FYS3410 Condensed matter physics
Lecture 20: pn-junctions and electrooptics
Randi Haakenaasen
UniK/UiO
Forsvarets forskningsinstitutt
14.03.2014
Outline
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Why pn-junctions are important
Physics of pn-junction
What does a pn-junction look like?
Two electrooptic applications – LED and IR detector
IR detector technology at FFI
Demo – IR detector
Importance of pn-junction
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pn-junctions have diode characteristics
– Conduct current well in one direction: exp with V
– Conduct current poorly in the other direction
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Used as rectifier, two pn-junctions back-to-back make a
transistor (used as electrical amplifiers and switches),
basic building block of all integrated circuits (ICs),
advanced microprosessor can have > 3 billion transistors
– Billions of pn-junctions in computer, phone, Ipod….
– about 60 million transistors made per person on
Earth (2002)
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Electrooptics
– Light emitting diodes LEDs
– Photodetectors
– Solar cells
Physics of the pn-junction
Ɛ
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Abrupt junction at equilibrium (no external excitation,
no net currents flowing in the device)
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Large carrier concentration gradients at the junction:
diffusion of majority electrons from n- to p side where
they become minority carrier and recombine with a
majority carrier hole
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Same for holes but opposite direction
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Ionized donor atoms (Nd+) are left uncompensated on
the n-side and ionized acceptor atoms (Na-) on p-side
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This space charge is fixed in place, and it gives an Ɛ field from n-side to p-side (positive to negative charge)
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The Ɛ -field opposes Jdiff for both electrons and holes
and only the majority carriers with enough energy to
overcome the E-field will make it across
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Any minority carrier that enters the depletion region
will immediately be swept across by the Ɛ -field and
create a drift current Jdrift in the opposite dir. of Jdiff
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The field builds up until Jdrift exactly cancels Jdiff and
no net current flows in the junction at equilibrium
Junction characteristics
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The Ɛ-field appears in a narrow region around the junction
called the ‘space charge region’ or the ‘depletion region’ W
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An equilibrium potential difference called the ‘contact
potential’ V0 across W (Ɛ = - dV/dx) is a bult-in potential
barrier (does not imply an external potential). No net
(external) current can result from it.
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The contact potential separates the bands: they are higher
on the p side by qV0 (Fermi level constant at equilibrium)
Doping concentrations and the contact potential
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No net current can flow across the junction at equilibrium: Jdrift and Jdiff cancel
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Furthermore – no net buildup of electrons or holes on either side as function of time
-> Jdrift and Jdiff cancel for each carrier type. For holes:
D: cm2/s
µ: cm2/Vs
Einstein relation
𝐷 𝑘𝑘
=
𝑞
𝜇
V and p functions of x only
V and p at edges of depl reg
Contact potential in terms of equilibrium hole or
electron concentrations outside junction
Equilibrium Fermi levels
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EF constant through device in equilibrium
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The energy bands on either side of the junction are separated by qV0
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When bias is applied to the junction, the potential barrier is raised or lowered from V0,
and the Fermi levels on either side are shifted by energy q*Vapplied
Space charge at junction
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Consider only space charge in transition region due to uncompensated Na and Nd, and no
effect outside W
Dipole - equal number of charges in either side:
Use Poisson equation
Do we want to go through this? Many equations to get V0, W, dp and dn
Depletion region
Qualitative description of current flow at junction
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Apply an external voltage to junction – almost all
voltage appears across transition region
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Forward bias - Vf is positive on the p-side
– Potential barrier at junction is lowered to V0-Vf
– the Ɛ-field decreases
– The transition width W decreases
– Jdiff increases because more majority carriers
have enough energy to cross the potential
barrier
– Majority carriers-> large currents
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Reverse bias – Vr is positive on the n-side
– Potential barrier at junction is raised to V0+Vr
– the Ɛ-field increases
– The transition width W increases
– Almost no majority carriers have enough
energy to cross the potential barrier, so Jdiff
negligible
– Left with Jdrift which is indep of Ɛ-field , it is
minority carriers that wander into transition
region and are swept across
Biasing the junction – changing the diffusion current
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Holes in Jdrift are generated by thermal excitation of EHP. If generated within a
diffusion length of the depletion region, the hole can diffuse to the junction and be
swept across. This generation current Jgen is a drift current which is independent of V
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We assume Jdrift and Jdiff are proportional to the carrier densities. For electrons at
zero bias:
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𝐽𝑑𝑑𝑑𝑑 0 = 𝐽𝑑𝑟𝑟𝑟𝑟 0 = 𝐽𝑔𝑔𝑔 = 𝐶𝑒 (𝐸𝐸+𝑞𝑉0 −𝐸𝐸)⁄𝑘𝑘 ∝ 𝑛𝑝
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When applying a voltage V the bands shift by qV. The electron diffusion current
changes because EF on the n-side is shifted:
• 𝐽𝑑𝑑𝑑𝑑 = 𝐶𝐶 (𝐸𝐸+𝑞𝑉0−(𝐸𝐹−𝑞𝑞))⁄𝑘𝑘 = 𝐽𝑔𝑔𝑔 𝑒 𝑞𝑞⁄𝑘𝑘
IV curve
For each type of carrier:
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An applied bias V changes number of carriers that
diffuse across by 𝑒 𝑞𝑞 ⁄𝑘𝑘
𝐽𝑑𝑑𝑑𝑑 = 𝐽𝑔𝑔𝑔 𝑒 𝑞𝑞⁄𝑘𝑘
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So
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Total current is
𝐽𝑑𝑑𝑑𝑑 − 𝐽𝑔𝑔𝑔
that
and
(they are in opposite direction) for both carriers
𝐽 = (𝐽𝑔𝑔𝑔,𝑛 + 𝐽𝑔𝑔𝑔,𝑝 )(𝑒 𝑞𝑉⁄𝑘𝑘 −1)
𝐽 = 𝐽𝑔𝑔𝑔 (𝑒 𝑞𝑉⁄𝑘𝑘 −1)
The total current must be constant through the device. There is a flow of electrons from the negative
battery terminal to the junction. These supply the extra electrons that diffuse across the junction as
well as resupply the electrons lost by recombination in the excess hole distribution near the junction
(on the n-side). In the p-material the current is carried by holes that flow from the positive battery
terminal. Since the electrons and holes flow in opposite direction, the current throughout the device is
in the same direction.
Another way to get the variation of diffusion current with bias
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We expect the minority carrier conc. next to junction on each side to vary with V because of
variations in diffusion across junction. When more carriers diffuse across, there will be a higher
concentration of these immediatelty on the other side, but further away from the junction they
decrease to the equilibrium values. For junction without bias we found (slide 6)
This becomes with bias V
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For ‘low-level injection’ (not too large increase in diffusion current) we neglect changes in majority
carrier concentrations which vary only slightly with bias.
𝑝𝑝
𝑝 𝑥𝑛𝑛
=
𝑝𝑛 𝑒 𝑞𝑉0 ⁄𝑘𝑘
𝑝 𝑥𝑛𝑛
= 𝑒 𝑞(𝑉0−𝑉)⁄𝑘𝑘
In forward bias, increased p(xn0)
– minority carr injection – steady state injection of holes
In reverse bias, V is negative, p(xn0) reduced below equilibrium value
Same for electrons on p-side of junction n(-xn0)
What does a pn-junction look like?
Electroplated Au bonding pad
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Schematic drawing
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SEM cross-section
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EBIC image of current through diode
Sputtered Au
ZnS (0.3 µm)
CdTe
passivation (0.5 µm)
n
p
CMT (9-10 µm)
CZT (211)B substrate
R. Haakenaasen et al., J. Electron. Mater. 29, 849 (2000).
R. Haakenaasen et al., J. Appl. Phys. 91, 427 (2002).
Photon detectors
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Photon absorbed -> e-h pair gives current/voltage in ROIC
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Photoconductor
– measure changes in σ
– large bias current, small signal (mA,nA)
– dissipates heat, only small arrays (linear)
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Photovoltaic, photodiode
– pn-junction
– Reverse bias: small dark current Id (nA-pA,nA-µA)
– Measures photocurrent (or voltage)
Eg
Photodiode in reverse bias
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In reverse bias dark current is small and ∼ constant
– It comes from generation currents in junction + background radiation
– Signal is easy to measure
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Important characteristics:
– RA, quantum efficiency, noise equivalent temperature difference NETD,
response time
– Small power dissipation, can have many detector elements
Light emitting diode LED
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Photodiode in forward bias
– The carriers that diffuse through the junction recombin radiatively in or
near the depletion region
– Almost all the current is converted into light
A semiconductor laser-photodetector is used in CDs
Summary