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High quantum yields generated by a multi-band quantum dot photocell
Journal Pre-proof High quantum yields generated by a multi-band quantum dot photocell Shun-Cai Zhao, Qi-Xuan Wu
PII: DOI: Reference:
S0749-6036(19)31010-9 https://doi.org/10.1016/j.spmi.2019.106329 YSPMI 106329
To appear in:
Superlattices and Microstructures
Received date : 6 June 2019 Accepted date : 31 October 2019 Please cite this article as: S.-C. Zhao and Q.-X. Wu, High quantum yields generated by a multi-band quantum dot photocell, Superlattices and Microstructures (2019), doi: https://doi.org/10.1016/j.spmi.2019.106329. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
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Shun-Cai Zhao
a1
ro o f
High quantum yields generated by a multi-band quantum dot photocell , Qi-Xuan Wub
a
e-p
Department of Physics, Faculty of Science, Kunming University of Science and Technology, Kunming, 650500, PR China; b College English department, Faculty of foreign languages and culture, Kunming University of Science and Technology, Kunming, 650500, PR China
Abstract
We perform the quantum yields in a multi-band quantum dot (QD) photocell via doping an intermediate band (IB) between the conduction band (CB) and
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valence band (VB). Under two different sub-band gap layouts, the output power has a prominent enhancement than the single-band gap photocell and the achieved peak photo-to-charge efficiency reaches to 74.9% as compared to the limit efficiency of 63.2% via the IB approach in the theoretical solar cell prototype. The achieved quantum yields reveal the potential to improve
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efficiency by some effective theoretical approaches in the QD-IB photocell. Keywords: Quantum yields, photo-to-charge efficiency, a multi-band
1
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quantum dot photocell 1. Introduction
Recently, the quantum photovoltaic system has attracted extensive atten-
3
tion because it is believed that its yield can be enhanced via some quantum
4
mechanism[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. In the seminal work[1], it shows that
5
the photocell power can achieve a substantial enhancement via the coherence
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1
Corresponding E-mail: [email protected].
Preprint submitted to Superlattices and Microstructures
June 6, 2019
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induced by the driving field, even if the actual photo-to-charge efficiency of
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the photocell was not calculated. However, another mechanism of coherence
8
without an external source, the noise-induced coherence or Fano-induced co-
9
herence can yield the enhancement of power in recent papers[2, 3], in which
10
the detailed balance[12] was broken and the photocell power delivered to the
11
load was increased.
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As it is well known, two major factors limit the quantum yield of the solar
13
cell prototype. One is losing excess kinetic energy of photo-generated carriers
14
as multiple phonon emission due to the absorption of photons with the energy
15
greater than the energy gap between the conduction and valence bands[13].
16
The second one is the loss of photons with energy lower than the band gap.
17
These result in the Shockley-Quiesser detailed balance limit and the energy
18
conversion efficiency is found[12] to be about 33%. Due to their quantum
19
confinement in three dimensions resulting in the tunable size and accordingly
20
tunable band gap, QDs are playing a vital role in the solar cells domain and
21
have achieved a considerable attention in the recent decades[14, 15, 16, 17,
22
18, 19]. Not only that, but QDs have the great potential to significantly
23
increase the photo-to-charge efficiency via the formation of IBs in the band
24
gap of the background semiconductor, which can absorb photons with energy
25
below the semiconductor band gap through transitions from the VB to the IB
26
and from the IB to the CB [20, 21, 22, 23, 24, 25, 26, 27, 28, 29]. In the QD-
27
IB solar cell approach, the limiting efficiency of 47% at 1 sun, 63.2% at full
28
solar concentration[23] were achieved, which exceeds the previous maximum
29
33% efficiency proposed by Shockley and Queisser in 1961[12].
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30
In this paper, we have theoretically calculated the quantum yields en-
31
hancement of the QD-IB photocell with an intermediate level. This QD-IB
32
photocell can be introduced by the doping technology, and its prototype comes from the seminal quantum photovoltaic system[1]. It is proven that
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the output power has a prominent enhancement in this QD-IB photocell as
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compared to the single gap QD photocell[1, 2, 3, 4, 5]. And the quantum
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peak photo-to-charge efficiency comes to 74.9%, which also exceeding 63.2%
37
mentioned in Ref.[23] is confirmed.
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In order to clarify our work, this paper is organized as follows: we describe
39
the quantum dot photocell model with an IB and deduce the power and
40
photo-to-charge efficiency generated by this photocell model in Sec.2. And
41
the power and photo-to-charge efficiency are evaluate by two different sub-
42
band gap layouts with different parameters in Sec.3. Sec.4 our conclusions
43
and outlook are presented.
44
2. Quantum dot photocell model with an intermediate band
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The proposed QD-IB photocell model can be generated by the doping
46
IB |c3 ⟩ via the doping technology in the theoretical prototype mentioned in
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45
47
Ref.[1]. Therefore, the band gap between the CB and the VB was divided
48
into two sub-bands, i.e., the upper sub-band gap Ei3(i=1,2) and the lower
49
sub-band gap E3b . And the doublet CBs |c1 ⟩ and |c2 ⟩ may be produced
by splitting of two degenerate QD levels due to electron tunneling between
51
two adjacent dots [see Fig. 1(a)]. The subdivided energy gaps can absorb
52
the solar photons with energy below the semiconductor band gap shown
53
in Fig. 1(a). Then, due to the IB |c3 ⟩, photons with energy below the
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50
band gap can be absorbed to excite electrons from the VB to the IB and
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from the IB to CB. Fig. 1(b) is the corresponding energy levels diagram for
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the QD photocell model, in which the two upper levels |c1 ⟩, |c2 ⟩ depict the
57
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CBs and level |b⟩ is on behalf of the VB, and the level |c3 ⟩ is interpreted as the IB. When the electronic system interacts with radiation and phonon
59
thermal reservoirs, the thermal solar photons with frequency midway between
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ωi3 (i = 1, 2) and ω3b are assumed to directing onto the cell. They drive |c1,2 ⟩
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61 62
↔ |c3 ⟩ and |c3 ⟩↔ |b⟩ transitions and have average occupation number n1 = [exp( kEBi3Ts ) − 1]−1 and n3 = [exp( kEB3bTs ) − 1]−1 , where Ei3 = (E13 + E23 )/2, Ts 3
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is the solar temperature. The ambient thermal phonons at temperature Ta
64
drive the low-energy transitions |c⟩ ↔ |c1 ⟩, |c⟩ ↔ |c2 ⟩, and |v⟩ ↔ |b⟩. Their
65 66
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corresponding phonon occupation numbers are n2 = [exp( kEB12Ta ) − 1]−1 and n4 = [exp( kEBvbTa ) − 1]−1 , where E12 = (E1c + E2c )/2.
Èc2\
Èc1\
æ
ë ë
Èc1\ Èc2\
Μc
~
~ Γ1
Γ1
Γ2
Γ2
ÑΝsi
e-p
æ
Èc\
Èc3\
Èc3\ ÑΝs j
Γ3
ë
æ
Μv
Èb\
G
j
ΛG Èv\ ~
G
(b)
Pr
(a)
Figure 1: (color online) (a) Quantum dots having two upper level conduction band states, |c1 ⟩and |c2 ⟩. The two different monochromatic solar photons(νsi , νsj ) are tuned to the midpoint between the two upper levels and intermediate band |c3 ⟩, the intermediate band
|c3 ⟩ and level |b⟩ in the valence band. The host semiconductor system, in which the
quantum dots are embedded, has effective Fermi energies µc and µv for the conduction and
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valence bands. (b) Corresponding energy levels diagram of this QD-IB photocell model. Solar radiation drives transitions between the ground state |b⟩ and the intermediate band
|c3 ⟩, the intermediate band |c3 ⟩ and two upper levels |c1 ⟩, |c2 ⟩. Transitions |c1 ⟩, |c2 ⟩ and
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|v⟩, |v⟩ and |b⟩ are driven by ambient thermal phonons. Levels |c⟩ and v⟩ are connected to a load.
The interaction Hamiltonian in the rotating-wave approximation for the
68
electronic system interacting with radiation and phonon thermal reservoirs
69
is given as follows,
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∑
∑
gi [ei(ω13 −νi )t σ ˆ13 + ei(ω23 −νi )t σ ˆ23 ]ˆ ai +
i
go [e
i(ω1c −νo )t
σ ˆ1c + e
i(ω2c −νo )t
σ ˆ2c ]ˆbo +
o
70
∑
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Vˆ (t) = ~{
∑ p
gj ei(ω3b −νj )t σ ˆ3b a ˆj +
j
gp ei(ωbv −νp )t σ ˆbvˆbp } + h.c. (1)
where gi,j,o,p are the coupling constants for the corresponding transition,
73
tors and phonon annihilation operators, respectively. σ ˆij (ˆ σji ) is the Pauli rise
74
or fall operator. The equation of motion for the electronic density operator
75
ρ reads ⊗
∫t
Pr
ρ(t) ˙ = − ~i T rR [Vˆ (t), ρ(t0 )
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~ωij = Ei − Ej is the energy spacing between levels |i⟩ and |j⟩. νi is the photon or phonon frequency, and a ˆi,j , ˆbo,p are the photon annihilation opera-
71
ρR (t0 ] −
1 T rR ~2
t0
[Vˆ (t), [Vˆ (t′ ), ρ(t′ )
⊗
ρR (t0 ]]dt′(2) ,
where the density operator ρR describes the phonon thermal reservoirs. In
77
the Weisskopf-Wigner approximation, we assume that the levels |c1 ⟩ and |c2 ⟩
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are degenerate and obtain the following master equations,
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ρ˙11 = −γ1 [(1 + n1 )ρ11 − n1 ρ33 ] − γ˜1 [(1 + n2 )ρ11 − n2 ρ33 ] + γ12 (1 + n1 )Re[ρ12 ] − γ˜12 (1 + n2 )Re[ρ22 ],
ρ˙22 = −γ2 [(1 + n12 )ρ22 − n1 ρ33 ] − γ˜2 [(1 + n2 )ρ22 − n2 ρ33 ] +
e-p
γ12 (1 + n1 )Re[ρ12 ] − γ˜12 (1 + n2 )Re[ρ22 ], 1 ρ˙12 = − [(γ1 + γ2 )(1 + n1 ) + (˜ γ1 + γ˜2 )(1 + n2 )]ρ12 2 1 − γ12 [(1 + n1 )ρ11 + (n1 + 1)ρ22 − 2n1 ρ33 ] 2 1 − γ˜12 [(1 + n2 )ρ11 (1 + n2 )ρ22 − 2n2 ρ33 ] − τ12 ρ12 , 2 ρ˙33 = −γ3 [(1 + n3 )ρ33 − n3 ρbb ] − (γ1 + γ2 )n1 ρ33 + γ1 (1 + n1 )ρ11 +γ2 (1 + n1 )ρ22 + 2γ12 (1 + n1 )Re[ρ12 ],
(3)
Pr
ρ˙cc = γ˜1 [(1 + n2 )ρ11 − n2 ρcc ] + γ˜2 [(1 + n2 )ρ22 − n2 ρcc ] + 2˜ γ12 (1 + n2 )Re[ρ12 ] − Γ(1 + λ)ρcc ,
˜ 4 ρbb − (1 + n4 )ρcc , ρvv ˙ = Γρcc + Γn
81 82 83
decay rates of the corresponding transitions [see Fig.1(b)]. For maximum √ √ Fano coherence, γ12 = γ1 γ2 , γ˜12 = γ˜1 γ˜2 , while γ12 = γ˜12 =0 for no interfer-
al
80
where γi and γ˜i are modeled the electrons’ decaying process as spontaneous
ence. In this model, levels |c⟩ and |v⟩ are connected to a load, and the load is
yielding a decay of the level |c⟩ into level |v⟩ at a rate Γ. The recombination
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79
84
between the acceptor and the donor is modeled by a decay rate of λΓ [also see
85
Fig. 1(b)], where λ is a dimensionless fraction, τ12 is the decoherence time.
86
And we focus on steady-state operation of the photocell model, voltage V
87
across the load is expressed in terms of populations of the levels |c⟩ and |v⟩ as[1, 2, 3]
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eV = Ec − Ev + kB Ta ln( 6
ρcc ). ρvv
(4)
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where Ta is the ambient temperature circumstance. The current j through
90
the cell is interpreted as j = eΓρcc and power delivered to the load is P =
91
jV which is supplied by the incident solar radiation power Ps [1, 2], and their
92
ratio describes the photo-to-charge efficiency of this QD-IB photocell.
93
3. Power and photo-to-charge efficiency
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The photocell power enhanced by the noise-induced or Fano-induced co-
95
herence has been investigated detailedly by the former work[2, 6]. In the
96
following, we abnegate the discussion on the output power influenced by the
97
coherence, while turn to discuss the quantum power and photo-to-charge
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100
between this QD-IB photocell model and the QD photocell theoretical proto-
101
type in Ref.[1] is the introduced IB. Therefore, the roles of different sub-band
102
gaps in the quantum yield will attract much attention.
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conversion efficiency under the condition with the maximum coherence in√ √ terference, γ12 = γ1 γ2 , γ˜12 = γ˜1 γ˜2 . And in present paper, the difference
98
With the stationary solutions to the master equations(3), we explore
104
the power and photo-to-charge efficiency through the numerical calculations.
105
And several typical parameters should be selected before the calculation. The
106
energy gaps E1c =E2c =Evb =0.005ev, Ecv =1.49ev, Ta =0.0259ev, Ts =0.5ev[1].
108 109
And other parameters are scaled by γ: γ1 =1.2γ, γ2 =0.8γ, γ3 =1.5γ, γ e1 =1.05γ, γ e2 =1.15γ, Γ1 =1.25γ, Γ2 =1.35γ. The dimensionless fraction is set as λ=0.2.
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103
The Shockley and Queisser efficiency [12] is accessible in semiconductors with
band gaps ranging from about 1.25 ev to 1.45 ev. However, the solar spec-
111
trum contains photons with energies ranging from about 0.5 eV to 3.5 eV.
112
Photons with energies ranging from about 0.5 ev to 1.25 ev is not absorbed
113
and photons with energies within [1.45ev, 3.5ev] can incur the thermalization
114
loss in the Shockley and Queisser efficiency. Therefore, the lower sub-band
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110
115
gap (E3b ) simulated as the solar spectrum ranging from 0.5 ev to 3.5 ev will
116
be discussed in Fig.2, while the upper sub-band gap(Ei3(i=1,2) ) between the 7
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0.55
E13 =E23 =0.45ev
70
70
E13 =E23 =0.65ev 60
E13 =E23 =1.05ev Photon-to-charge efficiency H%L
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E13 =E23 =1.25ev E13 =E23 =1.45ev
P HevL Γ
0.45
0.42 0.40
0.40
0.38 0.36 0.35
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E13 =E23 =0.85ev 0.50
0.34
50 40
50
30
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 E13 =E23 =0.45ev
40
E13 =E23 =0.65ev E13 =E23 =0.85ev E13 =E23 =1.05ev
30
E13 =E23 =1.25ev
0.32
E13 =E23 =1.45ev
0.30
(a) 0.5
1.0
0.28 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.5 2.0 2.5 Sub-band gap E3 bHevL
3.0
20
(b)
e-p
0.30
3.5
0.5
1.0
1.5 2.0 2.5 Sub-band gap E3 bHevL
3.0
3.5
Figure 2: (Color online) Power P and photo-to-charge efficiency generated by the QDIB photocell versus the lower sub-band gaps(E3b ) for different upper sub-band gaps
Pr
(Ei3(i=1,2) ).
117
CB and IB will select values from the range of [0.45 ev, 1.45 ev] with the
118
output voltage being 1.5 volts in Fig.2 (And the data for Fig.2 are in the SI
119
Word).
Figs.2 (a) and (b) show the output power and photo-to-charge efficiency
121
across the load as a function of the lower sub-band gap E3b , and the insert
122
diagrams depict the output power and photo-to-charge efficiency when the
123
lower sub-band gap E3b absorbs the solar photons within the range of [0.5ev,
124
1.25ev], whose energy is below the band gaps mentioned in the Shockley and
125
Queisser efficiency[12]. Fig.2 (a) shows an enhancement power as compared
126
to the single-band gap photocell[2, 6], and shows a steep rise for the output
127
power about in the range [0.5ev, 2.5ev] while its growth is slowing down
128
within the range [2.5ev, 3.5ev]. The insert diagram in Fig.2 (a) displays the
129
enhanced power by increasing the lower sub-band gaps(E3b ) within [0.5ev,
130
1.25ev]. The enhanced power demonstrates that photons with energy below
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the band gap can contribute to the cell photocurrent on account of the IB.
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Owing to the IB isolation from the VB with a zero density of states, the
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carrier relaxation to the VB become difficult and more electrons are stored
134
in the IB[28]. However, the increasing carriers form the delocalized state in
135
the IB and increase their density of states until their wave functions overlap
136
each other and facilitate Mott transition[30]. This process brings out the
137
smooth solid lines within the range [2.5ev, 3.5ev] in Fig.2 (a). What’s more,
138
the much higher energy photons within the range [2.5ev, 3.5ev] produce much
139
more thermal phonons which also decreases the growth of the output power.
140
However, the upper sub-band gap E13 =E23 display an opposite evolutionary
141
behavior when it absorbs the solar photons with energies ranging from 0.5
142
eV to 1.5 eV. And Figs.2 (a) shows the maximum output power with the
143
upper sub-band gaps E13 =E23 =0.45 ev while the minimum output power
144
with the upper sub-band gaps E13 =E23 =1.45 ev. These results indicate
145
that the narrower upper sub-band (E13 =E23 ) can easily excite more charge
146
carriers to the CB and produces an enhanced photocurrent. The phenomena
147
is physically caused by the doping IB which adds a ladder for the solar
148
photons below the semiconductor band gap, and much charge carriers stored
149
in the IB can easily transit to the CB with little input energy.
Pr
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133
Does the greater output power imply the greater photo-to-charge efficien-
151
cy ? The photo-to-charge efficiency in Fig.2 (b) displays an opposite evolu-
152
tionary behavior within the range from 0.5 eV to 3.5 eV. It notes that the
153
photo-to-charge efficiency decreases accompanying with the wider and wider
154
lower sub-band gap E3b . When the the lower sub-band gaps E3b equals 0.5ev,
155
the photo-to-charge efficiency achieves the maximum peak around 72.4% and
156
36.0% with the upper sub-band gap E13 =E23 =0.45ev, 1.45ev, respectively.
157
However, the minimum conversion efficiencies are below 20.0% with the low-
158
er sub-band gap E3b =3.5ev when the upper sub-band gaps E13 =E23 are set
159
as 0.45ev and 1.45ev, respectively. And the insert diagram in Fig.2 (b) dis-
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150
plays much higher photo-to-charge efficiency than the Shockley and Queisser
161
efficiency[12] when the lower sub-band gap E3b absorbs photons in the range
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of [0.5ev, 1.25ev]. The results indicate that the wider lower sub-band gap
163
E3b can promote the output power but weaken the photo-to-charge efficien-
164
cy, while the narrower upper sub-band gap Ei3(i=1,2) promotes not only the
165
output power but also the photo-to-charge efficiency. And the main underly-
166
ing physical significance comes from the absorbed solar photons. The higher
167
energy photons can excite multi-exciton to the IB which leads to much more
168
electron carriers shored in the IB, then the enhanced power is advent even-
169
tually. Meanwhile, the absorbed higher photons incur the decreasing ratio
170
between the output energy and the incident solar photons energy, i.e., the
171
photo-to-charge efficiency decreasing with the much higher solar photons.
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It is noted that Fig.2 has examined the quantum yield when this QD-
173
IB photocell was manipulated by the upper or lower sub-band gaps with a
174
fixed output voltage, and the sub-band gap layout is the narrow upper sub-
175
band gap accompanying with the wider lower sub-band gap. However, the
176
quantum yield of the QD-IB photocell with an opposite sub-band gap layout
177
is also worthy attention. Fig.3 shows the quantum yields versus the output
178
voltage with a different layout of sub-band gaps, i.e., E13 =E23 =1.43ev and
179
E3b =0.25ev. Considering the actual ratio has an order of magnitude around
180
20 between the solar temperature and the ambient temperature circumstance,
181
the solar temperature in this toy model is set as Ts =7ev comparing to the
182
selected ambient temperature values in Fig.3 (And the data for Fig.3 are in
183
the SI Word), and other parameters are the same to those in Fig.2.
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Pr
172
184
Totally different behavior for the quantum yields are advent in Fig.3.
185
Under the specify finite temperature, the output power sharply increases to
186
the peak firstly but then drops to the minimum slowly, and the peak value
187
decreases by an ambient temperature increment being 0.02ev in Fig.3(a). At
188
the ambient temperature Ta =0.40ev, the output power rapidly increases to the peak within the voltage range [0, 0.4v] and slowly declines to the min-
190
imum within the voltage range [0.4v, 1.5v], and it outputs the maximum
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T =0.40ev
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T =0.42ev T =0.44ev T =0.46ev T =0.48ev
0.6
0.4
0.2
0.0
T =0.50ev
40
30
20
10
0
æ
0.0
50
0.2
0.4
0.6 0.8 1.0 Sub-band gap E3 bHevL
1.2
1.4
0.0
0.2
0.4
0.6
0.8 Voltage HvL
e-p
P HevL Γ
0.8
60 Photon-to-charge efficiency H%L
1.0
ë ëë ëëë ë Ta=0.40ev ë ë ë ë ë Ta=0.42ev ë ë ë ë Ta=0.44ev ë ë ë Ta=0.46ev ë ë ëëëëëë ë ë ëë ë ë Ta=0.48ev ë ë ëë ë ëë ë ë ë Ta=0.50ev ë ë ëëëëë ë ë ëë ë ë ëë ëë ëë ë ë ëë ë ëëëëë ëëë ëë ëë ëëë ë ë ë ëë ëë ëë ëë ë ë ëë ëëëëëëëë ëëëë ëëë ëë ëë ëë ë ëëë ë ë ë ëëëëëëë ëëëë ëëë ëëëëëëëë ëëëë ëë ëë ë ë ëë ëëëëëëëëë ëëë ëëë ëë ëë ëë ë ëëë ëë ëë ëë ëëëë ë ëëëëëëëëëëë ë ëë ëëëë ëëëëëëëëëëëëëëëë ëëëëëëëëëëëëëëëë ëëë ëëëëëëëëëëëëëëëëëëëëëë ëë ëëëëëëëëëëëëëëëëë ëëë ëëëë ëëë ëëë ëëë ëëë ëëëëëëëë ëëëë ëë ëëëëëëëëëë ëëë ëëëëë ëëëëëëë ëëëëë ëëë ëëëëëëë ëëëë ëëë ëëëë ëëëëë ëëëë ëëë ëë ë
(b)
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(a) 1.2
1.0
1.2
1.4
Figure 3: (Color online) Power P and photo-to-charge efficiency generated by the QD-IB photocell versus the output voltage V under the different ambient temperatures Ta .
power at the voltage around 0.4v. While at the highest ambient temperature
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Ta =0.50ev, the curve for the power has the similar distribution pattern except
193
the much smaller peak within the voltage range [0, 1.5v]. Fig.3(a) indicates
194
that the photocurrent can be enhanced by the increasing of the voltage in the
195
range of [0, 0.4v] while the photocurrent decrease when the voltage exceeds
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0.4v, and these results show the negative influence of the ambient temper-
197
ature on the output power. It demonstrates that the higher temperature
198
circumstance can improve the collision probability then decrease the photon-
199
generated carrier transferring across the load, which results in the decreased
200
output power. Although the similar distribution curves for the photo-to-
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charge efficiency is shown in Fig.3(b), it observably displays the voltages cor-
202
responding to peak efficiencies are around 0.2v, as is different from the voltage
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corresponding to the peak power in Fig.3(a), which demonstrates the asyn-
204
chrony of the voltages corresponding to the peak power and peak efficiency.
205
What’s more, it shows the peak efficiency is significantly affected by the am-
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bient temperature circumstance. The peak photo-to-charge efficiency reaches
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74.9% at the lowest ambient temperature circumstance Ta =0.40ev, while it
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declines to 21.21% at the maximum temperature circumstance Ta =0.50ev.
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These indicates the higher ambient temperature circumstance can produce
210
much hot electrons and hot holes, and the increasing thermalization loss de-
211
stroy the photo-to-charge conversion. Then the efficiencies begin to decline
212
at around 0.2v, which incurs the efficiencies are much smaller at the voltage
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V=0.4v than those at the voltage V=0.2v.
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This QD-IB photocell displays the output power has a prominent en-
215
hancement than the single-band gap photocell[2, 6] in two different sub-band
216
gap layouts, and the achieved maximum quantum photo-to-charge conver-
217
sion efficiencies are higher than the limiting efficiency of 47% at 1 sun, 63.2%
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at full solar concentration for the IB approach in the former work Ref.[23].
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What’s more, the maximum quantum photo-to-charge conversion efficiency
220
are also higher than 43% at 1 sun, 55% for full solar concentration[23] for
221
two-gap tandem solar cell. However, it should be noted that this study has
222
focus only on the quantum yields for the photons below the energy gap or
223
for ambient operating temperature circumstance, the lost efficiency due to
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thermalization and the inter-band transition rate and surface recombination
225
rate of carriers were not discussed here. Designing a model of quantum ther-
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malization for photocell and with the consideration of inter-band transition
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rate and surface recombination rate of carriers will be explicitly discussed in
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our coming analysis work.
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4. Summary and discussion
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In conclusion, the quantum yields were discussed in this proposed QD-IB
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photocell. Owing to the IB inserted between the CB and VB, the higher
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quantum yields were achieved in two different sub-band gap layouts between
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the upper sub-band gap E13 =E23 and the lower sub-band gap (E3b ). The
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achieving output power has a prominent enhancement than the single-band
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gap photocell, and the achieving peak photo-to-charge efficiency reaches to 12
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74.9% as compared to the limit efficiency of 63.2% via the IB approach in
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the theoretical solar cell prototype. And the quantum behavior of thermal-
238
ization, inter-band transition rate and surface recombination rate of carriers
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in the quantum photocell may be other effective parameters to promote the
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quantum yields, they are worthy of attention in the QD-IB photocell in the
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future.
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Acknowledgment
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We gratefully acknowledge support of the National Natural Science Foun-
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dation of China ( Grant Nos. 61205205 and 61565008 ), the General Program
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of Yunnan Applied Basic Research Project, China ( Grant No. 2016FB009
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).
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References
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[3] K. E. Dorfman, K. R. Chapin, C. H. Raymond Ooi, A. A. Svidzinsky, and M. O. Scully, AIP Conference Proceedings 1411 256 (2011). [4] K. E. Dorfman, M. B. Kim, and A. A. Svidzinsky, Phys. Rev. A 84, 053829 (2011).
[5] C. Creatore, M. A. Parker, S. Emmott, and A. W. Chin, Phys. Rev. Lett. 111, 253601 (2013). [6] A. A. Svidzinsky, K. E. Dorfman, and M. O. Scully, Coherent Optical
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Journal Pre-proof 1) Proposed a novelty scheme for the enhancement of quantum yields in QDIB photocell. 2) A prominent enhanced output power than those single-band photocell .
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3) 74.9% photo-to-charge efficiency as compared to the limit efficiency of 63.2% via the theoretical IB approach in the solar cell prototype.
PII: DOI: Reference:
S0749-6036(19)31010-9 https://doi.org/10.1016/j.spmi.2019.106329 YSPMI 106329
To appear in:
Superlattices and Microstructures
Received date : 6 June 2019 Accepted date : 31 October 2019 Please cite this article as: S.-C. Zhao and Q.-X. Wu, High quantum yields generated by a multi-band quantum dot photocell, Superlattices and Microstructures (2019), doi: https://doi.org/10.1016/j.spmi.2019.106329. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
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Shun-Cai Zhao
a1
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High quantum yields generated by a multi-band quantum dot photocell , Qi-Xuan Wub
a
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Department of Physics, Faculty of Science, Kunming University of Science and Technology, Kunming, 650500, PR China; b College English department, Faculty of foreign languages and culture, Kunming University of Science and Technology, Kunming, 650500, PR China
Abstract
We perform the quantum yields in a multi-band quantum dot (QD) photocell via doping an intermediate band (IB) between the conduction band (CB) and
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valence band (VB). Under two different sub-band gap layouts, the output power has a prominent enhancement than the single-band gap photocell and the achieved peak photo-to-charge efficiency reaches to 74.9% as compared to the limit efficiency of 63.2% via the IB approach in the theoretical solar cell prototype. The achieved quantum yields reveal the potential to improve
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efficiency by some effective theoretical approaches in the QD-IB photocell. Keywords: Quantum yields, photo-to-charge efficiency, a multi-band
1
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quantum dot photocell 1. Introduction
Recently, the quantum photovoltaic system has attracted extensive atten-
3
tion because it is believed that its yield can be enhanced via some quantum
4
mechanism[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. In the seminal work[1], it shows that
5
the photocell power can achieve a substantial enhancement via the coherence
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Corresponding E-mail: [email protected].
Preprint submitted to Superlattices and Microstructures
June 6, 2019
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induced by the driving field, even if the actual photo-to-charge efficiency of
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the photocell was not calculated. However, another mechanism of coherence
8
without an external source, the noise-induced coherence or Fano-induced co-
9
herence can yield the enhancement of power in recent papers[2, 3], in which
10
the detailed balance[12] was broken and the photocell power delivered to the
11
load was increased.
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As it is well known, two major factors limit the quantum yield of the solar
13
cell prototype. One is losing excess kinetic energy of photo-generated carriers
14
as multiple phonon emission due to the absorption of photons with the energy
15
greater than the energy gap between the conduction and valence bands[13].
16
The second one is the loss of photons with energy lower than the band gap.
17
These result in the Shockley-Quiesser detailed balance limit and the energy
18
conversion efficiency is found[12] to be about 33%. Due to their quantum
19
confinement in three dimensions resulting in the tunable size and accordingly
20
tunable band gap, QDs are playing a vital role in the solar cells domain and
21
have achieved a considerable attention in the recent decades[14, 15, 16, 17,
22
18, 19]. Not only that, but QDs have the great potential to significantly
23
increase the photo-to-charge efficiency via the formation of IBs in the band
24
gap of the background semiconductor, which can absorb photons with energy
25
below the semiconductor band gap through transitions from the VB to the IB
26
and from the IB to the CB [20, 21, 22, 23, 24, 25, 26, 27, 28, 29]. In the QD-
27
IB solar cell approach, the limiting efficiency of 47% at 1 sun, 63.2% at full
28
solar concentration[23] were achieved, which exceeds the previous maximum
29
33% efficiency proposed by Shockley and Queisser in 1961[12].
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In this paper, we have theoretically calculated the quantum yields en-
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hancement of the QD-IB photocell with an intermediate level. This QD-IB
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photocell can be introduced by the doping technology, and its prototype comes from the seminal quantum photovoltaic system[1]. It is proven that
34
the output power has a prominent enhancement in this QD-IB photocell as
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compared to the single gap QD photocell[1, 2, 3, 4, 5]. And the quantum
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peak photo-to-charge efficiency comes to 74.9%, which also exceeding 63.2%
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mentioned in Ref.[23] is confirmed.
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In order to clarify our work, this paper is organized as follows: we describe
39
the quantum dot photocell model with an IB and deduce the power and
40
photo-to-charge efficiency generated by this photocell model in Sec.2. And
41
the power and photo-to-charge efficiency are evaluate by two different sub-
42
band gap layouts with different parameters in Sec.3. Sec.4 our conclusions
43
and outlook are presented.
44
2. Quantum dot photocell model with an intermediate band
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The proposed QD-IB photocell model can be generated by the doping
46
IB |c3 ⟩ via the doping technology in the theoretical prototype mentioned in
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47
Ref.[1]. Therefore, the band gap between the CB and the VB was divided
48
into two sub-bands, i.e., the upper sub-band gap Ei3(i=1,2) and the lower
49
sub-band gap E3b . And the doublet CBs |c1 ⟩ and |c2 ⟩ may be produced
by splitting of two degenerate QD levels due to electron tunneling between
51
two adjacent dots [see Fig. 1(a)]. The subdivided energy gaps can absorb
52
the solar photons with energy below the semiconductor band gap shown
53
in Fig. 1(a). Then, due to the IB |c3 ⟩, photons with energy below the
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band gap can be absorbed to excite electrons from the VB to the IB and
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from the IB to CB. Fig. 1(b) is the corresponding energy levels diagram for
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the QD photocell model, in which the two upper levels |c1 ⟩, |c2 ⟩ depict the
57
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CBs and level |b⟩ is on behalf of the VB, and the level |c3 ⟩ is interpreted as the IB. When the electronic system interacts with radiation and phonon
59
thermal reservoirs, the thermal solar photons with frequency midway between
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ωi3 (i = 1, 2) and ω3b are assumed to directing onto the cell. They drive |c1,2 ⟩
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↔ |c3 ⟩ and |c3 ⟩↔ |b⟩ transitions and have average occupation number n1 = [exp( kEBi3Ts ) − 1]−1 and n3 = [exp( kEB3bTs ) − 1]−1 , where Ei3 = (E13 + E23 )/2, Ts 3
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is the solar temperature. The ambient thermal phonons at temperature Ta
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drive the low-energy transitions |c⟩ ↔ |c1 ⟩, |c⟩ ↔ |c2 ⟩, and |v⟩ ↔ |b⟩. Their
65 66
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corresponding phonon occupation numbers are n2 = [exp( kEB12Ta ) − 1]−1 and n4 = [exp( kEBvbTa ) − 1]−1 , where E12 = (E1c + E2c )/2.
Èc2\
Èc1\
æ
ë ë
Èc1\ Èc2\
Μc
~
~ Γ1
Γ1
Γ2
Γ2
ÑΝsi
e-p
æ
Èc\
Èc3\
Èc3\ ÑΝs j
Γ3
ë
æ
Μv
Èb\
G
j
ΛG Èv\ ~
G
(b)
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(a)
Figure 1: (color online) (a) Quantum dots having two upper level conduction band states, |c1 ⟩and |c2 ⟩. The two different monochromatic solar photons(νsi , νsj ) are tuned to the midpoint between the two upper levels and intermediate band |c3 ⟩, the intermediate band
|c3 ⟩ and level |b⟩ in the valence band. The host semiconductor system, in which the
quantum dots are embedded, has effective Fermi energies µc and µv for the conduction and
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valence bands. (b) Corresponding energy levels diagram of this QD-IB photocell model. Solar radiation drives transitions between the ground state |b⟩ and the intermediate band
|c3 ⟩, the intermediate band |c3 ⟩ and two upper levels |c1 ⟩, |c2 ⟩. Transitions |c1 ⟩, |c2 ⟩ and
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|v⟩, |v⟩ and |b⟩ are driven by ambient thermal phonons. Levels |c⟩ and v⟩ are connected to a load.
The interaction Hamiltonian in the rotating-wave approximation for the
68
electronic system interacting with radiation and phonon thermal reservoirs
69
is given as follows,
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∑
∑
gi [ei(ω13 −νi )t σ ˆ13 + ei(ω23 −νi )t σ ˆ23 ]ˆ ai +
i
go [e
i(ω1c −νo )t
σ ˆ1c + e
i(ω2c −νo )t
σ ˆ2c ]ˆbo +
o
70
∑
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Vˆ (t) = ~{
∑ p
gj ei(ω3b −νj )t σ ˆ3b a ˆj +
j
gp ei(ωbv −νp )t σ ˆbvˆbp } + h.c. (1)
where gi,j,o,p are the coupling constants for the corresponding transition,
73
tors and phonon annihilation operators, respectively. σ ˆij (ˆ σji ) is the Pauli rise
74
or fall operator. The equation of motion for the electronic density operator
75
ρ reads ⊗
∫t
Pr
ρ(t) ˙ = − ~i T rR [Vˆ (t), ρ(t0 )
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~ωij = Ei − Ej is the energy spacing between levels |i⟩ and |j⟩. νi is the photon or phonon frequency, and a ˆi,j , ˆbo,p are the photon annihilation opera-
71
ρR (t0 ] −
1 T rR ~2
t0
[Vˆ (t), [Vˆ (t′ ), ρ(t′ )
⊗
ρR (t0 ]]dt′(2) ,
where the density operator ρR describes the phonon thermal reservoirs. In
77
the Weisskopf-Wigner approximation, we assume that the levels |c1 ⟩ and |c2 ⟩
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are degenerate and obtain the following master equations,
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ρ˙11 = −γ1 [(1 + n1 )ρ11 − n1 ρ33 ] − γ˜1 [(1 + n2 )ρ11 − n2 ρ33 ] + γ12 (1 + n1 )Re[ρ12 ] − γ˜12 (1 + n2 )Re[ρ22 ],
ρ˙22 = −γ2 [(1 + n12 )ρ22 − n1 ρ33 ] − γ˜2 [(1 + n2 )ρ22 − n2 ρ33 ] +
e-p
γ12 (1 + n1 )Re[ρ12 ] − γ˜12 (1 + n2 )Re[ρ22 ], 1 ρ˙12 = − [(γ1 + γ2 )(1 + n1 ) + (˜ γ1 + γ˜2 )(1 + n2 )]ρ12 2 1 − γ12 [(1 + n1 )ρ11 + (n1 + 1)ρ22 − 2n1 ρ33 ] 2 1 − γ˜12 [(1 + n2 )ρ11 (1 + n2 )ρ22 − 2n2 ρ33 ] − τ12 ρ12 , 2 ρ˙33 = −γ3 [(1 + n3 )ρ33 − n3 ρbb ] − (γ1 + γ2 )n1 ρ33 + γ1 (1 + n1 )ρ11 +γ2 (1 + n1 )ρ22 + 2γ12 (1 + n1 )Re[ρ12 ],
(3)
Pr
ρ˙cc = γ˜1 [(1 + n2 )ρ11 − n2 ρcc ] + γ˜2 [(1 + n2 )ρ22 − n2 ρcc ] + 2˜ γ12 (1 + n2 )Re[ρ12 ] − Γ(1 + λ)ρcc ,
˜ 4 ρbb − (1 + n4 )ρcc , ρvv ˙ = Γρcc + Γn
81 82 83
decay rates of the corresponding transitions [see Fig.1(b)]. For maximum √ √ Fano coherence, γ12 = γ1 γ2 , γ˜12 = γ˜1 γ˜2 , while γ12 = γ˜12 =0 for no interfer-
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where γi and γ˜i are modeled the electrons’ decaying process as spontaneous
ence. In this model, levels |c⟩ and |v⟩ are connected to a load, and the load is
yielding a decay of the level |c⟩ into level |v⟩ at a rate Γ. The recombination
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84
between the acceptor and the donor is modeled by a decay rate of λΓ [also see
85
Fig. 1(b)], where λ is a dimensionless fraction, τ12 is the decoherence time.
86
And we focus on steady-state operation of the photocell model, voltage V
87
across the load is expressed in terms of populations of the levels |c⟩ and |v⟩ as[1, 2, 3]
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eV = Ec − Ev + kB Ta ln( 6
ρcc ). ρvv
(4)
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where Ta is the ambient temperature circumstance. The current j through
90
the cell is interpreted as j = eΓρcc and power delivered to the load is P =
91
jV which is supplied by the incident solar radiation power Ps [1, 2], and their
92
ratio describes the photo-to-charge efficiency of this QD-IB photocell.
93
3. Power and photo-to-charge efficiency
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The photocell power enhanced by the noise-induced or Fano-induced co-
95
herence has been investigated detailedly by the former work[2, 6]. In the
96
following, we abnegate the discussion on the output power influenced by the
97
coherence, while turn to discuss the quantum power and photo-to-charge
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100
between this QD-IB photocell model and the QD photocell theoretical proto-
101
type in Ref.[1] is the introduced IB. Therefore, the roles of different sub-band
102
gaps in the quantum yield will attract much attention.
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conversion efficiency under the condition with the maximum coherence in√ √ terference, γ12 = γ1 γ2 , γ˜12 = γ˜1 γ˜2 . And in present paper, the difference
98
With the stationary solutions to the master equations(3), we explore
104
the power and photo-to-charge efficiency through the numerical calculations.
105
And several typical parameters should be selected before the calculation. The
106
energy gaps E1c =E2c =Evb =0.005ev, Ecv =1.49ev, Ta =0.0259ev, Ts =0.5ev[1].
108 109
And other parameters are scaled by γ: γ1 =1.2γ, γ2 =0.8γ, γ3 =1.5γ, γ e1 =1.05γ, γ e2 =1.15γ, Γ1 =1.25γ, Γ2 =1.35γ. The dimensionless fraction is set as λ=0.2.
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The Shockley and Queisser efficiency [12] is accessible in semiconductors with
band gaps ranging from about 1.25 ev to 1.45 ev. However, the solar spec-
111
trum contains photons with energies ranging from about 0.5 eV to 3.5 eV.
112
Photons with energies ranging from about 0.5 ev to 1.25 ev is not absorbed
113
and photons with energies within [1.45ev, 3.5ev] can incur the thermalization
114
loss in the Shockley and Queisser efficiency. Therefore, the lower sub-band
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110
115
gap (E3b ) simulated as the solar spectrum ranging from 0.5 ev to 3.5 ev will
116
be discussed in Fig.2, while the upper sub-band gap(Ei3(i=1,2) ) between the 7
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0.55
E13 =E23 =0.45ev
70
70
E13 =E23 =0.65ev 60
E13 =E23 =1.05ev Photon-to-charge efficiency H%L
60
E13 =E23 =1.25ev E13 =E23 =1.45ev
P HevL Γ
0.45
0.42 0.40
0.40
0.38 0.36 0.35
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E13 =E23 =0.85ev 0.50
0.34
50 40
50
30
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 E13 =E23 =0.45ev
40
E13 =E23 =0.65ev E13 =E23 =0.85ev E13 =E23 =1.05ev
30
E13 =E23 =1.25ev
0.32
E13 =E23 =1.45ev
0.30
(a) 0.5
1.0
0.28 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.5 2.0 2.5 Sub-band gap E3 bHevL
3.0
20
(b)
e-p
0.30
3.5
0.5
1.0
1.5 2.0 2.5 Sub-band gap E3 bHevL
3.0
3.5
Figure 2: (Color online) Power P and photo-to-charge efficiency generated by the QDIB photocell versus the lower sub-band gaps(E3b ) for different upper sub-band gaps
Pr
(Ei3(i=1,2) ).
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CB and IB will select values from the range of [0.45 ev, 1.45 ev] with the
118
output voltage being 1.5 volts in Fig.2 (And the data for Fig.2 are in the SI
119
Word).
Figs.2 (a) and (b) show the output power and photo-to-charge efficiency
121
across the load as a function of the lower sub-band gap E3b , and the insert
122
diagrams depict the output power and photo-to-charge efficiency when the
123
lower sub-band gap E3b absorbs the solar photons within the range of [0.5ev,
124
1.25ev], whose energy is below the band gaps mentioned in the Shockley and
125
Queisser efficiency[12]. Fig.2 (a) shows an enhancement power as compared
126
to the single-band gap photocell[2, 6], and shows a steep rise for the output
127
power about in the range [0.5ev, 2.5ev] while its growth is slowing down
128
within the range [2.5ev, 3.5ev]. The insert diagram in Fig.2 (a) displays the
129
enhanced power by increasing the lower sub-band gaps(E3b ) within [0.5ev,
130
1.25ev]. The enhanced power demonstrates that photons with energy below
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the band gap can contribute to the cell photocurrent on account of the IB.
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Owing to the IB isolation from the VB with a zero density of states, the
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carrier relaxation to the VB become difficult and more electrons are stored
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in the IB[28]. However, the increasing carriers form the delocalized state in
135
the IB and increase their density of states until their wave functions overlap
136
each other and facilitate Mott transition[30]. This process brings out the
137
smooth solid lines within the range [2.5ev, 3.5ev] in Fig.2 (a). What’s more,
138
the much higher energy photons within the range [2.5ev, 3.5ev] produce much
139
more thermal phonons which also decreases the growth of the output power.
140
However, the upper sub-band gap E13 =E23 display an opposite evolutionary
141
behavior when it absorbs the solar photons with energies ranging from 0.5
142
eV to 1.5 eV. And Figs.2 (a) shows the maximum output power with the
143
upper sub-band gaps E13 =E23 =0.45 ev while the minimum output power
144
with the upper sub-band gaps E13 =E23 =1.45 ev. These results indicate
145
that the narrower upper sub-band (E13 =E23 ) can easily excite more charge
146
carriers to the CB and produces an enhanced photocurrent. The phenomena
147
is physically caused by the doping IB which adds a ladder for the solar
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photons below the semiconductor band gap, and much charge carriers stored
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in the IB can easily transit to the CB with little input energy.
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Does the greater output power imply the greater photo-to-charge efficien-
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cy ? The photo-to-charge efficiency in Fig.2 (b) displays an opposite evolu-
152
tionary behavior within the range from 0.5 eV to 3.5 eV. It notes that the
153
photo-to-charge efficiency decreases accompanying with the wider and wider
154
lower sub-band gap E3b . When the the lower sub-band gaps E3b equals 0.5ev,
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the photo-to-charge efficiency achieves the maximum peak around 72.4% and
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36.0% with the upper sub-band gap E13 =E23 =0.45ev, 1.45ev, respectively.
157
However, the minimum conversion efficiencies are below 20.0% with the low-
158
er sub-band gap E3b =3.5ev when the upper sub-band gaps E13 =E23 are set
159
as 0.45ev and 1.45ev, respectively. And the insert diagram in Fig.2 (b) dis-
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plays much higher photo-to-charge efficiency than the Shockley and Queisser
161
efficiency[12] when the lower sub-band gap E3b absorbs photons in the range
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of [0.5ev, 1.25ev]. The results indicate that the wider lower sub-band gap
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E3b can promote the output power but weaken the photo-to-charge efficien-
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cy, while the narrower upper sub-band gap Ei3(i=1,2) promotes not only the
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output power but also the photo-to-charge efficiency. And the main underly-
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ing physical significance comes from the absorbed solar photons. The higher
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energy photons can excite multi-exciton to the IB which leads to much more
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electron carriers shored in the IB, then the enhanced power is advent even-
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tually. Meanwhile, the absorbed higher photons incur the decreasing ratio
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between the output energy and the incident solar photons energy, i.e., the
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photo-to-charge efficiency decreasing with the much higher solar photons.
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It is noted that Fig.2 has examined the quantum yield when this QD-
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IB photocell was manipulated by the upper or lower sub-band gaps with a
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fixed output voltage, and the sub-band gap layout is the narrow upper sub-
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band gap accompanying with the wider lower sub-band gap. However, the
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quantum yield of the QD-IB photocell with an opposite sub-band gap layout
177
is also worthy attention. Fig.3 shows the quantum yields versus the output
178
voltage with a different layout of sub-band gaps, i.e., E13 =E23 =1.43ev and
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E3b =0.25ev. Considering the actual ratio has an order of magnitude around
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20 between the solar temperature and the ambient temperature circumstance,
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the solar temperature in this toy model is set as Ts =7ev comparing to the
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selected ambient temperature values in Fig.3 (And the data for Fig.3 are in
183
the SI Word), and other parameters are the same to those in Fig.2.
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Totally different behavior for the quantum yields are advent in Fig.3.
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Under the specify finite temperature, the output power sharply increases to
186
the peak firstly but then drops to the minimum slowly, and the peak value
187
decreases by an ambient temperature increment being 0.02ev in Fig.3(a). At
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the ambient temperature Ta =0.40ev, the output power rapidly increases to the peak within the voltage range [0, 0.4v] and slowly declines to the min-
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imum within the voltage range [0.4v, 1.5v], and it outputs the maximum
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T =0.40ev
70
T =0.42ev T =0.44ev T =0.46ev T =0.48ev
0.6
0.4
0.2
0.0
T =0.50ev
40
30
20
10
0
æ
0.0
50
0.2
0.4
0.6 0.8 1.0 Sub-band gap E3 bHevL
1.2
1.4
0.0
0.2
0.4
0.6
0.8 Voltage HvL
e-p
P HevL Γ
0.8
60 Photon-to-charge efficiency H%L
1.0
ë ëë ëëë ë Ta=0.40ev ë ë ë ë ë Ta=0.42ev ë ë ë ë Ta=0.44ev ë ë ë Ta=0.46ev ë ë ëëëëëë ë ë ëë ë ë Ta=0.48ev ë ë ëë ë ëë ë ë ë Ta=0.50ev ë ë ëëëëë ë ë ëë ë ë ëë ëë ëë ë ë ëë ë ëëëëë ëëë ëë ëë ëëë ë ë ë ëë ëë ëë ëë ë ë ëë ëëëëëëëë ëëëë ëëë ëë ëë ëë ë ëëë ë ë ë ëëëëëëë ëëëë ëëë ëëëëëëëë ëëëë ëë ëë ë ë ëë ëëëëëëëëë ëëë ëëë ëë ëë ëë ë ëëë ëë ëë ëë ëëëë ë ëëëëëëëëëëë ë ëë ëëëë ëëëëëëëëëëëëëëëë ëëëëëëëëëëëëëëëë ëëë ëëëëëëëëëëëëëëëëëëëëëë ëë ëëëëëëëëëëëëëëëëë ëëë ëëëë ëëë ëëë ëëë ëëë ëëëëëëëë ëëëë ëë ëëëëëëëëëë ëëë ëëëëë ëëëëëëë ëëëëë ëëë ëëëëëëë ëëëë ëëë ëëëë ëëëëë ëëëë ëëë ëë ë
(b)
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(a) 1.2
1.0
1.2
1.4
Figure 3: (Color online) Power P and photo-to-charge efficiency generated by the QD-IB photocell versus the output voltage V under the different ambient temperatures Ta .
power at the voltage around 0.4v. While at the highest ambient temperature
192
Ta =0.50ev, the curve for the power has the similar distribution pattern except
193
the much smaller peak within the voltage range [0, 1.5v]. Fig.3(a) indicates
194
that the photocurrent can be enhanced by the increasing of the voltage in the
195
range of [0, 0.4v] while the photocurrent decrease when the voltage exceeds
196
0.4v, and these results show the negative influence of the ambient temper-
197
ature on the output power. It demonstrates that the higher temperature
198
circumstance can improve the collision probability then decrease the photon-
199
generated carrier transferring across the load, which results in the decreased
200
output power. Although the similar distribution curves for the photo-to-
201
charge efficiency is shown in Fig.3(b), it observably displays the voltages cor-
202
responding to peak efficiencies are around 0.2v, as is different from the voltage
203
corresponding to the peak power in Fig.3(a), which demonstrates the asyn-
204
chrony of the voltages corresponding to the peak power and peak efficiency.
205
What’s more, it shows the peak efficiency is significantly affected by the am-
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bient temperature circumstance. The peak photo-to-charge efficiency reaches
207
74.9% at the lowest ambient temperature circumstance Ta =0.40ev, while it
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declines to 21.21% at the maximum temperature circumstance Ta =0.50ev.
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These indicates the higher ambient temperature circumstance can produce
210
much hot electrons and hot holes, and the increasing thermalization loss de-
211
stroy the photo-to-charge conversion. Then the efficiencies begin to decline
212
at around 0.2v, which incurs the efficiencies are much smaller at the voltage
213
V=0.4v than those at the voltage V=0.2v.
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This QD-IB photocell displays the output power has a prominent en-
215
hancement than the single-band gap photocell[2, 6] in two different sub-band
216
gap layouts, and the achieved maximum quantum photo-to-charge conver-
217
sion efficiencies are higher than the limiting efficiency of 47% at 1 sun, 63.2%
218
at full solar concentration for the IB approach in the former work Ref.[23].
219
What’s more, the maximum quantum photo-to-charge conversion efficiency
220
are also higher than 43% at 1 sun, 55% for full solar concentration[23] for
221
two-gap tandem solar cell. However, it should be noted that this study has
222
focus only on the quantum yields for the photons below the energy gap or
223
for ambient operating temperature circumstance, the lost efficiency due to
224
thermalization and the inter-band transition rate and surface recombination
225
rate of carriers were not discussed here. Designing a model of quantum ther-
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malization for photocell and with the consideration of inter-band transition
227
rate and surface recombination rate of carriers will be explicitly discussed in
228
our coming analysis work.
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4. Summary and discussion
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In conclusion, the quantum yields were discussed in this proposed QD-IB
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photocell. Owing to the IB inserted between the CB and VB, the higher
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quantum yields were achieved in two different sub-band gap layouts between
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the upper sub-band gap E13 =E23 and the lower sub-band gap (E3b ). The
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achieving output power has a prominent enhancement than the single-band
235
gap photocell, and the achieving peak photo-to-charge efficiency reaches to 12
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74.9% as compared to the limit efficiency of 63.2% via the IB approach in
237
the theoretical solar cell prototype. And the quantum behavior of thermal-
238
ization, inter-band transition rate and surface recombination rate of carriers
239
in the quantum photocell may be other effective parameters to promote the
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quantum yields, they are worthy of attention in the QD-IB photocell in the
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future.
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Acknowledgment
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We gratefully acknowledge support of the National Natural Science Foun-
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dation of China ( Grant Nos. 61205205 and 61565008 ), the General Program
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of Yunnan Applied Basic Research Project, China ( Grant No. 2016FB009
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).
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References
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Journal Pre-proof 1) Proposed a novelty scheme for the enhancement of quantum yields in QDIB photocell. 2) A prominent enhanced output power than those single-band photocell .
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3) 74.9% photo-to-charge efficiency as compared to the limit efficiency of 63.2% via the theoretical IB approach in the solar cell prototype.