President UniversityErwin SitompulSDP 4/1 Dr.-Ing. Erwin Sitompul President University Lecture 4...

President University Erwin Sitompul SDP 4/1

Dr.-Ing. Erwin SitompulPresident University

Lecture 4

Semiconductor Device Physics

http://zitompul.wordpress.com


Electron kinetic energyIn

crea

sing

ele

ctro

n en

ergy

Ec

EvHole kinetic energy In

crea

sing

hol

e en

ergy

c referenceP.E. E E

Potential vs. Kinetic EnergyChapter 3 Carrier Action

Ec represents the electron potential energy:


Ec

Ev

E

x

Band BendingChapter 3 Carrier Action

Until now, Ec and Ev have always been drawn to be independent of the position.

When an electric field E exists inside a material, the band energies become a function of position.

• Variation of Ec with position is called “band bending”


c reference

1( )V E Eq

qVP.E.

VdV

dx

E

c v i1 1 1dE dE dE

q dx q dx q dx E

Band BendingChapter 3 Carrier Action

The potential energy of a particle with charge –q is related to the electrostatic potential V(x):

• Since Ec, Ev, and Ei differ only by an additive constant


DiffusionChapter 3 Carrier Action

Particles diffuse from regions of higher concentration to regions of lower concentration region, due to random thermal motion (Brownian Motion).


1-D Diffusion ExampleChapter 3 Carrier Action

Thermal motion causes particles to move into an adjacent compartment every τ seconds.


e

N|diff N

dnqD

dxJ P|diff P

dpqD

dxJ

Diffusion CurrentsChapter 3 Carrier Action

• D is the diffusion coefficient [cm2/sec]

n

x

Current flowElectron flow

hp

x

Current flowHole flow


N N|drift N|diff n N dn

q n qDdx

E J J J

N P J J J

P P|drift P|diff p P dp

q p qDdx

EJ J J

Total CurrentsChapter 3 Carrier Action

Drift current flows when an electric field is applied. Diffusion current flows when a gradient of carrier concentration

exist.


N n N 0dn

q n qDdx

EJ

Current Flow Under Equilibrium ConditionsChapter 3 Carrier Action

In equilibrium, there is no net flow of electrons or :

N 0,J P 0J

The drift and diffusion current components must balance each other exactly.

A built-in electric field of ionized atoms exists, such that the drift current exactly cancels out the diffusion current due to the concentration gradient.


F cC cE E kTN dEdne

dx kT dx

F c

CE E kTn N e

Ev(x)

Ec(x)

EF

dn qn

dx kT E

Current Flow Under Equilibrium ConditionsChapter 3 Carrier Action

Consider a piece of non-uniformly doped semiconductor:

n-type semiconductor

Decreasing donor concentration

• Under equilibrium, EF inside a material or a group of materials in intimate contact is not a function of position

cdEn

kT dx


N

n

D kT

q

Similarly, P

p

D kT

q

N n N 0dn

q n qDdx

EJ

n N 0q

qn qn DkT

E E

Einstein Relationship between D and Chapter 3 Carrier Action

But, under equilibrium conditions, JN = 0 and JP = 0

• Einstein Relationship

Further proof can show that the Einstein Relationship is valid for a non-degenerate semiconductor, both in equilibrium and non-equilibrium conditions.


P p

kTD

q

1 eV1 V

1 e

191 eV 1.602 10 J

Example: Diffusion CoefficientChapter 3 Carrier Action

What is the hole diffusion coefficient in a sample of silicon at 300 K with p = 410 cm2 / V.s ?

2 1 125.86 meV410 cm V s

1e

2cm25.86 mV 410

V s

210.603 cm /s

• Remark: kT/q = 25.86 mV at room temperature


Recombination–Generation Chapter 3 Carrier Action

Recombination: a process by which conduction electrons and holes are annihilated in pairs.

Generation: a process by which conduction electrons and holes are created in pairs.

Generation and recombination processes act to change the carrier concentrations, and thereby indirectly affect current flow.


Band-to-Band R–G Center Impact Ionization

EG

c1 dE

q dxE

ET: trap energy level

Generation ProcessesChapter 3 Carrier Action

Release of energy

• Due to lattice defects or unintentional impurities

• Also called indirect generation

• Only occurs in the presence of large E


Band-to-Band R–G Center Auger

Collision

Recombination ProcessesChapter 3 Carrier Action

• Rate is limited by minority carrier trapping

• Primary recombination way for Si

• Occurs in heavily doped material


Ev

Ec

Ec

EvGaAs, GaN(direct semiconductors)

Si, Ge(indirect

semiconductors)

PhotonPhoton

Phonon

Direct and Indirect SemiconductorsChapter 3 Carrier Action

E-k Diagrams

• Little change in momentum is required for recombination

• Momentum is conserved by photon (light) emission

• Large change in momentum is required for recombination

• Momentum is conserved by mainly phonon (vibration) emission + photon emission


0nnn

0ppp

, 0n p

Equilibrium valuesDeviation from

equilibrium values

Excess Carrier ConcentrationsChapter 3 Carrier Action

Positive deviation corresponds to a carrier excess, while negative deviations corresponds to a carrier deficit.

Values under arbitrary conditions

pn Charge neutrality condition:

, 0n p


Often, the disturbance from equilibrium is small, such that the majority carrier concentration is not affected significantly:

For an n-type material

For a p-type material

0 0, p n n n

0 0, n p p p

“Low-Level Injection”Chapter 3 Carrier Action

However, the minority carrier concentration can be significantly affected.

0p p

0n n • Low-level injection condition


p TR

pc N p

t

G G-equilibrium

p p

t t

NT : number of R–G centers/cm3

Cp : hole capture coefficient

Indirect Recombination RateChapter 3 Carrier Action

Suppose excess carriers are introduced into an n-type Si sample by shining light onto it. At time t = 0, the light is turned off. How does p vary with time t > 0?

Consider the rate of hole recombination:

In the midst of relaxing back to the equilibrium condition, the hole generation rate is small and is taken to be approximately equal to its equilibrium value:

R-equilibrium

p

t

p T 0c N p


R G R G

p p p

t t t

p TR G p

p pc N p

t

n TR G n

n nc N n

t

pp T

1

c N where

where nn T

1

c N

Indirect Recombination RateChapter 3 Carrier Action

The net rate of change in p is therefore:

p T p T 0c N p c N p p T 0c N p p

• For holes in n-type material

• For electrons in p-type material

Similarly,


pp T n T

1 1 nc N c N

Minority Carrier LifetimeChapter 3 Carrier Action

The minority carrier lifetime τ is the average time for excess minority carriers to “survive” in a sea of majority carriers.

The value of τ ranges from 1 ns to 1 ms in Si and depends on the density of metallic impurities and the density of crystalline defects.

The deep traps originated from impurity and defects capture electrons or holes to facilitate recombination and are called recombination-generation centers.


16 30 10 cmp

p n

Example: PhotoconductorChapter 3 Carrier Action

Consider a sample of Si doped with 1016 cm–3 Boron, with recombination lifetime 1 μs. It is exposed continuously to light, such that electron-hole pairs are generated throughout the sample at the rate of 1020 per cm3 per second, i.e. the generation rate GL = 1020/cm3/s

a) What are p0 and n0?

2i

00

nn

p

210

16

10

10 4 310 cm

b) What are Δn and Δp?

LG 20 610 10 14 310 cm• Hint: In steady-state,

generation rate equals recombination rate


Example: PhotoconductorChapter 3 Carrier Action

Consider a sample of Si at 300 K doped with 1016 cm–3 Boron, with recombination lifetime 1 μs. It is exposed continuously to light, such that electron-hole pairs are generated throughout the sample at the rate of 1020 per cm3 per second, i.e. the generation rate GL = 1020/cm3/s.

c) What are p and n?

d) What are np product?

• Note: The np product can be very different from ni

2 in case of perturbed/agitated semiconductor

0p p p 16 1410 10 16 310 cm

0n n n 4 1410 10 14 310 cm

16 1410 10np 30 310 cm 2in


2i

R G R G p 1 n 1( ) ( )

n npp n

t t n n p p

• ET : energy level of R–G center

Net Recombination Rate (General Case)Chapter 3 Carrier Action

For arbitrary injection levels and both carrier types in a non-degenerate semiconductor, the net rate of carrier recombination is:

T i( )1 i E E kTn n e

i T( )1 i

E E kTp n e

where


1.(4.27)Problem 3.12, from (a) until (f), for Figure P3.12(a) and Figure P3.12(f),Pierret’s “Semiconductor Device Fundamentals”.

Chapter 2 Carrier Action

Homework 3

2.(5.28)The electron concentration in silicon at T = 300 K is given by

Deadline: 10 February 2011, at 07:30.

16 3( ) 10 exp cm18

xn x

where x is measured in μm and is limited to 0 ≤ x ≤ 25 μm. The electron diffusion coefficient is DN = 25 cm2/s and the electron mobility is μn = 960 cm2/(Vs). The total electron current density through the semiconductor is constant and equal to JN = –40 A/cm2. The electron current has both diffusion and drift current components.

Determine the electric field as a function of x which must exist in the semiconductor. Sketch the function.

President UniversityErwin SitompulSDP 4/1 Dr.-Ing. Erwin Sitompul President University Lecture 4...

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