1 ECE 4243/6243 Fall 2015 Nanoscience and Nanotechnology-I L1 Overview, September 1, 2011 UConn, F. Jain Office hours: Tu 1:30-2:30pm, W 1:00-2:30pm •Improved performance of systems drives the incorporation of nanodevices. •Nanostructures has at least one dimension approaches 7-8nm as quantum effects manifests. This quantization leads to formation of quantum well lasers and quantum well FETs. •Carrier transport in carbon nanotubes and nanowires (1-D) exhibits very high electron mobility. In CNTs mobility approaches 200,000 cm 2 /V-sec. This also results in quantization of conductance (resistance at room temperature) G=i2e 2 /h (I = 1, 2, 3, ). Last year CNT computer was demonstrated by Shulaker et al. (Nature 501, pp. 526, 26 September 2013) using p-FETs. •FETs with quantum dot channel and/or quantum dot gate manifest multi-state characteristics which can
Transcript
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ECE 4243/6243 Fall 2015 Nanoscience and Nanotechnology-I L1 Overview, September 1, 2011 UConn, F. Jain
Office hours: Tu 1:30-2:30pm, W 1:00-2:30pm
•Improved performance of systems drives the incorporation of nanodevices.
•Nanostructures has at least one dimension approaches 7-8nm as quantum effects manifests. This quantization leads to formation of quantum well lasers and quantum well FETs.
•Carrier transport in carbon nanotubes and nanowires (1-D) exhibits very high electron mobility. In CNTs mobility approaches 200,000 cm2/V-sec. This also results in quantization of conductance (resistance at room temperature) G=i2e2/h (I = 1, 2, 3, ). Last year CNT computer was demonstrated by Shulaker et al. (Nature 501, pp. 526, 26 September 2013) using p-FETs.
•FETs with quantum dot channel and/or quantum dot gate manifest multi-state characteristics which can process 2 or more bits simultaneously.
•Biosensors use nanoparticles to enhance surface plasmons, and bioluminescence. FETs are used in Gene sequencing, DNA identification and proteins identification.
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ECE 4243/6243 Fall 2014 Nanoscience and Nanotechnology-I L1 Overview, August 26, 2014 UConn, F. Jain
Office hours: Tu 1:30-2:30pm, W 1:00-2:30pm
1. Scaling of microelectronic (sub-14nm FETs, memories) and photonic devices, MEMs, and biosensors leads to nanostructures. Does scaling to sub-8nm leads to novel phenomena that provide new characteristics in quantum devices?
2. Si nanophotonics provides a way to integrate electronic and photonic devices on same substrate.
3. Electronic and photonic devices involve p-n homo- and heterojunctions, FETs and memory devices. P-n junctions are basic to LEDs, lasers, photodetectors, MOS imaging and displays, and solar cells.
4. Carrier transport and optical transitions in 1-D (e.g. carbon nanotubes and nanowires), 2-D (e.g. graphene, MoSe2, quantum well layers), and 0-D quantum dot based layers requires carrier concentration (density of states and Fermi-Dirac statistics, phonons) and tunneling through barriers.
5. Fabrication of nanostructures is dependent on materials processing.
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Overview cont.
1. Quantum effects manifests when at least one dimension where electrons exist become comparable to 5-8nm.
2. One-dimensional constraint results in the formation of quantum wells, multiple quantum wells, and superlattices. Energy density of states in quantum wells is different than in layers which are not constrained (called 3-d or bulk material). Two-dimensional graphene does not exhibit a band gap until an electric field is applied. Field-induced band gap has been observed.
3. Two-dimensional constraints result in the formation of nanowires, nanotubes. Energy density of states in quantum wires/nanotubes is different than in quantum wells.
4. The effective band gap in quantum wells is higher than bulk layer and band gap in nanowire/tube is higher than in a well.
5. Photon absorption or emission involves electronic transitions which depend on the density of states. Absorption coefficient in quantum wires is higher than in wells. It also starts at higher energy than band gap in bulk materials.
4
Overview cont.
6. Quantum wells are realized using barrier layers (e.g. AlGaAs barrier and GaAs well). Their shapes may be rectangular, parabolic, or mixed. Energy levels are obtained by solving Schrodinger equation using appropriate boundary conditions shape and effective mass of the material.
7. Carriers may tunnel from one quantum well to other or one quantum well to quantum dot if they are in vicinity and a finite probability exist. The probability or rate of tunneling is computed by solving the Schrodinger equation in various regions and finding the relative amplitude of wavefunctions.
8. Optical transitions may involve free carriers or formation of excitons.
9. Most of the electronic and photonic devices use semiconductor materials.
10. Semiconductors are direct energy gap or indirect gap. Metals do have not energy gaps. Insulators have above 4.0eV energy gap.
Examples of Nanodevices (p. 5)
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Fig. 5. Topology of a fabricated FINFET.Ref. Bin Yu, L. Chang, S. Ahmed, H. Wang, S. Bell, C. Yang, C. Tabery, C. Ho, Q. Xiang, T-J. King, J. Bokor, C. Hu, M-R. Lin, and D. Kyser, “FinFET Scaling to 10nm Gate Length,” IEDM Tech. Digest, p. 251, December 2002.
A. Hokazono, k. Ohuchi, M. Takayanagi, Y. Watanabe, S. Magoshi, Y. Kato, T. Shimizu, S. Mori, H. Oguma, T. Sasaki, H. Yoshimura, K. Miyano, N. Yasutake, H. Suto, K. Adachi, H. Fukui, T. Watanabe, N. Tamaoki, Y. Toyoshima, and h. Ishiuchi, “14 nm gate length CMOSFETs utilizing low thermal budget process with poly SiGe and Ni salicide,” IEDM Tech. Digest, p. 639, December 2002.Fig. 7. Topology of a 14 nm fabricated FET.
Why quantum well, wire and dot lasers, modulators and solar cells?Quantum Dot Lasers:•Low threshold current density and improved modulation rate.•Temperature insensitive threshold current density in quantum dot lasers. Quantum Dot Modulators:•High field dependent Absorption coefficient (α ~160,000 cm-1) : Ultra-compact intensity modulator •Large electric field-dependent index of refraction change (Δn/n~ 0.1-0.2): Phase or Mach-Zhender ModulatorsRadiative lifetime τr ~ 14.5 fs (a significant reduction from 100-200fs). Quantum Dot Solar Cells: High absorption coefficent enables very thin films as absorbers. Excitonic effects require use of pseudomorphic cladded nanocrystals (quantum dots ZnCdSe-ZnMgSSe, InGaN-AlGaN)
Table I Computed threshold current density (Jth) as a function of dot size in for InGaN/AlGaN Quantum Dot Lasers (p.11)
q and Jth
Quantum Dot Size 100100100Å 505050Å 353535Å
Defect Status
q Jth A/ cm2 =418nm
q Jth A/ cm2 =405nm
q Jth A/ cm2
=391nm
Negligible Dislocations
(ideal)
0.9 76
0.9 58
0.9 54
Traps N t=2.9x1017cm-
3 (Dislocations =1x1010 cm-2)
0.0068 10,118 0.0068 7,693 0.0068 7,147
Excitonic Enhancement (in presence of dislocations)
0.049 1,404 0.17 304 0.358 136
(Ref. F. Jan and W. Huang, J. Appl. Phys. 85, pp. 2706-2712, March 1999).
Quantum confinement of carriers• Energy bands and carrier concentrations.
• Density of states in bulk, quatnum wells, quantum wires/nanotubes, nano-rods and quantum dots.
• Confinement and tunneling of carriers across potential barriers.
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Optical transitions in nanostructures• Band to band free carrier transitions.
• Band to band transitions involving exciton formation.
• Light emission and absorption.
9
Energy bands
10
Fig. 8 and 9. p.119
k vector
Energy
E-K diagram of an indirectsemiconductor
Energy Gap Eg
k vector
Energy
E-K diagram of an directsemiconductor
Energy Gap Eg
Energy bands
11Fig. 13(b) and Fig. 13c. p.123-124
(Ref. F. Wang, “Introduction to Solid State Electronics”, Elsevier, North-Holland)
V(R) V0
2b<a-b 0 a a+b
)ba)(kcos()acos().bcosh()asin().bsinh(2
22
Absorption and emission of photons
12
Fig. 2 p.138
Conduction Band
Light Hole Band
Heavy Hole Band
So
)(
)()(
VtI
tPh CV
0
00 )()()( mmCV dhtPtP
Eghm0
21
23
3)2(
4)( gr Ehm
hVh
1)
2)
(Transition Probability)here, (h) is the joint density of states in a volume V (the number of energy levels separated by an energy
o
The joint density of states is expressed as Eq. 2B)
Pmo probability that a transition has occurred from an initial state ‘0’ to a final state ‘m’ after a radiation of intensity I(h) is ON for the duration t.
Nanophotonics
• Si nanophotonics
• Surface enhanced Raman effect via plasmon formation in thin metal films or gold nanoparticles.
• Plasmons are modified by functionalized nanoparticles enabling biosensing of proteins etc.
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Si Nanophotonics (pp. 60-65)
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Figure 1: Simple examples of 1D, 2D, and 3D photonic crystals. The different colors represent materials with different refractive indexes. Ref: Photonc Crystals: Molding the Flow of Light, by J. D. Joannopoulos
A physical device that possesses a photonic band gap (PBG) can be classified as a PBG structure. A photonic band gap is similar to the band gap of a semiconductor material, except that instead of comprising a range of energies, a PBG consists of a range of optical frequencies that cannot exist in the structure. PBGs arise because of the symmetry of a structure. For example, for a DBR (refer to previous write up on DBRs), a basic type of PGB structure, the PBG exists only for light normal to the plane of incidence. If the wavelength of light incident on the DBR is close enough to the wavelength for which it was designed, the light will be reflected at each layer interface. The light penetrating into the DBR is evanescent, i.e. decaying exponentially. Thus, modes within a frequency range centered at a frequency corresponding to this wavelength cannot exist within the DBR. We designate this range of frequencies the PBG of this particular DBR structure (it is possible for a structure to have multiple PBGs).
Photons are confined in a waveguide which comprise of a higher index of refraction layer (waveguide) sandwiched between two lower index (or cladding) layers). If there is a stack of these layers and spacing between cladding and waveguide layer is such that there is coupling between waveguides, we have a 1D photonic crystal which allows certain wavelengths and blocks others. This is considered having a photonic band gap. If this is done in two dimensions, we have a 2D photonic crystal as shown below. 2D and 3D photonic crystals are used to design narrow waveguides which can turn light 90 degrees.
Nanophotonics (pp.506-508)
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Fig. 9(a) Flowchart showing nanophotonic devices based displays and energy efficient computing systems.
Fig. 9 (b) Si nanophotonics: Mach–Zehnder interferometer using photonic crystal waveguides 56.
Fig. 10(a) Energy conversion (solar cells) and storageSystem.
Fig. 10(b). Schematic of a dye-sensitized solar cell57.
QDot Optical Modulators &
LEDs/Si Nanophotonics
Pixel Addressing Platform/
Computing Architecture
Novel Displays/Energy Efficient
ComputingSolar Cells
Ultra-Capacitors Nanotechnology
Tracking, Storage & Power System
Interface
Alternate Energy System
Biophotonics
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Fig. 6(a) Overview of DNA sequencing system.
Fig. 6 (b) Flow chart showing pH based DNA sequencing.
Fig. 7(a) Implantable glucose sensor platform.
Fig. 7(b) Glucose sensing system architecture.
Floating-Gate FETs for pH
Sensing
pH Sensor Used for the Detection
of DNA Synthesis
System Architecture
Electronic Gene Sequencing
Floating Gate Transistor
pH detection using proton (H+) release and transistor gate
charge change
Shift in transistor characteristics proportional to change in pH
pH changes as a single DNA strand is
attached with complementary base
pairs, releasing protons (H+)
Glucose, Lactate, pH, O2
Implantable Nano-Sensors
Signal Processing, Solar Powering, & Communications
System Architecture
Continuous Monitoring of
Analytes
Figs. 6(a) and 6(b) address DNA/gene sequencing describing current methods (using optical detection and pyro-sequencing) and the emerging methods (chem-FET based pH sensing21). Figure 6(a) shows a system view with details in Figs. 6(b) and additional details in Fig. 12. The new electronic method provides faster DNA synthesis/gene sequencing 22-
23 in contrast to luminescence-based pyro-sequencing methods24. A one-hour teaching module (Figure 6) will expose students how a transistor (FET) can sense the H+ concentration (or pH value), which depends on number of bases of a reference DNA matching with the bases of a gene fragment DNA present in a target solution.
Figs. 7(a) and 7(b) show how an implantable sensor monitors glucose levels by producing a current.
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Semiconductor Background Review
Energy bands in semiconductors: Direct and indirect energy gap
Current density J in terms of conductivity and electric field E: J = E = (-V) = - V
I = J A = E (W d),
In n-type Si, nq n nno + q p pno
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Carrier Transport: Drift and Diffusion
Drift Current: In = Jn A = - (q n n) E A
Diffusion Current density: Jn= +q Dn n, [Fick's Law]
Total current = Diffusion Current + Drift Current
Einstein’s Relationship: Dn/μn =kT/q
Pnonno=ni2 n-Si ND=Nn=nno
Pponpo=ni2 p-Si NA=Pp=Ppo
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Drift and Diffusion of holes in p-Si
In p-type Si,
The conductivity is: nq p ppo + q n npo
Drift Current: Ip drift = Jp A = (q p p) E A
Diffusion Current density: Jp= - q Dp p, [Fick's Law]
Diffusion current: Ip diff = - q A Dp p
Einstein’s Relationship: Dn/μn =kT/q
Total hole current = Diffusion Current + Drift Current
Ip= - q A Dp p + (q p p) E A
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Carrier concentrationWhen a semiconductor is pure and without impurities and defects,
the carrier concentration is called intrinsic concentration and it is denoted by ni. i.e.
n=p=ni.
ni as a function of Temperature, see Figure 17 (page 28) and Fig. 11 (page 69).
Also, ni can be obtained by multiplying n and p expressions (apge 68 of notes)
2kT
E3/4
pn
2/3
2i
kT
E3/2
4
2pn
22
g
g
e)mm(h
kT 22n
eh
(kT)mm π44
in
22
Extrinsic Semiconductors: Doped n- and p-type Si, GaAs, InGaAs, ZnMgSSe IIIrd or Vth group elements in Si and Ge are used to dope them to increase their hole and electron concentrations, respectively.
Vth group elements, such as Phosphorus, Arsenic, and Antimony, have one more electron in their outer shell, as a result when we replace one of the Si atoms by any one of the donor, we introduce an extra electron in Si.
These Vth group atoms are called as donors. Once a donor has given an electron to the Si semiconductor, it becomes positively charged and remains so. Whether a donor atom will donate its electron depends on its ionization energy ED. If there are ND donor atoms per unit cm3, the number of the
ionized donors per unit volume is given by
e
2
1+1
1-1 NN
kT
)E-E(D+D
fD
23
Fermi-Dirac Statistics
We have used a statistical distribution function, which tells the probability of finding an electron at a certain level E. This statistics is called Fermi-Dirac statistics, and it expresses the probability of finding an electron at E as
Ef is the energy at which the probability of finding an electron is ½ or 50%.
In brief, donor doped semiconductors have more electrons than holes.
e+1
1 Ef
kT
)E-E( f )(
E
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Acceptors and p-type semiconductors: We can add IIIrd group elements such as Boron, Indium and Gallium in Si. When they replace a Si atom, they cause a deficiency of electron, as they have three electrons in their outer shell (as compared to 4 for Si atom). These are called acceptor atoms as they accept electrons from the Si lattice which have energy near the valence band edge Ev. Eq. 12 expresses the concentration of ionized acceptor atoms (on page 71).
N-A is the concentration of the ionized acceptor atoms that have accepted
electrons. EA is the empty energy level in the acceptor atom.
Hole conduction in the valence band: The electron, which has been accepted by an acceptor atom, is taken out of the Si lattice, and it leaves an empty energy state behind. This energy state in turn is made available to other electrons. It is occupied by other electrons like an empty seat in the game of musical chairs. This constitutes hole conduction.
e41
+1
1*N=N
kT
)E-E(A-A
fA
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Donors and acceptors in compound semiconductors (see Problem set before chapter 1, p. 26)
Semiconductors such as GaAs and InGaAs or ZnMgSSe are binary, ternary, and quaternary, respectively. They represent III-V and II-VI group elements.
For example, the doping of GaAs needs addition of group II or VI elements if we replace Ga and As for p and n-type doping.
In addition, we can replace Ga by Si for n-type doping. Similarly, if As is replaced by Si, it will result in p-type doping. So Si can act as both n and p-type dopant depending which atom it replaces.
Whether Si is donor or acceptor depends on doping temperature.
26
Calculation of electron and hole concentrations in n-type and p-type semiconductors
Method #1: (simplest)Simple expressions for electron and hole concentrations in n-Si having ND
concentration of donors (all ionized). Electron concentration is n = nn or nno =ND, (here, the subscript n means on the n-side or in n-Si; additional subscript ‘o’ refers to equilibrium). Hole concentration is pno =ni
2/ND.
For p-Si having NA acceptor concentration (all ionized), we have p= pp =NA, and electron concentration npo= (ni
2)/NA,
Method#2 (simpler)Here, we start with the charge neutrality condition. Applying charge neutrality, we get: total negative charge density = total positive charge densityi.e. qND
+ + qpno = qnno, here pno and nno are the hole concentrations in the
n-type Si at equilibrium. But pno or hole concentration = ni2/ND. Substituting pno
in the charge neutrality equation, we get electron concentration by solving a quadratic equation [Eq 8, page 71]. Its solution is: n4+NN
2
1=n 2
i2DDn
27
Method#3 (Precise but requires Ef calculations)
qND+ + qpno = qnno, Charge neutrality condition in n-type
semiconductor can be written as:[Eq. 6 on page 70]
eh
kTm22 = e
h
kTm22+
e+1
1-1N kT
E
2
n2
3
kT
)EE(-
2
p2
3
kT
)E-E(D
fgf
fD
Here, we have ignored the factor of ½ from the denominator of the first term. In this equation, we know all parameters except Ef. One
can write a short program and evaluate Ef or assume values of Ef
and see which values makes left hand side equal to the right hand side.
28
Effect of Temperature on Carrier Concentration
The intrinsic and extrinsic concentrations depend on the temperature.
For example, in Si the intrinsic concentrations at room temperature (~300K) is ni =1.5x1010 cm-3. If you raise the temperature, its value
The electron concentration in conduction band between E and E+dE energy states is given by
dn = f(E) N(E) dE.To find all the electrons occupying the conduction band, we need to integrate the dn expression from the bottom of the conduction band to the highest lying level or energy width of the conduction band. That is, [see page 56 notes]The density of states N(E) will change if we are dealing with quantum wells, wires, dots. This leads to electron concentration (see page 57): This equation assumes that the bottom of the conduction band Ec = 0.
0
)()( dEEfENn
e h
kTm22=n kT
E
2
n
3/2f
An alternate expression results, if Ec is not assumed to be zero.
e h
kTm22=n kT
)E-E(
2
n
3/2fc
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Direct and Indirect Energy Gap Semiconductors
k vector
Energy
E-K diagram of an indirectsemiconductor
Energy Gap Eg
k vector
Energy
E-K diagram of an directsemiconductor
Energy Gap Eg
Fig. 10b. Energy-wavevector (E-k) diagrams for indirect and direct semiconductors (page 17). Here, wavevector k represents momentum of the particle (electron in the conduction band and holes in the valence band). Actually momentum is = (h/2)k = k
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Electrons & Holes Photons Phonons
Statistics F-D & M-B Bose-Einstein Bose-Einstein
Velocity
vth ,vn
1/2 mvth2 =3/2 kT
Light c or v = c/nr
nr= index of refraction
Soundvs = 2,865 meters/s in GaAs
Effective Mass
mn , mp
(material dependent)
No mass No mass
Energy
E-k diagramEelec=25meV to 1.5eV
ω-k diagram (E=hω)ω~1015 /s at E~1eVEphotons = 1-3eV
ω-k diagram (E= ω)ω~5x1013/s at E~30meVEphonons = 20-200 meV
Momentum
P= kk=2π/λλ=2πvelec/ω
momentum: 1000 timessmaller than phonons and electrons
P= kk=2π/λλ=2πvs/ω
(page 17).
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P-n Junctions (pp. 20-28)
n
NNq
kT=
p
p
q
kT=voltage in-Built=V 2
i
DA
no
pobi lnln
)NN(2
NNqp
p
qkT
=)NN(2
NNqV
=W
DAor
DA
no
po2
1
DAor
DA
bi2
1
ln
Use (Vbi – Vf) for forward-biased junctions, and (Vbi + Vr ) for reverse-biased
junctions.
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Shockley's equation (p. 28)
1)-e(J=J kTVq
s
f
1)-e(I=I=A J kTVq
s
f
Here, the reverse saturation current Is = A Js, and reverse saturation current
density Js is
Here, Dp is the diffusion coefficient of holes, pno is the hole concentration
under equilibrium on n-Si side, Lp is the diffusion length of holes (L2p = Dp x
p). p is the average lifetime of injected holes.
Similarly, Ln is the diffusion length of electrons injected from n-side into p-
side and npo is the minority electrons on p-side at equilibrium.
L
nDq+
L
pDq=J
n
pon
p
nops
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Charge distribution, Field, Built-in Voltage (p.22)
xNq
-=xNq
-=E noDoAlGaAs
pooGaAs
A
max
Poisson's Equation ·D = ·V
Or, 2V= -r,= q(ND+ + p- NA
- -n)]
(W)E2
1-=)x+x(E
2
1-=V=- mponombipn
WxNq
2
1=V or,
WxNq
2
1=V
or
noAbi
or
poAbi
W=xx nopo
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Vbi
W
0-Xp0 Xn0
P N
X
q Voltage=q
Vbi
W
0-Xp0Xn0
P N
X
Voltage
Edx-=d
Edx-=-=d xx-pnno
po
n
p
(a) Voltageas a function of distance (Since field E is negative, the negative sign makes itpositive. As a result the potential increases parabolically as we go from p-side to the n-side).
p
n
(b) Electron energy as a function of distance (Multiply the voltage with electroncharge which is negative q. The negative q makes q to change sign with respect topart (a). That is, the energy of electron is higher in p-Si than in n-Si).
P N
qVbi
(c) Energy band diagram of a p-n junction. Electron energy in the conduction bandof p-Si is higher than of electron in the conduction band of n-Si.
-Xp0Xn0
0
Fig. 4. Schematic representation of energy band diagram for a p-n junction showing electron energy.
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Energy band diagrams: Homojunction & Heterojunction
Vbi
W
0-Xp0 Xn0
Ec
Ev
Ef
P N
p-AlGaAs n-GaAs
Ec
Ev
W
0-Xp0 Xn0
Ec
Ev
Ef
Eg ~ 1.9 eV
Eg = 1.424 eV
Homojunction
Heterojunction
37
Equilibrium
(VA)
-xp xn0 lnlp
p n
NA = 1019 cm-3
NA = 1019 cm-3
VA
I
Non-equilibrium
x
nepe
-xpo xno0 lnlp
p n
o
NA = 1019 cm-3
ND = 1016 cm-3
n(x)o
p(x)o
E(x)
NA
NDFig. 5.Carrier distribution in a p-n junction under equilibrium and under non-equilibrium (under forward biasing).
38
Energy band diagrams in Heterojunctions (p.25)
N-AlGaAsp-GaAs
Eg1
Eg2
EfN2
Efp1
Ec2
Ec1
Ev2
Ev1
q2 q1
Ec
Reference vacuum level
q2
q1
Ei Ei
Ec-Efp
Ei-Efn
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Energy band diagrams in Heterojunctions (p.25)
By definition, the built in voltage is the difference between the two Fermi levels (Efp1 and Efn2 for p-GaAs and n-AlGaAs, respectively. Here, we have not used
the Ei we use the difference between the Fermi level and the band edge (i.e.
either Ec2-EfN2 or Efp1-Ev1).
qVbi = - q(q[(c2 - Efn2) –{gp1 – (Efp1 –Ev1)}]
= - q[(gp1 + (Ec2 - Efn2) + (Efp1 –Ev1)]
qVbi = Ec + gp1 -(Ec2 - Efn2) - (Efp1 –Ev1)
Vbi =1/q[Ec + gp1 -(Ec2 - Efn2) - (Efp1 –Ev1)]
Here, (Ec2 - Efn2) = (kT) ln(NC/n)
and, (Efp1 –Ev1) = + (kT) ln(Nv/p)
40
p-AlGaAs n-GaAs
Ec
Ev
W
0-Xp0 Xn0
Ec
Ev
Ef
Eg ~ 1.9 eV
Eg = 1.424 eV
Energy band diagram in a heterojunction P-AlGaAs/n-GaAs.
41
Heterojunctions and Junction Fabrication Techniques
Heterojunctions General: • Higher injection efficiency with lower doping levels in the wider energy gap
semiconductor
• Laser Diodes: Carrier confinement in a narrow layer, if needed (useful in lasers to generate photons in a narrow layer (smaller d); minority carriers are not as readily injected from a narrower gap material into wider gap material.
• Laser Diodes:Photon confinement in a three layer sandwich of low-high-low index of refraction (e.g. AlGaAs-GaAs-AlGaAs); nrAlGaAs)<nr(GaAs). See homework #1.
• Quantum Well Lasers: thin low energy gap active layer permits confinement of carriers in very narrow layer (~50-70Angstroms) forming quantum wells and providing lower threshold operation.
• Quantum wire and quantum dot lasers: Lower threshold and temperature insensitivity
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
pninj
f
f
42
• Solar cells: wider gap semiconductor acts as the window where photons enter the device and are absorbed in the lower energy gap material
• Solar cells: Provides higher operating voltage for a given current; and minimize recombination of carriers at the surface.
• Heterojunction Bipolar transistors (HBTs): High injection efficiency even with lower emitter concentrations permits the use of a very highly doped base. This in turn reduces the base transit time 9one of the main factors limiting the unit gain cutoff frequency fT.
• Flexibility in designing higher current gain, reducing resistance (e.g. sub-collector).
