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Band alignment and conversion efficiency in Si/Ge type-II quantum dot intermediate band
solar cells
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2007 Nanotechnology 18 405401
(http://iopscience.iop.org/0957-4484/18/40/405401)
Nanotechnology 18 (2007) 405401 (12pp) doi:10.1088/0957-4484/18/40/405401
Band alignment and conversion efficiency
in Si/Ge type-II quantum dot intermediate
band solar cells
A M Kechiantz
1,2,4, L M Kocharyan
3and H M Kechiyants
11Department of Applied Chemistry and Institute of Molecular Science, National Chiao Tung
University, Hsinchu, Taiwan
2Scientific Research Division, State Engineering University of Armenia, Yerevan, Armenia 3Department of Physics, Yerevan State University, Yerevan, Armenia
E-mail:arakech@mail.nctu.edu.tw
Received 6 April 2007, in final form 1 August 2007
Published 11 September 2007
Online at
stacks.iop.org/Nano/18/405401
Abstract
The concept of the intermediate band (IB) solar cells (SC) offers the promise
of achieving 63% conversion efficiency devices. The effect of the type II
band alignment in the quantum dot (QD) IB SCs on the above percentage is
analyzed and the potential of the Ge/Si system for fabrication of the type II
QD IB SC is discussed. Also, it is shown that the increase of the sunlight
concentration leads to the rise of the potential barrier around QDs and the
concentration of S
x≈ 700 can induce the ε
L= 0.2 eV height barrier in the
Ge/Si system, making this a significant result. Furthermore, the increase of
the sunlight concentration leads to the separation of the quasi-Fermi levels
from the confined states and also leads to the decrease of the recombination
activity in QDs. The two-photon absorption in QDs increases rapidly and
dominates over recombination at the moderate concentration. As the
contributions of QDs to both the photo- and dark currents in the type II QD
IB SC are evaluated it is shown that, compared to the conventional Si SCs,
the type II Ge QD IB Si SCs can generate about 25% higher photocurrent and
conversion efficiency.
(Some figures in this article are in colour only in the electronic version)
List of symbols
αCandαV The absorption coefficient for the direct
electron transitions from the confined state into the conduction band and from the valence band into the confined state within the Ge QDs,
αC= βC(NDϑ − pD)andαV= βVpD,
αC= αV≈2.4×103cm−1
α The absorption coefficient for the direct electron transitions in the bulk Ge,
α ≈ βNC,α5×103cm−1
ϑ The number of confined states per QD involved in the absorption,ϑ =10
4 Permanent e-mail:MRS Armenia@yahoo.com
βC, βVandβ The relevant absorption cross sections,
ϑβC≈8×10−13cm2[21], ϑβV=2×10−13cm2[20], β≈2.5×10−14cm2, ϑ =10, βC=3×10−14cm2and βV=2×10−14cm2are a realistic approximation
CA The Auger coefficient,
CA=10−31cm6s−1[17]
DV The in-plane diffusion coefficient of
holes within the Si1−xGexlayer,
DV=10 cm2s−1
d The thickness of the n-doped
multilayer absorber
coordinate, and the electric dipole, respectively
εJ The potential barrier for the dark
current in the depletion layer of the ideal p–n junction
εSiandεGe Indirect fundamental bandgap of the
strained Ge and Si,εSi=1.12 eV
ε1andε2 The offsets in the conduction and
valence bands at the heterojunction between the Si and Si1−xGex layers
εSG Bandgap of the Si1−xGexlayer of the
spacer,ε2= εSi− εSG
εL The illumination-induced barrier
around the Ge QD,εL= e2pD/εRND
ε The dielectric constant of the Si spacer,
ε =11.9
R The height of the Ge QDs,
R≈3 nm [26]
εandεV The bandgaps between the confined
state and thevalley in the conduction band, and between the confined state and thevalley in the valence continuum band,ε=0.87 eV [40],
εV=0.43 eV
gC, gV, gSiandg The integral intensities of infrared photons in theεV< ¯hω < ε+ εV,
εV< ¯hω < ε, εSi< ¯hωand
ε+ εV< ¯hωregions of the solar spectrum,
gC= gV=1.05×1017cm−2s−1,
gSi=2.37×1017cm−2s−1and
g =1.95×1017cm−2s−1[36];
G The intensity of the net electron
transitions from the valence band into the conduction band via the confined electronic state in the QDs
jCand jV The intensity of irradiation-induced
transitions from the confined electronic state into the conduction band and from the valence band into the confined electronic state in the QDs
jRCand jRV The increase in the intensity of
recombination per QD from the conduction band into the confined state, and from the confined state into the valence continuum band
j The total photocurrent generated in the Ge QD buried Si solar cell,
j ≈47.5 A cm−2at the concentration ofSX≈1000
jSi The total photocurrent generated in the
conventional Si solar cells,
jSi≈38 A cm−2[36] at the
concentration ofSX≈1000
L The distance between buried contacts
shown in figure2,L=10μm
L The symmetry point of the Brillouin
zone
The symmetry point in the center of the Brillouin zone
The symmetry line of the Brillouin zone
2 and4 The valleys on thesymmetry line of the Brillouin zone in the conduction band
m The electron mass in thevalley in the conduction band of the bulk Ge,
m =0.041mo[40]
n The ideality factor of the p–n junctions
ND The volume density of the Ge QDs,
ND=2×1016cm−3[26]
NC The effective number of oscillators
involved in the direct transitions in bulk Ge,NC =2×1017cm−3[40]
NV The density of electronic states in the
valence band of the Si1−xGex layer,
NV≈2NDV
NDV The density of states in the valence
continuum band of the Ge QDs
The volume of the Ge QD,
=103nm3[22,26]
pD The volume density of confined holes
pV The density of holes within the
Si1−xGex layer of the n-doped
Si/Si1−xGex/Si spacer (including
photo-generated holes),
pV≈ αV(gV+ g)SX(L2/DV)/[1+
( NDNDVL2/τVDVNV)exp(−εL/kT )]
SX The concentration of sunlight,
SX=103
VOC The open-circuit voltage induced in the
Ge QD buried Si solar cell
VOCSi The open-circuit voltage induced in the
conventional Si solar cells
η The conversion efficiency of the Ge QD buried Si solar cell
ηSi The conversion efficiency of the
conventional Si solar cells,
ηSi=37% [36]
τC The inter-band recombination lifetime
that includes all radiative and nonradiative (and interface)
mechanisms for the electron transitions from the conduction band of the Si/Si1−xGex/Si spacer into the confined
state in the QD,τC=1μs in the
type-II Ge QDs buried in the Si matrix [14],τC=1μs in the type-II
GaSb QDs buried in the GaAs matrix [15]
τV The intra-band relaxation lifetime that
includes both radiative and nonradiative mechanisms for the electron transitions from the confined state into the valence continuum band in the Ge QD,τV=50 ps for the
intra-band relaxation lifetime [16]
τA The Auger recombination lifetime
given byτA=1/CApV2
z The distance from the front-side surface
ε The energy gap for the direct optical transitions within the Si/Si1−xGex/Si
spacer, from thevalence band(EV) into theconduction band(EC),
ε= EC− EV
EandE The energies of theandbands in the conduction and valence bands
E2andE4 The energies of the splitbands in the conduction band
lh and hh The light and heavy holes
1. Introduction
The concept of intermediate band (IB) solar cells (SC) has attracted much attention in the last decade. This concept aims to bring about higher conversion efficiency devices than the multi-junction SCs [1]. Like the conventional solar cells, IB SCs exploit one-photon absorption for generating the photocurrent. However, these SCs also exploit the two-consecutive-photon-induced electron transitions via the intermediate states for generating an extra photocurrent [1]. In fact, the IB SC concept exploits nonlinearity in the absorption and therefore the concept will gain from the concentration of sunlight. The compatibility with the high concentrator technology gives IB SCs an additional advantage for reducing electricity costs due to the substitution of expensive semiconductor cells with low-cost optics [2].
In the past decade, considerable insight into the optical and photoelectrical features of IB SCs has been achieved [3–9]. Recently the IB SCs have been fabricated from InAs QDs sandwiched between n- and p-doped GaAs layers and their operation demonstrated [10, 11]. However, the induced photovoltage was lower than in the control GaAs SC. A possible explanation of the low photovoltage is the thermal generation of carriers in InAs QDs. These carriers can escape from the QDs embedded in the build-in electric field [12] producing an extra dark current that may reduce the separation of the quasi-Fermi levels and suppress the photovoltage. It seems that the InAs/GaAs system may not be the best material choice for IB SCs [10,11].
The separation of quasi-Fermi levels is a paramount problem for the energy conversion in IB SCs [3–5]. The QD confined states in IB SCs are like the electronic states of impurity centers. The states easily convert into fast recombination centers and come into equilibrium either with the conduction band or with the valence band. For example, impurity centers embedded in GalnNAs solar cells arrest the quasi-Fermi level, increase the recombination and impact the photovoltage in the cells [13]. However, the recombination at QDs also depends on the potential barriers around QDs. The recombination is reduced when the potential barrier separates the electrons and the holes in a real space. For instance, the inter-band recombination in the type-II GaSb QDs buried in GaAs and in the type-II Ge QDs buried in Si is extended to 1 μs, due to the potential barrier in the conduction band [14,15]. Another feature of the type-II QDs is the irradiation-induced potential barrier around QDs [16]. The higher the sunlight concentration, the higher is the barrier induced. Despite its importance for the operation of IB SCs
εΓ
εv εc
εJ
Figure 1. A simplified energy band diagram of the type II QD IB SCs.
there has been little work done on integration of type II QDs with the IB SCs.
Figure 1 displays the simplified energy band structure of the type II QD IB SCs. Unlike the conventional QD IB SCs [10,11], the stack of QD layers of type II QD IB SCs is shown as not being sandwiched by the p- and n-doped layers. First, QDs are embedded far from the depletion layer and the built-in electric field, though at a distance less than the carrier diffusion length. Second, QDs have the type II energy band alignment that creates potential barriers for majority carriers and potential wells for minority carriers.
In this paper we report on the energy conversion in type II QD IB SCs. The mathematical model is developed in section2. It is shown that the increase of the sunlight concentration leads to the rise of the potential barrier around QDs. The raised barrier suppresses the recombination activity in QDs. The two-photon absorption in QDs increases rapidly and dominates over recombination along with the increase in the sunlight concentration. We have revealed that the photocurrent and the conversion efficiency may be higher than in the conventional SCs. The potential of the Ge/Si system for fabricating type II QD IB SCs is analyzed in section3. The assumed device structure is shown in section4. Discussions are presented in section5.
2. Model
2.1. Electron transitions in QDs
The simplified energy-band diagram of the type-II QD SCs in thermal equilibrium is shown in figure1. The p–n junction and the stack of QD layers sandwiched by n-doped spacers are seen to be connected in series. QDs have the type II energy band alignment with potential barriers in the conduction band and potential wells in the valence band. QDs are embedded in the n-doped base of the p–n junction, far from the depletion layer and the built-in electric field, but at a distance less than the carrier diffusion length. A detailed balance exists among generation and recombination processes. The Fermi energy lies at the same value for all bands and states. QDs are uncharged since electronic states of the type II QDs are empty in the conduction band and full in the valence band.
We assume the concentrated sunlight is absorbed in QDs only. The photovoltage is induced by the electron–hole pairs generated in the stack and injected from the stack into the p–n junction.
The concentrated sunlight destroys the detailed balance and it induces additional electron transitions from the confined states into the conduction band and brings pD holes into the
confined states. The destroyed balance splits the Fermi level into the quasi-Fermi levels of (a) the conduction band, (b) the valence continuum band and (c) the confined states [1,10]. The additional electron transitions also take away a negative charge ofepD/NDfrom the QDs, whereNDis the volume density of
the QDs. Along with the removing of the charge, the potential barrierεLarises in the valence band around the QDs [16]. The
induced barrier blocks any transfer of mobile holes back from the semiconductor into the charged QDs. Simultaneously the potential barrier in the conduction band blocks the transfer of mobile electrons into the QDs. The equation of continuity governs separation of the quasi-Fermi levels by the induced occupation of the confined states.
Under the ideal IB SC conditions [1], the balance of transitions,G/ND= jC− jRC= jV− jRV, and the equation of
continuity,jC+ jRV= jV+ jRC, in QDs reduce to equations (6) and (7) in [1], respectively. The transitions jC, jV, jRV and
jRC must be calculated by equation (5) in [1]. Here jC and
jVare the irradiation-induced electron transitions going from
the confined electronic state into the conduction band and from the valence band into the confined electronic state in the QD;
jRV and jRC are the recombination-induced transitions into
the confined state from the valence continuum band and the conduction band, respectively.
In order to take into account the nonradiative transitions, we rewrite the transitions per QD [8,9] as
jC= αCgCSX/ND (1)
jV= αVgVSX/ND (2)
jRV= αV(gV+ gV)SX/[ND+ (τVDVNV/ NDVL2) × exp(εL/kT )] (3)
jRC= pD/NDτC. (4)
Here τC is the inter-band recombination lifetime for the
electron transitions from the conduction band in the spacer into the confined state in QDs;τVis the intra-band relaxation
lifetime for the electron transitions from the confined state into the valence continuum band within QDs; both τC and
τV lifetimes include all radiative and nonradiative (including
interface) mechanisms of transitions; SX is the concentration
of the sunlight; NDis the volume density of the QDs;gC,gV
and g are the integral intensities of infrared photons in the
ε< ¯hω < ε+ εV,εV< ¯hω < εandε+ εV< ¯hωranges of the solar spectrum, respectively;εis the bandgap between the ground confined state and the valley in the conduction band of QDs;εVis the bandgap between the ground confined
state and thevalley in the valence continuum band of QDs; is the volume of the QD;NVis the density of electronic states
in the valence band in the spacer; NDVis the density of states
in the valence continuum band in QDs; DV is the diffusion
coefficient of holes in the spacer; Lis the distance from QDs to the depletion layer;αCandαVare the absorption coefficients
for the direct optical transitions in QDs from the confined state into the conduction band and from the continuous valence band
into the confined state, respectively. We assumeαV = βVpD
andαC = βC(NDϑ − pD)whereβCandβVare the relevant
absorption cross sections; ϑ is the number of the confined states per QD involved in the absorption. Equation (3) is derived under the condition that QDs have more electrons in the confined state than holes in the valence continuum band;
(NDϑ − pD)/ND> pV (NDV/NV)exp(−εL/kT ), wherepV
is the density of holes in the roughly 1/αV-thick stack of QD
layers:
pV≈ αV(gV+ g)SX(L2/DV)/[1
+ ( NDNDVL2/τVDVNV)exp(−εL/kT )]. (5)
Substituting the photo-induced barrier εL = e2pD/εRND
and the transitions jC, jV, jRV and jRC into the equation of
continuity yields pD= ϑ ND 1+ 1 τCgCβCSX +βVgV βCgC −βV(gV+ g) βCgC × NDNDVL2 τVDVNV ×exp − e2 εkT R pD ND −1 (6) G= 1− gV+ g gV × NDNDVL2 τVDVNV × exp − e2 εkT R pD ND × SXαVgV (7)
whereε is the dielectric constant of the spacer and R is the height of the QD.
2.2. Photocurrent
For simplicity, we assume a weak surface recombination in the type II QD IB SCs. Then approximately all mobile carriers generated in the stack of QDs must be collected by the p– n junctions. The generated photocurrent can be calculated by integrating the two-photon transitions G and adding the result to the photocurrenteSXg(0) induced by conventional one-photon transitions, eSXg(0) + eG(z)dz. We can simplify the integration by substituting ∂gV/∂z = −αVgV
in the integral and g(0)/gV(0) for g/gV in equation (7).
Calculations reduce the total photocurrent j generated in the type II QD IB SCs to j = eSXgV(0) × 1−gV(d) gV(0) × 1+ g(0) gV(0) × 1+ NDNDVL 2 τVDVNV ×exp − e2 εkT R pD ND −1 (8) wheredis the thickness of the stack.
2.3. Dark current
The stack of QD layers and the p–n junction are connected in series in the type II QD IB SC. In this circuit, the stack of QDs operates as a pump engine injecting electron–hole pairs into the p–n junction while the p–n junction generates the photovoltage and the photocurrent. Since the junction and the stack are separated in the space, one can expect that the dark current of the type II QD IB SCs is induced by the p–n junction only. In fact, the stack embedded at a distance less than the carrier diffusion length may have some contribution to the dark current. To evaluate this contribution to the dark current, we call the detailed balance arguments firstly [1].
According to equation (6) from [1] under the condition (7) from [1], the dark current jDK can be written as jDK =
jDJ+ jDV under the condition jDC = jDV, where jDC and
jDVare the dark components of the electron transitions from
the confined state into the conduction band and from the valence band into the confined states in QDs, and jDJis the
dark current of the ideal p–n junction. Using equation (5) from [1], these currents can be expressed as jDJ ≈
(2kTε2
J/h3c2) ×exp[−εJ/kT ]exp(V/kT )and jDV= jDC≈
(2kTεCεV/h3c2) × exp[−(εV+ εC+ V )/2kT]exp(V/kT ).
The ratio of the currents, jDJ/ jDV, gives the condition for
omitting the contribution of QDs to the dark current in the type II QD IB SCs on the basis of the detailed balance arguments
exp[(εV+ εC−2εJ + V )/2kT] > εCεV/ε2J. (9)
For taking into account the nonradiative transitions, we assume that the distance from QDs to the depletion layer is large enough to prevent tunneling of confined carriers from QDs into the depletion layer. Then the dark current in the p–n junction is dominated either by electron (hole) diffusion over the potential barrier in the depletion layer,
jDDV (DV/L)NV×exp[−(εJ − V )/kT ], or by the electron
transitions involving both tunneling and recombination in the depletion layer. Evidently, if the contribution from QDs
jRV dominates in the total dark current, jRV > jDJ, it
must also dominate over the diffusion component of the dark current, jRV > jDDV. Since the density of holes is
pV = NV × exp[−(εJ− V )/kT ] at the depletion layer,
equations (3) and (5) can be used to rewrite the contribution of QDs to the dark current as jRV ≈ ( NDNDVd/τV) ×
exp[−(εL+ εJ− V )/kT ]. The ratio jDDJ/ jRV gives the
condition for omitting the contribution of both radiative and nonradiative transitions in QDs to the dark current in the type II QD IB SCs:
exp[εL/kT ] > NDNDVLd/NVDVτV. (10)
2.4. Photovoltage and conversion efficiency
Under the open-circuit condition, the bias VOC is induced,
creating the precise balance jDK(VOC) = j between the
generated photocurrent jand the set currentjDK(VOC). Under
the conditions (9) and (10), the contribution of QDs to the dark current is small. The set current jDK(VOC) is reduced
to the dark current of the p–n junction jDJ(VOC). Therefore,
the open-circuit voltageVOCinduced in the type II QD IB SC
will be approximately the same as that VOCO induced in the
conventional SC, VOC = VOCO+ nkT × ln( j/ jO), if both
devices have the same quality p–n junctions with the same parameters like dark currents, ideality factorsnand fill factors
F F. On the other hand, the conversion efficiency of the type II QD IB SCηwill increase,η = ηO×( j/ jO). HereηOand jOare
the conversion efficiency and the photocurrent generated in the conventional SC, jO = eSXgO(0);gOis the integral intensity
of solar photons in the absorption spectrum of the conventional SC,εO < ¯hω. Substituting j from equation (9) and jO inη
yields η = ηO gV(0) + g(0) gO(0) 1−gV(d) gV(0) × 1+ NDNDVL 2 τVDVNV ×exp − e2 εkT R pD ND −1 . (11)
2.5. The Auger limit
Under the concentrated light irradiation, the Auger recombi-nation provides an intrinsic constraint upon the recombina-tion lifetime, the open-circuit voltage and the efficiency of conventional Si SCs [17]. For the electron–hole recombina-tion in the spacer between QDs in the stack of QD layers in the type II QD IB SCs, the Auger limit can be written as
τA = 1/CApV2 > L2/DV, whereτA andCA are the Auger
recombination lifetime and the Auger coefficient, respectively. SubstitutingpVfrom equation (5) inτAreduces the Auger limit
to
SX(gV+ g)αL3
CA/D3V<1. (12)
2.6. Recombination limits
While the recombination transitions balance the irradiation-induced electron transitions, the net generation G and the separation between the quasi-Fermi levels are very small. However, these parameters essentially increase as the irradiation-induced transitions become more intensive than the recombination transitions in QDs. After substituting jC, jRC,
jV and jRV from equations (1) to (4) into jC > jRC and
jV > jRV, the following conditions can be found for the
separation of the quasi-Fermi levels
τCgC>1/SXβC (13) gVτVexp e2 εkT R pD ND > g NDNDVL2 DVNV . (14) These conditions reduce equations (6), (7) and (11) to
pD(z) = ϑ NDβCgC(z)/(βCgC(z) + βVgV(z)) (15) G(z) = −SX ∂gV(z) ∂z (16) η − ηO ηO = gV(0) + g(0) − gO(0) gO(0) . (17) 2.7. Coordinate dependence Equations∂gC/∂z = −αC(z)gC(z),∂gV/∂z = −αV(z)gV(z),
αC = βC[NDϑ − pD(z)]andαV = βVpD(z)determine the
integral intensities, gC(z) and gV(z), as a function of the
distancezfrom the illuminated surface in the cell. If
gC(0) = gV(0) (18)
the conditions (13) and (14) reduce the integral intensities to
gC(z) = gV(z) = gV(0)exp(−αVz). Simultaneously, the
dependence onzdisappears in the confined state occupation,
pD= ϑ NDβC/(βC+ βV), and in the absorption coefficients
αC= αV= ϑ NDβCβV/(βC+ βV). (19)
Since gV(0) = (ε− εV)γ and gC(0) = εVγ, where γ ≈
2.5×1017cm−2s−1eV−1is the density of photon flux in the solar spectrum in the range of 0.6 eV< ¯hω <1.5 eV [41], the condition (18) also yields
Figure 2. Schematic of the device structures.
3. Potential of Ge/Si system
3.1. Motivation
The choice of the Ge/Si material system for the type II QD IB SCs is motivated by its specific technological and photoelectrical properties. Ge and Si are indirect band semiconductors that offer very slow electron–hole recombination. The type II Ge QD has the real-space indirect fundamental bandgap at the interface with the Si matrix and the large discontinuity in the valence band. The band offset in the conduction band can grow up to 0.3 eV. The offset can be tuned by the strain at the interface, by the composition of the Si spacer and by the carbon-induced compensation of the strain [18, 19]. Experiments revealed large absorption cross sections in Ge QDs [20, 21]. The electron inter-band recombination lifetime is extended to 1 μs [14]. All of these data on Ge/Si material system are favorable for the type II QD IB SCs and offer the promise of achieving higher conversion efficiency devices. The compatibility with the Si-based integrated-circuit technologies gives the type II Ge QD IB Si SCs the advantage of having a lower cost for launching it into industrial production5.
3.2. Technological aspect
These materials are completely miscible forming Si1−xGex
alloys with a gradually varying bandgap over the entire compositional range, from pure Si to pure Ge. Numerous studies have reported on the formation of the type II QD multilayer structures in Ge/Si system by MBE and MOCVD using the Stranski–Krastanow growth mode [20, 22–26]. A stack of ND = 2×1016cm−3Ge QDs, similar to the stack
shown in figure 2, has been grown recently [26]. The stack was composed of 50 QD layers with about 2×1011cm−2Ge
5 The compatibility with Si-based integrated-circuit technologies is very
important for investors. As a result, the production of silicon solar cells has increased since the 1990s and now composes 93% of all photovoltaic products despite strong competition from other promising photovoltaic materials.
QDs per layer. The 40 nm thick Si spacers separate the QD layers from each other [26].
A large interfacial strain induced by the 4% lattice mismatch between Ge and Si drives the growth of a strained Ge layer in the Stranski–Krastanow growth mode. The strained layer is converted into nanometer-sized Ge QDs to relax the strain when the deposited layer exceeds a critical thickness [20,22,24,27]. The control over the strain is now successively used for tailoring energy bands in Ge/Si1−xGex
multilayer nanostructures [18,28–32]. Composition of those QDs is also dependant on parameters of the Si spacer. For example, when the spacer is thinner than the critical thickness, the atomic inter-diffusion from the Si spacer into Ge QDs occurs to relax the residual strain further [20,22,28,29]. The residual strain and the inter-diffusion may essentially modify both offset and profile of bandgaps at the Ge/Si interface [29]. The control over the composition may be used for tailoring the energy bands. An additional degree of freedom for tailoring both the band offsets and the strain in the Ge QDs can be provided by adding carbon [33]. Carbon has the smaller lattice constant and as experiments have shown it can completely compensate the strain at the Ge/Si interface [19,34].
3.3. Conduction band alignment
3.3.1. Unstrained Ge. The lowest conduction band minima of unstrained Ge lie at the L points of symmetry in the111 directions on the surface of the Brillouin zone. These minima constitute a 0.66 eV-wide indirect bandgap [35]. Another conduction band minimum lies in thevalleys in the100 directions of the Brillouin zone. It constitutes a 0.85 eV-wide indirect bandgap. The point of symmetry in the center of the Brillouin zone constitutes a 0.80 eV-wide direct band. The unstrained Ge/Si interface has the type-II band alignment with a 0.51 eV-wide offset in the valence band and a 0.05 eV-wide indirect band offset in the conduction band [35,36].
3.3.2. Strained Ge/Si. Like the bulk samples, strained Si/Ge nanostructures have indirect fundamental bandgaps, εSi and
εGe, in Ge and Si layers. However, the residual interfacial
strain essentially modifies both offsets and profile of the energy bands at the strained Ge/Si interface [14, 37]. The fundamental bandgap acquires the real-space indirect character at the interface [32, 37]. The real-space indirect bandgap dramatically reduces the oscillator strength of the radiative inter-band recombination at Ge QDs [38].
Both thermal expansion coefficient and lattice constant are larger in Ge than in Si. Usually a compressive strain is induced in Ge QDs while a tensile strain is induced in Si spacers [18,28]. The energy band diagram of Si spacers with Ge QDs is shown in figure 3. The strain lifts the sixfold degeneracy of the conduction band invalleys of the Brillouin zone and splits the valleys into2 and4 valleys. The strain shifts these valleys in the opposite directions so that the 2 valley constitutes the conduction band minimum in the tensile strained Si spacer. The strain relaxing in the thick Si spacer may also lead to a confining potential of less than 25 meV for electrons in the conduction band of the Si at the Ge/Si interface [28, 29]. This small wrinkle drops to 0 at about 20 nm from the interface [28, 29]. The compressive
Figure 3. An energy band diagram of the multilayer absorber.εis
the energy gap for the direct optical transitions within the Si/Si1−xGex/Si spacer, from the valence band (EV) into the
conduction band(EC), ε= EC− EV; Eis the energy of the
band in the conduction and valence bands; E2and E4are the energies of the split bands in the conduction band; lh and hh are the light and the heavy holes.
strain pushes up the L valley and switches the conduction band minimum from the L valley to the 4 valley in Ge QDs [18, 28, 29]. The band offset in the conduction band,
ε1, increases up to 0.2 eV in the valley [28, 30]. The
band offset ε1 can grow up to 0.3 eV in the type-II Ge/Si
heterojunction, however, its growth is dependent on the strain and on the composition of the Si spacer and on the carbon-induced compensation of the strain in Ge QDs [18,19].
Thepoint in the center of the Brillouin zone constitute a 3.4 eV-wide direct bandgap in Si and a 0.8 eV-wide direct bandgap in Ge [18]. Therefore, the potential energy profiles of the conduction and valence band edges in thevalleys exhibit the type-I alignment with theband offset of about 2 eV in the conduction band at the Ge/Si interface. The potential energy profile over the interface also acquires the type-II alignment in the2 valley: however, it may acquire the type-I alignment in the4 valley [18,28,29]. The fundamental bandgap retains indirect in Ge QDs since under the strain the conduction band minimum at the4 valley is lower than at thevalley.
3.4. Valence band alignment
The strain lifts the degeneracy between heavy and light holes atvalleys in the valence band. The heavy holes constitute the upper band edge in the compressively strained Ge QDs while the light holes constitute the upper band edge in the tensile strained Si spacer [18,28,29].
A confinement potential of the Ge QDs essentially modifies the energy band profile in the valence band. The confinement potential takes some electronic states from the valence continuum band edge at the valley in the center of the Brillouin zone and confines them into Ge QDs. Instead the electronic states retained in thevalley constitute a new
continuum band edge below the confinement potential in the valence band of the Ge QDs. The new band edge merges with the valence band edge at the QD/Si spacer interface. Simultaneously, the new continuum band edge constitutes a larger direct gap at thepoint in the center of the Brillouin zone in the Ge QDs. As shown in figure3, the confinement increases the direct bandgap in the Ge QDs by adding the valence band offset, εV = 0.51 eV, to the gap, ε + εV.
The confinement also increases the directε and indirectεGe
bandgaps between the confined state and both the and4 valleys of the conduction band in the Ge QDs.
3.5. Absorption cross sections
The absorption cross section, β, can be roughly appraised from the absorption coefficientα and the effective number of oscillators NC involved in the direct optical transitions
between thevalleys,α ≈ βNC [39]. Bothαand NC
are proportional to m3r/2, wheremr is the reduced electron–
hole mass mr = memh/(me+ mh). Electrons involved in the direct transitions between the valleys in the bulk Ge essentially have a smaller mass than the involved holes,
me = 0.041 mo and mh = 0.28mo [40]. Therefore, the
effective number of oscillators in the bulk Ge is approximately equal to the density of states in thevalley of the conduction band, NC = 2×1017cm−3. The effective cross section is aboutβ≈2.5×10−14cm2.
A strong carrier confinement increases both oscillator strengths and absorption cross sections in QDs [3, 39]. Nevertheless, we will use the absorption cross sections of the bulk Ge,β ≈ 2.5×10−14 cm2, as a scale to appraise the
absorption cross sections,βCandβV, in Ge QDs.
The absorption cross sections are also proportional to the dipole transition matrix elementsψFuF|er|ψIuI, where
ψF,I(r)anduF,I(r)are the envelope function and the periodic Bloch function of the relevant final and initial wavefunctions (F and I, respectively) [39],eis the electronic charge,ris the electron space coordinate, ander is the electric dipole. This dipole matrix element is reduced toψF|er|ψIfor transitions between electronic states with the same Bloch function since
uV|er|uV = 0, e.g. for transitions in the same band (the intra-band transitions). On the other hand, the matrix element is reduced to uC|er|uVψC|ψV for transition between electronic states of different bands (the inter-band transitions) since the Bloch functions of conduction and valence bands are orthogonal to each other [39]. Therefore, the type-I alignment of thebands never affects the periodic Bloch functions and the matrix elementuC|er|uVof the direct optical transitions from the confined state to the conduction band at thevalley in Ge QDs. Moreover, the type-I alignment of the bands induces resonant electronic states in the valley within Ge QDs. This makes the overlapping of the envelope functions
ψC|ψV and the oscillator strength stronger. Therefore, the larger cross sectionβCis expected in Ge QDs,βC > β. For
the same reason, the absorption cross sectionβVfor the
intra-band absorption must be ψVF|er|ψVI/uC|er|uVψC|ψV times stronger thanβ.
Measurements of the inter-band absorption coefficient performed in the waveguide geometry for Ge QDs buried in the Si matrix revealed 103 cm−1per 23 nm thick layer [21].
The absorption cross section of ϑβC ≈ 8 × 10−13 cm2
per QD can be deduced from these experiments. The result is 30 times larger than β = 2.5 × 10−14 cm2. A
photoinduced spectroscopy technique used to measure the intra-band absorption cross sectionϑβV per QD in Ge QDs
buried in Si has revealed the experimental value of ϑβV =
2×10−13cm2[20]. This result is about ten times stronger than
β. The discrepancy between estimatedβ and the measured values of the absorption cross sections per QD,ϑβCandϑβV,
demonstrate that about ϑ = 10 confined states per QD are effectively involved in the absorption in the Ge QDs. Then,
βC = 3×10−14 cm2 andβV = 2×10−14 cm2are realistic
values reflecting the large measured values of the absorption cross sections in Ge QDs.
4. Device structure
In the type II QD IB SC applications it is crucial to maintain relatively high carrier mobility. The electrons and the holes generated in the stack of QD layers should be able to travel to the p–n junction before they recombine. Recent experiments have shown that the mobility in the stack of Ge/Si QD layers mainly depends on the structural and morphological properties of QDs [23]. Evidently, the mobility in the layered structure must be higher in the plane direction.
The buried contact approach provides an effective way of in-plane collecting the photogenerated carriers from the stack of QD layers. This approach also provides an additional performance improvement, a reduced shading loss arising from the top contact metal [41]. The assumed buried-contact structure of the type-II QD IB SC is shown in figure2. The cell looks similar to the buried-contact conventional Si SC [41]. The stack of the type-II Ge QDs embedded in the n-doped Si is grown on the n-doped Si-wafer. The Si layers in the stack act as the spacers between the approximately 3 nm thick Ge QD layers. About 50 layers of these spacers make up an approximately 5 μm thick n-doped multilayer absorber with the silicon oxide layer covering this absorber. The oxide serves as a top surface passivation coating, reducing surface recombination rate along the solar cell surface. The p–n junctions of the type-II QD IB SC shown in figure2are formed with the p-doped shells buried deep in the grooves incorporated into the n-doped absorber. The processing developed for the buried-contact solar cells [41] can be also used for putting the p-doped shells into the graves in the n-doped QD absorber. For example, first, a laser can be used to cut grooves through the top silicon oxide layer and the underlying multilayer absorber; second, boron deposition and diffusion can be used to form p-doped shells around the grooves in the absorber; third, the electrodeless plating can be used selectively to deposit a metal contact on the p-doped conducting shell in the grooves. Like the buried p–n junctions of the buried-contact solar cells [41], these p–n junctions collect holes generated in the n-doped absorber in the type-II Ge QD buried Si solar cell.
The spacer can also have a more complex structure. In particular, the spacer shown in figure 4 is a three-layer heterostructure. The 50 nm thick n-doped Si1−xGex alloy
layer is built in between the two 20 nm thick n-doped Si barrier layers in this spacer. The spacer can serve as an in-plane channel collecting mobile holes. The amount of Ge
Figure 4. An energy band diagram of the three-layer heterojunction Si/Si1−xGex/Si spacer.
in the Si1−xGex alloy layer,x < 0.2, determines the energy
band offset and the height of the barrierε2at the Si/Si1−xGex
interface in the three-layer spacer. A small amount of Ge,
x = 0, lets the Si layers in the Si/Si1−xGex/Si spacer to act
as the wide-band shell barrier around Ge QDs.
5. Results and discussions
5.1. Potential barriers
According to equations (6)–(11) and (13) and (14), the potential barriers around QDs are extremely important for the type II QD IB SCs performance. The potential barrier ε1
separates mobile electrons from QDs in the conduction band while the potential barrierεL+ ε2separate mobile holes from
QDs in the valence band. Both separations occur in a real space; therefore, mobile electrons and holes recombine very seldom with confined electrons and holes.
The band offset in the conduction band,ε1, depends on
technological parameters like the strain, the composition of the Si spacer and the carbon-induced compensation of the strain in Ge QDs. The value ofε1=0.2 eV was reported for the offset
in thevalley [28,30], however, the offset can grow up to 0.3 eV [18,19].
The barrierε2is created by heterojunctions in the complex
three-layer spacers while the barrierεLis induced by sunlight
illumination. Evidently, the stack with a simple one-layer Si spacer has an application advantage and, due to its importance here, we discuss the case of the one-layer spacers only,ε2=0.
The Ge QDs buried in n-doped Si have a dense quasi-continuous energy spectrum of the confined states [42, 43]. About 55 confined states per QD were estimated from the capacitance measurements [43]. While the irradiation-induced barrierεL is small, the irradiation-induced mobile holes drop
very fast from n-doped Si spacer into the Ge QDs. These holes relax very fast through the dense quasi-continuum of confined states into the ground confined state. The dropped holes fill the QDs very fast with positive charge. The accumulation (electron–hole inter-band recombination) time is long in the indirect bandgap semiconductors like Si and Ge [42]. Therefore, the accumulated charge can be large even at moderate excitation powers. The accumulated positive charge of the pDconfined holes induces the potential barrier
Figure 5. Conversion efficiencyη/ηSi≈ j/ jSi(solid line) and
irradiation-induced barrierεL(dashed line) as a function of the concentration Sx.
ofεL = e2pD/εRNDin the valence band. This barrier arising
around the Ge QDs blocks diffusion of mobile holes from the Si spacer into the charged Ge QDs. The calculation shows that the potential εL grows about e2/εR = 40 meV per
confined hole in Ge QDs that ε = 11.9 and R = 3 nm. In facte2/εRis the confined exciton binding energy, i.e. the
energy gain that the mobile electron and the confined hole have due to attracting each other in the Ge QDs. The barrier ε1
in the conduction band separates electron and hole in a real space and disallows them to screen each other in the QDs. Therefore, the potential appears around the QDs. Noteworthy, the exciton binding energy extracted from experiments on carrier transports through a photoexcited Ge QD system was also 40 meV [44].
Obviously, the irradiation-induced barrierεLcan grow up
from 0 toε1but no more. Otherwise the mobile electrons begin
to overwhelm the barrierε1and screen the holes confined in
the Ge QDs. Substituting pD from equation (6) into εL =
e2p
D/εRND, one can calculate the irradiation-induced barrier
εLas a function of the sunlight concentrationSx. The following
numerical values involving experimental data for parameters have been used in the calculations:ε1=0.2 eV [28,30],kT =
26 meV,e2/εR = 40 meV [44],N D =2×1016cm−3[26], NV ≈ 2NDV, ϑ = 10, τV = 50 ps [16], τC = 1μs [14], L = 10 μm, gC = gV = 1.05 × 1017 cm−2s−1 [36], g =1.95×1017cm−2s−1[36],β C=3×10−14cm2,βV= 2×10−14cm2, =103nm3[14,26],D V=10 cm2s−1. The
graph shown in figure 5reveals that this irradiation-induced barrier can be as large as 0.18 eV at the concentration of
Sx = 400 suns and as large as 0.2 eV at the concentration
ofSx =700 suns. It is noteworthy that the irradiation-induced
large barrier around Ge QDs,εL≈0.17 eV, was also extracted
from experiments [16].
5.2. Imposed limits
5.2.1. Equation (20). The band offsets at the Ge/Si interface determine the two-photon absorption spectra in the type II QD IB SCs. It is crucial to maintain relatively high two-photon generation of mobile electrons and holes. Therefore, the band
p
Figure 6. Irradiation-induced filling of the confined states with holes pD/ϑ NDand conditions in equations (12)–(14) as a function of the concentration Sx: 1—pD/ϑ ND; 2—equation (12); 3—equation (13);
4—equation (14).
offsets should be adjusted to yield the effective absorption and generation by tuning parameters like the strain at the Ge/Si interface, the composition of the Si spacer and the carbon-induced compensation of the strain [18, 19]. According to equation (20) the most effective two-photon absorption occurs when ε = 2εV. As reported in [40], the direct bandgap
between the confined state and thevalleys in the Ge QD is
ε = 0.87 eV. This yieldsεV = 0.43 eV for the offset in the
valence band. The same value is the energy gap between the valence continuous band and the confined state in the type II Ge QD IB Si SCs. The band offset at the QD Ge/Si interface is 0.25 eV in the conduction band between the2 valley of the Si spacer and thevalley of the Ge QD.
5.2.2. Equation (13). Equation (13) gives the condition for separation of the quasi-Fermi level of the confined states from that in the conduction band. The separation depends on the inter-band recombination lifetime, τC. This lifetime
includes both radiative and nonradiative (including interface) mechanisms of the electron transitions from the conduction band in the Si spacer into the confined state in the Ge QD. Equation (13) shows that the separation depends on the type-II band alignment of QDs via the barrier ε1 as a parameter.
This barrier creates the indirect real-space separation of the carriers that prevents the conduction band electrons from the fast recombination with the confined holes [14,15]. As long as τC ≈ 1 μs inter-band recombination lifetime has been
extracted from experiments on the type-II Ge QDs buried in the Si [14] and the type-II GaSb QDs buried in the GaAs [15]. The inter-band recombination in the Si spacer has been estimated about 1μs [14]. It is not clear yet how the real-space indirect-band separation in the conduction indirect-band suppresses inter-indirect-band recombination of mobile electrons with confined holes in the type-II QDs. Nevertheless, the suppression makes possible to liberate the quasi-Fermi level of the confined holes from that of the mobile electrons.
Equations (6) and (13) as a function of the sunlight concentration Sx are displayed in figure 6. Calculations
Figure 7. Conversion efficiencyη/ηSias a function of the barrier heightεL.
and (13) for the numerical values given in section5.1. The separation of the quasi-Fermi levels is seen to be at the concentration ofSx =300. Under this concentration, the 42%
of the confined states relevant to the absorption in the QDs,ϑ, are filled with holes.
5.2.3. Equation (14). Equation (14) gives the condition for separation of the quasi-Fermi level of the confined states from that of the continuum valence band. The separation depends on the intra-band recombination lifetime, τV. This lifetime
includes both radiative and nonradiative transitions of electrons from the confined state into the valence continuum band in the Ge QDs. Equation (14) show that the separation depends on the irradiation-induced barrierεL. This barrier prevents mobile
holes from dropping into the confined state inside the QDs. Moreover, the barrier supports diffusion of mobile holes in the plane of the Si spacer. Mobile holes must diffuse the distance
Lalong the spacers to get the p–n junction in the type II Ge QD IB Si SCs. The mid-IR pump–probe experiments on Ge QDs buried in Si revealedτV = 50 ps-long intra-band relaxation
lifetime [16]. The ‘phonon bottleneck’ effect and the acoustic phonon emission were suggested to be responsible for so much long intra-band relaxation lifetime [16].
Equations (6) and (14) as a function of the sunlight concentrationSx are displayed in figure6. Calculations have
been made by substituting parameters in equations (6) and (14) for the numerical values given in section5.1. The separation of the quasi-Fermi levels is seen to be at the concentration of
Sx =130. Under this concentration, the 34% of the confined
states relevant to the absorption in the QDs,ϑ, are filled with holes.
It is noteworthy that the conditions (13) and (14) are also relevant to the electronic states of recombination centers in doped and compound materials. For instance the abrupt decrease in the performance of GaInNAs solar cells by adding nitrogen, as noted in [13], indicates a fast relaxation of mobile electrons and an arrest of its quasi-Fermi levels by the nitrogen traps.
5.2.4. Equation (12). Equation (12) gives the Auger limit of the recombination lifetime in the type II Ge QD IB
Si SCs. For the high conversion efficiency, the in-plane diffusion towards p–n junctions must be faster than the Auger recombination lifetime between the electrons and holes within the Si spacer layers. The Auger limit as a function of the sunlight concentrationSxis displayed in figure6. Calculations
have been made by substituting parameters in equation (12) for CA = 10−31 cm6s−1 [17], α = 5 × 103 cm−1
and the numerical values given in section 5.1. The Auger recombination that is seen to be small must be omitted in the type II Ge QD IB Si SCs.
5.3. Dark current
5.3.1. Equation (9). Equation (9), exp[(εV+ εC−2εJ+ V )/
2kT] > εCεV/ε2J, where 2εJ > εV+ εC > εJ > εV, εC,
evaluates the contribution of QDs into the dark current in the frame of the detailed balance arguments [1]. It is seen that this contribution dominates and the QDs operate as a fast recombination center until the biasV <2εJ − εV+ εC. The
contribution of the QDs into the dark current is reduced along with the biased increase. The contribution can be omitted from consideration at large biases,V >2εJ− εV+ εC, e.g. under
concentrated sunlight, when the large photovoltage is induced and the potential barrier appears around the QDs.
5.3.2. Equation (10). Equation (10), exp[εL/kT ] >
NDNDVLd/NVDVτV, also evaluates the contribution of the
QDs into the dark current of the type II QD IB SCs. However, this equation takes into account nonradiative transitions. Substituting the numerical values of parameters given in section 5.1 into the right-hand side of equation (10) yields
NDNDVLd/NVDVτV ≈10. It is seen that this contribution
dominates and the QDs operate as a fast recombination center until εL < 0.1 eV. The contribution into the dark
current reduces along with the irradiation-induced barrier as
εL increases. Under the concentrated sunlight, when εL >
0.1 eV, the contribution of the QDs to the dark current is small. Therefore, it can be omitted from consideration.
5.4. Photon flux
Photons from theε < ¯hω < ε+ εV,εV < ¯hω < ε and
ε + εV < ¯hωregions of the solar spectrum can induce the direct optical transitions in the Ge QDs in the type II Ge QD IB Si SCs. For simplicity, we assume that the sunlight is absorbed in the Ge QDs only. The direct bandgap isε =0.87 eV [40]. According to equation (20), under the condition (18), the offset in the valence band must beεV=0.43 eV. For these bandgaps,
the integral intensities of irradiation aregC = gV = 1.05×
1017cm−2s−1andg =1.95×1017cm−2s−1[36].
5.5. Absorption coefficients
According to section5.2.1, the confinement potential and the interfacial strain increases the direct energy bandgap between
valleysεfrom 0.8 eV in the bulk Ge toε+ εV =1.3 eV in the Ge QDs [20,40]. Photons with higher energy, 1.3 eV<
¯hω, directly transfer electrons from the valence continuum bands into the conduction band in the Ge QDs. Obviously, the absorption coefficientαfor these direct optical transitions
between the valleys must be as large as it is in the same quality bulk Ge,α 5×103cm−1.
The confined states of the Ge QDs are at the point of symmetry in the center of the Brillouin zone. Photons from both ε < ¯hω < ε + εV and εV < ¯hω < ε
spectral regions, therefore, directly transfer electrons from the confined states into the valley in the conduction band and from the valley of the valence continuum band into the confined states, respectively. The two-photon transitions via these confined states are proportional to both illumination intensity and recombination lifetime. Either the intensity or the lifetime must be so large that, after the first-photon induced electron transition from the valence band into the confined state, this electron has a large probability for the second-photon induced transition from the confined state into the conduction band. Equations (13) and (14) show how large the product of the illumination intensity and the recombination lifetime must be for the illumination to induce the effective two-photon transitions. Evidently, the concentration of light
SX and the real-space separation of carriers support the net
electron transitions in the QDs.
The equation of continuity sets the proper occupationpD
of the confined electronic state. The filling of the confined state with holespD/ϑ NDas a function of the sunlight concentration
Sx is displayed in figure6. Calculations made by substituting
the numerical values of parameters given in section (5.1) into equation (6). The occupation grows to pD/ϑ ND≈0.5 at the
concentration of SX ≈ 700 suns. The striking consequence
of the type-II band alignment is the irradiation-induced barrier in the valence band around the QDs. Figure5shows that this barrier can be as high asεL = 0.2 eV at the concentration
ofSX≈700 suns. Under the concentration ofSx =130 suns,
34% of confined states relevant to the absorption in the QDs are filled with holes. The confined states are already very close to the optimal filling for the two-photon absorption. Substituting
ND = 2×1016cm−3,ϑ = 10,βC = 3×10−14 cm2, and
βV = 2×10−14 cm2into equation (19) givesαC = αV ≈
2.4×103cm−1for the two-photon absorption in the type II Ge QD IB Si SCs.
5.6. Photocurrent and conversion efficiency
In a few femtoseconds the irradiation-induced mobile electrons and holes slide from the 3 nm thick Ge QDs into the Si spacer. These electrons relax in the spacer in picoseconds, e.g. by emission of optical phonons. In particular, the electrons relax from thevalley into the2 valley in the conduction band. The potential barriers around the Ge QDs,ε1andεL, separate
mobile electrons and holes from the confined electronic states in a real space and suppress both the radiative and nonradiative transitions back into the QDs.
The equation of continuity sets the proper intensityGof the net transitions through the confined state. This equation also sets the proper injection of the mobile electron–hole pairs into the p–n junction in the type II Ge QD IB Si SCs. Equation (8) and figure6reveal an exponential dependence of the injection-induced photocurrent j on the barrier height in the valence band, εL = e2pD/εRND. The concentrationSX
also impacts the photocurrent jand the conversion efficiency
ηof the type II Ge QD IB Si SCs via the induced barrier. The
ratioη/ηSi≈ j/ jSiis plotted as a function of the concentration
SXin figure7. The numerical values of parameters are given in
section5.1. The conversion efficiencyηof the type II Ge QD IB Si SCs is even seen to drop below the conversion efficiency
ηSi of the conventional Si solar cells when the concentration
SX < 200 suns andεL < 0.15 eV since the conditions (13)
and (14) are not met. At these concentrations, the QDs are seen to act as active recombination centers.
The conversion efficiency of the type II Ge QD IB Si SCs,
η, however, grows fast with the concentrationSX. It already
becomes η = 1.2 ηSi at the concentration of SX ≈ 500
that εL ≈ 0.184 eV as shown in figure5. The conversion
efficiency of η = 1.25 ηSi is achieved at the concentration
of SX ≈ 1000 suns such that εL ≈ 0.21 eV. At this
concentration, equations (8) and (10) give j ≈ 47.5 A cm−2 for the photocurrent induced in the type II Ge QD IB Si SCs, and jSi ≈ 38 A cm−2 [36] for the photocurrent induced in
the conventional Si solar cell. Assuming the same parameters like dark current, ideality factor n and fill factor F F for both devices, the enhanced photocurrent increases nearly 25% the conversion efficiency of the type II Ge QD IB Si SCs in comparison to the same quality conventional Si SC. In particular, the conversion efficiency limit calculated with the detailed balance arguments for the ideal one-p–n-junction Si SC will increase from 37% [36] to 46% in the type II Ge QD IB Si SCs.
6. Conclusion
In this work we have modeled the effect of the type II band alignment on the energy conversion in QD IB SCs. The important factor of this modeling is that increasing the sunlight concentration leads to suppressing the recombination activity in QDs. Simultaneously, the two-photon absorption rapidly increases in QDs. The contributions of QDs into the dark current in the type II QD IB SC is reduced and can be neglected. The photocurrent and the conversion efficiency may be higher than in the conventional SCs. The potential of Ge/Si system for fabrication of the type II QD IB SC has been analyzed. The main conclusion of this analyzes is that the type II Ge QD IB Si SCs will generate about 25% higher photocurrent and conversion efficiency than the same quality conventional Si SC.
Acknowledgments
We thank Daniel L Clinciu, and the referees for their comments. This work was supported by National Science Council of Taiwan under grant no. NSC 95-2112-M-009-046 and partly supported by Armenian Ministry of Education and Science under grant 0441-136-01.02.2005.
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