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

Semiconductor Physics 1-2

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

Semiconductor Physics 1-3

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

Semiconductor Physics 1-4

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

Semiconductor Physics 1-9

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)

Semiconductor Physics 1-12

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

Semiconductor Physics 1-18

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)

Semiconductor Physics 1-20

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.

Semiconductor Physics 1-22

Semiconductor Physics 1-23

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