Contributions from the Depletion Region - KNUbkict-ocw.knu.ac.kr/include/download.html?fn=559E057A862B5.pdf · Solar Cells, Light Emitting Diode, Laser Diode, Photodiode Solar Cell

Chapter 4. PN and Metal-Semiconductor JunctionsModern Semiconductor Devices for Integrated Circuits

Contributions from the Depletion Region

at reverse bias,

E

EFp

EFn

ideal reverse current

added reverse generation

current due to generation of

carriers from trap level in the

depletion region

ET

EV

EC

I0

Space-charge-region (SCR) currents

at small forward bias,

EFp

EFn

ET

ideal diffusion current

ideal diffusion current

recombination current

EC

EV

E

ISCR

ISCR

0 SCRI I I

ideal diffusion SCRI I I


Space-charge-region (SCR) currents

Inside the depletion region

( ) /( ) / 2 /Fn FpC VE E kTE E kT qV kT

C V ipn N N e e n e

The recombination rate is the largest where / 2 .qV kT

in p n e

/ 2( ) ( 1)qV kTi

dep

nNet recombination generation rate per unit volume e

/ 2

: / .

:

( 1) : 0 :

:

dep

qV kT

the generation recombination lifetime in the depletion layer

net generation

e equilibrium

net recombination

/ 2 / 2( 1) ( 1)N

P

x i depqV kT qV kTiSCR

xdep dep

qnWnI qA e dx A e

/ / 2

0, ( 1) ( 1)i depqV kT qV kT

ideal SCR

dep

qnWTotal diode current I I I I e A e


Total diode current can be written as,

/ / 2

0

/

0

( 1) ( 1)

( 1), 1 2 :

i depqV kT qV kT

dep

qV kT

qnWI I e A e

I e idealty factor

Junction leakage current is a very important

issue in DRAM technology and generate

noise in major devices. Manufacturing these

devices requires special care to make the

generation/recombination lifetime long with

super-clean and nearly crystal-defects free

processing to minimize the density of

recombination traps.

Under reverse bias,

0( )i dep

leakage

dep

qnWI I A

leakage dep rI W V


Stored excess minority carrier

charge in neutral region (Q)

negligible

( , )Px

Q qA n x t dx

Charge Storage

For forward biased one sided N+P junction,

2

2

( , )

1

n

n

n

n

n x t d n nD

t dx

dJ n

q dx

, since 0in neutral region .En n

dnJ qD

dx

By multiplying (-qA ) at both sides of the continuity equation and integrating,

( )

( )

1n

P n P P

J

nx J x x

n

dqA n dx A dJ qA n dx

dt

: Continuity equation

,( ) ( ) ( )n n P n P nP diffusion diffusionAJ AJ x AJ x AJ i

diffusion

n

dQ Qi

dt : Charge control equation

(continuity equation for excess electron)

include both ac and DC


( )n

dQ Qi t

dt

In steady state (DC),

0 diffusion diffusion

dQand i I I

dt for one-sided junction

n s

Q QI

s is called the charge-storage time.

• In a one-sided junction, is the recombination lifetime ( )

on the lighter-doping side.s ,n p

s n • For N+P one-sided junction,

In general, is an average of the recombination lifetime on the N side

and the P side.s

Similarly, for forward biased one sided P+N junction,

( )p

dQ Qi t

dt

For one sided N+P junction, ( ) :diffusioni i t total current


Small-Signal Model of the Diodea.c. small signal,V sin ,

acac

kTwhere v

qV v t

I i

The small-signal equivalent circuit of a PN diode.

V

SR

intrinsic part

I i

R

/ /

0 0( 1)qV kT qV kTI I e I e I

V-I0

V

I

Slope = 1/R

V0

0

/

0

/ /

0 0

1( ) ( 1)

/

qV kT

V V

qV kT qV kT

DC

dI dG I e

R dV dV

d q kTI e I e I

dV kT q

R is called diffusion

resistance

0( ) /d V V S S S DC

dQ dI kTC G I

dV dV q Small signal

diffusion

capacitance

Diffusion capacitance:

dominant in forward

bias

Junction capacitance:

dominant in reverse

bias


Transient and A-C Conditions

• Most solid state devices are used for switching or for processing a-c

signals.

• We investigate the important influence of excess carriers in transient

and a-c problems.

Time Variation of Stored Charge

• Any change in current a change of charge stored in the carrier

distributions.

• Since time is required in building up or depleting a charge distribution, the

stored charge must inevitably lag behind the current in a time-dependent

problem. This is inherently a capacitive effect.

• For a proper solution of a transient problem, we must use the time-

dependent continuity equations


For P+-N junction; two charge storage effects:

(1) The usual recombination term Qp/p in which the excess carrier distribution

is replaced every p seconds

(2) A charge buildup (or depletion) term dQp/dt, which allows for the fact that

the distribution of excess carriers can be increasing or decreasing in a time-

dependent problem

• Solving the equation with Laplace transform, with I (t > 0)=0 and

Qp(0)=Ip, we obtain

10 (0)

10

p p p

p

p p p

p

Q s sQ s Q

Q s sQ s I

, ,p p

P diffusion

p

Q t dQ ti total diode current i t

dt

Turn-off transient

i t

I

t=0

t

0( )p p p

p p

Q t dQ t Q ti t I for t at steady state

dt


( )

1( )

atf t e

fs a

L

• The stored charge dies out exponentially from its initial value Ip with a time

constant equal to the hole lifetime in the n material.

1

( ) p

p

p

p

t

p p

IQ s

s

Q t I e

P+ N

i(t)

v(t)

N

NxPx


becomes non-exponential as the transient proceeds.

• Even though the current is suddenly terminated, the voltage across the

junction persists until Qp disappears.

• At any time during the transient, the excess hole concentration at xN is

/' 1

qv t kT

np t p e

• The gradient of the hole distribution at xN = 0 (zero current implies zero

gradient).

• An approximate solution for v(t) can be obtained by assuming an

exponential distribution for at every instant during the decay

quasi-steady state approximation

'p

xNx

Transient Junction Voltage, v(t)?

'p

'p


( ) /

' , '( ) N px x Lp x t p t e

• For the stored charge at any instant

( ) /

' 'N p

N

x x L

p px

Q t qA p e dx qAL p t

/

'( ) 1pqv t kT

n

p

Q tp t p e

qAL

/

ln 1ptp

p n

IkTv t e

q qAL p

During turn-off, v(t) cannot be changed

instantaneously

Quasi-Steady State Approximation

( ) pt

p pQ t I e


hole distribution in the N-region as

a function of time during the transient

'( , )p x t

Reverse Recovery Transient• For t < 0 (positive bias steady I = If E/R)

• After the generator voltage is reversed (t > 0), the current must initially reverse to I = Ir -

E/R (temporarily).

The reason for this unusually large reverse current through the diode is that the stored

charge (and hence the junction voltage) cannot be changed instantaneously.

Nx

Switching voltage

Diode current


• As the current is reversed, the junction voltage remains at the small forward-bias it had before t = 0.

• While the current is negative through the junction, the slope of the distribution must be positive at xN.

• As long as pn is positive, the junction voltage v(t) is positive and small.

• When the stored charge is depleted and becomes negative, the junction exhibits a negative voltage.

• As time proceeds, the magnitude of the reverse current becomes smaller as

more of –E appears across the reverse-biased junction, until finally the only current is

the small reverse saturation current.

• The time tsd ( ) required for the stored charge (and therefore the junction voltage) to

become zero is called the storage delay time.

The critical parameter determining tsd ( ) is the carrier lifetime (p for the P+-N junction)

s

s

s


Part II: Application to Optoelectronic Devices

Solar Cells

Photonic Devices:

Solar Cells, Light Emitting Diode, Laser Diode, Photodiode

Solar Cell Basics

• Commonly made of silicon, solar cells, also known as photovoltaic cells, can convert sunlight

to electricity with 15 to 30 % energy efficiency.

• The structure of solar cell is identical to a PN junction diode but with finger-shaped or transparent

electrodes so that light can strike the semiconductor.


Depletion of fossil-fuel deposits and recent history

and projection of world energy consumption

assuming 3% annual growth. (From [3]. © 1992 IEEE.)

pn Junction Si solar cells at work. Honda„s two seated Dream car

is powered by photovoltaics. The Honda Dream was first to finish

3,010 km in four days in the 1996 World Solar Challenge.

SOURCE: Courtesy of Centre for Photovoltaic Engineering,

University of New South Wales, Sydney, Australia.

SOURCE: Courtesy of NASA, Dryden Flight Center


Solar cell inventors at Bell Labs (left to right) Gerald Pearson, Daryl Chapin

and Calvin Fuller are checking a Si solar cell sample for the amount of

voltage produced (1954).

SOURCE: Courtesy of Bell Labs, Lucent Technologies


The principle of operation of the solar cell (exaggerated features tohighlight principles)

Neutral

n-regionNeutral

p-region

W

Eo

Voc

Medium

Long

Depletion

region

DiffusionDrift

Finger

electrode

Back

electrode

n

p

Lh

Short

Le


• Photogenerated carriers within the volume Lh + W + Le give rise to a photocurrent Iph.

• The variation in the photogenerated EHP concentration with distance is also shown

where α is the absorption coefficient at the wavelength of interest.

Le

Lh W

Iph

x

EHPs

exp(x)

scI


(a) The solar cell connected to an external load R and the conventionfor the definitions of positive voltage and positive current. (b) Thesolar cell in short circuit. The current is the photocurrent, Iph. (c) The

solar cell driving an external load R. There is a voltage V and current Iin the circuit.

R

I

(a)

Light

Iph

V = 0

Isc

= Iph

(b)

Iph

I = Id

Iph

V

Id

R

(c)

V

Dry Battery +-

I

V


V

I (mA)

Dark

Light

Twice the light

0.60.40.2

20

20

0

Voc

Iph

Short circuit solar cell current in light

IKII phsc

Constant that depends on the particular device

Light intensity

Photocurrent generated by light

Solar cell I-V

1expph

kT

eVIII o

where Io is the reverse saturation current

and is the ideality factor: 1 - 2

short circuit

current (Isc)

open circuit

voltage

Typical I-V characteristics of a Si solar cell. The I-V curves for positive

current requires an external bias voltage. Photovoltaic operation is always

In the negative current region.


V

I (mA)

0.60.40.20

Voc

100

Isc = Iph

The load line for

R = 3

(I-V for the load)

I-V for a solar cell

under an illumination

of 700 W m-2

Operating point

Slope = 1/R

P

I

I

I

R

V

I

(a) (b)

0.50.30.1

V

200

(a) When a solar cell drives a load R. R has the same voltage as the solar cell but the current

through it is in the opposite direction to the convention that current flows from high to low

potential.

(b) The current I and voltage V in the circuit of (a) can be found from a load line construction. Point

P is the operating point .The load line is for R = 3 Ω.( ', ')I V

Load lineR

VI (The actual current I and voltage V in the circuit must satisfy both the

I - V characteristics of the solar cell and the load).

Fill factor

ocsc

FFVI

VI mm (The FF is a measure of the closeness of the solar cell I-V curve to the

rectangular shape (the ideal shape)).


• Electron-hole pair (EHP) generation by light illumination.

EHPs generated in SCR move toward to their respective majority-carrier regions,

due to electric field in SCR and form generation current called, - Isc.

• The power dissipated by the diode is negative (i.e., the product (V×I) is negative)

power generator (Solar power electrical power)

light illumination

EHP generation

(a) Light can produce a current in PN junction at V = 0.

(b) Solar cell IV product is negative, indicating power

generation.

/

0

,

( 1)qV kT

sc

Total diode current I

I I e I

ocV


Light Penetration Depth-Direct-Gap and Indirect-Gap Semiconductors

1.24( ) ( )

hcPhoton energy eV m

Photons with energy less than Eg are not absorbed

by the semiconductor. Photons with energy larger

than Eg are absorbed but some photons may travel

a considerable distance in the semiconductor

before being absorbed.

Light intensity( )x

x e :

1:

absorption coefficient

penetration depth

1The thickness of solar cell :

• The Si or Ge solar cell must be thick ( > 50 μm)

: due to low α

• The GaAs or InP solar cell is thin (~ 1 μm)

: due to high α

low

high

Related to the specific energy band structure

in order to capture nearly all the photons.

Documents

Contributions from the Depletion Region - KNUbkict-ocw.knu.ac.kr/include/download.html?fn=559E057A862B5.pdf · Solar Cells, Light Emitting Diode, Laser Diode, Photodiode Solar Cell