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SEMICONDUCTORS 2 (Junctions (Fabrication of P-N junctions (Etching methods…
SEMICONDUCTORS 2
Junctions
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Reverse bias breakdown
- If reverse bias voltage high enough
- Does not necessarily destroy the component if the current is limited
- Used for example in voltage regulation
Zener breakdown
- When the doping levels are high (thin depl. region)
- Carriers can tunnel through the depl. region
- Condition: Ev of the p-side coincide with Ec band on the n-side
Avalanche breakdown
- Carrier multiplication, impact ionization
- Carriers in high E-field of the junction area obtain enough energy to knock off more e from the bonds by impacts
- Vbr increases when Eg increases
- Vbr decreases when the doping level increases
Simple models
- :warning: Simple models did not take into account the effects of the junction potential and majority carrier changes on the injection, recombination, and generation in the junction area
- Ohmic effects were omitted
- Junction was assumed to be step-like
- Effect impurities as recombination centers
Metal-SC junction
Schottky-junction
- Work function: qΦm and qΦs (distance of Ef from the Evac)
- qΦm ~4 - 5 eV
- Schottky-phenomenon: - charge brought close tometal surface > + charge induced onto the surface > lowers the work function
- No depl. region is formed on the metal side of the junction
- If qΦm > qΦs:
Step qV0=q(Φm-Φs) for e from SC to metal
Metal side: the step is steep wall, qΦb =q(Φm-χ) (χ: e affinity of SC)
W=sqrt(2.perm.V0/q Nd)
- If Φm<Φs:
e moved from the metal towards the SC
for holes: depl. region = barrier towards the metal, qV0=q(Φs-Φm)
Rectifying junctions
- Forward barrier can be lowered by an external voltage V
- Reverse barrier is ct: qΦb=q(Φm-χ), so I prop. to exp(-qΦb/kT)
- Current is carried by majority carriers (drift) > components are fast compared to pn-junctions
Ohmic junctions
- Junction which has linear I-U characteristics
- (1) If Φm < Φs (in n-type SC) and Φm > Φs (p-type SC): no depletion region is formed to the SC but excess amount of majority carriers is formed
- (2) Use very high doping of the SC, depletion region very narrow and the carriers can easily tunnel
- (3) Eutectics can be used, metal which is used as a dopant directly to the SC
Heterojunctions
- SC on both sides of the junction are of different materials
- Used in transistors and in quantum structures
- In ideal case the for conduction and valence band discontinuities it holds
- Anderson’s affinity rule: ΔEc=q(χ2-χ1), ΔEv=ΔEg-ΔEc
- flux of E-field: ε1E1= ε2E2
- Junction potential is divided according to the ratio of doping levels and permittivities
Excess carrier in SC
Optical absorption
- Eelectron-hole pair: hν>Eg
- Absorption coeff. (dep. on wavelength):
dI/dx= α I(x), I(x)=I0.exp(-α.x)
- Eg of some common semiconductors ~ wavelengths
Luminescence
Def: process in which the matter emits light
as a consequence of discharging an excitation level
Photoluminescence
- Recomb. of e/holes in SC: (direct) fast process, time constants about 10-8 s > fluorescence
- Phosphorescence: very slow luminescence processes
Electroluminescence
- When e and holes brought to the junction by electric current
- Injection luminescence: energy released in the recombination process is emitted as light
- Uses: characterization of current spreading solar cells, light extraction from LEDs
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Carrier diffusion
Diffusion
- Consequence of random thermal movement
- Carrier fluxes gen. by diff:
Φn(x)=-Dn dn(x)/dx, Φp(x)=-Dp dp(x)/dx
- Diff. coeff.: Dn, Dp
- Diff. current densities:
Jn= qDn dn(x)/dx, Jp=-qDp dn(x)/dx
Drift and Internal Electric Fields
- If E(x) is applied:
Jn= q μn n(x) E(x) + qDn dn(x)/dx
Jp= q μp p(x) E(x) - qDp dp(x)/dx
- Total current density: J(x)=Jn(x)+Jp(x)
- Drift current prop. to the carrier conc.
- Diff. current prop. to the gradient of carrier conc.
- Minority carrier diff current bug (even at small carrier conc.)
- For e: E(x)=1/q dEi/dx with Ei=-q(V(x)+V0)
- Slope of the bands prop. to E(x)
- In eq. : no net movement of carriers, constant electrochemical potential
- Einstein relation: D/μ=kT/q
Diffusion, recombination and continuity equation
- Take into account recomb. (dep. on conc.)
- Continuity eq.:
d(dn/dt)=1/q dJn/dx-dn/τn, d(dp/dt)=-1/q dJp/dx-dp/τp
- e diff. eq. (if drift current are small):
d(dn/dt)=Dn d2(dn/dx2)-dn/τn, d(dp/dt)=Dp d2(dp/dx2)-dp/τp
- Control of spatial and time dep. of excess carrier conc.
“Steady state” injection
- Steady state > time derivatives of the diff. eq.=0
d2(dn/dx2)=dn/(τn Dn)=dn/(Ln^2)
d2(dp/dx2)=dnp(τp Dp)=dn/(Lp^2)
- Diff lengths: Ln=sqrt(τn Dn), Lp=sqrt(τp Dp)
- If holes are injected to the other end:
dp(0)=Dp > dp(x)=Dp e(-x/Lp)
- Causes a current density: Jp(x)=q Dp/Lp dp(x)
- Diff current prop. to the excess carrier conc.
Haynes-Schokley Experiment
- Used for measuring the mobility+ diff. coeff. of minority carriers
- A pulseof light igenerates an excess minority carrier
concentration in an end of the SC tube
- When a voltage is applied: excess carrier “pulse” will move from where they were generated to the other end of the rod
- Gaussian distribution: dp(x,t)=DP/sqrt(Pi.4Dp.t) e(-x^2/(4.Dp.t))
Gradient of the Quasi-Fermi Level
- Jn(x)=μn n(x) dFn/dx
- Rewritten: Jn(x)=S(x) d(Fn/q)/dx
Optoelectronics
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Light emitting diode
- Direct Eg mat. recmb. of carriers produces light
- In forward biased: controlled strong recomb. > electroluminescence
Light emitting diodes
- Eg of compound SC are btw 0.18 eV (InSb) and 3.4 eV (GaN)
- Alloy composition: can tune Eg and the type of band structure (direct/indirect) + change in lattice param.
- Optoelectronic pair= light emitting diode/laser + photodiode
Used in CD/DVD/bluray players, electrically isolated data transfer
- III-V alloys more popular than II-VI alloys: doping/formation of junction and ohmic contact formation is more difficult
Fiber optic communication
- Transfer of light, emitter to detector usually done via glass or plastic optical fibers with a diameter of 5-25 µm
- Inner part:(core) has a higher refractive index
- Outer part: (cladding) made of SiO2
=> keeps the light due to total internal reflection
- Intensity decreases along the length of a fiber: I=I0.exp(-α(λ)x)
- α(λ): attenuation factor
- Most suitable λ: 1.55 um and1.3 um
- Chromatic dispersion: different λ have different n and move in the fiber at different speeds
Multilayer heterojunction LEDs
- When the signal f not very high + the signal is analog
- Intensity of a LED: linearly dep. on I in a wide range
Lasers
- Light Amplification by stimulated Emission of Radiation
-Produces and amplifies collimated and monochromatic light ray
- *Size: from barely visible to “house-sized”
- Power: 10^-9 – 10^20 W
- Wavelength: microwaves – x-rays, 10^11-10^17 Hz
- Continuous wave operation (pulsed operation-
- Usage: Light source, electronics, thermal treatments, surgery, metering, Radar, data storing, data transfer, etc.
- Characteristics: coherent, monochromatic, collimated, large power density
- Stimulated emission:
In eq.: n2/n1= exp(-(E2-E1)/kT)=exp(-hv12/kT)
By taking into account the energy density of the optical field:
B12.n1.ρ(v12)=A12.n2+B21.n2.ρ(12)
B12, A21 and B21: Einstein coefficients
Eemis(sti)/Eemis(spo)=B21.ρ(v12)/A21
- Population inversion: n2>n1, necessary for laser
- Interferometer: mirrors of distance L=mλ/2
- If the laser medium has n: λ0=nλ
Semi-conductor laser
- Small dimensions: 0.1 x 0.1 x 0.3 mm3
- Modulation of SC diode lasers is easy, because the pumping mechanism is simple
- EH recomb. process can be used for realizing laser
Population inversion
- Pumping: forward biasing a pn-junction (general), optical pumping
- Forward bias: brings a large amount of charge carriers to the junction area > inversion region
- If carrier supply is high enough: achieve continuous recomb.
- Threshold current density: smallest J that generates high
enough recomb. rate for the laser operation
- Formation of population inversion in the inversion region, can be described by the quasi-Ef
- EH recomb. follows a condition: (Fn-Fp)>hv
For SC: (Fn-Fp)>Eg
:warning: Need direct band-gap
Emission spectrum of a pn-junction
- Photon's energy: Ec-Ev=Eg<hv<Fn-Fp
Upper limit is dep. on the bias voltage
- λ of spont. emiss. is within those limits, but the λ of a laser is det. by the resonator (cavity): λ/2(m)=2Ln/λ0
Fabrication of a laser diode
- pn-junction made of highly doped SC
- Resonator (cavity)
- Metal contacts and thermal sink
Heterojunction lasers
- Problem of homojunctions: too thick layer in which the recomb. takes place, cannot be used
- Heterojunction:With a proper forward bias V the population inversion is achieved only in the middle layer
- Confinement of the active region > reduce threshold current I
- Using different n in the layers > guide the photons (waveguide structure) > keep the photons oscillating within the resonator
- Double heterostructure: more efficient for confining the carriers, n between the cladding and the waveguide layers confines the optical field better and smaller Eg
- Lasing action can be controlled in lateral direction by using contact stripes
Quantum well (QW) laser
- Carriers can be confined by different layer structures
- typical multilayer structure
- continuously changing, GRINSCH
- Separate confinement heterostructure: a structure in which the light confinement is controlled by a n difference btw the cladding and the waveguide region + additional (separate) material layer (active region) which has a smaller Eg
Vertical Cavity Surface Emitting laser (VCSEL)
- Vertical emitting lasers: resonator is formed using a distributed Bragg mirror (DBR)
- Control easier (thanks to the length of the resonator = emission λ)
- Threshold I can be very small <50 µA
+ low cost, integration in 1D and 2D arrays on chip, high speed modulation, high beam quality, low power, high power efficiency
The materials used in lasers
- Optoelectronics mostly based on InP and GaAs
technology (=substrate materials)
- Ex: GaInAs/GaAs, GaInAsP/GaAs, GaInAsP/InP, AlGaInAs/InP, GaInP/GaAs,GaInNAs(Sb)/GaAs, GaN/Sapphire, InGaN/sapphire + many more