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MSE 141 Electronic Materials. Semiconductors and Devices Dr. Benjamin O. Chan Associate Professor February 2012. Problem Set 3. Hummel 3 rd edition Chapter 8 1, 4, 6, 7, 9, 13, 15, 22 Due Feb. 16 Final Exam Thursday Feb. 23. Semiconductors. Active electrical component - PowerPoint PPT Presentation
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MSE 141 Electronic MaterialsSemiconductors and DevicesDr. Benjamin O. ChanAssociate ProfessorFebruary 2012
Problem Set 3•Hummel 3rd edition•Chapter 8
▫1, 4, 6, 7, 9, 13, 15, 22
•Due Feb. 16•Final Exam
▫Thursday Feb. 23
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
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
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
Overlapping sp Levels
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!
Band Structure of Si
Energy Gap at 0 KElement Eg (eV)
C (diamond) 5.48
Si 1.17
Ge 0.74
Sn (gray) 0.08
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)(eVE
m
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()(
Eg vs. T•Eg decreases with
increasing temperature
•For Si, ▫D=650K, ▫Eg reduction = -2.4
x 10-4 eV/K
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)?
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
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
Fermi Energy
Seatwork/Homework•Using the Fermi distribution, calculate
the probability of occupation for E > Ec for Si and GaAs at room temperature.
Why should EF be in the middle of the energy gap?
Density of Electrons and Holes
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*
Intrinsic Carrier Concentration
Mobility •Conductivity is not determined by carrier
concentration alone!
•Drift velocity v per unit electric field E
Ev
Conductivity• Recall
and
• Substituting m expression,eNe
EvN
Nvej
Ej
Temperature Dependence of Mobility, Carrier Density and Conductivity
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
Group V Impurity in Si
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
Donor and Acceptor Levels
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!
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!
Solid Solubilities of Impurities
Carrier Concentration•Intrinsic
•n-type
•p-type
Carrier Concentration vs. Temperature
Conductivity and Temperature
Fermi Energy Changing with Doping and Temperature
Determining Carrier Concentration•Indirect measurement
▫Resistivity is easier to measure compared to conductivity
▫Correlate resistivity with carrier concentration
•Direct Measurment▫Hall Effect
Resistivity Measurements
lRA
R IV
sample ammeter
voltmeter
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
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)(CF
IVRs
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 thicknesswRs
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
Why do you need a constant current source for the four point
probe set-up?(Why is a constant voltage source
not sufficient?)
Resistivity and Carrier Concentration
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)
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
Hot Probe (ASTM F42-77(87))
Voltmeter/Ammeter
+
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!?)
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
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
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
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
eEBjN
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
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 m▫Depends on carrier concentration
Affects reverse bias conditions
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)
What are the conditions that determine whether you will get an ohmic or
rectifying contact?
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!)
Band Bending at the Semiconductor Surface
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
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
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
Metal-Semiconductor Interface I
Metal-Semiconductor Interface II
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
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
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
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)
Forward and Reverse Bias on Metal Semiconductor Interface
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
I-V Characteristic
Comparison with pn Junction
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
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
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
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
Ohmic Contacts
Aluminum on Silicon• Common material for metallization on Si or SiO2
▫ Relatively good conductor▫ Low melting/annealing temperatureAl < 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!
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
p-n Junction
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
Forward and Reverse Bias
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
DCLDC
AeI
Diffusion•D related to mobility via Einstein relation
•Minority carrier diffusion length L
▫ tep = lifetime of electrons in p (before recombination)
ekT
D epep
epepep DL t
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!
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
Ideality Factor
where n is the ideality factorn=2 recombination
current dominatesn=1 diffusion current
dominates1<n<2 both currents
contribute
1 nkTeVS eII
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
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
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)
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
Solar Cell (Photodiode)
Carrier Collection
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
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
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)
inPVI maxmax
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
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
Tunnel Diode
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
Transistors•Bipolar junction
transistor▫npn or pnp▫Back-to-back pn
junctions▫Three terminal device
Base Emitter Collector
BJT’s•Biasing conditions for amplifier
applications▫Base-emitter forward biased▫Base-collector strongly reverse biased▫Electrons injected into emitter, amplified at
collector
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!
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
Transistor Switch•The electron flow from emitter to
collector can be arrested via an appropriate base voltage
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 (~1m)
Beneficial side-effect: higher frequency response•Doping of collector usually not critical
▫Lightly doped for high gain and low capacitance
Collector I-V Characteristics
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
Depletion-Type MOSFET
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
Enhancement-Type MOSFET
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)
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
JFET
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)
MESFET
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
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)
Quantum Dot
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
Q Dot Band Structure
Negative Differential Resistance•Tunneling can come to a near standstill at
slightly higher voltages▫Available empty energy levels not aligned
with free electrons
Q Dot I-V Characteristic