semiconductor device: pn junctionmil.ee.nctu.edu.tw/course/semiconductor/review_modern... · 2012....

IEE5017, NCTU, 鄭裕庭

Semiconductor Device: PN Junction

Prof. Yu-Ting Cheng

Microsystems Integration Laboratory

Department of Electronics Engineering &

Institute of Electronics

National Chiao Tung Univesity


Fermi Level of PN Junctions

In forward and reverse bias:

φbi → φbi −V

Space Charge

Region (SCR)

Quasi Neutral

Region (QNR)


Thermal Equilibrium

2

0

0

00

ln

)0(

)0(ln

)()(

i

ADbi

xFcxFcsnspbi

n

NN

q

kTV

xn

xnkT

EEEEWWqV


Carrier Profile in Thermal Equilibrium of

PN Junction

1-D Poisson’s Eq.:

Gauss Law:

E

VEV 2


Electrostatic Potential (Build-in Potential)

V(x)

V(x)

V(x)

V(x)

1. Two unknowns: xn and xp.

:Overall charge neutrality: qNAxp = qNDxn

2. Potential difference across structure must be Vbi:

V(xn) - V(-xp) Vbi

Vbi Vbi

Vbi

Vbi


PN in Non-equilibrium State

I. Qualitatively, electrostatics unchanged out of equilibrium, but SCR widens

and shrinks, as needed:

Vbi Vbi+V

Vbi-V

V

V

V

V


I-V Characteristics

In thermal equilibrium:

balance between electron and hole flows across

SCR

Balance between G and R in QNR’s

I =0

In forward bias:

energy barrier to minority carriers reduced

minority carrier injection

R>G in QNR’s

I ∼ eqV/kT

In reverse bias:

energy barrier to minority carriers increased

minority carrier extraction

G>R in QNR’s

I saturates to a small value


Quasi Fermi Level

Review:

Let’s define:

Then

v

B

Fv

C

B

cF

E

v

Tk

EE

E

C

Tk

EE

dEEFEgpep

dEEFEgnen

))(1)((

)()(

00

00

v v


I. Interested in energy band diagram representations of complex situations in

semiconductors outside thermal equilibrium.

In TE, Fermi level makes statement about energy distribution of carriers in bands

⇒ EF relates no with Nc and po with Nv:

Outside TE, EF cannot be used. Define two ”quasi-Fermi levels” such that:

Under Maxwell-Boltzmann statistics (n <<Nc, p<<Nv):


What Can we implement the concept of quasi-Fermi levels?

Take derivative of n = f(Efe) with respect to x:

Then, from

Similar

Gradient of quasi-Fermi level: unifying driving force for carrier flow.


I. Quasi-Fermi levels: effective way to visualize carrier phenomena outside equilibrium

in energy band diagram.

Visualize carrier concentrations and net recombination

Visualize currents:

∇Efe =0 ⇒ Je =0

∇Efe 0 ⇒ Je 0

if n high, ∇Efe small to maintain a certain current level

if n low, ∇Efe large to maintain a certain current level

1. If Efe >Efh ⇒ np > ni 2⇒ U> 0

2. Efe <Efh ⇒ np < ni 2 ⇒ U< 0

3. If Efe = Efh ⇒ np = ni 2 ⇒ U = 0 (carrier conc’s in TE)


I. Quasi-equilibrium: carrier distributions in energy never depart too far from TE in

times scales of practical interest.

Quasi-equilibrium appropriate if:

scattering time << dominant device time constant

⇒ carriers undergo many collisions and attain thermal quasi-equilibrium with the

lattice and among themselves very quickly.


In forward bias

Compute diode current density as follows:

J = Je(−xp)+Jh(xn)

Compute each minority carrier current contribution as follows:

Je(−xp)= −qn 0(−xp)ve(−xp)

Jh(xn)= qp0(xn)vh(xn)

Boundary conditions across SCR. In thermal equilibrium, Boltzmann relations:

If net current inside SCR is much smaller than drift and diffusion components, then

quasi-equilibrium⇒ Boltzmann relations apply:

http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-720j-integrated-microelectronic-devices-spring-2007/


I. Quasi-Fermi levels across long diode:

•Inside SCR:


•In terms of excesses:

Boundary conditions have all expected features. For electrons (for example):


I. Minority carrier velocity at edges of SCR (”long” diode: Wn �>> Lh,Wp �>>Le).

•Carrier velocities:

•Excess minority carrier currents:


I. Total current: sum of electron and hole current:

Define Js ≡saturation current density (A/cm2):

If diode area is A, current is:


Rectifying Behavior of a Diode

Rectifying behavior arises from boundary conditions across SCR:

In forward bias: carrier concentrations at SCR edges growup exponentially

In reverse bias: carrier concentrations at SCR edges reduced quickly to zero (can’t go

below!)


Quasi-neutrality in QNR’s demands n’ p’ .Consequences:

In n-QNR,quasi-neutrality implies:

Also, if V ↑→ Qhn ↑→|Qen|↑ with:

ΔQhn supplied from p-contact, ΔQen

supplied from n-contact.

Looks like a capacitor ⇒ diffusion capacitance.

Minority Carrier Storage


Diffusion capacitance(per unit area):

where

For a long diode

For a short diode: with τtn and τtp are the minority carrier transit times through QNR’s:

Similar result to long diode!


Cd grows exponentially in forward bias, negligible in reverse bias:


Series Resistance Effect

I. Accounts for ohmic drop in QNR’s

:Reduces internal diode voltage → I ↓

Higher VF required to deliver desired

IF →more power dissipation, potential

process control problems

RC time constant degraded.


Second Order Effect:

Space-charge generation and recombination In real devices, non-ideal I −V characteristics often

Anomalies often due to:

*Recombination through traps in SCR (in forward bias)

*Generation through traps in SCR (in reverse bias)

Simple model for SCR generation and recombination:

Starting point: trap-assisted G/R rate equation:


I. In SCR:

II.SCR G/R current:

*Since n and p changing quickly with x in SCR, no analytical solution.

Since np constant, point of SCR with highest Utr where: τhon = τeop

Thus,

Use this across entire SCR upper limit to current:


High Voltage Effects in Diode

I. Forward Bias: High Injection Region

One of the assumption in the device model is that the injection of minority carriers was

at a fairly low level, so that essentially no voltage dropped across the bulk of the

structure. All the voltage was assumed to be dropping over the depletion region.

However, Iforward, the injection level the injected minority carrier density the

majority carrier density. At that time, an increasely larger fraction of the external

bias drops across the undepleted region. The diode current will then stop growing

exponentially with the applied voltage, but will tend to saturate and the whole diode

will behave like a conductor. (Thus, as the forward bias increase, the current is now

controlled by the resistance of the n- and p- type regions as well as the contact

resistance.

II. Reverse Bias: Punchthrough

As the reverse bias is increased, the diode current may abruptly run away with the

current being only limited by the external circuit. This phenomena called breakdown

may be due to any of three causes: Punchthrough, Impact Ionization and Zener

Breakdown.


Cont. on Reverse Bias: Punchthrough

As the reverse bias is increased, the depletion region across which the potential

drops also increases. Consider a situation where we have, a heavily doped p-region

next to a lightly doped n-region. The n-side depletion region is then much larger than

that of the p-side. At sufficiently large voltage, the n-side depletion region will reach

the n-side ohmic contact. If the voltage is further increased, the contact will feel the

electric field penetration and will supply electrons to the p-n diode. The diode

essentially then suffers a short and the current is simply limited by the outside circuit

resistance. If Vrp is the punchthrough voltage, the current for Vr> Vrp is essentially

Where RL is the resistance in the circuit and includes the effect of the diode resistance.

L

rpr

R

VVI


Zener Breakdown

http://www.ecse.rpi.edu/~schubert/Course-ECSE-2210-Microelectronics-Technology-2010/A-MT-Ch13-PN-junction-Reverse-bias.pdf


Tunneling breakdown will occur in lightly doped pn junctions at sufficiently high

reverse voltages. Tunneling breakdown is called Zener breakdown. Such diodes are

called Zener diodes. Typical Zener voltages = 5 – 20 V


Impact Ionization

I. Physical basis: Impact ionization at high electric fields. Generation of electron-hole

pairs by impact ionization.

During impact ionization a rapidly propagating electrons hits the electron shell of an

atom and “kicks” an electron out of its orbit thereby ionizing the atom

The free carriers created this way will create further free carriers by impact ionization

carrier multiplication higher current


I. Avalanche breakdown is caused by impact ionization of electron-hole pairs. When

applying a high electric field, carriers gain kinetic energy and generate additional

electron-hole pairs through impact ionization. The ionization rate is quantified by the

ionization constants of electrons and holes, n and p. These ionization constants are

defined as the change of the carrier density with position divided by the carrier

density or:

The ionization causes a generation of additional electrons and holes. Assuming that the

ionization coefficients of electrons and holes are the same, the multiplication factor M,

can be calculated from:

ndxdn n

2

1

1

1x

x

dx

M

Avalanche breakdown


I. The integral is taken between x1 and x2, the region within the depletion layer where

the electric field is assumed constant and large enough to cause impact ionization.

Outside this range, the electric field is assumed to be too low to cause impact

ionization. The equation for the multiplication factor reaches infinity if the integral

equals one. This condition can be interpreted as follows: For each electron coming

to the high field at point x1 one additional electron-hole pair is generated arriving at

point x2. This hole drifts in the opposite direction and generates an additional

electron-hole pair at the starting point x1. One initial electron therefore yields an

infinite number of electrons arriving at x2, hence an infinite multiplication factor.

II.The multiplication factor is commonly expressed as a function of the applied voltage

and the breakdown voltage using the following empirical relation:

62 ,

1

1

n

V

VM

n

br

a

semiconductor device: pn junctionmil.ee.nctu.edu.tw/course/semiconductor/review_modern... · 2012....

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