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MSE 141 Electronic MaterialsSemiconductors and DevicesDr. Benjamin O. ChanAssociate ProfessorFebruary 2012
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Problem Set 3
•Hummel 3rd edition•Chapter 8
▫1, 4, 6, 7, 9, 13, 15, 22
•Due Feb. 16•Final Exam
▫Thursday Feb. 23
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Semiconductors•Active electrical component
▫Metals and their alloys are usually passive▫Non-linear I-V characteristics
Diodes, transistors, lasers Sensors, amplifiers, light source
•Can manipulate conductivity•Si the most common material
▫Ge: first material used▫Other semiconductors
GaAs, AlGaAs, GaN, InP, CdTe
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Si Success•Ease of oxidation
▫Wet or dry oxidation Natural oxide forms after a few days when
exposed to air▫SiO2 layer provides good insulating and
masking functions Photolithography
Masking function Circuit Fabrication
Electrical insulation
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Bond Modification
•Hybrid states▫2 s states and 6 p states combine to form 8
sp states▫8 sp states split into 2 branches containing
1 s and 3 p states Lower s state: 1 electron per atom Lower p states: 3 electrons per atom
•Valid for covalently bonded materials
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Overlapping sp Levels
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Energy Bands
•Valence band contains 4N electrons▫Completely filled
•Conduction band can accommodate 4N electrons▫But of course it is empty!
•States are filled like water fills a vessel!
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Band Structure of Si
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Energy Gap at 0 KElement Eg (eV)
C (diamond) 5.48
Si 1.17
Ge 0.74
Sn (gray) 0.08
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The Energy Gap
•Decreases with atomic number▫Artificial diamond: C-based IC▫Ge: good IR detector▫Sn easily conducts at room temperature
•Wavelength equivalent
)(
24.1)(
eVEm
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Temperature Dependence
▫where Eg(0) is the energy gap at 0 K▫ = 5 x 10-4 eV/K and▫ D = Debye temperature (Table 19.2)
Temperature needed to reach 96% of the final value for heat capacity CV
T> D : classical region T< D : QM consideration
Dgg T
TETE
2
)0()(
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Eg vs. T
•Eg decreases with increasing temperature
•For Si, ▫ D=650K,
▫Eg reduction = -2.4 x 10-4 eV/K
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Intrinsic Semiconductors
•Intrinsic = pure•Electrical conduction
▫Electrons must be excited from the valence to the conduction band
▫Small Problem Thermal energy at room temperature (kBT) is
only 25.8 meV. How can electrons cross Eg (1.10 eV for Si at T=300K)?
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Interband Transition•Electron goes from valence
to conduction band▫“hole” appears in valence band
•Intrinsic carrier concentration (298 K)▫Si: 1.5 x 1010 cm-3
▫GaAs: 1.1 x 106 cm-3
•Seatwork▫Determine the concentration of intrinsic
carriers relative to the number of atoms in Si and GaAs.
Ec
Ev
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Fermi Energy
•Probability of occupation= F(EF) = ½•T = 0K
▫E<Ev: F(E)=1
▫E>Ec: F(E)=0
•EF located in the middle of the energy gap•At higher temperatures F(E) can become
less than 1 for E<Ev and F(E) can be bigger than 0 for E>Ec
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Fermi Energy
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Seatwork/Homework
•Using the Fermi distribution, calculate the probability of occupation for E > Ec for Si and GaAs at room temperature.
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Why should EF be in the middle of the energy gap?
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Density of Electrons and Holes
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Electrons and Holes
•Number of electrons in the conduction band = number of holes in the valence band
•Expression for Nh similar to Ne
•Although me* ≠ mh*
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Intrinsic Carrier Concentration
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Mobility m•Conductivity is not determined by carrier
concentration alone!
•Drift velocity v per unit electric field E
E
v
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Conductivity• Recall
and
• Substituting m expression,
eNeE
vN
Nvej
Ej
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Temperature Dependence of Mobility, Carrier Density and Conductivity
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Extrinsic Semiconductors
•Extrinsic=Impure▫No such thing as pure semiconductor▫Defective by nature
•Doping=Intentionally Impure▫Group III impurity
Missing electron=hole=p-type▫Group V impurity
Extra electron=n-type
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Group V Impurity in Si
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Intentional Impurities
•Usually in the ppm range•Group V
▫Donates an electron to the material▫Impurity energy level just below conduction
band•Group III
▫Accepts an electron from the material▫Impurity energy level just above valence band
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Donor and Acceptor Levels
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Majority and Minority Carriers
•Majority carrier▫Usually from dopant (extrinsic carriers)
•Minority carrier▫Usually from interband transitions (intrinsic
carriers)•Valid for reasonably low T•The picture can change at high T
▫Intrinsic carriers become the majority!
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How many carriers can you put in the material?•Limited by solid solubility curve for
impurity▫Hume Rothery rules!
•Crystal structure should be preserved▫Complete solubility not required!
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Solid Solubilities of Impurities
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Carrier Concentration•Intrinsic
•n-type
•p-type
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Carrier Concentration vs. Temperature
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Conductivity and Temperature
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Fermi Energy Changing with Doping and Temperature
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Determining Carrier Concentration
•Indirect measurement▫Resistivity is easier to measure compared
to conductivity▫Correlate resistivity with carrier
concentration•Direct Measurment
▫Hall Effect
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Resistivity Measurements
l
RA
RIV
sample ammeter
voltmeter
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Problems with Resistivity Measurements•Geometrical shape required for specimen
▫Uniform cross-sectional area•Contact resistance•Loading effects from meter
▫Voltmeter: should not draw current High impedance required
▫Ammeter: should not impede current flow Zero resistance desired
•Stray capacitance and inductance
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Four Point Probe Technique(ASTM F84-84, F374-84)•Suitable for wafer geometry
▫Rectangular/circular/cylindrical/slab•Minimizes contact resistance and loading
effects•Four probes separated equally by distance
s▫Outer probes: constant current supply▫Inner probes: voltmeter
•Sheet resistance Rs
)(CFI
VRs
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Four Point Probe•Correction Factors
▫Geometrical in nature▫Something to do with
s and how big the sample dimensions are with respect to it
•Computing resistivity
▫w=sample thickness
wRs
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Correction Factor Limit
•Rs formula valid for w « a or d
•BONUS PROBLEM▫In the limit as d»s, show that
CF = (/ln 2) = 4.54
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Why do you need a constant current source for the four point
probe set-up?(Why is a constant voltage source
not sufficient?)
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Resistivity and Carrier Concentration
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Empirically Generated Curves!
•There are other ways to determine carrier concentration!▫Non-destructive▫Destructive
Rutherford Backscattering (RBS) Secondary Ion Mass Spectrometry (SIMS) Neutron Activation Analysis (NAA)
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Carrier Type Determination
•Is the material n-type or p-type?•Seebeck Effect
▫Double thermocouple•Works for
▫Bulk material▫Films on high resistivity material▫Films on opposite type substrate
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Hot Probe (ASTM F42-77(87))
Voltmeter/Ammeter
+
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How it works…
•Hot probe has greater carrier concentration
•Positive terminal of meter must be on the hot probe▫If p-type, electrons flow from cold to hot
junction: meter records positive reading▫If n-type, electrons from flow from hot to cold:
meter records negative reading•If the tester leads are inverted, the
deflections will be inverted! (this can be confusing!?)
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Determining Resistivity and Carrier Type Simultaneously
•Hall Effect Apparatus▫Can measure
concentrations down to 1012 electrons/cm3
▫Sensitivity is several orders of magnitude better than any chemical analysis
▫Applies to bulk material▫Pass a current in a material
immersed in a magnetic field
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Hall Effect
•Consider a rectangular block of n-type semiconductor immersed in a magnetic field with a magnetic induction B in the z-direction
•Let a current density j flow through the material in the +x direction
•Flowing electrons experiencea Lorentz force deflecting them from their pathBvqF
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Hall Effect• Lorentz force makes the electrons drift to one
side of the material• Accumulation of charge sets up an electric field
▫ Hall field
• Hall field builds up until it balances the Lorentz force
• The current density j in the material iseNvj x
zxy BvE
EeF
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N and the Hall CoefficientWe can calculate the number of conduction electrons N (per unit volume)
•Define the Hall constant/coefficient
▫coefficient is inversely proportional to N▫sign indicates carrier type
NeRH
1
y
zx
eE
BjN
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Limitations of the Hall Technique•Heating Effects
▫An electromagnet is usually used▫Current required is in the AMPS range
typically•Do the measurements quickly•Demagnetization is necessary when
repeating the experiment
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Capacitance-Voltage Technique
•Junction or schottky barrier needed•The variation of capacitance with voltage
is indicative of carrier concentration•Depth profiling is possible
▫5 to 10 mm▫Depends on carrier concentration
Affects reverse bias conditions
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Metal-Semiconductor Contacts• Desired effect: Ohmic contact
▫ Obeys Ohm’s law (linear I-V characteristics)▫ Interconnection between devices▫ Interface to external circuit
• Another effect: rectifying contact▫ Schottky Barrier▫ Conducting in forward bias, non-conducting in reverse
bias▫ Undesirable for ohmic contacts▫ Can fabricate devices based on this effect
MOS (Metal-Oxide-Semiconductor) MIS (Metal-Insulator-Semiconductor)
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What are the conditions that determine whether you will get an ohmic or
rectifying contact?
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Surface States
•Consider an n-type free surface▫Surface states generate free electrons making
it charged▫Negative charge repels electrons near the
surface, exposing ionized donors▫Depletion layer results (layer with fewer
electrons compared to the bulk material)▫Energy bands curve upwards towards the
surface indicating repulsion of electrons from the surface (potential barrier!)
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Band Bending at the Semiconductor Surface
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Band Bending for p-type Semiconductor•Consider p-type free surface
▫Holes migrate to free surface▫Band edges bent downward toward the
surface▫Potential barrier for holes is established
near the surface
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The Work Function •Energy required to take an electron from
EF to ▫Appendix 4▫Difference between EF and vacuum (free
electron state) Metals: Ionization energy Semiconductors: depends on carrier type
▫Different from electron affinity
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Metal/n-type Semiconductor Interface
•Before contact▫ M> S
•Upon contact▫Electrons from conduction band of
semiconductor flow into conduction band of metal until EF equalizes
▫Metal is negatively charged▫Potential barrier for electrons forms▫EC in bulk semiconductor is lowered by M - S
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Metal-Semiconductor Interface I
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Metal-Semiconductor Interface II
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Metal/p-type Semiconductor Interface
•Before contact▫ M < S
•Upon contact▫Electrons diffuse from metal to semiconductor ▫Metal is positively charged▫Downward potential barrier for holes forms▫EC in bulk semiconductor is lowered by M - S
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Contact Potential
•The difference between work functions of the metal and semiconductor (or any two materials in contact with each other)▫M- S
•Potential barrier height from metal side▫M- ▫ is the electron affinity
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Currents
•Diffusion Current▫Current driven by concentration gradients▫Equilibrium state: Electrons flowing from the
semiconductor to the metal and vice versa must be equal
•Drift Current▫Current driven by electric fields (drift velocity)▫Bent bands imply an electric field in the
material: holes are swept in the direction of the field and electrons opposite to it
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Current Across the Barrier
•Metal/n-type semiconductor junction▫DC bias: metal negative bias▫Metal becomes more negative▫Electrons in semiconductor repelled more▫Potential barrier increases making depletion
region wider▫Diffusion currents become negligible▫Voltage-independent drift current produces
small and constant electron current from metal to semiconductor (reverse bias)
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Forward and Reverse Bias on Metal Semiconductor Interface
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Forward Bias
•Positive terminal on metal▫Potential barrier reduces▫Electrons driven over the barrier▫Large current results from semiconductor to
metal▫Depletion layer reduces
•Rectifying property useful for converting AC to DC
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I-V Characteristic
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Comparison with pn Junction
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Current Equations•Metal to semiconductor
▫A = contact area, C = constant•Semiconductor to metal
▫V = bias voltage•Saturation current
kTMS
MeACTI 2
kTeVSM
SMeACTI 2
kTS
SMeACTI 2
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Net Current
• Forward bias: V>0▫ Inet increases exponentially
▫ Watch out for the knee! For Si, knee voltage = 0.7
• Reverse bias: V<0▫ Inet ~ -Is
▫ Graphs exagerrate Is so you can see it 3 orders of magnitude smaller than forward current (A – mA)
1 kTeVSMSSMnet eIIII
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Advantages of Schottky Diode
•Involves only one type of conduction carrier (electrons)▫No mutual annihilation (recombination) of
electrons and holes can occur▫Can be switched more rapidly from forward to
reverse bias Suitable for microwave-frequency detectors
•Metal contact provides better heat removal ▫Helpful in high power devices
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Metallization (Ohmic Contact)Metal/n-type interface▫ M < S
▫ Electrons flow from metal to semiconductor▫ Bands bend downward▫ No potential barrier forms impeding electron flow in
either direction▫ Current can be injected in and out of the semiconductor
without significant power loss▫ Ohmic contact is formed!
• Metal/p-type interface▫ M > S
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Ohmic Contacts
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Aluminum on Silicon• Common material for metallization on Si or SiO2
▫ Relatively good conductor▫ Low melting/annealing temperature
Al < Si
▫ Ohmic contact formed with p-type Si Improve contact by diffusing Al into Si generating a p+
(heavily doped) region at the contact point▫ Rectifying contact on n-type Si
Avoid rectification by heavily doping (n+) contact region Depletion layer becomes thinner Makes electron tunneling possible! Ohmic contact formed!
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p-n Junction
•Diffuse n-type impurity into p-type material (or vice versa)
•EF equalizes ▫Electrons flow from n to p▫Holes flow from p to n▫Depletion layer is formed▫Electric field across junction builds up until no
net charge transfer occurs across the junction
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p-n Junction
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The Biased Junction• Forward bias
▫ p-side positive▫ Electrons driven from p to n, holes from n to p▫ Depletion layer narrows and barrier height decreases▫ Large electron flow from n to p
• Reverse bias▫ n-side positive▫ Electrons driven from n to p, holes from p to n▫ Depletion layer widens and barrier height increases▫ Small drift current
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Forward and Reverse Bias
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Shockley Equation
• Ideal diode law
▫ where the reverse saturation current is
▫ Cep ,Chn = equilibrium concentration of electrons in p, holes in n
▫ D’s and L’s = diffusion constants and diffusion lengths
1 kTeVS eII
hn
hnhn
ep
epepS L
DC
L
DCAeI
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Diffusion•D related to mobility via Einstein relation
•Minority carrier diffusion length L
▫ tep = lifetime of electrons in p (before recombination)
e
kTD ep
ep
epepep DL
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Is•Keep Is small
▫Keep minority carrier concentrations (Chn and Cep) low compared to electrons and holes introduced by doping
▫Selecting semiconductors with with large energy gaps and high doping levels will help!
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Deviation from Ideal Behavior
•Surface effects▫Surface channels/depletion region form▫Leakage current generated
•Generation-recombination of carriers in the depletion region
•Tunneling of carriers between states in the bandgap
•High injection condition (np~pp or pn~nn)•Series resistance effect
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Ideality Factor
where n is the ideality factorn=2 recombination
current dominatesn=1 diffusion current
dominates1<n<2 both currents
contribute
1 nkTeVS eII
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Junction Breakdown• Usually under reverse bias• Junction conducts a large current (>Is)• Irreversible when current becomes too large (mA
range)• Reverse bias bigger than critical value can result
in impact ionization▫ Can excite other electrons into the conduction band▫ Results in breakdown (reverse current increases
rapidly)▫ Avalanche process▫ Depends on degree of doping
Higher doping = lower breakdown voltage
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Zener Diode
•Zener breakdown▫Tunneling effect at low reverse voltages
(<4V for Si diodes)▫Occurs under heavy doping
Barrier width very thin Some valence electrons on the p-side are
opposite empty conduction band states on the n-side
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Zener Diode
• Breakdown voltage is quite consistent
• Zener diode is not destroyed by breakdown▫ Unless excessive
heat dissipation causes it to melt
• Useful in circuit protection devices, e.g., voltage regulators (power supplies)
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Photodiodes
•Bare p-n junction▫Exposed to light of energy > Eg
▫Electron-hole pairs generated▫Electrons in the depletion layer are swept
to the n-side▫Holes are swept to the p-side▫External circuit can detect the presence of
these charge carriers
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Solar Cell (Photodiode)
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Carrier Collection
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Basic Features
•Open circuit voltage▫Connect voltmeter across the solar cell▫Typically 500-700 mV
•Short circuit current▫Connect ammeter across solar cell (short
circuit!)▫More indicative of the carriers generated by
light•I-V Characteristics
▫Diode curve shifted down by light generated current: Ilight=Idark-IL
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I-V Characteristics
•Fourth quadrant curve▫Negative power! (P=IV)▫Power generated!
•Efficiency▫Ratio of output power over input power
•Fill Factor▫How well diode curve fills box bounded by
I-, V- axes and Voc, Isc
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I-V Curve
•Desired solar cell operation at the maximum power point▫Determined by the resistive load in the circuit
and the intensity of light impinging on the cell•Rated efficiency
▫Pin=1000 W/m2 on earth’s surface (high noon)▫Temperature dependent (std. temp. = 25C)
inP
VI maxmax
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Avalanche Photodiode
•p-n photodiode operated at high reverse bias (near breakdown)
•Generated electron-hole pairs are accelerated and ionize lattice ions▫Secondary electron-hole pairs generated▫10 to 1000 photocurrent gain
•Suitable for low-light-level and very high frequency applications
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Tunnel Diode
•Narrow depletion layer due to heavy doping
•Occupied valence band of p-side higher than occupied conduction band of n-side▫Small reverse bias▫Electrons tunnel from p to n side
•Empty valence band lower than occupied conduction band of n-side▫Small forward bias▫Electrons tunnel from n to p side
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Tunnel Diode
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Negative Resistance
•Moderate forward bias: non-conducting▫Negative resistance region▫Current drops with voltage
•Normal forward bias: conducting•Applications
▫Positive resistance dissipates energy▫Negative resistance generates energy▫Oscillators with zero net resistance won’t lose
energy
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Transistors•Bipolar junction
transistor▫npn or pnp▫Back-to-back pn
junctions▫Three terminal device
Base Emitter Collector
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BJT’s•Biasing conditions for amplifier
applications▫Base-emitter forward biased▫Base-collector strongly reverse biased▫Electrons injected into emitter, amplified at
collector
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Amplification
•Forward biased emitter = small resistivity•Reverse biased base collector = much
larger resistivity•Power is larger in larger at the base
collector▫Current is identical in both junctions▫Power gain!
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AC Amplification
•Base voltage controls current from emitter to collector▫Large forward bias decreases potential barrier
and electron injection into the p area is relatively high
▫Small forward voltage results in smaller electron injection
•Strong collector bias mimics and magnifies base voltage
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Transistor Switch
•The electron flow from emitter to collector can be arrested via an appropriate base voltage
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Desirable Characteristics (npn)
•Large electron density in the emitter requires it to be heavily doped (n-type)
•Recombination with holes in the base area should be kept to a minimum▫Base should be lightly doped (p-type)▫Base should be thin (~1mm)
Beneficial side-effect: higher frequency response
•Doping of collector usually not critical▫Lightly doped for high gain and low
capacitance
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Collector I-V Characteristics
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MOSFET
•Metal-Oxide-Semiconductor Field Effect Transistor
•FET▫Channel connecting a source S to a drain D▫Channel has the same type as source and drain▫Unipolar: only one type of charge carrier▫Gate voltage applied to channel controls the
flow of charge carriers through it▫Gate has MOS structure: gate voltage produces
field controlling channel width
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Depletion-Type MOSFET
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Types of MOSFET
•Depletion type▫Normally on: channel is conducting when VG =
0▫As VG becomes more and more negative,
electrons accumulating at the oxide interface repel electrons in the channel into the substrate until the channel is pinched off (turned off!)
•Enhancement type▫Normally off: no channel when VG=0
▫Channel forms when VG>0: holes are driven from oxide interface
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Enhancement-Type MOSFET
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More MOSFET’s
•NMOSFET▫n channel
•PMOSFET▫p channel
•CMOSFET▫p and n channels integrated into a single chip▫Complementary MOS▫Dominant technology for IT
Low voltage (0.1V), low power consumption, short channel length (high speed performance)
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JFET
•Junction FET▫Channel consists of a pn junction▫Normally on: zero bias provides maximum
source to drain current▫Reverse bias increases depletion layer until
it pinches off the channel
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JFET
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Types of JFET• n-JFET
▫ n-type channel
• p-JFET▫ p-type channel
• BIFET▫ Combined bipolar transistors with JFET
• MESFET▫ Uses a metal semiconductor junction
• MODFET▫ Modulation doped (thin AlGaAs film on undoped GaAs
substrate)
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MESFET
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Advantage of GaAs Over Si
•Faster switching speeds▫Electron mobility 6-fold compared to Si▫Hole mobilities lower
Stick to n-type material
•More setbacks?▫Si has larger thermal conductivity
More power needed for faster switching rates
▫Electron mobilities are comparable at high fields
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Quantum Structures
•How small can you make transistor?•Quantum Dot
▫3-D confinement (0-D freedom)•Quantum Wire
▫2-D confinement (1-D freedom)•Quantum Well
▫1-D confinement (2-D freedom)
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Quantum Dot
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Q Dot Device
•GaAs sandwiched in wider gap AlGaAs▫AlGaAs conduction band higher than GaAs▫Potential barrier between GaAs regions
•At sufficiently large bias filled conduction band levels of n-GaAs levels out with empty conduction band levels in the middle n-GaAs▫Tunneling can occur
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Q Dot Band Structure
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Negative Differential Resistance•Tunneling can come to a near standstill at
slightly higher voltages▫Available empty energy levels not aligned
with free electrons
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Q Dot I-V Characteristic