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LW 5 February 14, 2017 UCONN ECE 4211 F. Jain

Review of BJT parameters and Circuit Model

Heterojunction Bipolar Transistors (HBTs)

BJT Design

LEDs

PowerPoint for two lectures

p+n+ p-base

n+

n-collectorn Epi n Epi

n+

BURIED LAYERp-Si (substrate)

E B C

Collector

Contact Diffusion n Epi

Emitter

E

BC

P+

P+

(a) cross-sectional view

Collector

Diffusion

(b) Top View

Base

Diffusion

Emitter

Diffusion

p+

Circuit model, p.234

2

Si eSi= 11.8

Circuit model, p. 235

3

HBT Eqb. p.241

4

HBT Biased . p.242

5

3B. 6 Design of a Bipolar Junction Transistor

p+n+ p-base

n+

n-collectorn Epi n Epi

n+

BURIED LAYERp-Si (substrate)

E B C

Collector

Contact Diffusion n Epi

Emitter

E

BC

P+

P+

(a) cross-sectional view

Collector

Diffusion

(b) Top View

Base

Diffusion

Emitter

Diffusion

p+

Figure 5. Cross-section and Top view of a n-p-n transistor

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Design specifications: Design an n-p-n transistor with a common emitter gain, bo = 500. The device cross-

section and a typical layout is given in Fig. 5. The cut-off frequency fa = wa/2p value in GHz is also provided.

Starting substrate is an epitaxial wafer with a 10 Ohm-cm n-Si epitaxial layer on p-Si substrate. Epi thickness

is not known. Given for guideline purposes are the following device parameters:

3B. 6 Design of a Bipolar Junction Transistor

7bo

8

Step (b) Estimate base-emitter and base-collector capacitances under zero bias and biased conditions.

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Step (e) Selection of :

•Isolation region width and size

•Separation between buried layer and isolation diffusion and other features

•Collector contact diffusion as you may seem fit (i.e. deep plug going to the buried

layer or like emitter diffusion)

•Buried layer parameters

Using diffusion coefficients as obtained during the diffusion experiments. List the

process data needed in the fabrication of the transistor.

tC = Collector capacitance charging time

= rscCTE

rsc = collector resistance, CTE = collector capacitance

Q. 3. BJT Design Problem: Equivalent to one home work set. You can substitute it for any missed homework or any bad grade in a

home work set.

Design an n-p-n bipolar junction transistor with a common emitter gain, bo = 500. The device cross-section and a typical layout are given

in Figure 3. Provide:

(a) doping levels of emitter, base, and collector,

(b) width of the base,

(c) determine the cut-off frequencies fa and fb, and

(d) How would you increase cut-off frequency by a factor of 100 or 1000; what parameter(s) would you vary. Name the most important

parameter for a given device size.

Given: Starting substrate is an epitaxial wafer with a 10 Ohm-cm n-Si epitaxial layer on p-Si substrate.

Epi thickness is not known you have to find it from base width W used in your design..

Given for guideline purposes are the following device parameters:

Emitter: Base:

Dp,E =20 cm2/sec. Dn,B =40 cm2/sec (diffusion coefficient for electrons)

tp =10 msec (lifetime of holes injected from base) tn =2 msec (electrons injected from the emitter)

Emitter area AEB = 2 mm x 2 mm Base-collector area ABC = 6 mm x 6 mm

Emitter-collector voltage VCE = 5 Volts

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LEDs Figure 8(a) shows the performance of various diodes in lumens per watt as a function of peak emission wavelength. It also shows the eye response curve that shows the theoretical limit of a light source. That is, if the internal and extraction efficiencies are 100%, then the output in lumens will be for every watt of electrical power. The curve shows about maximum value at 670 lm/W in the green (550nm). This figure also shows the optical out put from other technologies. REFERENCE: M. R. Krames et al, (Reference#3-APL 1999). Fig. 7 (right, from Appendix) shows the InGaN white light LED. Fig. 7 Notes shows the TIP LED reported by Krames et al cited above.

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Figure 8(b) shows a chronological map presenting LED evolution and comparing them to other technologies. Note that Organic LEDs (OLEDs) is an emerging competitor.

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4.4. Chronology of development of LEDs:Although GaP is an indirect gap semiconductor exhibiting very poor quantum efficiency,

n-p GaP diodes were fabricated in 1970s to obtain red and green emitting LEDs. Here, we took advantage of excitonic transitions rather than free band-to-band type transitions. For example, the p-side doped with Zn and oxygen (on p-side, Zn is p-type dopant in GaP) resulted in efficient emission of red light, and nitrogen doping (in addition to the regular n and p dopants; Se,Te being the n-type dopants) resulted in efficient green light emission. The efficiency resulted from excitonic transitions in place of free electron-hole pair recombination.

Subsequently, engineers sought to work with direct gap materials. They are listed as follows in terms of chronological order. (see Fig. 6).

l = 1.24/1.42 = 0.55µm1. AlGaAs on GaAs substrates for red (1980-1985)2. AlInGaP on GaAs substrates for red and yellow (early to mid 1990s)3. AlInGaP on GaP for red and yellow (better than on GaAs from absorption in the GaP (Eg=2.24eV) window region (1995-p)4. AlInGaN-InGaN diodes grown on sapphire or SiC substrates for blue and green (1996-p)5. ZnO-ZnHgO; ZnCo

4.2. Optical Transitions: 4.2.1 Conservation of energy and momentum

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The properties of the material or region in which photons are generated determine theoperating wavelength and the quantum efficiency ηq with which the photons are generated.The nature of transitions producing photons depends on the material in which recombinationtakes place. For example, in a direct energy gap semiconductor Fig 2(b), the recombination isgenerally direct between conduction band electrons with and valence band holes. However,in an indirect gap material (Fig. 2(a)) such as Si or Ge, the electrons and hole have quitedifferent momentum. The momentum is conserved by external scattering or interaction. Acommon mechanism of momentum conservation is with the help of phonons. Somesemiconductors such as GaAs1-yPy and AlxGa1-xAs are direct gap in certain range ofcomposition, and indirect in other range.

The energy band of a semiconductor is the relationship between the electron and holeenergy E as a function of their wavevector k. This is referred as E-k diagram. Here, k isrelated to momentum (for free particles, (h/2π)k is the momentum). For direct energy gapsemiconductors, the conduction band minimum and valence band maximum occur at thesame k (=2 π /λ) value. Whereas they occur at different k-values in the case of indirectsemiconductors.

)(

24.1)(

evEm =ml hE = l=c

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Direct and Indirect Energy Gap Semiconductors

Energy-wavevector (E-k) diagrams for indirect and direct semiconductors. Here, wavevector k represents momentum of the particle (electron in the conduction band and holes in the valence band). Actually momentum is = (h/2p)k = k

Semiconductors are direct energy gap or indirect gap. Metals do have not energy gaps. Insulators have above 4.0eV energy gap.See E-k diagram in Fig. 2 below.

k wavevector

Energy

E-K diagram of an indirect energy gap semiconductor

Energy Gap Eg

k wavevector

Energy

E-K diagram of an direct semiconductor

Energy Gap Eg

Conduction Band

Electrons

Valance Band

Holes

Ec

Ev

Ec

Evh

Phonon emission

Photon h emission

Energy and momentum conservation: hν of emitted photons

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Direct gap semiconductors: In a direct energy semiconductor, the transitions from conductionband to the valence band results in the emission of a photon with energy h as expressed by:Photon energy h = Ec,elec – Ev,hole = Energy gap Eg. (A)The momentum conservation requires:

(h/2π) kc,elec + (h/2π) kv, hole + (h/2π) kphoton = 0 (B)h/2π h=

Direct gap λ(µm)= 1.24/Eg(eV)Ee-Eh is approximately equal to Eg

The wavevector k is 2π/λ. The momentum associated with photon is very small as its wavelength is much larger than those of electrons and holes. So equation (B) becomes:

(h/2π) kc,elec ~ -(h/2π) kv,hole (C)The wavelength of light in the visible spectrum ranges from ~6800-4500A. Whereas the wavelength of electrons λ = h/p ranges between 20-200A. Here, the momentum p is related to the kinetic energy E= p2/2mn; the kinetic energy is 3/2 kT for electrons in equilibrium with the lattice and it is higher for hot electrons (p2/2mn >> 3/2kT).

Energy and momentum in Indirect semiconductors

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Indirect gap semiconductors: In indirect gap semiconductors, the electrons and holes havesignificantly different k values. As a result we need another particle or scattering mechanismthat can conserve momentum. One way the indirect transition takes place is with the helpof phonons. Phonons have small energy 0.02-0.12 eV and large momentum. Theypropagate with the speed of sound.

Photon emission associated with phonon emissionh(photon) = Ec,elec – Ev,hole – hq (phonon emission) (D)

or h(photon) = Ec,elec – Ev,hole + hq (phonon absorption) (E)

The conservation of momentum can be seen from the vectors in Fig. B(b).(h/2π) kc,elec + (h/2π) kv, hole + (h/2π) kphoton + (h/2π) kphonon = 0 (F)

Neglecting photon momentum, we get(h/2π) kc,elec + (h/2π) kv, hole + (h/2π) kphonon = 0 (G)

The sign of phonon momentum depends if a phonon is generated or absorbed.

4.2.4 Region of the p-n diode where photons are generated:

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0

p+ n

X

ne

npo

pe

pno

Concentrations

pn(x)p(x)

x>x> for e1)-e(p=eppxp=p(x) nL

)x--(x

kT

Vq

noL

)x--(x

non p

nf

p

n

=)(

Internal efficiency

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injqint =

)+(=

rnr

nr

qtt

t

L

)pD(+

L

)nD(L

)nD(

=

1)-e(L

pDqA+

L

nDqA

1)-e(L

nDqA

=)x(-I+)x(I

)x(I

p

nop

n

pon

n

pon

kT

Vq

p

nop

n

pon

kT

Vq

n

pon

nppn

pn

injf

f

=

)n+(1

n4=T

2

r

r

(1) 50% Loss due to travel towards the back contactFigure 14 shows that about 1/2 of the generated light is lost as it travels towards the back electrode.

2. Surface reflection

3. Critical angle related loss

n

1-1-1=)-(1-1=-1=T

2r

2

1

2

1

c2

c sincos

Extraction efficiency

External efficiency

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n

1-1-1*

)n+(1

n4*

2

1*

L

pD+

L

nD

L

nD

*+

=2r

2

1

2

r

r

p

nop

n

pon

n

pon

rnr

nr

exttt

t

intextractionext =

Overall conversion efficiency

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Overall Conversion EfficiencyOverall efficiency is defined as the Light output (integrated in all directions) in watts/Electrical power input (VI) supplied to the device.

V J area unitper power d.c. Input

area junction unitper flux light Luminous=

FF

c_

Sometimes the power conversion efficiency is defined as

VJ

dd

dP

=FF

p

ll

Here, P(λ) = light output at wavelength

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Upward Transitions involve:• Valence band-to-conduction band

-Direct band-to-band -Indirect band-to-band-Direct and indirect transitions with exciton formation

• Band to impurity band or levels, • Donor level-to-acceptor level, and • Intra-band or free carrier absorption.

Similar transitions in downward direction result in emission of photons.

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4.5. Light Emission via Excitonic TransitionsThe recombination of electrons and holes in a diode gives rise to the emission of photons. The recombination probabilitydepends on the energy band type (i.e. direct gap or indirect gap). The probability of recombination is higher in direct gapmaterials such as GaAs and it is not as good in Si (or indirect semiconductors). Recombination can takes place either viaemitting a photon or without emission of a photon (non radiative recombination, here the energy is given up in terms oflattice vibrations and raises the temperature of the material. This is refereed to as producing phonons or quanta ofvibrations). Many times electrons and holes form a meta-stable pair (known as exciton) via Coulomb attraction and photonis emitted when exciton ceases to exist or electron and hole recombine. This process is more efficient in indirect gapmaterials.a) GaP: Zn-O system (Red light)b) GaP: N system (Green light)In both of these systems the emission of light is much more intense than expected in a n-p junction GaP device havingindirect band-to-band type transitions. The reason is the formation of excitons in the p-region where minority electrons areinjected. The decay of excitons, yielding photons, is more probable than photon emission involving indirect transition (band-to-band).

4.5.1 GaP - Zn-O system (RED-Emitting LEDs)Figure 9 shows the n-p GaP diode under forward-biased condition. (n-type dopants in GaP are Se and Te. p-type dopants inGaP are Zn and Cd.)

Figure 11. Energy levels in GaP: Zn-O system

Material Selection of layer where photons are generated

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Material Selection: Fig. 21 (page 301)

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Point A: Project GaAs-A-InAs curve on the horizontal O-C-2 line. Find the fraction OC/O2 = 0.528 C2/O2 = 0.472. Therefore, at point A the composition is Ga0.472In0.528As.

Material Selection

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InP

InAs

GaAs

0 C

A

GaP

2

Lattice Constant

EgB

Material Selection

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Spectral width of emitted radiation

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Electron and hole concentration as a function of energy

The electron concentration ‘n’ in the entire conduction band is given by

=

cE

dEEfENn )()( (EC is the band edge)

This equation assumes that the bottom of the conduction band is =0.

=0

)()( dEEfENn

dEEm

kTEEn n

f

2/12/3

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0

)2

(2

1

)/exp(1

1

=

p

=vE

dEEfENp )](1)[(

Density of states in bulk is N(E)dE = dEEmh 2/12/3

22)

2(

2

1

p

)/(1

1)(

kTEEFDfe

Ef

=

2/3

22

2/12/3 )2

(2

1*]/exp[*

2

1*)/1(

n

f

mkTEkTn

pp=

e h

kTm22=p kT

)EE(-

2

p

3/2gf

p

Graphical method to find carrier concentration in bulk or thick film (Chapter 2 ECE 4211)

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E

Ec

Ef

Ev

Density of states

N(E)

E

01/2 1 f(E)

dn electron conc.

between E and E+dE

dp

E

Fig. 28 (a) Density of states, Fermi-Dirac distribution function f(E), and distribution of

electrons and hole in conduction and valence band. The electron concentration increases

as Ef gets closer to the conduction band edge (see Fig. 28b).

(a)

dp hole conc. between

E and E+dE

dp = N(E)[1-f(E)]

Here, N(E) is for the

valence band

Graphical method to find carrier concentration in quantum well

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E

0=Ec

Ef

Ev

Density of states

N(E)

E

01/2 1 f(E)

dn electron conc.

between E and E+dE

dp

E

Fig. 28 (a) Density of states, Fermi-Dirac distribution function f(E), and distribution of

electrons and hole in conduction and valence band. The electron concentration increases

as Ef gets closer to the conduction band edge.

(a)

dp hole conc. between

E and E+dE

dp = N(E)[1-f(E)]

Here, N(E) is for the

valence band

E1e

E2e

E1hh

E2hh

=-Eg

Tuning of band gap by strain

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Ref: W. Huang, 1995 UConn doctoral thesis with F. Jain1.Under the tensile strain, the light hole band is lifted above the heavy hole, resulting in a smaller band gap.2.Under a compressive strain the light hole is pushed away from heavy. As a result the effective band gap as well as light and heavy hole m asses are a function of lattice strain. Generally, the strain is +/- 0.5-1.5%. "+" for tensile and "-" for compressive.3.Strain does not change the nature of the band gap. That is, direct band gap materials remain direct gap and the indirect gap remain indirect.

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•Downward transitions result in photon emission. This is called radiative transition. When there is no photon emission it is called non-radiative transition.

Rate of emission in quantum wells is higher than in bulk layers.

Rate of emission in quantum wires is higher than in quantum wells.

Rate of emission in quantum dots is higher than in quantum wires.

Rate of emission has two components:

1.Spontaneous rate of emission

2.Stimulated rate of emission.

Spectral width in quantum well active layer is smaller than bulk thin film active layer

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Spectral width of emitted radiation

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4.8. Methods to Reduce Losses in LEDsVarious mechanisms are identified which lead to losses of generated photons in a p-ndiode. Design methods are outlined to reduce these losses.We have seen that if all the loss mechanisms are considered, the light extraction efficiencycomes out to be very low (1-2%). The following steps are taken to reduce photon losses (or improve photon extraction):

•To recover part of the photons traveling towards the bottom contact.There are various ways to achieve this. One may be have a reflecting contact. Thisinvariably results in poor electrical characteristics; due to increased Ohmic voltage drop(contact resistance * current). Another way is to incorporate a layer, shown dotted inFigure 16, having a lower index of refraction than the layer in which the photons aregenerated.

Excitonic Transitions in Quantum Wires

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Excitonic Transitions: This gets modified when the exciton binding energy in a system is rather large as compared to phonon energies (~kT). In the case of excitonic transitions, the gain coefficient is:

1)]-f+f()E(dzzzdyyy

|M[|LLcmn

e2=)(g

vcexexhehe

ex

2

b

hl,zyoro

2

ex

L)|)()(||)()((|

|)0(| 2

22

21/2

pwe

pw

LED Design Index of refraction for ternary semiconductors

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x0.091+0.71x-3.59=n(x) 2

y)-x)(1-3.56(1+x)-3.60y(1+y)-3.39x(1+3.52xy=y)n(x,

4.7. Refractive Index as a funciton of semiconductor compositionThis section provides information on the index of refraction for semiconductors we use for visible or infrared sources. The compositional dependence of refractive index in the case of AlxGa1-xAs is given by[1]

(22)and for InxGa1-xAsyP1-y

[2]

[1]H.C. Casey Jr. & M.B. Panish, Heterostructure Lasers Part A: Fundamental Principles, Academic Press, 1978, Chapter 2[2]G.H.Olsen et al, Journal of Electronic Materials, vol 9, pp. 977-987, 1980.