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Chemistry and Physics of Solar Cells - Coggle Diagram
Chemistry and Physics of Solar Cells
General
Main concept Solar cells
3 Charge collection
1 Light absorption
2 Charge seperation
Why solar cells
Immense amount of solar energy reaches earth
Efficiency's has gone up and prices gone down
Sustainable method for creating energy
Performance quantities
Jsc
FF
Voc
Efficiency
IPCE = photon to current efficiency
AM = Air mass = 1/cos(theta)
AM1.5 is the normal spectrum (1000W/m2)
Structure
Elemental semiconductors = group IV elements
Silicium has the diamond structure
Group III+V elements can be used together
GaAs has the zincblende structure
Volume density (atoms/volume)
Surface density (atoms/area)
High refractive index leads to reflection
Polycrystallinity should be avoided --> intrabandgap states
Quantum mechanics
Introduction to quantum mechanics
Photovoltaic effect (work function) --> de broglie wavelength (L = h/p) --> Time dependent SE --> Time independent SE --> general solution free electron --> BC (infinite) well --> solution (infinite) well --> solution step potential --> Reflection/Transmission/Tunneling --> Formation energy bands
Quantum theory of solids
Effective mass m*
Negative for holes = have opposite direction
The effective mass of electrons and holes takes into account the particle weight and all internal forces acting on it. F = m*a
m
= h*
2/d2E/dk2
Sharp energy bands = low effective mass
Broad energy bands = large effective mass
Density of states
Differential density of quantum states
2
1/8
volume shell/Vk
Energies
Three dimensional potential well --> E = h2k2(x,y,z)/2m
Volume
Vk = (pi/a)^3
Fill in to get DOS
Integrate to get number of state between E and E + iets
For SC
Vb
Depends on hole mass and Ev - E
Cb
Depends on electron mass and E-Ec
Number of states per unit energy and volume
Kronig-penny 1d model
By assuming periodic step wise periodic potentials around atoms
Can be used to describe the energy state in solids with the bloch function phi = u(x)exp(ikx)
Resulting function: p'sin(aa)/aa + cos(aa) = cos(ka)
a = atom distance, alpha = measure for energy(root(2me/h2), p'= (barrier height (v0), barrier depth b, mass particle)
for certain energys the function on the left side is greater than |1|, cos(ka) can be maximal be |1| so for those energys there is no k- value/wavenumber--> origin band gap.
Bandgap energy can be determined by filling in the two alpha values at the same k-value
Formation energy bands in crystalline solids
Fermi-dirac distribution function
Can be used to determine he probability that a state with energy E is filled.
Goal
Emerging PV (application)
Operations of solar cells (theory)
Semiconductor material
Equilibrium
No forces acting on the semiconductor
Intrinsic SC
Amount of charge carriers
Electrons in CB
n0 = ni = Nc*exp(Ef-Ec)/kt
Nc = effective DOS
Holes in VB
p0 = ni = Nv*exp(Ev-Ef)/kt
Using density of states * fermi-dirac(simplif)
ni2 = p0
n0 = Nv
Nc*exp(-Eg/kt)
So smaller bandgap = more cc
Both nv and nc are T dependent
Pure SC with no impurities or lattice deffects
Fermi position
Dependent on electron mass/hole mass ratio
Extrinsic/doped SC
Addition of donor/acceptor atoms = doping
Dopant ionisation statistics
nd = Nd-Nd+
Nd = density of dopants
Nd+ = density of ionized dopant
nd = density of nonionized dopants
nd/(n0+nd)
Usually very small above 200 K
Vast energy levels above pull out all electrons
Types
n-type doping
The addition of group 5 element that have an extra electron that is loosely bound. Thermal excitation can excite these electron to the conduction band and a positive charge stays on the element
Electrons are now the dominant charge carriers. n = ne
Increases the fermi level
p-type doping
The addition of group 3 elements result in that it can take up an extra electron. Thermal excitation can excite electrons from the vb to the energy state above the vb that creates holes in the vb
Dominant charge carriers are p0
Decreases the fermi level
ni2 = p0*n0 still holds
Overcompensated SC
Semiconductor that contains both acceptor and donor atoms
n-type overcompensated
p-type overcompensated
It behaves like intrinsic if both are present in same conc --> annihilation and ni2=n0*p0
Use electroneutrality formula to determine final concentrations
Temperature dependence
Region 2 = Extrinsic >> intrinsic so T independent
Region 3(high T) = intrinsic >= extrinsic so no longer T ind (fermi back)
Region 1 = higher conductivity with T due to ionisation (100 k)
Use to have constant sigma or to create junction
Relation fermi level/ conc
p0 = ni*exp(Efi-Ef)/kt
n0 = ni*exp(Ef-Efi)/kt
Transport phenomena
Charge carrier Diffusion
Due to an concentration gradient
Diffusion current density
J = e
Dn
dn/dx
Current follows direction of the holes
D = kbt*Mu/e
Charge carrier drift
Due to an electric field
Inbalance in +k and -k = net momentum
Drift current density
J = N
e
vc = N
e
mu
E = e(mun
N+mup*P)E
Mobility
Increases with lower m* and longer scattertime
Hence electrons have higher mobility
Factor causing scattering
Phonon scattering, mu = T^-1.5
Ionized inpurity scattering, mu = T^3/2/Ni
Goes with T^3/2 because electrons get less stuck
Flux = electron/hole drift + electron/hole diffusion
J = e(mun
N+mup
P)E + eDn
dn/dx - e
Dp*dp/dx
Non-equilibrium
Excess charge carriers
Generation and recombination
Terminology
Generation = the creation of holes/electrons
Recombination = The annihilation of electron/holes
n = total conc = constant + dn(t)
no = thermal equilibrium electrons = constant
dn = excess electrons = n-n0
tau-n0 = excess minority carrier lifetime
gn' = excess generation rate
Rn' = excess recombination rate
Low level injection = generation of charge carriers is small compared to the majority carriers. So p0>>dn or n0>>dp
Equilibrium
Gn0=Gp0=Rn0=Rp0
Generation holes/electrons equal --> come in pairs
Non-equilibrium
Minority carriers determine the properties
n*p = ni^2 does not hold anymore
Ambipolar transport
Continuity equation
Diffusion
Generation
Drift
Recombination
Can be made for both holes and electrons
Movement of electrons and holes is coupled because an electric field will arise if they are seperated or have different diffusivities = Ambipolar diffussion
Ambipolar transport equation
Depends only on the minority carrier
Because majority carrier has much higher conductivity and can easily adjust
D' and mu' = ambipolar diffusion coeficient and mobility
Are functions of concentrations
But for extrinsic, low level injection. The diffusion coeficients are that of the minority carriers. So use faster minority = use p-type
Simplification help solve the problem
Shine light/change T
Recombination kinetics
Radiative recombination
R = ar
n(t)
p(t) (2nd order)
Extrinsic SC + low-level injection
n-type, d(dp)/dt = -arn0*(dp(t)) = p(t)/tau-po
So majority carrier is a constant (+-first order)
p-type, d(dn)/dt= -ar(dn(t))*p0 = n(t)/tau-no
Recombination lifetime
tau-no = 1/arPo
tau-po = 1/arN0
Trap assisted/ Non-radiative
Origin
Defects/Dangling bond in lattice or at the surface(diffusion gradient)
Non-bonding orbitals might give energy states inside the bandgap --> deep traps willl assist recombination
Usually faster than Radiative recombination
Processes
Electron from trap to CB
Hole from VB to trap
Electron from CB to trap
Hole from Trap to VB
Extrinsic semiconductor
N-type
Fermi level is above trap energy --> filled trap states
First recombination with excess holes (minority), then majority carrier will instantaniously follow
Low level injection, Et near Ef, Rp = Cp
Nt
dp = dp/tp0
P-type
Fermi level is below trap energy --> empty trap states
First recombination with excess electrons (minority), then majority carrier will follow instantaniously
Low level injection, Rn = Cn
Nt
dn = dn/tn0
Quasi fermi levels
Fermi levels of holes (Efp) and electrons (Efn) with excess carriers
Fermi level of majority carrier will not deviate much from Ef
Use the given that you can relate states using only the energy difference
Semiconductor device
PN-junction
Basic structure
Space charge region
Region near juntion where complete depletion occurs
Because of diffusion of majority carriers
N-type side becomes positively charged
P-type side becomes negatively charged
No carriers are present and drift/diffusion are in equilibrium
Junction between an uniformly doped n-type and p-type material
Zero-applied bias
Electric field
Gauss law
dE = p/eta
Poisson equation
-d^2(phi)/dx^2 = p/eta
Flat junctions
Constant E if uniformely doped
E = sigma/2eta
Space-charge width
Electric field
Approx
Uniform
Fully depleted/ionized
Abrupt junction
Ndxn = Naxp
p-region
Emax = -eNaxp/eta
E = -e(Na)(xp-x)/eta
n-region
Potential in n-type region contains built in potentail vbi
Can be used to calculate space charge width = use formula
Always below zero
Depends on doping densities, Vbi and dielectric constant
W = xp + xn
|Emax| = 2 Vbi / W
Energy band diagram
Built-in potential barrier
Difference in energy Efp, Efn
Vbi = Efn-Efp = kT/e * ln(NaNd/ni^2)
Vbi is between 0 and the band gap energy
Vbi is difficult to go the bandgap = much doping required
Maximum energy that can be extracted
In equilibrium band bending must occur such that the fermi level (with conc term) of the n-type and p-type material are at the same level = no current
P-type increases in energy and n-type decreases (electrostatic)
Fermi levels are equal
Reverse applied bias
Junction capacitance
Charge that is extra stored when the SCR is increased
C' = eta/W
Can be determined via an (1/C^2) vs iets plot
One sided junction
When the doping densities differ so much that the space charge region is almost at one side. So if Na>>>Nd or Nd>>>Na
Space charge width
Increases when applying a potential
Because doping remains the same
Potential is applied such that n-type gets more positive and p-type gets more negative
Replace Vbi with Vbi+Vr in all formulas
Fermi levels not equal anymore
Forward applied bias
Potential barrier is lowered with e(Vbi-Va), such that
diffusion
can now overcome the potential. Electron flow from n to p and hole flow from p to n.
Nomenclature
Nn
N = electrons or holes n/p
n = in n-type or p-type = n,p,n0,p0
From forward bias to ideal diode current
Concentration profile minority carrier
Assumptions
g'=0
ss
E = 0 in neutral region
Decreases exp with distance (rec)
Determined using ambipolar transport equation
Diffusive current
If assumed no recombination in junction
Current = hole diffusive current + electron diffusive current
Gradient of concentration profile next to SCR (xn,-xp)
Concentration mc next to SCR
Increases exponentially with Va
np=np0*exp(eva/kt)
Ideal diode equation
J = Js * (exp(eva/kt)-1)
Js = reverse bias saturation current density
If Va < 0, -Js is maximum reached
Non-idealities
Forward bias recombination current
So additional charges must be injected to compensate for recombination
Jrec = Jr0*exp(eVa/2kt)
Injected charges may recombine in SCR
Dominates at low applied potentials
More rec = lower Voc
Reverse bias generation current
Jgen = eniW/2t0
In SCR with n=p=0 there must be generation (via traps)
Derive R
E- field neutral region
To balance current away from SCR, there is a small gradient in majority carrier --> small electric field
Balance diode current with drift current majority carrier to obtain E
Small because majority carriers has much higher conductivity
Overal diode relation
J = Jd + Jrec = Js(exp(eVa/nkt)-1)
n = ideality factor between 1-2, 1 at high v, 2 at low v
Quasi fermi level splitting is constant in SCR
The SCR decreases for an forward bias until the built in potential is reduced to zero = Voc
Quandrants pn junction diode
2nd
No current
3th
Reverse bias, negative current, Photo diode
1st
Forward bias, consumes energy = LED
4th
Forward bias, negative current, pv quadrant
Open potential < Vbi (entropic terms)
At high V, the chance of recombination is much higher
Metal-semiconductor junction
Metal SC ohmic contact
When
Ef, n-type < Ef, metal
Ef, p-type > Ef, metal
Barrier is now (Ec-Ef)
Favourable to have no resistance from electrons/holes flowing when positive voltage is applied
Behave via the rules of ohms law
Schottsky barrier diode
General
Properties
Barrier that forms that prevent the diffusion of holes/electrons into the semiconductor in ss
Space charge region is completely in the semiconductor (no charges in metal = one sided juntion)
For n-type there is a flow of electrons towards the metal
When
Ef,p-type < Ef, metal
Metal gets into contact with semiconductor
Ef, n-type > Ef, metal
Nomenclature
X
From vacuum level to CB
Electron affinity
Work function
From fermi-level metal to vacuum
Phim
Phis
Ideal juction
Schottsky barier
Phib0 = (Ec-Ef,m)/e = phim - X
Difference fermi level metal and energy CB to metal
Remains the same, independent of applied bias
Built-in potential
Vbi = Phib0 - (Ec -Ef,s)/e = Phib0 - phin
So difference CB to metal en CB in neutral SC
Vacuum level goes up in the SC
Is functioin of applied bias
Width SCR SC
Same as for an one sided juntion
Non-ideal junction
Schottsky barrier loading
Polarisation can occur that lowers the energy of electrons close to the metal --> barrier gets lower energy
Interface states
Surface gets-charge due to traps at the surface
For many trap states: Charge occurs until Ef, surface = phim = phi0
Phi0 = local neutrality level of interface defects
Barrier height is now phi0-Xs ipv Phim - Xs
The experimental Phibn can differ from the theoretical Phib0
Current-voltage relationship
Flux depends on direction electrons, velocity, energy states, fermi dirac
J = Js(exp(eVa/kt)
Js = A
T^2*exp(-eVa/kt)
A = Richardson constant for thermionic emission
Watch out, use constants with cm
The flux of electrons that have enough energy (Ec') to move to the metal
Metal contacts are needed for charge extraction
Semiconductor heterojunction
General
Formula's get more complex because have not the same properties
Junction between two different SC materials
Naming
Nn
Larger bandgap is denoted with capital letter
n-n juntion are also now possible
Types
2 Bandgap partially in each other (energy allignment)
3 Bandgaps have no overlap (rare)
1 Bandgap inside the other (no charge T)
Band diagram
Fermi levels still equal
Because potential is the same at the interface, dEc and dEv must be unchanged at interface
Bending is now not that predictable
If fermi-level > Ec, highly doped at that position
Solar cells
Thin films
Cheap but lower efficiency
Amorphous silicon
Properties
Absorption is stronger --> disordered state relaxes the dk=0 selection rule. In between (in)direct bandgap.
1 um thick
Way shorter diffusion length than thickness (low mob/lifetime)
Many defects (dangling bond) 10^16 --> passivate with H (10^15)
Doping of a-Si
Really hard because defect density is so high --> no effect
Transport in a-Si
Diffusion
Much shorter than thickness
Drift
More efficient in a-Si (1 um)
Ld = mu
E
tau
p-i-n juntion
Undoped i has very large SCR --> needed for drift extraction
To thick i = dead regions without E
Fabrication of a-Si
Deposit Si using CVD
Use transparant conducting oxide as contact
Polycrystalline
CI(G)S
Copper, indium, gallium, selenide
Less toxic and has good bangap tunability
CdTe
3 um thick
II-VI semiconductor with bandgap close to SQ limit
Has high defect density, treat with CdCl2 to go to 22% efficiency
Challanges
Toxicity of Cd
Price of Te
Defects at suface and grain boundaries
Around same diffusion lengths as thickness
Properties
Thinner layers, less material needed
More defects, lower diffusion length
Stronger absorption (direct bandgap)
Cheaper production method
Perovskite + Organic
'Efficient and cheap'
Perovskite solar cell
SC properties
Strong absorption
Doping
Point defects
Results in self-doping
Occurs due to low bond strength
Can either be n or p-type defects
Structure PRK not suited for doping
Can change Ef, by altering precursor ratio
Cell designs
n-i-p configuration
p-i-n configuration
Transport layers should have large bandgaps and allign with the VB and CB
Fermi level splitting denotes Voc
Structure and composition
Metal halide PRK
ABX3
B = metal (pb2+,Sn)
X = halide (I,Br,Cl)
A = cation (MA,Cs,FA)
Used for solar cell applications
Compostion influences bandgap
Cation
Eg, Cs>MA>FA
Halide
Eg, Cl>Br>I
Metal
Eg, Pb>Sn
Crystal structure
Orthorombic for T<161K (a niet b niet c)
Tetragonal for T>161K (at room T, a = b niet c)
Cubic for T>330 k
Tandem cells
Four terminal tandem cell (seperate)
Two terminal tandem cell (needs current matching)
Organic solar cells
Present developments
Optimize energy levels to reduce energy losses
Enhance charge transport
Reduce bandgap close to 1000 nm
Configuration
TCO
Bulk heterojunction
Mixture of polymer and electron acceptor
Both have 3d structure to move hole/electron to contact with electronic hopping
Metal contact
Efficiencies over 10% and is cheap,flexible and easy to process
Charge extraction
Excition diffusives towards junction that seperates electron from hole using E-field
Diffusion length is very small --> need many interfaces inside material
SC properties
Have low electron permitivity --> large exciton binding energy compared to kt--> exciton remains until charge separation
Can form VB and CB due to bonding of MOs
Molecules are held by VDW interactions and can easily be modified
Few charge carriers due to large bandgap and non-charged imperfections
1st generation(Si)
Fabrication silicon
Crystallinity silicon
Single (10 cm)
Multi (most used)
Poly (to much defects)
Higher crystallinity is more expensive but results in less grain boundaries
Process
Obtaining pure silicon
Step 1 SiO2 + C --> Si + CO2 (metullurgical grade silicon)
Step 2 Si + 3HCl --> SiHCl3 + H2 --> Si + 3HCl (electronic grade)
99.999% purity required to have low trap states
Obtaining crystalline silicon
Czochralski process (Specific cooling to 1 crystal)
Float zone crystallisation (heated into 1 crystal)
Production solar cell
Screen printed solar cells
Put block in phosphor environment (800K) to n-dope outside (no abrupt juntion)
Cut away bottom n-type and screen print Al back contact
Start with silicon block (low doped p-type naturally)
Al diffuses into p-type --> heavely doped p+ --> pp+ junction that extracts holes
Than apply AR coating otherwise 30% reflection
Add silver contacts on top such that series resistance is low, shunt high
Solar cell efficiency
Current I = IL - IS(exp(eV/nkt-1)
IL = light induced current
Unwanted diffusive current
Limiting cases
R = 0, J=Jsc=IL Short circuit current
R = inf J = 0
Occurs at Voc
Voc = nkT/e ln(1+IL/IS)
Voc increaes with light intensity
Voc decreases by recombination
Conversion efficiency = Im
Vm/Pin = Jsc
Voc*FF/Pin
Fill factor = Im
Vm/Isc
Voc
Solar cell has power point tracking to extract as much power as possible. Power point can change depending on conditions (varies the external resistance)
Series resistance should be as low as possilbe and shunt as high as possible --> can be optimized using fingers and bushbars
Properties absorber layer
Light absorption
Absorption Si low = indirect bandgap, need phonons
Should absorb 80-90% light
Using tricks (reflection)
Increasing layer size (300 um)
Generation rate g' = alpha*Iv(x)/hv
Number of electrons/hole pairs at position x s-1
Charge separation
During illumination, E-field pn junction will extract electrons to n-type and holes to p=type
Diffusive current at junction counteracts this = unfavourable
Charge extraction
Long diffusion distances
lifetime
Better at low doping
Reduce trap states
High mobilities
use electron minority
Good efficiency but more costly production method
High efficiency Concepts + QDs
Limitations of conversion
Thermalisation (goes to CB +3KT^, in 10^-12s)
Fermi level splitting (thermo)
Absorbed efficiency
Maximum power point (FF)
Quantum dots
Concept solar cells
Carrier multiplication
Energy of thermilisation of two created charge carriers excites electron to CB
Stronger effect in smaller QD
Tandem solar cell
Using different size PbS quantum dots
Hot carriers
Not yet made into solar cell
Extract hot carriers in quantum dots by using extration far above CB
SC behaviour
Bandgap
Depends on size crystals
Can be related to particle in the box = discrete energy levels
Enp = Eg + quantum confinement term + coulombic term
Due to discrete energy levels, phonon creation is decreases, less thermilisation
Colloidal SC nanocrystals
Difficulties
Quantum dots have large surface area and thus problems with surface recombination
Thermodynamic maximum efficiency
Solid angle
Part of sunlight seen by earth = A/r^2 (steradian)
This can be increases using a lense up to max 46200 times
Limit = Carnot efficiency = 1 - Tcold/Thot
Emitting and absorption of solar cell (use J=sigmaT^4)
Solar cell cannot use energy that it emmits
Maximum ideal solar cell
1 sun
67% (with tandem)
Maximum concentrated
86%
= etacar times etaemm
Methods to break SQ
SQ only assumes radiative recombination +AM1.5
Proven
Concentrator cells
Advantages
Higher efficiency
Voc increases (high IL)
FF increases = 1 - KT/Voc
Less area solar cell needed
Difficulties
Efficiency drops with temperature
High current means large voltage drop
Tandem and multijunction solar cells
Difficulties
Expensive
Lattice matching
Use alloying to steer lattice size
Otherwise many dangling bonds
Current matching (monolithic)
Lowest current limits whole cell
Depends on light spectrum
No contacts in between
Uses tunnel junctions
High dopant conc --> small SCR --> tunneling possible for electrons to recombine with holes in next layer
Advantages
Absorb more light
More energy use of absorbed light
Max = 44% for two junctions
More theoretical
Intermediate band solar cells
Create energy band with electrons in the middle such that low energy photons are absorbed. But also lead to more recombination
Upconversion
2 small energy photons are combined to 1 photon
Can happen in some organic molecules and can be applied on the back of a solar cell.
Downconversion
To high photon energies are converted to two lower energy
Apply on surface SC but problems that created phons go up and down.
Absorb hole spectrum, no thermilisation
Economics
Cost per Wp (AM1.5)
BOS
Cost/m2
Lifetime
Grid parity
Cost per kWh