitative p-n Diode Solution
Similarly for electrons on the p-side…
Quisineutral Region Quisineutral Region
x”=0 x’=0
Quisineutral Region Quisineutral Region
Depletion Region
Negligible thermal R-G implies Jn and Jp are constant throughout the depletion region. Thus, the total current can be define in terms of only the current at the depletion region edges.
Quantitative p-n Diode Solution
0 0
0 0 NPppP
pNppN
xJxxxJ
xJxxxJ
)x(J)x(JJ pPpN
Continuity equation
...light as suchprocesses other All
GR Thermal
P
...light as suchprocesses other All
GR Thermal
N
t
p
t
pJ
qt
p
t
n
t
nJ
qt
n
1
1
Continuity Equations
Quantitative p-n Diode Solution
Quisineutral Region Quisineutral Region
x”=0 x’=0
Quantitative p-n Diode Solution
Total on current is constant throughout the device. Thus, we can characterize the current flow components as…
-xp xn
J
pn-junction diode structure used in the discussion of currents. The sketch shows the dimensions and the bias convention. The cross-sectional area A is assumed to be uniform.
Hole current (solid line) and recombining electron current (dashed line) in the quasi-neutral n-region of the long-base diode of Figure 5.5. The sum of the two currents J (dot-dash line) is constant.
Hole density in the quasi-neutral n-region of an ideal short-base diode under forward bias of Va volts.
The ratio of generation-region width xi to space-charge-region width xd as a function of reverse voltage for several donor concentrations in a one-sided step junction.
The current components in the quasi-neutral regions of a long-base diode under moderate forward bias: J(1) injected minority-carrier current, J(2) majority-carrier current recombining with J(1), J(3) majority-carrier current injected across the junction. J(4) space-charge-region recombination current.
(d) Adapted from [8]. Current-voltage characteristic for a diode near the boundary between (a) and (c), showing diffusion current at lower voltages and a transition to thermionic-emission current at higher biases.
Current in a Heterojunction
(a) Transient increase of excess stored holes in a long-base ideal diode for a constant current drive applied at time zero with the diode initially unbiased. Note the constant gradient at x = xn as time increases from (1) through (5), which indicates a constant injected hole current. (Circuit shown in inset.) (b) Diode voltage VD versus time.
(a) Transient decay of excess stored holes in a long-base ideal diode. In the case shown, the initial forward bias applied through the series resistor is abruptly changed to a negative bias at time t = 0. (Circuit shown in inset.) (b) Diode current ID versus time.
Junction and Free-Carrier Storage
Jelec
x
n-region
J = Jelec + Jhole
SCL
Minority carrier diffusioncurrent
Majority carrier diffusionand drift current
Total current
Jhole
Wn–Wp
p-region
J
The total current anywhere in the device is constant.
Just outside the depletion region it is due to the diffusion of minority carriers.
Quantitative p-n Diode Solution
Quantitative p-n Diode Solution
Thus, evaluating the current components at the depletion region edges, we have…
Note: Vref from our previous qualitative analysis equation is the thermal voltage, kT/q
J = Jn (x”=0) +Jp (x’=0) = Jn (x’=0) +Jn (x”=0) = Jn (x’=0) +Jp (x’=0)
Ideal Diode Equation Shockley Equation
Current-Voltage Characteristics
of a Typical Silicon p-n Junction
Quantitative p-n Diode Solution
ExamplesDiode in a circuit