Volume 1 photovoltaic solar energy 1 25 – downconversion

1.25

Downconversion

MJY Tayebjee and TW Schmidt, The University of Sydney, Sydney, NSW, Australia
G Conibeer, University of New South Wales, Sydney, NSW, Australia
© 2012 Elsevier Ltd. All rights reserved.

1.25.1
1.25.2
1.25.3
1.25.3.1
1.25.3.2
1.25.3.3
1.25.4
References

Introduction
Equivalent Circuits
Practical Applications
QC in Rare-Earth Materials
MEG in Semiconductor Nanostructures
SF in Organic Materials
Prospects

Glossary
Carrier multiplication The generation of two low-energy
charge carriers from one high-energy charge carrier.
Downconversion The conversion of a high-energy photon
into two or more low-energy photons.
Downconverter A device capable of downconversion.

Exciton fission A general term for the generation of two
or more low-energy excitons from one high-energy
exciton.

549
550
554
555
557
559
560
560

Multiple exciton generation Exciton fission within a
semiconductor nanostructured system.
Quantum cutting Exciton fission within a rare-earth ion.
Shockley–Queisser limit The limiting energy conversion
efficiency of a single threshold solar cell under one sun.
Singlet fission Exciton fission within an organic
molecular system. The initial exciton is in a singlet state,
which then undergoes fission into two correlated triplet
states.

1.25.1 Introduction
As explained in Chapter 1.24.2, and in detail in Chapter 1.14, one of the principal efficiency losses of all single threshold
solar cells is that the energy absorbed in excess of the threshold is converted to heat. This mechanism accounts for the
greater part of energy losses in solar cells with lower thresholds such as crystalline silicon. A strategy to counter this loss
mechanism is to absorb photons well in excess of the threshold, and reradiate this energy with two photons at or above
threshold. In this way, the current of the cell is increased with no penalty to operating voltage. This process is known as
downconversion.

In this chapter we will consider the case where a photon with energy greater than an upper threshold, E > Eb, is converted
into two or more photons with energy greater than a lower threshold, E > Er. These photons are optically coupled to a single
threshold solar cell (STSC), allowing for a reduction in the thermalization losses. In practice, this may be achieved via
exciton fission (EF) processes: multiple exciton generation (MEG), singlet fission (SF), or quantum cutting (QC). (We will
adhere to popular definitions. EF will be used a general term for the generation of two or more low energy excitons from
one high energy exciton. The term MEG will be reserved for inorganic semiconductor nanostructures; SF will refer to an
organic molecule in an excited singlet state and a molecule in the ground state evolving into two molecules in lower energy
triplet states; QC will refer to rare-earth ion systems that undergo EF.) In this chapter, we also consider carrier multiplication
(CM), where, instead of multiple photon generation, an absorber directly creates multiple charge carriers from a single
absorbed photon.
Apart from increasing the efficiency of a solar cell, one might wish to protect a solar cell from damaging effects of higher energy
photons. Organic cells are the only current solar technology which are constructed from materials that are abundant enough to scale
up power generation to terawatt scales [1]. They, however, suffer from photostability issues. A downconverter placed at the front of
these devices would play the dual role of increasing the photon flux and reduce degradation due to the absorption of high-energy
photons. Furthermore, compared to tandem devices, which require current matching [2], downconversion and CM solar cells do
not suffer from this restriction.
Before we proceed, be careful to note the difference between downconversion and downshifting. Downconversion does not
conserve exciton number. Downshifting, on the other hand, is a linear process that alters the illumination spectrum such that its
overlap with a device’s incident photon conversion efficiency (IPCE) curve is maximized. In this chapter, we establish the efficiency
limits of downconversion-assisted STSCs and solar cells with absorbers that undergo CM. Different practical approaches, imple­
mentations, and developments within the field will then be discussed.

Comprehensive Renewable Energy, Volume 1

doi:10.1016/B978-0-08-087872-0.00129-3

549


550

Technology

1.25.2 Equivalent Circuits
The details of the efficiency limits of STSCs have been covered briefly in Chapter 1.24.2, and Reference 3. Further details of the
following derivation are given in Reference 4. In keeping with the preceding chapter, we will use the STSC current–voltage


characteristic [5]
I
ðeVc − Er Þ
0
½1Š
¼ kr − kr exp
e
kB T
for a cell operating at a voltage Vc, where e, kB, and T = 300 K are the elementary charge, Boltzmann’s constant, and operating
temperature, respectively. The rate of absorption, kr = kS(Er, ∞, 1), from the highest occupied molecular orbital (HOMO) to the
lowest unoccupied molecular orbital (LUMO), with energy difference Er, is
kS ðE1 ; E2 ; σÞ ¼

σ
hc

hc ð
= E1

λFλ⊙ dλ

½2Š

hc = E2

where σ is the step-function cross section of the absorber and Fλ⊙ is the solar spectrum irradiance in J m−2 nm−1 s−1 at a wavelength λ.
Planck’s constant and the speed of light in a vacuum are denoted h and c, respectively. This rate is countered by the rate of emission
kr′ into a medium with refractive index n, where


ð∞
−ðE − E1 Þ
σn2
kA ðE1 ; n; σ Þ ¼ 2 2 E2 exp
kB T
4π c
E1
"
#





3
σn2
kB T
E1 2
E1
¼ 2 2
þ2
þ2

ħ
kB T
kB T
4π c
2
σn kB T
≈ 2 2 3 E21
½3Š
4π c ħ
The rate of stimulated emission can be ignored given the low irradiance and the fact that Em ≫ kBT [3]. As such, the lower order terms
in E1 can also be omitted.
We will consider three devices and establish their energy conversion efficiency limits. Figure 1 shows their equivalent
circuits and architectures. Device A consists of two photocells with respective band gaps of Er and Eb. The CM process is
provided by a direct current (DC) transformer (Buck converter) that doubles the current and halves the voltage. In practice,
of course, the process would be provided by the absorber within a single photocell. Devices B and C are luminescent
downconverters which have the same equivalent circuits. These are optically coupled to an STSC. The difference arises from
the overall device architecture: B is placed at the rear of the STSC, whereas C is placed at the front. As we shall see, this gives
rise to different absorption spectra.
In A, we must match the outgoing current of the cell, r, with twice the Buck converter’s incoming current:


ðeVc − Er Þ
IA
0
¼ kr − kr exp
e

 kB T

½4Š

2eVc − Eb
0
¼ 2 kb − kb exp
kB T
When considering B and C, the operating voltage of the downconverters, Vd, differs from that of the STSC, Vc. The current passing
through the downconverters is determined by equating the currents passing through each photocell:


IC
ð2eVd − Eb Þ
IB
0
¼
¼ kb − kb exp
e
e
kB T

½5Š
ð2eVd − Er Þ
0
−ðkr þ ðV c Þ=2Þ
¼ kr exp
kB T
The photon flux passing from the STSC to the downconverter is denoted (Vc) and is equally partitioned between the two identical
light-emitting diodes (LEDs). The forms of the downconverted flux, kd, are shown in Table 1 for B and C. The I–V characteristic of
the STSC assisted by luminescent downconversion is given by


ðeVc − Er Þ

Ic
0
½6Š
¼ kc þ kd − kc exp
e
kB T
We are now in a position to calculate the efficiency of each device
Pmax
η ¼ ð∞

Fλ⊙ dλ

0

where Pmax is the maximum power point obtained from IAVc for A and IcVc for B and C.

½7Š


Downconversion

2Vc

551

2Vd
r

Vc

Vc

Vd
r
b

r

b

r
A

B/C

Eb

|3

STSC

Eb

|3

abs

abs

EF

EF

|2

|2

Er

em
abs

abs
|1

|1
A

B/C

‘red’

‘blue’

‘blue’

STSC

‘blue’

‘red’

‘red’

‘red’
b

r
-

+

b

‘red’

-

+

r
A

r
r

‘red’

b

STSC/B

+
r

C/STSC

Figure 1 (Top) The equivalent circuits of A, B, and C. The square component in A represents a DC step-down transformer, such as a Buck converter with
an operating efficiency of 100% that links a higher threshold photocell, b, to a lower threshold photocell, r. The luminescent circuits, B and C, consist of a
high-threshold photocell, b, and two lower threshold LEDs, r, which drive an STSC. (Middle) Generalized energy-level diagram of the three devices. The
labels |1>, |2>, and |3> will be used to describe systems undergoing EF. Absorptive and emissive transitions are, respectively, labeled abs and em.
(Bottom) Schematics of the device architectures.

Table 1

Parameter values for the three devices considered

Parameter

A

B

C

kr

kS(Er, Eb, 1)

0

kS(Er, Eb, 1/2)

kA(Er, 1, 1)

kA(Er, nr, 1/2)

 pffiffiffiffiffiffiffiffiffiffiffiffiffi

kA Er ; 1 þ nr2 ; 1=2

kb

kS(Eb, ∞, 1)

kS(Eb, ∞, 1)

kS(Eb, ∞, 1)

kb′

kA(Eb, 1, 1)

kA(Eb, nr, 1)

 pffiffiffiffiffiffiffiffiffiffiffiffiffi 
kA Eb ; 1 þ nr2 ; 1

kd

2kr′ exp ((eVd – Er)/kBT)

F(2kr′ exp ((eVd – Er)/kBT) + kb′ exp ((2eVd – Eb)/kBT))

kc

kS(Er, Eb, 1)

0

k′c

kA

kA(Er, nr, 1)



Fkc′ exp ((eVc – Er)/kBT)

′

kr



pffiffiffiffiffiffiffiffiffiffiffiffiffi 
Er ; 1 þ nr2 ; 1

kc′ exp ((eVc – Er)/kBT)

Note that an internal refractive index, nr, of 3.6 was chosen for B and C in order to compare with Reference 6. The fraction,
f = nr2/(1 + nr2), denotes the fraction of photon flux that is directed into the device by virtue of its internal refractive index.


552

Technology

(a) 2.8

(b) 2.8
32

32
2.4

Eb /Er

Eb /Er

2.4

2.0
40

44

28

32

36

24

1.6
36
1.2
0.8

2.0

1.0

1.2

1.4

1.6

1.8

1.2
0.8

2.0
(d)

24

28

32

Energy conversion efficiency (%)

2.4

Eb /Er

28

24

1.0

1.2

36
40

1.6

24
1.0

1.4

1.6

1.8

2.0

Band gap (eV)

(c) 2.8

1.2
0.8

32

1.6

Band gap (eV)

2.0

36

40

1.2
1.4
1.6
Band gap (eV)

1.8

2.0

50
45

A

40

B
C

35
30
SQ
25
20
0.8

1.0

1.2

1.4

1.6

1.8

2.0

Band gap (eV)

<16 16 20 24 28 32 36 40 44 >44
Figure 2 Contour plots of the limiting energy conversion efficiencies as a function of band gap and the ratio Eb/Er for (a) A, (b) B, and (c) C under the
AM1.5G spectrum [7]. (d) The maximum energy conversion efficiencies for each device. The SQ is shown for reference.

Figure 2 summarizes the energy conversion efficiencies of devices A, B, and C, under AM1.5G illumination, and their global
maxima (45.9%, 42.9%, and 38.9%, respectively) are shown in Table 2. The three devices have energy conversion efficiency limits that
are significantly greater than the the Shockley–Quesser limit of 33.7% under AM1.5G illumination. In all three cases, the greatest

Table 2
The maximum efficiency for devices operating under 6000 K black
body and AM1.5G illumination

Device
A
B
C
STSC

6000 K black body

AM1.5G [7]

η
(%)

η

(%)

42.6
(39.6)
40.3
(39.6)
37.9
(36.8)
31.1

Eb/Er
1.73
1.93
1.89
-

45.9
(41.9)
42.9
(41.9)
40.5
(38.9)
33.7

Eb/Er
1.72
1.91
1.87
-

In all cases, the optimal values of Er were 1.05 and 0.95 eV, for a device operating under black
body and AM1.5G illumination, respectively. The values for an unassisted STSC are shown for
comparison, with optimal band gaps of 1.30 and 1.34 eV, respectively. The values in
parentheses denote the cases where the restriction Eb/Er = 2.0 has been applied. Again,
nr = 3.6 was used for B and C.


Downconversion

553

conversion efficiency is obtained when the ratio Eb/Er < 2. We can equivalently say that the sum of the enthalpies of the two low-energy
excitons is greater than the enthalpy of the high-energy exciton. As such, the process is endothermic and must be driven by entropy.
This is best understood from a statistical thermodynamic viewpoint. Given a system of N absorbers and the vector p containing
, |2〉
, and |3〉(see middle of Figure 1), the total number of
normalized state occupancies p1, p2, and p3, respectively, for |1〉
microstates in the system is




N
N
N
ΩðpÞ ¼
½8Š
p1 N
p2 N
p3 N

 
n
where the definition of the binomial coefficient,
¼ n!=½k!ðn −kÞ!Š, is used. The EF process involves a change in the number of
k
microstates:
Δf ΩðpÞ ¼ Ωf ðpÞ − Ωi ðpÞ



 



N
N
N
N
N
N
¼
−
p2 N þ 2
p3 N−1
p1 N
p2 N
p3 N
p1 N−1

½9Š

The entropy generated in the EF process is ΔfS = kb ln (Δf Ω):


p1 Np3 NðN − p2 NÞðN − p2 N−1Þ
Δf SðpÞ ¼ kB ln
ðN − p1 N þ 1Þðp2 N þ 1Þðp2 N þ 1ÞðN − p3 N þ 1Þ
As N→ ∞ ; collecting all the terms in N 4 ;


p1 p2 ðp2 −1 Þ 2
¼ kB ln 2
p2 ð1− p1 Þð1− p3 Þ

½10Š

Examining the above equation, we can see that as p1 or p3 approaches unity, the process becomes infinitely entropically
favorable. This is also shown in Figure 3, where the value of ΔfS is plotted on a ternary diagram as a function of p. Horizontal
lines correspond to iso-p2 values, which are symmetric over the occupancies of p1 and p3. EF corresponds to movement vertically up
the diagram. As such, entropy generation is maximized at the point (1/2, 0, 1/2). At the point (1/3, 1/3, 1/3), the EF process is at an
entropic equilibrium (ΔfS = 0). Note that in the devices of interest the very large majority of the carrier population is in |1>, that is,
the bottom right corner of the diagram.
Of course, the component values of p and therefore ΔfS depend on the operating voltage of the device. The voltage of the device
is a measure of the free energy (chemical potential) within each state of the system, thus, under steady-state conditions in A:
1
ZA


1
eVc − Er

p2 ¼
exp
kB T
ZA


1
2eVc − Eb
p3 ¼
exp
kB T
ZA
p1 ¼

0.2

−0.2

½12Š
½13Š

0.8

−0.1

0.6

p2

p3

0.4

½11Š

0.6

0.4
0.0

0.8

0.2
0.1

0.2

0.4

0.6

0.8

p1
Figure 3 Ternary contour plot of TΔfS in eV as a function of p. EF (fusion) corresponds to moving vertically up (down) the plot. Since |TΔfS| → ∞ as any
component of p approaches unity, the vertices of the plot have been truncated. Here T=300 K.


554

Technology

(a) 2.8
2.6

2.4

0.3
0.6

0.0

−0.9

−0.6

0.0

0.3

2.2

0.3

2.0

0.6

1.8

0.9

Eb /Er

Eb /Er

2.6

0.0

2.4
2.2

(b) 2.8

−0.6

1.8

−0.3
−0.6
−0.9

1.2

1.6

2.0

1.6

1.5

1.4

1.4

1.2
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

1.2
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Voltage (eV)

Voltage (eV)

Figure 4 The value of (a) TΔfS and (b) ΔfG in eV as a function of voltage and Eb/Er for A, B, and C, where Er = 1 eV. The white lines from left to right
correspond to the operating voltage (at the maximum power point) of A, C, and B.

The partition function of the entire system is

ZA ¼





2eVc − Eb
eVc − Er
1 þ exp

þ exp
kB T
kB T

½14Š

We can establish similar equations for B and C:
p1 ¼

1
Z



1
eVd − Er
exp
Z
kB T


1
2eVd − Eb
p3 ¼ exp
Z
kB T






eVd − Er
2eVd − Eb
Z ¼ 1 þ exp
þ exp
kB T
kB T
p2 ¼

½15Š
½16Š
½17Š
½18Š

Figure 4 shows the changes in free energy, ΔfG, and entropy, ΔfS, associated with the EF process for A, B, and C as a function of
operating voltage and Eb/Er, where Er = 1 eV. The white lines from right to left show the voltages of A, C, and B when operating at the
maximum power point. We note that the ratio Eb/Er can be lowered without lowering the operating voltage since EF becomes more
entropically favorable. As such, EF is an endothermic process. This effectively means that a greater portion of the solar spectrum can be
absorbed into states that undergo EF, increasing the photocurrent without penalizing the device voltage. This result is clarified in
Figure 4(b), where isoenergetic contours are almost parallel to operating voltages. In practice, this is probably only realizable in
organic chromophores, since endothermic SF has been observed as a dominant relaxation pathway (cf. Section 1.25.3.3).

1.25.3 Practical Applications
A downconverter must be placed in front of a standard cell and can boost current by converting a UV photon to more than one
photon just above the band gap of the solar cell, thus boosting current. However, the downconverter does require that more lower
energy photons are emitted than high-energy photons absorbed, that is, its quantum yield (QY) must be greater than 1. Hence, there
must be at least as many photons emitted at the lower energy as are absorbed at the higher, or else the DC layer will decrease the
number of photons absorbed by the cell. In fact, due to the partial transmission of photons from a low refractive index in air to a
higher one in the DC layer, the QY must be greater than 1 in order not to be parasitic – a QY of about 1 for a refractive index of 3.6 –
similar to that for a Si solar cell [8]. DC devices have been attempted experimentally but so far an overall QY > 1 has not been

achieved, resulting in a downshifting of energies in, for example, Si nanocrystals [9] or porous silicon [10], which nonetheless can
give a useful enhancement in spectral response at short wavelengths for some materials, due to better absorption of the downshifted
photons. This effective narrowing of the bandwidth of the absorbed spectrum allows the solar cell design to be optimized with
respect to absorption coefficient as a function of wavelength, junction depth, and surface recombination [11]. Similarly, lumines­
cent downshifting layers based on luminescent dyes have been demonstrated to boost the short wavelength response of CdTe cells
in which short wavelengths are usually attenuated in the CdS window layer [12]. True downconversion or QC, as first suggested by


Downconversion

555

Dexter [13], requires absorption of a short wavelength photon and reemission of at least two photons of about twice the
wavelength. In turn, this requires an appropriately located intermediate energy halfway between the excited state and the ground
state. Most work has focused on lanthanide materials because of their varied and discrete energy levels.

1.25.3.1

QC in Rare-Earth Materials

The unique properties of rare-earth ions lend themselves to QC applications. A recent review by Zhang and Huang [14] detailed
rare-earth ion QC phosphors, and the development of these systems has largely been inspired by applications in the lighting
industry or in electronic displays. Nevertheless, in light of their rich energy-level structure, the promise of rare-earth ion systems for
use in downconverters has been recognized and remains an active area of research [15].
The spectroscopy of rare-earth ions was discussed briefly in Chapter 1.24.6.1. Radiative electronic transitions in rare-earth ions
are ‘quasi’-atomic due to the tight binding of 4f electrons. Unlike molecular systems, electronic states are denoted by term symbols
of the form 2S+1LJ. Here the spin multiplicity is S = eu/2, where eu is the number of unpaired electrons with the same spin. The total
orbital quantum number L ¼ ∑enu¼1 jmℓ j, where mℓ is the magnetic orbital quantum number of a unpaired electron; in the case of
rare-earth ions mℓ = − 3, − 2, − 1, 0, 1, 2, 3, as the highest energy electrons exist in the 4f orbital. By convention, the value of L is
denoted with a letter (S = 0, P = 1, D = 2, F = 3, G = 4, H = 5, I = 6 …). The total angular momentum quantum number takes values in

the range |L − S| ≤ J ≤ L + S in integer steps, where J = L + S corresponds to the lowest energy state.
There are several possible mechanisms for QC, which have been discussed by Wegh et al. [16], and are summarized in Figure 5.
Rare-earth ions exist as pairs of sensitizers and emitters. The trivalent ytterbium cation (Yb3+) was suggested as an emitter in QC
systems in 1957 by Dexter [13]. This is particularly applicable to solar cells since the Yb3+ $ 1.24 eV 2F5/2 → 2F7/2 transition could be
used in conjunction with a crystalline silicon (Er $ 1.1 eV) STSC. Luminescent QYs greater than unity were actually achieved in a
Tb3+–Yb3+ couple in 2005 [17]. Several other trivalent cationic rare-earth couples have been suggested, and they are summarized in
Figure 6.
Praseodymium (Pr3+) is a good choice because of its widely dispersed energy levels well matched for photon cutting [27] (see
Figure 7). The 3P2, 1I0, and P0 levels at between 440 and 490 nm can absorb blue photons which can then radiatively recombine via
the 1G4 level at 1010 nm – at just greater than twice this wavelength, thus emitting two photons at just above the silicon band gap,
although nonradiative recombination via the other levels at longer wavelengths than 1G4 is also likely. Experiments indicating such
photon cutting have been carried out on Pr3+ embedded in various phosphors [28, 29], and also for other lanthanide-doped
materials [25, 30]. Transition metals with their partially screened ‘d’ shell electrons also have partially discrete levels and work on
photon cutting in transition metal-doped materials has also been carried out [31, 32].
An alternative approach is to absorb a short wavelength photon high up in the conduction band of various semiconductors.
There is then the possibility of an impact ionization event (i.e., reverse Auger recombination) in which the high-energy electron
excites an additional electron to the conduction band, thus creating two or more electron–hole pairs at the band gap energy [32].
Luminescent recombination of these electron–hole pairs is then usually enhanced by choice of an appropriate doping level within
the band gap and an increased number of photons emitted. The QY of such impact ionization depends on the energy of the initial
photon and is reduced by nonradiative thermalization and recombination. QYs greater than 2 have been achieved in some

E

I

II

III

IV

Eb

1

1
2

1

Er
1

1

0
S&E

E

S

E

S

E

S

E

Figure 5 The mechanisms of QC with rare-earth ion sensitizers (S) and emitters (E). Scheme I shows QC within a single ion. II shows a two-step energy
transfer process, where part energy from an excited sensitizer is transferred to an emitter by cross-relaxation. The emitter returns to the ground state
through radiative recombination. The sensitizer then transfers the remainder to a second emitter, which also radiatively returns to the ground state. III and
IV both show QC with only one energy step, that is, the sensitizer also emits one of the lower energy photons. Redrawn and adapted from Wegh RT,
Donker H, Oskam KD, and Meijerink A (1999) Visible quantum cutting in LiGdF4:Eu3+ through downconversion. Science 283(5402): 663–666 [16].


556

Technology

6

1

S0


40


1

D7/2

S

9/2

38


3
6

4

G9/2

36


7/2
5

D4


34


6

5

32

F3

D3

3

P0

2

D5/2
7/2

3

L8
M10


P3/2

3

2

K13/2

3

5/2
7/2

2

P3/2

2

1

0

30


3
4

D1/2

28


F2

5

G3

3

3/2

5

D2

4


2

26


P3/2

D2

2

24


D5/2
2
P1/2

D3

G5
D2
3
G3
5
G4

G

11/2
3/2 9/2

1

P0

5
4

3

1

D2


3
5/2
3

2

16


H11/2
3

F9/2
5

4

S3/2

2

2

K6

1
4

G5/2
0


5

F5

4

F9/2

3

F2
3


6

F1/2
5

7/2

I4


3/2

4

2
1

I9/2

5/2

6

10


S3/2

S2


3/2

1

4

4
5

4


S2

4

5

7/2

F11/2

6

H5/2

G4

9/2

9/2

2

F5/2

11/2

7/2

3

6
7/2

8

3

5

I8

F4

4

I15/2

3

6

3

11/2
6

3/2

H15/2

7

13/2

7
7

13/2

H6


4


11/2

1
2


7


1.1 eV

3

5


11/2

6

13/2

4

4


F7/2

9/2

5

11/2

5


3


5

7/2

0

F0

F6

13/2

2


H5


9/2

5/2

1/2

2

4

2

G4


F7/2

H11/2

1


F5

5/2

12


5/2

3

3


H9/2


F3/2

6


2

F3/2

H4

5

4

14


K7


4

D4

G7/2


4
7/2

G7/2

H9/2

4

5
G11/2 F1

3
K
4
F9/2 82

2

G9/2


2

2

4

2

18


G11/2

5

5

I6

20


G4

3

2

D2


4

5

L8


P2

1

1

9/2

K7

3

3

22


G7/2
2
K15/2

3

5

P0

2

G5


L10
D3


1

2

H6

5

5

3

Energy (×103 cm−1)

P2

I6

3
P
1

1

I

2

1


2

F5/2

3

H4

4

5

Ce

Pr

Nd

Pm

I9/2

I4

H5/2

7

8

7

Sm

Eu

Gd

Tb

6

F0

S

F6

6

H15/2

5

Dy

Ho

I8

4

I15/2

3

Er

Tm

H6

2

F7/2

Yb

Figure 6 Dieke diagram showing the excited-state energies of trivalent rare-earth cations. Excited states that can be used for downconversion are shown
in color: blue and red, respectively, represent the upper and lower excited states involved in QC. We consider rare earth couples where the emitter is Yb3+ in
the 2F7/2 state. To date, this includes coupling with Pr3+ [15, 18, 19], Nd3+ [20], Tb3+ [18, 21, 22], Er3+ [23, 24], or Tm3+ [18] sensitizers. An extension of
this diagram for energies greater than 40 Â 103 cm− 1 has been provided by Wegh et al. [25]. Reproduced and adapted from Dieke GH and Crosswhite HM
(1963) The spectra of the doubly and triply ionized rare earths. Applied Optics 2(7): 675–686 [26].


Downconversion

3

20

P2
1
I0

P0

557

440 nm
490 nm

1

D2

Energy (�103 cm−1)

15

10

1

G4

1010 nm

3
3

5

F4
F3

3

H6

3

H5

0

3

H4
Pr3+

3+

Figure 7 Energy levels for Pr based on data from Reference 27 and extracted detail from Figure 6. Also shown is the possible photon-cutting
mechanism for a photon absorbed around 450 nm and emitted as two photons via the 1G4 level.

materials, usually based on wide band gap oxides (at least 5 eV) doped with lanthanide or transition metal atoms, but with incident
photon energies of at least twice or thrice the band gap [30, 31]. QYs up to about 1.20–1.40 have also been achieved with the
relatively narrow gap (3.4 eV) ZnS doped with Zn, Cu, or Ag, but only with photons in excess of 20 eV [32].
However, at the incident photon energies required for this impact ionization, there are almost no photons in the solar spectrum.
Also, the efficiency of the impact ionization mechanism is very low. Hence, these are not good materials for downconversion for
solar cells. But, in some materials based on quantum dot (QD) arrays, this efficiency can be increased dramatically such that several
excitons can be generated from one incident high-energy photon.

1.25.3.2

MEG in Semiconductor Nanostructures

MEG is a process whereby a high-energy electron–hole pair in a nanostructured inorganic semiconductor undergoes impact
ionization, yielding two lower energy excitons (see Figure 8). Quantum confinement is a key concept for EF, since bulk
semiconductors usually require Eb/Er = 4 – 6 due to (1) the conservation of carrier momentum and (2) extremely short hot carrier
lifetimes as a result of rapid electron–phonon interactions [33–36]. Nanostructured materials, on the other hand, lend themselves
to EF because
•
•
•
•

electron–hole pairs are correlated, giving rise to excitons rather than free carriers [2];
exciton cooling is slowed due to the discretization of electronic states [37];
momentum is no longer a good quantum number, and thus does not need to be conserved [37]; and
Auger processes (such as EF) are enhanced due to the increased Coulomb interaction between electrons and holes [2]

In the previous section, we suggested that EF could proceed even if Eb/Er < 2. However, theoretical calculations of PbSe, CdSe, and
InAs structures with quantum confinement suggest that MEG will only be appreciably observed when Eb/Er ≥ 2.2 [38, 39]. In
practice, time-resolved spectroscopy of lead sulfide, selenide, and telluride QDs has shown MEG thresholds in the range
Eb/Er = 2.7–3.0 [40–43]. More precisely, the efficiency of MEG has been defined in terms of the QY at a given photon energy, hν [44]:

QY ¼


hv
−1 ηEHPM
Er

½19Š


558

Technology

E

Eb

MEG

Er

0
Figure 8 The creation of two excitons via MEG. MEG will occur in QD systems, where a band structure describes electronic states. Closed and open
circles represent electrons in the conduction band and holes in the valence band, respectively.

Table 3
The MEG efficiency for a number of bulk QD
and single-walled carbon nanotube (SWCNT) samples, as
analyzed by Beard [45]
Sample

ηEHPM

References

Bulk Ge

Bulk Si
Bulk PbSe
Bulk PbS
PbSe QDs
InP QDs
SWCNTs

0.3
0.4
0.2
0.3
0.4
0.9
0.7

[46]
[47]
[48]
[48]
[49, 50]
[51]
[52]

The quantity ηEHPM is the electron–hole pair multiplication efficiency and is defined as the minimum energy required to produce an
electron–hole pair, divided by the actual energy required. Very recently, Beard [45] quantified ηEHPM for a number of experimental
results, which are tabulated in Table 3. Much higher values are obtained in confined structures, suggesting that quantum
confinement is indeed a promising method for the promotion of EF. It should be noted, however, that there is still significant
disagreement among researchers about the QY that can be obtained from such systems. For instance, some report a QY ≫ 1 in PbS
and PbSe, while other investigations suggest that QY < 1.25 (see Reference 44 and references therein). These differences have chiefly
been attributed to surface effects or charge delocalization, and a better understanding of these will stimulate further research into the

field [45].
For a MEG material to be used directly as a DC with an STSC, a few conditions are required. The MEG QDs would need to have
an appropriate band gap to illuminate a solar cell – for a Si STSC, Si QDs would be appropriate, and MEG has been shown in
well-passivated Si QDs [41]. But, much more challenging would be the need for a high luminescent efficiency of the multiple
excitons such that there would be a net QY greater than unity. However, it is not yet clear whether such a luminescent efficiency from
these materials is feasible. The currently observable rate of MEG and subsequent Auger decay processes back to a single exciton at
about 200 ps [41, 45], and the long radiative lifetimes of these materials, at about 10 ns, would make efficient multiple photon
emission unlikely.
An alternative approach is to directly incorporate the MEG QDs in a solar cell in order to boost the current in the device
through direct CM. Several attempts have been made to do this, which until recently have not successfully shown an increase in
current. However, very recent results have shown a PbSe QD solar cell device with QYs greater than 1 for 3.5 eV illumination
[53]. This very significant result demonstrates the feasibility of the approach and further significant improvement is likely to
follow.


Downconversion

1.25.3.3

559

SF in Organic Materials

SF can occur in molecular crystals, thin films, aggregates, dimers, or polymers. An excited single-state organic chromophore
undergoes fission with a nearby chromophore in the ground state giving rise to two triplet chromophores, as shown in Figure 9.
These triplets may either undergo phosphorescence or spatial separation and be directly injected into the external circuit. A key
advantage of using molecular systems is that triplet states are generally long lived due to the spin-forbidden transition to the ground
singlet state. It is important to note, however, that the SF process does not violate spin conservation: the two triplets produced will
be correlated such that their tensor product is a singlet state.
Since phosphorence is a slow spin-forbidden transition, these organic molecules are more suited to CM than downconversion

since the yields would be too low. Alternatively, the system could be altered by the addition of a highly phosphorescent species, as
shown in Figure 10. Sensitizers that undergo SF transfer their excited state energy to emitter molecules via triplet energy transfer
(TET). In practice, the TET process would be exothermic; however, entropy could also be exploited by having a large emitter­
to-sensitizer ratio. Unfortunately, to date, phosphorescent yields have not exceeded 50% - any gain from SF would be squandered.
SF first appeared in peer-reviewed literature in 1965, when Singh and coworkers [54] suggested that it occurred in anthracene.
Further evidence of SF in other polyacene structures, including anthracene [55, 56], tetracene [56–61], and pentacene [59, 62–65],
has also been shown. Investigations into other conjugated oligomer and polymer systems have also shown evidence of SF (see, for
instance, the review by Smith and Michl [66]). Examining the body of literature, SF was initially avidly studied in the 1970s, before
interest lapsed. We have experienced renewed interest over the last decade in light of the development of novel, efficient,
photovoltaic devices.
Many authors have introduced their studies with the requirements for efficient SF, and invariably state the restriction Eb ≥ 2Er, in
spite of some of the earliest observations of SF occurring in systems where this was not the case (for instance, SF in anthracene is
highly endothermic [55]). The fact that SF is nevertheless a dominant relaxation process cannot be explained by thermal activation
alone. A far more viable explanation is that entropy is acting as a driving force for the process, and the simple derivation given in
Chapter 1.25.2 displays this. Very recently, Jadhav and coworkers [67] have demonstrated a working solar cell containing the singlet
fissile organic compound, tetracene (Tc). The Tc/copper phtalocyanine/C60 device displays SF with an efficiency of 71 Æ 18%.

E
Eb

S1

S1
1

Er

2

T1

T1
2

0

S0

S0

Figure 9 The creation of two excitons via SF. SF proceeds in molecular systems where electronic states are described by molecular orbitals. The first
process (1) represents the absorption transition S1 ← S0, and the second (2) represents SF.

E
S1

Eb

S1

1

2

T1
Er

T1

3

4

0

T1

S0

2

3

3
S0

Emitter

T1

3
4

S0
Sensitizers

S0
Emitter

Figure 10 SF within sensitizer molecules, followed by phosphorescence of emitter molecules. The first process (1) represents the absorption transition
S1 ← S0, and the second (2) represents SF. Process (3) is TET which leaves emitters in an excited triplet state from which they return to the ground state

by phosphorescing (4).


560

Technology

While there is an extremely wide body of experimental studies with evidence of SF in organic materials, a fundamental and
universal understanding of the mechanism is still an active area of research. In their review, Smith and Michl [66] presented
quantum mechanical formalisms for SF by direct coupling and through a charge transfer state. Greyson et al. [68, 69] proposed SF
mechanisms using density matrix theory and density functional theory. Zimmerman et al. [70] used ab initio molecular orbital
calculations to show that SF proceeds in pentacene via a dark state.

1.25.4 Prospects
Chapter 1.24 dealt with the prospects of upconversion. One of the major obstacles for the realization of a working upconverter is the
fact that it is an unfavourable process from an entropic standpoint. An enthalpic sacrifice is required in order for upconversion to be
exergonic. By contrast, downconversion and carrier multiplication involves the creation of two (quasi-) particles from one (quasi-)
particle: an entropically favourable process. That is, an exergonic reaction proceeds even where there is a gain in enthalpy. Therefore
downconversion may prove to be more effective than upconversion at circumventing the energy conversion efficiency limits
associated with conventional photovoltaic devices.
A further advantage of a luminescent downconverter is that it can be added to the front face of existing photovoltaic installations.
This is especially advantageous when they are used to enhance an organic device as these often suffer from degradation due to
photo-activated reactions with high energy photons. A luminescent downconverter can play the dual role of decreasing the number
of such photons, while increasing the photon number, and therefore the current of the device. While downconversion technology is
still currently in its infancy, the sheer extent of research can allow us to be optimistic about the realization of these devices in the near
future.

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