Chemistry and Physics of Solar Cells
General
Main concept Solar cells
3 Charge collection
1 Light absorption
Why solar cells
Immense amount of solar energy reaches earth
Efficiency's has gone up and prices gone down
Sustainable method for creating energy
2 Charge seperation
Performance quantities
Jsc
FF
Voc
Structure
Elemental semiconductors = group IV elements
Group III+V elements can be used together
Quantum mechanics
Efficiency
Volume density (atoms/volume)
Surface density (atoms/area)
Introduction to quantum mechanics
Goal
Emerging PV (application)
Operations of solar cells (theory)
AM = Air mass = 1/cos(theta)
AM1.5 is the normal spectrum (1000W/m2)
High refractive index leads to reflection
Silicium has the diamond structure
GaAs has the zincblende structure
Polycrystallinity should be avoided --> intrabandgap states
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
Semiconductor material
Equilibrium
No forces acting on the semiconductor
Intrinsic SC
Effective mass m*
Density of states
Kronig-penny 1d model
Formation energy bands in crystalline solids
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
Fermi-dirac distribution function
Can be used to determine he probability that a state with energy E is filled.
Differential density of quantum states
For SC
Number of states per unit energy and volume
Vb
Cb
Depends on hole mass and Ev - E
Depends on electron mass and E-Ec
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
Amount of charge carriers
Pure SC with no impurities or lattice deffects
Extrinsic/doped SC
Addition of donor/acceptor atoms = doping
Dopant ionisation statistics
Electrons in CB
Holes in VB
Fermi position
Using density of states * fermi-dirac(simplif)
n0 = ni = Nc*exp(Ef-Ec)/kt
p0 = ni = Nv*exp(Ev-Ef)/kt
Nc = effective DOS
Dependent on electron mass/hole mass ratio
Types
n-type doping
p-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
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
Overcompensated SC
Temperature dependence
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
Semiconductor that contains both acceptor and donor atoms
Electrons are now the dominant charge carriers. n = ne
ni2 = p0*n0 still holds
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)
n-type overcompensated
p-type overcompensated
It behaves like intrinsic if both are present in same conc --> annihilation and ni2=n0*p0
2 1/8volume shell/Vk
Energies
Volume
Three dimensional potential well --> E = h2k2(x,y,z)/2m
Vk = (pi/a)^3
Fill in to get DOS
Integrate to get number of state between E and E + iets
ni2 = p0n0 = NvNc*exp(-Eg/kt)
So smaller bandgap = more cc
Both nv and nc are T dependent
Use to have constant sigma or to create junction
Dominant charge carriers are p0
Increases the fermi level
Decreases the fermi level
Relation fermi level/ conc
p0 = ni*exp(Efi-Ef)/kt
n0 = ni*exp(Ef-Efi)/kt
Use electroneutrality formula to determine final concentrations
Transport phenomena
Non-equilibrium
Excess charge carriers
Charge carrier Diffusion
Charge carrier drift
Flux = electron/hole drift + electron/hole diffusion
Due to an electric field
Due to an concentration gradient
J = e(munN+mupP)E + eDndn/dx - eDp*dp/dx
Drift current density
Inbalance in +k and -k = net momentum
J = Nevc = NemuE = e(munN+mup*P)E
Mobility
Increases with lower m* and longer scattertime
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
Hence electrons have higher mobility
Diffusion current density
J = eDndn/dx
Current follows direction of the holes
D = kbt*Mu/e
IPCE = photon to current efficiency
Generation and recombination
Ambipolar transport
Shine light/change T
Terminology
Generation = the creation of holes/electrons
Recombination = The annihilation of electron/holes
Equilibrium
Gn0=Gp0=Rn0=Rp0
Generation holes/electrons equal --> come in pairs
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
Non-equilibrium
Minority carriers determine the properties
n*p = ni^2 does not hold anymore
Recombination kinetics
Radiative recombination
R = arn(t)p(t) (2nd order)
Low level injection = generation of charge carriers is small compared to the majority carriers. So p0>>dn or n0>>dp
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)
Recombination lifetime
tau-no = 1/arPo
tau-po = 1/arN0
Continuity equation
Diffusion
Generation
Drift
Recombination
Movement of electrons and holes is coupled because an electric field will arise if they are seperated or have different diffusivities = Ambipolar diffussion
Can be made for both holes and electrons
Ambipolar transport equation
Depends only on the minority carrier
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
Because majority carrier has much higher conductivity and can easily adjust
Simplification help solve the problem
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
p-type, d(dn)/dt= -ar(dn(t))*p0 = n(t)/tau-no
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
P-type
Fermi level is above trap energy --> filled trap states
First recombination with excess holes (minority), then majority carrier will instantaniously follow
Fermi level is below trap energy --> empty trap states
First recombination with excess electrons (minority), then majority carrier will follow instantaniously
Low level injection, Et near Ef, Rp = CpNtdp = dp/tp0
Low level injection, Rn = CnNtdn = dn/tn0
Semiconductor device
PN-junction
Basic structure
Zero-applied bias
Reverse applied bias
Electric field
Space-charge width
Energy band diagram
Junction capacitance
One sided junction
Space charge width
Space charge region
Junction between an uniformly doped n-type and p-type material
Built-in potential barrier
Gauss law
Poisson equation
Region near juntion where complete depletion occurs
No carriers are present and drift/diffusion are in equilibrium
Because of diffusion of majority carriers
N-type side becomes positively charged
P-type side becomes negatively charged
dE = p/eta
-d^2(phi)/dx^2 = p/eta
Flat junctions
Constant E if uniformely doped
E = sigma/2eta
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)
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
Electric field
Approx
Uniform
Fully depleted/ionized
Abrupt junction
p-region
n-region
Emax = -eNaxp/eta
Ndxn = Naxp
Always below zero
E = -e(Na)(xp-x)/eta
Potential in n-type region contains built in potentail vbi
Can be used to calculate space charge width = use formula
Depends on doping densities, Vbi and dielectric constant
W = xp + xn
|Emax| = 2 Vbi / W
Increases when applying a potential
Potential is applied such that n-type gets more positive and p-type gets more negative
Replace Vbi with Vbi+Vr in all formulas
Because doping remains the same
Charge that is extra stored when the SCR is increased
C' = eta/W
Can be determined via an (1/C^2) vs iets plot
When the doping densities differ so much that the space charge region is almost at one side. So if Na>>>Nd or Nd>>>Na
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
Diffusive current
Non-idealities
Forward bias recombination current
Reverse bias generation current
Overal diode relation
Concentration mc next to SCR
Increases exponentially with Va
np=np0*exp(eva/kt)
Assumptions
Decreases exp with distance (rec)
g'=0
ss
E = 0 in neutral region
Quasi fermi level splitting is constant in SCR
If assumed no recombination in junction
Current = hole diffusive current + electron diffusive current
Ideal diode equation
Determined using ambipolar transport equation
E- field neutral region
Gradient of concentration profile next to SCR (xn,-xp)
J = Js * (exp(eva/kt)-1)
Js = reverse bias saturation current density
If Va < 0, -Js is maximum reached
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
Jgen = eniW/2t0
In SCR with n=p=0 there must be generation (via traps)
Derive R
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
J = Jd + Jrec = Js(exp(eVa/nkt)-1)
n = ideality factor between 1-2, 1 at high v, 2 at low v
The SCR decreases for an forward bias until the built in potential is reduced to zero = Voc
Quandrants pn junction diode
2nd
3th
1st
4th
Forward bias, consumes energy = LED
No current
Reverse bias, negative current, Photo diode
Forward bias, negative current, pv quadrant
Open potential < Vbi (entropic terms)
Metal-semiconductor junction
Semiconductor heterojunction
Metal SC ohmic contact
Schottsky barrier diode
General
When
At high V, the chance of recombination is much higher
Metal contacts are needed for charge extraction
Properties
Ideal juction
Non-ideal junction
Current-voltage relationship
Schottsky barrier loading
Interface states
When
Ef,p-type < Ef, metal
Metal gets into contact with semiconductor
Ef, n-type < Ef, metal
Ef, p-type > Ef, metal
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)
Nomenclature
X
Work function
From fermi-level metal to vacuum
From vacuum level to CB
Phim
Phis
Electron affinity
Ef, n-type > Ef, metal
For n-type there is a flow of electrons towards the metal
Schottsky barier
Phib0 = (Ec-Ef,m)/e = phim - X
Built-in potential
Vbi = Phib0 - (Ec -Ef,s)/e = Phib0 - phin
So difference CB to metal en CB in neutral SC
Difference fermi level metal and energy CB to metal
Vacuum level goes up in the SC
Remains the same, independent of applied bias
Is functioin of applied bias
Width SCR SC
Same as for an one sided juntion
The experimental Phibn can differ from the theoretical Phib0
Polarisation can occur that lowers the energy of electrons close to the metal --> barrier gets lower energy
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
Flux depends on direction electrons, velocity, energy states, fermi dirac
J = Js(exp(eVa/kt)
The flux of electrons that have enough energy (Ec') to move to the metal
Js = A T^2*exp(-eVa/kt)
A = Richardson constant for thermionic emission
Barrier is now (Ec-Ef)
Favourable to have no resistance from electrons/holes flowing when positive voltage is applied
Solar cells
Thin films
Perovskite + Organic
1st generation(Si)
High efficiency Concepts + QDs
More rec = lower Voc
Watch out, use constants with cm
Behave via the rules of ohms law
General
Formula's get more complex because have not the same properties
Types
2 Bandgap partially in each other (energy allignment)
3 Bandgaps have no overlap (rare)
1 Bandgap inside the other (no charge T)
Junction between two different SC materials
Band diagram
Naming
Nn
n-n juntion are also now possible
Larger bandgap is denoted with capital letter
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
Fabrication silicon
Production solar cell
Solar cell efficiency
Properties absorber layer
Light absorption
Charge separation
Charge extraction
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
During illumination, E-field pn junction will extract electrons to n-type and holes to p=type
Diffusive current at junction counteracts this = unfavourable
Long diffusion distances
lifetime
High mobilities
use electron minority
Better at low doping
Reduce trap states
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 = ImVm/Pin = JscVoc*FF/Pin
Fill factor = ImVm/IscVoc
Solar cell has power point tracking to extract as much power as possible. Power point can change depending on conditions (varies the external resistance)
Crystallinity silicon
Process
Series resistance should be as low as possilbe and shunt as high as possible --> can be optimized using fingers and bushbars
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)
Single (10 cm)
Multi (most used)
Poly (to much defects)
Higher crystallinity is more expensive but results in less grain boundaries
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
Good efficiency but more costly production method
Cheap but lower efficiency
Amorphous silicon
Polycrystalline
CI(G)S
Properties
Fermi levels are equal
Fermi levels not equal anymore
Thinner layers, less material needed
More defects, lower diffusion length
Stronger absorption (direct bandgap)
Cheaper production method
Properties
CdTe
'Efficient and cheap'
Economics
Cost per Wp (AM1.5)
BOS
Cost/m2
Lifetime
Grid parity
Cost per kWh
3 um thick
Absorption is stronger --> disordered state relaxes the dk=0 selection rule. In between (in)direct bandgap.
1 um thick
Doping of a-Si
Transport in a-Si
Fabrication of a-Si
Challanges
Diffusion
Drift
Way shorter diffusion length than thickness (low mob/lifetime)
Around same diffusion lengths as thickness
Many defects (dangling bond) 10^16 --> passivate with H (10^15)
Really hard because defect density is so high --> no effect
More efficient in a-Si (1 um)
Much shorter than thickness
Ld = muEtau
p-i-n juntion
Undoped i has very large SCR --> needed for drift extraction
To thick i = dead regions without E
Deposit Si using CVD
Use transparant conducting oxide as contact
Copper, indium, gallium, selenide
Toxicity of Cd
Price of Te
Defects at suface and grain boundaries
II-VI semiconductor with bandgap close to SQ limit
Has high defect density, treat with CdCl2 to go to 22% efficiency
Less toxic and has good bangap tunability
Perovskite solar cell
Organic solar cells
SC properties
Cell designs
Structure and composition
Tandem cells
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
Halide
Metal
Eg, Cs>MA>FA
Eg, Cl>Br>I
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
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
n-i-p configuration
p-i-n configuration
Transport layers should have large bandgaps and allign with the VB and CB
Four terminal tandem cell (seperate)
Two terminal tandem cell (needs current matching)
Fermi level splitting denotes Voc
Present developments
Configuration
Charge extraction
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
Excition diffusives towards junction that seperates electron from hole using E-field
Diffusion length is very small --> need many interfaces inside material
TCO
Bulk heterojunction
Metal contact
Mixture of polymer and electron acceptor
Both have 3d structure to move hole/electron to contact with electronic hopping
Efficiencies over 10% and is cheap,flexible and easy to process
Optimize energy levels to reduce energy losses
Enhance charge transport
Reduce bandgap close to 1000 nm
Limitations of conversion
Quantum dots
Thermodynamic maximum efficiency
Methods to break SQ
Solid angle
Limit = Carnot efficiency = 1 - Tcold/Thot
Emitting and absorption of solar cell (use J=sigmaT^4)
Maximum ideal solar cell
1 sun
Maximum concentrated
Thermalisation (goes to CB +3KT^, in 10^-12s)
Fermi level splitting (thermo)
Absorbed efficiency
Maximum power point (FF)
SQ only assumes radiative recombination +AM1.5
Proven
Concentrator cells
Tandem and multijunction solar cells
Difficulties
Advantages
Difficulties
Advantages
More theoretical
Intermediate band solar cells
Upconversion
Downconversion
Concept solar cells
Carrier multiplication
SC behaviour
Colloidal SC nanocrystals
Bandgap
Difficulties
Part of sunlight seen by earth = A/r^2 (steradian)
This can be increases using a lense up to max 46200 times
Solar cell cannot use energy that it emmits
= etacar times etaemm
67% (with tandem)
86%
Absorb hole spectrum, no thermilisation
Absorb more light
More energy use of absorbed light
Expensive
Lattice matching
Current matching (monolithic)
Max = 44% for two junctions
No contacts in between
Lowest current limits whole cell
Depends on light spectrum
Use alloying to steer lattice size
Otherwise many dangling bonds
Uses tunnel junctions
High dopant conc --> small SCR --> tunneling possible for electrons to recombine with holes in next layer
Higher efficiency
Less area solar cell needed
Voc increases (high IL)
FF increases = 1 - KT/Voc
Efficiency drops with temperature
High current means large voltage drop
Create energy band with electrons in the middle such that low energy photons are absorbed. But also lead to more recombination
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.
To high photon energies are converted to two lower energy
Apply on surface SC but problems that created phons go up and down.
Depends on size crystals
Can be related to particle in the box = discrete energy levels
Enp = Eg + quantum confinement term + coulombic term
Tandem solar cell
Due to discrete energy levels, phonon creation is decreases, less thermilisation
Using different size PbS quantum dots
Hot carriers
Not yet made into solar cell
Energy of thermilisation of two created charge carriers excites electron to CB
Stronger effect in smaller QD
Quantum dots have large surface area and thus problems with surface recombination
Extract hot carriers in quantum dots by using extration far above CB