Lecture 3 Semiconductor Physics...
Transcript of Lecture 3 Semiconductor Physics...
Lecture 3
Semiconductor Physics (cont’d)
Semiconductor Physics 1-1 Sunday 24/9/2017
Agenda Continue Semiconductor Physics
Charge Carrier Transport • Carrier Drift
• Carrier Diffusion
pn junctions (or diodes) Introduction
Construction
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Charge Carrier Transport (cont’d)
Carrier Drift Carrier movement is induced by a force of some
type
Apply electric field to semiconductor: • E ≡ electric field [V cm-1]
net force on carrier • F = ±qE
Between collisions, carriers accelerate in the direction of the electrostatic field:
• v(t) = a • t = (Force/Mass).time = ± qE t/mn,p
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Carrier Drift (cont’d)
But there is, on the average, a collision every τc (i.e. lifetime) and the velocity is randomized:
The average net velocity in direction of the field: v = vd = ± qE t/mn,p = ± qE τc /2mn,p = (± q τc /2mn,p) E
This is called drift velocity [cm s-1]
Define: μn,p=± q τc/2mn,p ≡ carrier mobility [cm2 V−1 s−1]
Then, for electrons: vdn = −μn E
and for holes: vdp = μp E
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mean free time between
collisions
Carrier Drift (cont’d) Mobility is a measure of ease of carrier drift
If τc ↑, longer time between collisions ⇒ μ ↑
If m ↓, “lighter” particle ⇒ μ ↑
At room temperature, mobility in Si depends on doping:
Holes “heavier”
than electrons
- For same doping
level, μn > μp
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Drift Current Net velocity of charged particles ⇒ electric
current:
The total current density consists of both electrons and holes.
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EEEpnq
EqpEqnqpvqnvJJJ
EqnqnvJ
pn
pndpdnpntot
ndnn
)(Conductivity [Ω-1 • cm-1]
Resistivity [Ω • cm]
The Equivalent Electrical Resistance
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Resistivity
commonly used to specify the doping level In n-type semiconductor: (n=Nd and Nd≫Na)
In p-type semiconductor: (p=Na and Na≫Nd)
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Example
Si with Nd = 3 x 1016 cm-3 at room temperature, and
knowing that μn ≈ 1000 cm2/V•s, ρn
≈ 0.21 Ω• cm, and applied Electric field E = 1 kV/cm
find
a) vdn
b) Jndrift
c) Time to drift through a Si rod of length
L = 0.1 μm
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Carrier Diffusion Diffusion = particle movement (flux) in response to
concentration gradient
Elements of diffusion:
A medium (Si Crystal)
A gradient of particles (electrons and holes) inside the medium
Collisions between particles and medium send particles off in random directions
• Overall result is to erase gradient
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distance
Carrier Diffusion (cont’d)
Charge particles move from a region of high concentration to a region of low concentration. It is analogous to an everyday example of an ink droplet in water.
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Carrier Diffusion (cont’d)
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Diffusion Current
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Einstein relation
At the core of drift and diffusion is same physics
(statistical thermodynamic phenomena): collisions among particles and medium atoms
There should be a relationship between D and μ
Einstein relation:
In semiconductors:
At room temperature:
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Total Current Density In general, total current can flow by drift and
diffusion separately
Total current density:
Carriers move fast in response to fields and gradients
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Introduction to pn junctions pn junction (or diode)
p region and n region in intimate contact
Why is the pn junction worth studying? It is present in virtually every semiconductor device!
Understanding the pn junction is essential to understanding transistor operation
Basic function of diodes Allow current to flow only in one direction (protection)
Related Applications: rectifiers, waveform clipping and clamping circuits, DC-DC converters, etc.
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Construction of pn junction
When n-type and p-type semiconductors are introduced side-by-side in a semiconductor, a pn junction or a diode is formed.
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Metallurgical junction
Construction of pn junction (cont’d) the carrier concentration distribution in thermal
equilibrium
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Construction of pn junction (cont’d) At bringing the n and p sides together
Far away from the metallurgical junction: nothing happens Two quasi-neutral regions
Around the metallurgical junction: diffusion of carriers must counterbalance drift (Space charge region ) Semiconductor Physics 1-19
current
p n
Construction of pn junction (cont’d)
Thermal equilibrium: balance between drift and diffusion
We can divide
semiconductor into
three regions:
• Two quasi-neutral n and p regions (QNR’s)
• One space charge region (SCR)
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depletion region
Construction of pn junction (cont’d)
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Lecture Question
Discuss how pn junctions can be used to design photovoltaic solar cells.
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Lecture Summary Covered material Continue Semiconductor Physics
Carrier Transport • Carrier Drift and Drift Current (produced by electric field ) • Carrier Diffusion and Diffusion Current (produced by
concentration gradient) • Einstein Relationship • Total Current Density
Introduction to pn junctions (diodes) pn junction construction
Material to be covered next lecture Continue pn junctions
Depletion rejoins Built-in potential I-V characteristics