SLIDE 1
Band diagram
On the vertical axis: potential energy
- f the electrons
The pn junction [Fonstad, Ghione] Band diagram On the vertical - - PowerPoint PPT Presentation
The pn junction [Fonstad, Ghione] Band diagram On the vertical - - PowerPoint PPT Presentation
The pn junction [Fonstad, Ghione] Band diagram On the vertical axis: potential energy of the electrons On the horizontal axis: now there is nothing: later well put the position q F s : work function ( F s : extraction potential),
SLIDE 2
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The same material, with different doping
If the two samples are
isolated from each other, we have ->
note: the electron affinity
does not change
We’ll first assume uniform
doping in each sample
The work function is larger
for the p side
p side n side
SLIDE 4
The same material, with different doping
We have a junction! How to build the band diagram:
the Fermi level is constant (if not, electrons would move from
zones with higher f(E) to zones with lower f(E), due to the different probability of occupation of the states)
electron affinity and forbidden gap width are constant
(depend on the material only)
far from the junction, the band structure is that of the isolated
material
the vacuum level is continuous
SLIDE 5
Band diagram in contact
1st approx. drawing... complete drawing
E0 is now the energy of the electron just outside the material
SLIDE 6
Depletion region
Where bands bend, there are two depletion layers,
where r ~ ND or r ~ NA
These are space-charge regions => E => potential The contact potential, or built-in potential, is in order to compute the width of the depletion region,
we’ll compute with (global neutrality)
SLIDE 7
The two components of the built-in potential Vi
SLIDE 8
Depletion region and potentials
Two integration steps:
- [div E=r/e0] constant r => linear E(x)
- [E=-dv/dx] linear E(x) -> parabolic j(x)
j: electric potential – conventionally referred to EFi U: potential energy of the electrons at EFi (well, they do not exist...) U=-qj U is also (apart from an offset) the potential energy
- f the electrons e.g. at the bottom of CB
SLIDE 9
Depletion region
So we get so that And we get
with NAxp=NDxn and Neq=(NAND)/(NA+ND)
So, higher doping => thinner depletion region
SLIDE 10
Out of thermal equilibrium
Reverse bias....................................... forward bias
SLIDE 11
Out of thermal equilibrium
SLIDE 12
Electrons potential energy and concentrations
E and j in the depletion region -> E => we have to spend energy to
move electrons from right to left
i.e. their potential energy U increases
when moving from right to left
U has the same behaviour of EFi (and
the same of j but with opposite sign)
So from [sl. 110/24]
we can write
<-- minus!
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The current
Let us consider a 1D model (i.e., the section is constant
along x)
Hypothesis:
low injection n, p neglectable in the depletion layers the sides of the junctions (wp, wn) are much longer than
the diffusion lengths Ln=(Dntn)1/2 and Lp=(Dptp)1/2
In any section low injection -> We need to compute the concentrations of minority carriers
dr dr
SLIDE 14
Junction law
The solutions of the
diffusion equations are here
We need to know
n’p(-xp) and p’n(xn)
From
we get
SLIDE 15
Junction law
From
we get
At equilibrium (V=0) Out of equilibrium (but with low
injection): junction law ->
SLIDE 16
Out of equilibrium
Carriers
profile ->
SLIDE 17
The current
E.g. at x=xn Jtot(xn)=Jp(xn)+Jn(xn)=Jp, diff(xn)+Jn(xn) Assuming that recombination is neglectable in the space
charge region, Jn(xn)=Jn(-xp)=Jn, diff(-xp)
so that
Jtot(xn)=Jp, diff(xn)+Jn, diff(-xp)
p n n p
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The current
And we finally get
with
SLIDE 19
Effect of temperature
Higher T implies higher current, due to changes in
- increase in carrier concentration
- VT
- changes in Dn/p and Ln/p
At constant voltage, I doubles for an increase of 10 oC At constant current, V decreases of about 2.5 mV/oC
SLIDE 20
Depletion (or transition) capacitance Due to variations in the width
- f the depletion layer ->
variations of the charge
SLIDE 21
Diffusion capacitance
Due to variations in the profile of the
carriers in the proximity of the depletion layer
The “extra” charge in the profile of the carriers concentrations,
close to the space charge region, is proportional to J:
The corresponding capacitive effect is also proportional to J:
SLIDE 22
Diodes and switching
[See spice Simulation]
SLIDE 23
Large signal model
So the large signal model of a
diode is ->
All these 3 parameters (1
conductance and 2 capacitors) change with bias
In inverse bias Cj prevails on Cd the opposite in direct bias
SLIDE 24
Small signal model
By linearising the model around the bias
point we obtain the small signal model ->
gd0=I/hVT
where I is the bias current
It is a linear model!
SLIDE 25
Zener diodes
All diodes are subject to breakdown for sufficiently high inverse
bias
Zener diodes are designed to work in this condition, normally as
voltage references
Two physical mechanisms: tunnel and avalanche Higher doping => thinner depletion
region => higher E => easier breakdown => lower Vz
In order to have higher Vz : lower doping (at least on one side)
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Tunnel and avalanche breakdown
Tunnel: for VZ<6V, high doping; VZ decreases with T Avalanche: for VZ>6V, lower doping; VZ increases with T
SLIDE 27
Photodiodes
- If suitable photons reach the junction, they
may generate electron-hole couples
- minority (and also majority) concentrations
will increase
- In reverse bias, current will be larger due to
an extra photo-generated current IS proportional to the # of photons
- and we have
I = -IS + I0 (expV/VT -1)
- Photodiodes can be used as light detectors
- Considering the opposite current (I’=-I)
I V I’ V
SLIDE 28
Photodiodes as power generators
- So we have an open circuit voltage
(photovoltaic effect)
- and a short circuit current
- And we can also extract power!
- Photovoltaic cells are diodes with
very large area (to get many photons), optimized for power generation
V V V I’ I’ I’ I’ V
SLIDE 29
LEDs
SLIDE 30
LEDs
[Please note: the right drawing is deceitful, electron and holes are on the lines, not above or below the lines]
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