• Why pn-junctions are important
• Physics of pn-junction
• What does a pn-junction look like?
• Three electrooptic applications – LED, IR detector, solar cell
• Demo – IR detector, modulated-LED-sound-transmitter
Excess carriers
• Most SC devices operate by creation of charge carriers in excess of thermal equil. values
– Optical excitation
– Electron bombardement
– Injected in forward biased pn-junction
Steady state: nonequil condition in which all processes are constant and are balanced by opposing processes (eg a sample with a constant current or optical generation of
EHPs just balanced by recombination)

Thermodyn. equilibrium: no net flows of matter, charge or energy, no phase changes, and no unbalanced potentials (or driving forces) within the system.
(a sample at constant temperature, in the dark, with no fields applied). A system in thermodyn. equil. experiences no changes when isolated from its surroundings

• pn-junctions have diode characteristics
– Conduct current well in one direction: exp with V
– Conduct current poorly in the other direction
• 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)
• Electrooptics
– Light emitting diodes LEDs
– Lasers
– Photodetectors
– Solar cells

• Abrupt junction at equilibrium (no external excitation, no net currents flowing in the device)
Ɛ
• 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
• Same for holes but opposite direction
• Ionized donor atoms (Nd+) are left uncompensated on the n-side and ionized acceptor atoms (Na-) on p-side
• This space charge is fixed in place, and it gives an
Ɛ
field from n-side to p-side (positive to negative charge)
• The
Ɛ
-field opposes J diff for both electrons and holes and only the majority carriers with enough energy to overcome the E-field will make it across
• Any minority carrier that enters the depletion region will immediately be swept across by the
Ɛ
-field and create a drift current J drift in the opposite dir. of J diff
• The field builds up until J drift
exactly cancels J diff and no net current flows in the junction at equilibrium

• The
Ɛ
-field appears in a narrow region around the junction called the ‘space charge region’ or the ‘depletion region’ W
• An equilibrium potential difference called the ‘contact potential’ V
0
across W (
Ɛ = - dV/dx
) is a built-in potential barrier (does not imply an external potential). No net
(external) current can result from it.
• The contact potential separates the bands: they are higher on the p side by qV
0
(Fermi level constant at equilibrium)

(need this for calculation of V
0
)
In a SC with a carrier gradient and an electric field,
𝐽 the current density for holes is 𝑝 𝑥 = 𝑞𝜇 ℎ drift 𝑝 𝑥 ℇ 𝑥 − 𝑞𝐷 diffusion ℎ 𝑑𝑝 𝑥 𝑑𝑥
At equilibrium, no net current flows. Thus a fluctuation which starts a diffusion current also sets up an electric field which redistributes carriers by drift
𝑝
= 0
ℇ 𝑥 =
𝐷 ℎ 𝜇 ℎ
1 𝑝 𝑥 𝑑𝑝 𝑥 𝑑𝑥
=
𝐷 ℎ 𝜇 ℎ 𝑛 𝑖 𝑛 𝑖 𝑒
− ( 𝐸𝑖−𝐸𝐹 ) ⁄ 𝑘𝑘 𝑒 − ( 𝐸𝑖−𝐸𝐹 ) ⁄ 𝑘𝑘
1 𝑘𝑘
𝐷 ℎ 𝜇 ℎ
=
𝐷 ℎ 𝜇 ℎ
1 𝑘𝑘 𝑑𝐸 𝑖 𝑑𝑥
=
𝐷 𝑒 𝜇 𝑒
= 𝑘
𝐵 𝑞
𝑇
= 0.026 V
− 𝑑𝐸
𝐹 𝑑𝑥
0
D: cm2/s
µ : cm2/Vs
=
𝐷 ℎ 𝜇 ℎ
1 𝑘𝑘 𝑞ℇ 𝑥 𝑑𝐸 𝑖 𝑑𝑥
− 𝑑𝐸
𝐹 𝑑𝑥

• Electrons drift in direction opposite to field
• -> Potential energy increases in direction of field
• The electrostatic potential
𝑉 𝑥 = 𝐸 𝑥 ⁄ −𝑞
• The electric field ℇ 𝑥 = − 𝑑𝑉 𝑥 𝑑𝑥
• Relate
ℇ 𝑥
to the electron potential energy in band diagram, choosing
𝐸 𝑖
as reference
•
ℇ 𝑥 = − 𝑑𝑉 𝑥 𝑑𝑥 = − 𝑑 𝑑𝑥
𝐸 𝑖
−𝑞
=
1 𝑞 𝑑𝐸 𝑖 𝑑𝑥
• To remember: e- drift ‘downhill’ in an
ℇ
-field, while holes float up like bubbles

• No net current can flow across the junction at equilibrium: J drift and J diff cancel
• Furthermore – no net buildup of electrons or holes on either side as function of time
-> J drift and J diff cancel for each carrier type. For holes:
D: cm2/s
µ : cm2/Vs
Einstein relation
𝐷 𝜇
= 𝑘𝑇 𝑞
V and p functions of x only
V and p at edges of depl reg
Step junction: use equil. values for p and n outside depletion region

Contact potential in terms of doping concentrations and n i
Contact potential in terms of equilibrium hole or electron concentrations outside junction

• E
F
constant through device in equilibrium
• The energy bands on either side of the junction are separated by qV
0
• When bias is applied to the junction, the potential barrier is raised or lowered from V
0
, and the Fermi levels on either side are shifted by energy q*V f

• Apply an external voltage to junction – almost all voltage appears across transition region
• Forward bias - Vf is positive on the p-side
– Potential barrier at junction is lowered to V
0
-V f
– the
Ɛ
-field decreases
– The transition width W decreases
– J diff increases because more majority carriers have enough energy to cross the potential barrier
– Majority carriers-> large currents
• Reverse bias – Vr is positive on the n-side
– Potential barrier at junction is raised to V
0
+V r
– the
Ɛ
-field increases
– The transition width W increases
– Almost no majority carriers have enough energy to cross the potential barrier, so J diff negligible
– Left with J drift which is indep of
Ɛ
-field , it is minority carriers that wander into transition region and are swept across

The diffusion current J diff depends strongly on the bias voltage
The drift current J drift is independent of bias voltage -
It is minority carriers generated by thermal excitation of EHP pairs. If they diffuse to the depletion region they are swept across by the
Ɛ-field. It is also called
generation current
J gen
For electrons at zero bias:
𝐽 𝑑𝑖𝑑𝑑 , 𝑒
0 = 𝐽 𝑑𝑟𝑖𝑑𝑟 , 𝑒
0 = 𝐽 𝑔𝑒𝑛 , 𝑒
An applied bias voltage V f junction by
( 𝑞𝑉 𝑓
) ⁄ 𝑘𝑘
increases the probability that a carrier can diffuse across the 𝑑𝑖𝑑𝑑 , 𝑒
𝑑
= 𝐽 𝑑𝑖𝑑𝑑 , 𝑒
0
( 𝑞𝑉 𝑓
⁄ 𝑘𝑘 ) =
𝑔𝑒𝑛 , 𝑒
( 𝑞𝑉 𝑓
⁄ 𝑘𝑘 )

For each type of carrier:
𝐽 𝑑𝑖𝑑𝑑
𝑉 𝑑
= 𝐽 𝑑𝑖𝑑𝑑
(0) 𝑒 𝑞𝑉 𝑓
⁄ 𝑘𝑘 = 𝐽 𝑔𝑒𝑛 𝑒 𝑞𝑉 𝑓
Total current each carrier is 𝐽 𝑑𝑖𝑑𝑑
− 𝐽 𝑔𝑒𝑛
⁄ 𝑘𝑘 total current 𝐽 = ( 𝐽 𝑔𝑒𝑛 , 𝑒
𝐽 = 𝐽 𝑔𝑒𝑛
( 𝑒
+ 𝐽 𝑔𝑒𝑛 , ℎ
)( 𝑒
− 1)
− 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.

f
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
This becomes with bias V
For ‘low-level injection’ (not too large increase in diffusion current) we neglect changes in majority carrier concentrations which vary only slightly with bias. 𝑝 𝑝 𝑝 𝑥 𝑛𝑛
= 𝑝 𝑛 𝑒 𝑞𝑉
0 𝑝 𝑥 𝑛𝑛
⁄ 𝑘𝑘
= 𝑒 𝑞 ( 𝑉
0
−𝑉 ) ⁄ 𝑘𝑘
• In forward bias, increased p(x n0
)
– minority carr injection – steady state injection of holes
• In reverse bias, V is negative, p(x n0
) reduced below equilibrium value
• Same for electrons on p -side of junction n(-x n0
)

ZnS (0.3
µ m)
CdTe passivation (0.5
µ m)
Electroplated Au bonding pad n
CMT (9-10
µ m)
CZT (211)B substrate
Sputtered Au p
•
Schematic drawing
•
SEM cross-section
•
EBIC image of current through diode
R. Haakenaasen et al.
, J. Electron. Mater. 29, 849 (2000).
R. Haakenaasen et al.
, J. Appl. Phys. 91, 427 (2002).

I positive I negative
𝐼 = 𝐼 𝑔𝑒𝑛
( 𝑒 − 1)

At equilibrium, V ext
= 0
• Diode with built-in contact potential V
0
• For electrons
– I diff
from n to p
– I drift
from p to n
– these cancel in equilibrium: no net current
Non-equilibrium: add a constant photocurrent I ph
• Get new higher level of carriers and gen/recomb current
• I ph
is a minority carrier current
– same direction as I drift
– proportional to incident light
– V=0, get short circuit I sc
= - I ph
– open circuit I = 0, V = V oc
(max V
0
)
𝐼 = 𝐼 𝑔𝑒𝑛
( 𝑒 − 1) becomes 𝐼 = 𝐼 𝑔𝑒𝑛
( 𝑒 − 1) − 𝐼 𝑝ℎ

𝐼 = 𝐼 𝑔𝑒𝑛 𝑒 − 1 − 𝐼 𝑝ℎ
Short-circuit current
𝐼 𝑜𝑝 and open circuit voltage
𝑉 𝑜𝑜
• In 1st quadrant, V and I positive -> LED, laser
• In 3rd quadrant, V and I are negative -> photodetector
• In 4th quadrant, V positive and I negative -> solar cell
– When P=VI is positive, power delivered from external circuit to junction
– When P=VI is negative, power delivered from junction to external circuit

• Photodiode with I ph in forward bias V f
– The carriers that diffuse through the junction recombine radiatively in or near the depletion region
– Almost all the current is converted into light

• In reverse bias dark current is small and
∼
constant (IR: 10 -7 – 10 -13 A)
– It comes from generation currents in depletion zone + within diffusion length of junction
• Signal current proportional to optical generation rate (10 -3 – 10 -6 A)
– Proportional to incoming light intensity
– Fast reponse time: high mobility or wide depletion layer
𝐼 = 𝐼 𝑔𝑒𝑛 𝑒 − 1 − 𝐼 𝑝ℎ
Short-circuit current
𝐼 𝑜𝑝 and open circuit voltage
𝑉 𝑜𝑜
• Important characteristics:
– Large signal/dark current ratio
– RA (10 3 – 10 7
Ω− cm 2 ), quantum efficiency (100%), noise equivalent temperature difference NETD (10 mK), response time (
µ s)
– Small power dissipation, can have many detector elements

• Voltage
≤
V oc
≤
V
0
generally
≤
E g
/q
• Si: V oc
1V, I op
10-100 mA for A=1cm 2
• But use many devices to generate enough power to run electronics or charge batteries