Lecture 3 OUTLINE Semiconductor Basics contd Carrier drift

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Lecture 3 OUTLINE • Semiconductor Basics (cont’d) – Carrier drift and diffusion • PN

Lecture 3 OUTLINE • Semiconductor Basics (cont’d) – Carrier drift and diffusion • PN Junction Diodes – Electrostatics – Capacitance Reading: Chapter 2. 1 -2. 2 EE 105 Fall 2011 Lecture 3, Slide 1 Prof. Salahuddin, UC Berkeley

Recap: Drift Current • Drift current is proportional to the carrier velocity and carrier

Recap: Drift Current • Drift current is proportional to the carrier velocity and carrier concentration: Total current Jp, drift= Q/t Q= total charge contained in the volume shown to the right t= time taken by Q to cross the volume Q=qp(in cm 3)X Volume=qp. AL=qp. Avht Hole current per unit area (i. e. current density) Jp, drift = q p vh EE 105 Fall 2011 Lecture 3, Slide 2 Prof. Salahuddin, UC Berkeley

Recap: Conductivity and Resistivity • In a semiconductor, both electrons and holes conduct current:

Recap: Conductivity and Resistivity • In a semiconductor, both electrons and holes conduct current: • The conductivity of a semiconductor is – Unit: mho/cm • The resistivity of a semiconductor is – Unit: ohm-cm EE 105 Fall 2011 Lecture 3, Slide 3 Prof. Salahuddin, UC Berkeley

Electrical Resistance I V + _ W t homogeneously doped sample L (Unit: ohms)

Electrical Resistance I V + _ W t homogeneously doped sample L (Unit: ohms) Resistance where r is the resistivity EE 105 Fall 2011 Lecture 3, Slide 4 Prof. Salahuddin, UC Berkeley

Resistivity Example EE 105 Fall 2011 Lecture 3, Slide 5 Prof. Salahuddin, UC Berkeley

Resistivity Example EE 105 Fall 2011 Lecture 3, Slide 5 Prof. Salahuddin, UC Berkeley

A Second Mechanism of Current Flow is Diffusion EE 105 Fall 2011 Lecture 3,

A Second Mechanism of Current Flow is Diffusion EE 105 Fall 2011 Lecture 3, Slide 6 Prof. Salahuddin, UC Berkeley

Carrier Diffusion • Due to thermally induced random motion, mobile particles tend to move

Carrier Diffusion • Due to thermally induced random motion, mobile particles tend to move from a region of high concentration to a region of low concentration. – Analogy: ink droplet in water EE 105 Fall 2011 Lecture 3, Slide 7 Prof. Salahuddin, UC Berkeley

Carrier Diffusion • Current flow due to mobile charge diffusion is proportional to the

Carrier Diffusion • Current flow due to mobile charge diffusion is proportional to the carrier concentration gradient. – The proportionality constant is the diffusion constant. Notation: Dp hole diffusion constant (cm 2/s) Dn electron diffusion constant (cm 2/s) EE 105 Fall 2011 Lecture 3, Slide 8 Prof. Salahuddin, UC Berkeley

Diffusion Examples • Linear concentration profile constant diffusion current EE 105 Fall 2011 •

Diffusion Examples • Linear concentration profile constant diffusion current EE 105 Fall 2011 • Non-linear concentration profile varying diffusion current Lecture 3, Slide 9 Prof. Salahuddin, UC Berkeley

Diffusion Current • Diffusion current within a semiconductor consists of hole and electron components:

Diffusion Current • Diffusion current within a semiconductor consists of hole and electron components: • The total current flowing in a semiconductor is the sum of drift current and diffusion current: EE 105 Fall 2011 Lecture 3, Slide 10 Prof. Salahuddin, UC Berkeley

The Einstein Relation • The characteristic constants for drift and diffusion are related: •

The Einstein Relation • The characteristic constants for drift and diffusion are related: • Note that at room temperature (300 K) – This is often referred to as the “thermal voltage”. EE 105 Fall 2011 Lecture 3, Slide 11 Prof. Salahuddin, UC Berkeley

The PN Junction Diode • When a P-type semiconductor region and an N-type semiconductor

The PN Junction Diode • When a P-type semiconductor region and an N-type semiconductor region are in contact, a PN junction diode is formed. V – D + ID EE 105 Fall 2011 Lecture 3, Slide 12 Prof. Salahuddin, UC Berkeley

Diode Operating Regions • In order to understand the operation of a diode, it

Diode Operating Regions • In order to understand the operation of a diode, it is necessary to study its behavior in three operation regions: equilibrium, reverse bias, and forward bias. VD = 0 EE 105 Fall 2011 VD < 0 Lecture 3, Slide 13 VD > 0 Prof. Salahuddin, UC Berkeley

Carrier Diffusion across the Junction • Because of the differences in hole and electron

Carrier Diffusion across the Junction • Because of the differences in hole and electron concentrations on each side of the junction, carriers diffuse across the junction: Notation: nn electron concentration on N-type side (cm-3) pn hole concentration on N-type side (cm-3) pp hole concentration on P-type side (cm-3) np electron concentration on P-type side (cm-3) EE 105 Fall 2011 Lecture 3, Slide 14 Prof. Salahuddin, UC Berkeley

Depletion Region • As conduction electrons and holes diffuse across the junction, they leave

Depletion Region • As conduction electrons and holes diffuse across the junction, they leave behind ionized dopants. Thus, a region that is depleted of mobile carriers is formed. – The charge density in the depletion region is not zero. – The carriers which diffuse across the junction recombine with majority carriers, i. e. they are annihilated. quasineutral region width=Wdep region EE 105 Fall 2011 Lecture 3, Slide 15 Prof. Salahuddin, UC Berkeley

Some Important Relations Energy=-q. V EE 105 Fall 2011 Lecture 3, Slide 16 Prof.

Some Important Relations Energy=-q. V EE 105 Fall 2011 Lecture 3, Slide 16 Prof. Salahuddin, UC Berkeley

The Depletion Approximation Because charge density ≠ 0 in the depletion region, a large

The Depletion Approximation Because charge density ≠ 0 in the depletion region, a large E-field exists in this region: In the depletion region on the N side: r(x) In the depletion region on the P side: q. ND a -b -q. NA EE 105 Fall 2011 x Lecture 3, Slide 17 Prof. Salahuddin, UC Berkeley

Carrier Drift across the Junction EE 105 Fall 2011 Lecture 3, Slide 18 Prof.

Carrier Drift across the Junction EE 105 Fall 2011 Lecture 3, Slide 18 Prof. Salahuddin, UC Berkeley

PN Junction in Equilibrium • In equilibrium, the drift and diffusion components of current

PN Junction in Equilibrium • In equilibrium, the drift and diffusion components of current are balanced; therefore the net current flowing across the junction is zero. EE 105 Fall 2011 Lecture 3, Slide 19 Prof. Salahuddin, UC Berkeley

Built-in Potential, V 0 • Because there is a large electric field in the

Built-in Potential, V 0 • Because there is a large electric field in the depletion region, there is a significant potential drop across this region: (Unit: Volts) EE 105 Fall 2011 Lecture 3, Slide 20 Prof. Salahuddin, UC Berkeley

Built-In Potential Example • Estimate the built-in potential for PN junction below. – Note

Built-In Potential Example • Estimate the built-in potential for PN junction below. – Note that EE 105 Fall 2011 N P ND = 1018 cm-3 NA = 1015 cm-3 Lecture 3, Slide 21 Prof. Salahuddin, UC Berkeley

PN Junction under Forward Bias • A forward bias decreases the potential drop across

PN Junction under Forward Bias • A forward bias decreases the potential drop across the junction. As a result, the magnitude of the electric field decreases and the width of the depletion region narrows. r(x) q. ND a -b -q. NA x ID V(x) V 0 -b EE 105 Fall 2011 0 a x Lecture 3, Slide 22 Prof. Salahuddin, UC Berkeley