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Different nanocrystal systems for carrier multiplication

Nguyen, X.C.

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Chapter 4

Co-doped silicon nanocrystals and

carrier multiplication

This chapter illustrates the experimental results concerning the carrier multiplication

process in phosphor and boron co-doped silicon nanocrystals at room temperature.

The �rst �ngerprint of this process has been found for the excitation energies around

two times the optical bandgap. By a combination of photoluminescence quantum

yield measurements and induced absorption spectroscopy, carrier multiplication is

investigated in a broad excitation energy range. Bleaching of induced absorption in

the near infrared probe range is observed. The carrier multiplication mechanism in

co-doped nanocrystals is suggested to proceed via II of both core and dopant-related

states.

4.1 Introduction

Improving the conversion e�ciency of the solar cell is an interesting and important

topic of recent research. For a single-junction solar cell, the maximal theoretical

e�ciency limit, following from the detailed balance, is around 33 % for a material

with the optimal bandgap of approximately 1.35 eV [70]. One way to enhance the

e�ciency above this limit is by making use of the so-called CM process - an impact

excitation process in which a hot carrier, with a su�ciently large excess energy, cools

down by promoting another carrier into the conduction/valence band. By e�cient

CM in a material with an optimized bandgap of approximately 0.8 eV, the solar cell

conversion e�ciency can be enhanced up to ∼ 44 % [116]. CM is typically promoted

by QC and in view of its potential to increase the photovoltaic conversion e�ciency,

it is widely investigated in semiconductor NCs. In the past, CM in undoped Si NCs

has been studied by transient absorption [72], and PL QY [84]. Since the optimal

bandgap of 0.8 eV is lower than the bandgap of bulk Si, it cannot be realized in

pure Si NCs. However, by doping of Si NCs with donors or acceptors, impurity

levels are introduced in the bandgap, thus e�ectively reducing it. These change the

optical properties of Si NCs. Indeed, recent investigations report reduction of PL

energy upon doping with phosphor and/or boron of di�erent concentrations [117,

118]. At the same time PL intensity of doped Si NCs is signi�cantly reduced when

compared to the undoped ones [119]. This is commonly assigned to an e�cient Auger

58 Chapter 4. Co-doped silicon nanocrystals and carrier multiplication

process involving free carriers in the bands or localized at (shallow) impurity levels.

Such a process is diminished by dopant compensation, which can be obtained by

simultaneous co-doping of Si NCs with phosphor and boron, so that similar numbers

of donor and acceptor states are formed inside the band gap. For these materials,

an incomplete compensation is the main origin of the low PL quantum e�ciency.

For co-doped NCs, the Coulomb correction due to donor-acceptor pair interaction

varies strongly with the dopant concentration; consequently the PL emission energy

reduces at high doping levels [120].

In undoped Si NCs, the energy threshold for CM was reported to be at least twice

the bandgap energy 2Eg [84]; it is not clear whether CM will take place in (co-)doped

Si NCs and, if it does, how its threshold energy will change. Past investigations of

co-doped Si NCs revealed that the PL quantum e�ciency was strongly degrading

with the impurity concentration [120] and also that the PL decay dynamics was

in�uenced. CM in doped Si NCs has not been investigated yet; in this research we

report some results pertinent to that subject.

4.2 Preliminary study: A �ngerprint of carrier multipli-

cation in induced absorption spectroscopy

4.2.1 Samples

In the present study two single layer SiO2:Si NCs samples have been used. These

were produced by co-sputtering, with the same Si excess and the same layer thick-

ness. One of them was heavily co-doped with boron and phosphor with the same

atomic percentage of 1.25 % and the other one was undoped. Both samples had

Si excess of 18 % and the active layer thickness of 1.5 µm, and were deposited on

quartz substrates. The sputtered layers were annealed in N2 ambient at 1150 ◦C

for 30 mins to grow Si NCs and to enhance their PL intensity [121]. Subsequently,

room temperature optical characteristics of the materials were evaluated.

4.2.2 Experiment

Linear absorption was measured using a Perkin Elmer Lambda 950 spectrometer

with a detection energy range up to 3300 nm. The accuracy in the low absorption

range (at long wavelengths) was increased due to the dual beam mode. The PL

spectrum of the undoped sample was measured in a setup using a xenon L2273

Hamamatsu lamp coupled to a Solar MSA130 double grating monochromator as

an excitation source, and a CCD detector, with the sample being placed inside

a Newport integrating sphere with a 7.5 cm diameter - see reference [101] for a

more detailed description. To measure PL of the co-doped sample (emitting in

infrared), the CCD was replaced by an infrared detector (Ge detector-Edingburgh

4.2. Preliminary study: A �ngerprint of carrier multiplication in

induced absorption spectroscopy 59

Instruments) with a high sensitivity in the range of 0.73 - 1.46 eV, coupled to a high

resolution monochromator (Spex 1000M). The details of the relevant setup were

illustrated in �gure 2.7a. In order to enhance the signal-to-noise ratio, a lock-in

detection mode with a mechanical chopper was applied.

Optical generation of carriers has been studied using transient IA [72, 111, 15, 83]

in a pump-probe con�guration. The details of the setup were mentioned in section

2.3.1.

Using the experimentally measured optical density of the samples, the IA amplitude

could then be calibrated to the number of photons absorbed within the sample. The

number of absorbed photons NAbs was calculated as:

Nabs =P (εexc) ∗Abs(εexc)

εexc, (4.1)

where Abs(εexc), P(εexc) are the linear absorption of the sample at excitation energy

εexc and the excitation power, respectively.

4.2.3 Results and discussion

Figure 4.1: a): The redshift of PL spectra can be seen as a consequence of co-doping,

the peak of PL shifts down by approximately 0.43 eV (from 1.45 eV to 1.02 eV for the

undoped and co-doped sample respectively). b): The main graph - linear absorption

of the undoped and co-doped Si NCs; an enhancement of linear absorption as well as

the extension of the spectrum to the low excitation energy region for co-doped NCs

can originate from appearance of acceptor and donor levels in the bandgap. The inset

- the relative absorption of the co-doped sample in the low absorption range (marked

with a rectangle in the main graph), the shadowed area represents the deviation of

the absorption value due to the interference. The marker shows the average value of

relative absorption (3.82 %) with the relevant error bar (0.38 %) at 1.51 eV.


The normalized PL spectra of the two samples obtained upon the excitation

energy of 3.1 eV are shown in �gure 4.1a. The PL spectrum shifts by 0.4 eV (from

1.45 eV down to 1.05 eV) as both boron and phosphor were doped into the sample.

This has been observed before and assigned to radiative recombination of e-h pairs

localized at donor and acceptor levels inside the bandgap of Si NC [120]; in that

way emission at energies below the bandgap of bulk Si could be obtained. Concomi-

tantly, from �gure 4.1b, we conclude that also the absorption in the co-doped sample

is enhanced considerably; in particular we note that the absorption spectrum of the

co-doped sample extends to lower excitation energies. Also the saturation of the

absorption in this sample appears already at approximately 3.5 eV, i.e. at a lower

energy than for the undoped reference sample. We argue that these changes can be

related to the presence of impurities, and possibly also to defects introduced upon

doping.

In order to investigate a possibility of CM in the co-doped sample, the IA mea-

surements have been performed for two excitation energies of 1.51 eV and 2.48 eV.

These correspond to values below and above twice the optical bandgap which we

assume to be equal to the emission energy. The expectation is that CM, if present,

could appear for the high energy but not for the low energy pumping, since the

CM threshold must be above twice the optical bandgap [84]. In �gure 4.2, the IA

Figure 4.2: The decay dynamics of IA for excitation energies of 1.51 eV (a) and 2.48

eV (b). For each pumping energy, three di�erent powers were applied to con�rm the

linear excitation regime. Here two points, namely A and B are selected to show the

amplitude of IA for two delay time of 3 and 2500 ps, respectively.

dynamics obtained at the selected pump energies is shown in the delay time window

of 3 ns. In order to avoid nonlinear e�ects, it is necessary to conduct the experi-

ments in the range where each Si NC absorbs not more than a single photon, so that

multiple e-h pairs cannot be induced in the same Si NC by absorption of several

4.2. Preliminary study: A �ngerprint of carrier multiplication in

induced absorption spectroscopy 61

photons. In order to establish that this indeed is the case, the IA transients were

taken at di�erent excitation power levels, as in reference [15]. In the linear regime,

increasing the excitation �ux increases the number of excited NCs, each capturing a

single photon. Since excitation decay dynamics should be similar in all NCs of the

probed ensemble, the dynamics of the total IA signal, integrated over all the excited

NCs, should not change as long as the linear excitation regime is maintained; the

dynamics will change only when some NCs will capture more photons and a strong

interaction between carriers localized within the same NC will appear. In order to

check that, the ratios of IA amplitudes A and B, taken at delays of 3 and 2500 ps,

respectively, have been compared at three di�erent pump power levels. The results

are depicted in the inset of �gure 4.3. As can be seen, for the two excitation en-

Figure 4.3: The dependence of IA amplitude of the sample with co-doped Si NCs

at delay time of 2.5 ns on the number of absorbed photons. In the main graph, the

�tting function is linear, the error bars of horizontal axis are estimated from the

accuracy of the power meter (around 5 %), linear absorption measurements (around

5 %) and the error from interference in the absorption measurement (10 % for 1.51

eV, 0 % for 2.48 eV, see �gure 4.1b). The clear di�erence of line slope represents a

�ngerprint of CM. The inset shows the power dependence of the A/B ratio for the

two excitation energies.

ergies, the A-to-B ratio remains constant, which implies that changing the power

does not in�uence the IA dymanics, thus asserting that both experiments were in-


deed performed in the linear excitation regime, with the average number of photons

absorbed per NC being well below one: Nabs << 1. At the same time, this ratio

is somewhat higher for the higher excitation energy: this indicates that the initial

amplitude of IA, and thus the initial e-h pair concentration, could be higher under

this pump energy. As discussed in the past [111], this could be an indication of the

CM process, with the additional carrier undergoing fast non-radiative recombination

due to, e.g., AR process. This notion is further con�rmed in the main panel of �gure

4.3. Here the experimental points show the amplitude of IA at 2500 ps at di�erent

pump power settings for the two excitation energies as function of the number of

photons absorbed in the sample. In both cases a linear dependence is observed, but

with a clearly higher slope for the larger energy. This evidences a higher e-h pair

generation rate, being thus indicative of CM e�cient taking place.

4.2.4 Conclusions

Based on optical characterization and IA measurements, the �rst possible evidence

of CM in boron and phosphor co-doped Si NCs has been found. Further experiments,

possibly combining excitation dependencies of IA and PL QY, will be necessary to

further elucidate, and con�rm, this e�ect. These are described in the second part

of this chapter.

4.3 Detailed investigation of carrier multiplication in phos-

phor and boron co-doped silicon nanocrystals

4.3.1 Experiments

The phosphor and boron co-doped Si NCs used in this study (see section 4.2.1) emit

in the NIR region with a low emission e�ciency. Therefore their PL spectra and

PL QY at room temperature could not be measured with the VIS CCD. Another

setup, including a germanium detector (Edingburgh Instruments) and an integrating

sphere (in the con�guration with sample inside) were employed to detect the number

of emitted photons. Details of the setup were presented in �gure 2.6. However, in

the low excitation energy range, the shoulder of excitation peak with the same

photon energy as PL might be detected, leading to an overestimation of the number

of emitted photons. The IA setup can be used to solve this problem, details of this

setup and the explanation for the procedure have been presented in �gure 2.10.

In order to investigate the PL dynamics, pulsed laser beam excitation was used. In

this setup, the fundamental laser pulse at (3.5 eV) was produced and used to excite

an optical parameter oscillator (OPO), with a non-linear crystal. By changing the

incident angle of the fundamental laser beam (by rotating the crystal), photons of

di�erent energy were produced. The repetition rate of the laser was set to 100 Hz,

4.3. Detailed investigation of carrier multiplication in phosphor and

boron co-doped silicon nanocrystals 63

with a pulse width of 5 ns. The PL was collected by the monochromator Spex

1000M, with a high resolution grating. On the exit slit, photons of a narrow energy

range were detected by a photomultiplier tube (PMT) Hamamatsu R5509-73 which

can operate in the VIS and the NIR range. The operation temperature and the

voltage of this PMT was set at -80 ◦C and -1500 V, respectively, in order to reduce

the thermal noise and to improve the signal-to-noise ratio.

The PL spectral dependence of the co-doped sample was measured in the setup

illustrated in �gure 4.4. As a spinning grating is used to scan the whole PL spectrum,

the stability of the excitation power is compulsory; a Xenon lamp coupled with a

monochromator was employed to ful�ll this requirement. The inset of this �gure

shows the correction curve of the setup for the energies between 0.8 and 1.45 eV;

the small correction factor in the low energy range suggests that the setup responds

well to the low energy photons.

Figure 4.4: The setup used to measure PL spectra of the co-doped sample. The

details with some explanation for the excitation source, the chopper and the lock-in

ampli�er, have been given in �gure 2.7a. A monochromator Spex 1000M was used

to scan the whole PL spectra. The inset shows the correction curve of the setup for

PL energy between 0.8 and 1.45 eV.


4.3.2 Results and discussion

4.3.2.1 Photoluminescence dynamics: �tting typical decay characteris-

tics

Figure 4.5: a): The experimental PL decay dynamics of the undoped and co-doped

samples upon an excitation at 2.9 eV, detected at 1.45 and 1.03 eV, respectively,

and their �tting curves (the white and yellow lines, respectively). b): The excitation

energy dependence of the PL lifetime for the undoped and co-doped samples. For the

high excitation energy range (2.0 - 2.9 eV), the PL lifetime of the undoped Si NCs

varies only slightly, whereas that of the co-doped ones shows a signi�cant excitation

dependence, being shorter for higher pump energies.

The PL dynamic traces for the undoped and co-doped samples excited at the

energy of 2.9 eV and detected at the peak of their PL spectra, are presented in �gure

4.5. In the measurement, the PMT collects photons whose energy is in a certain

range, so that the PL dynamics represents contributions of NCs of di�erent sizes.

Therefore the detected dynamics does not obey a single exponential but the best �t

is obtained with a stretched exponential function [122], characteristic for multiple

contributions. This function for the PL dynamics with intensity of PL I(t), and

�stretched� lifetime τ0 is written as follow:

I(t) = I0 +A× e−(tτ0

)β, (4.2)

where I0 stands for the background signal of the PMT, and the stretched coe�cient

β varies between 0 and 1. The e�ective lifetime τ responding to the detection energy

can then be calculated from the �tting parameters τ0 and β as:

τ = τ0 ×1

β× Γ

(1

β

), (4.3)



where the Γ function of a variable x is de�ned as:

Γ(x) =

∫ ∞0

zx−1e−zdz. (4.4)

The �tting curves for the undoped and co-doped sample (the white and yellow

curves in �gure 4.5a, respectively) show that the co-doped sample is characterized

by a slower PL dynamics. In the high excitation energy region, the PL lifetime for

the undoped sample is almost excitation energy independent, with the value around

77 - 80 µs, whereas that of the co-doped NCs has decay times between 90 µs and

120 µs. Moreover, the co-doped sample shows a clear excitation energy dependence

of PL decay dynamics, in particular in the low excitation energy, being around τ ≈122 µs at the lowest pump energy.

4.3.2.2 Photoluminescence quantum yield: the excitation energy depen-

dence

The setup to measure the absolute PL QY of the undoped sample has been presented

in �gure 2.1; the relative PL QY of the co-doped sample was measured with the

setup depicted in �gure 2.6. In order to calculate the absolute PL QY of the co-

doped sample, the following steps needed to be conducted - see �gure 4.6 for an

illustration:

Figure 4.6: The steps to calculate the number of emitted photons upon the excitation

energy of 3.64 eV for the co-doped sample. a): The full PL scanned by the setup of

�gure 4.4 (black curve) in step 1 and a log-normal �tting yielding a particular peak

position and deviation. b) A partial, experimentally obtained PL spectrum (orange)

in step 2 measured by the setup in �gure 2.1; the PL spectrum was recorded down

to 1.2 eV. The full PL spectrum (pink) was reconstructed using the �tting function

and relevant parameters found in step 1; subsequently the number of emitted photons

was determined.


• Step 1: The complete PL spectrum of the co-doped sample upon an excitation

at 3.64 eV was recorded using the setup illustrated in �gure 4.4, and then �tted

with a log-normal function, with a particular peak and width.

• Step 2: The same sample and a quartz substrate excited by the excitation

energy of 3.64 eV were measured with the setup in �gure 2.1. The number

of absorbed photons was calculated in the excitation window (above 2 eV) in

the same way as in �gure 2.1. In the emission window (below 1.5 eV), only a

part of the PL spectrum (above 1.14 eV) was recorded with the VIS CCD, see

�gure 4.6b. The shape of this PL spectrum is identical to the full PL spectrum

measured in step 1, but the amplitude is unknown.

• Step 3: The total number of emitted photons was calculated from the area of

the �tting curve for PL spectrum in step 2; a log-normal �tting function with

the same peak and width values as obtained in the �rst step was applied for

the PL spectrum in the second step, and in that way the amplitude was found.

The reconstructed PL spectra and the number of photons emitted upon the

excitation energy of 3.64 eV was determined.

Figure 4.7: The PL QY of the undoped and co-doped samples. Because of the low

values, PL QY of the co-doped sample is multiplied 4 times; a somewhat similar

behavior can be seen, such as the initial raise and an onset of a sharp increase in

the high-energy excitation region.

By using the above procedure, the absolute PL QY of the co-doped sample upon the



excitation energy of 3.64 eV was determined from the number of emitted photons

in step 3 and the number of absorbed photons in step 2. Subsequently this absolute

PL QY value was used to scale with the relative PL QY measurements. In that way

the absolute PL QY for the whole 2.10 - 4.45 eV range was found. The excitation

dependence of the absolute value of PL QY for both the undoped and the co-doped

sample are shown in �gure 4.7. Some discussion of these data sets will be presented

further on.

4.3.2.3 Induced absorption: linear excitation regime for both samples

Figure 4.8: The ratios of A-to-B calculated in the same way as in section 4.2 for the

undoped a) and the co-doped sample b), respectively. For all the excitation energies,

the A-to-B ratios do not change with the number of absorbed photons; therefore the

linear regime is con�rmed for the whole dataset; we conclude that all the transients

have been obtained in the linear regime, i.e., with less than a single exciton per NC

<Nabs> <1. The A-to-B ratio for the undoped sample is around 2.5 for all excitation

energies, the ratio for co-doped one slightly depends on the excitation energy, and

its value varies in the range of 1.5 - 1.8.


CM was further investigated by IA in the second series of measurements (series

2) using the setup described in section 4.2.2. The excitation energy range was

expanded. The undoped sample was used as a reference to �nd the in�uence of

donor and acceptor levels on the CM process and the IA dynamics. In section

4.2, only two excitation energies of 1.51 and 2.48 eV were applied to explore the

possibility of CM in the co-doped NCs. Here in order to investigate CM further we

expand the measurements to higher excitation energies. The pump energies of 2.48,

3.1, 3.84 and 4.0 eV were used for the undoped sample. For the co-doped sample,

the IA measurements were conducted upon the excitation energy from 1.5 to almost

4 times its optical bandgap, namely 1.51, 1.77, 2.0, 2.48, 3.54 and 3.94 eV. Firstly,

the linear excitation regimes are investigated for all the excitation energies from the

A-to-B ratio as explained in section 4.2. As can be seen on panels a) and b) in �gure

4.8 for the undoped and co-doped sample, respectively, the values of A-to-B ratio

corresponding to each pump energy are found similarly for all numbers of absorbed

photons; this result implies that all measurements have been taken in the linear

excitation regime. Furthermore, the value of A by B is almost excitation energy

independent, thus indicating the single exciton nature of the recorded IA transients.

4.3.3 Induced absorption and carrier multiplication

4.3.3.1 Induced absorption dynamics

As mentioned above, the presence of the dopant states in the band structure of Si

NCs a�ects the PL dynamics, PL spectra and PL QY. The impact of dopant levels

on the IA dynamics is shown for the VIS (�gure 4.9a) and the NIR probe (�gure

4.9b) upon an excitation energy of 3.1 eV.

For the VIS probe: the dynamic traces of the two samples are normalized at the

maximum; the steeper slope for the co-doped sample implies faster IA dynamics.

The �tting function for the dynamics is proposed to include a single and a stretched

exponential component with the amplitudes Asingle, Astretched, respectively, and can

be written as follows:

IA(t) = Asingle × e− tτsingle +Astretched × e

−

(t

τstretched

)β+ IBGN , (4.5)

where τsingle and τstretched are the lifetimes for the single and the stretched compo-

nent, respectively, IBGN is the baseline of the �tting curve corresponding to a slowly

decaying background, and β is a coe�cient of the stretched exponential component.

The reason for the faster IA dynamics for the co-doped sample may be related to the

imperfect compensation between donor and acceptor concentrations, as mentioned

in section 4.1. The results of the �tting are presented in table 4.1.

For the NIR probe, the comparison for dynamics of the two samples is presented



Probe Sample Asingle τsingle(ps) Astretched τstretched(ps)AsingleAstretched

β

VISUndoped 0.15 1900 2.3 0.5 0.07 0.23

Co-doped 0.12 750 2.7 0.5 0.04 0.3

NIR Undoped 1.4 0.7 3.2 3 0.44 0.2

Table 4.1: The �tting parameters for IA decay for the undoped and co-doped samples.

The low value of theAsingleAstretched

ratio implies that the stretched component is dominant.

in �gure 4.9b with normalization at 200 ps. The �tting function of IA dynamics

for the undoped sample includes a single and a stretch exponential component, the

value for the parameters are shown in table 4.1. For the co-doped sample, an in-

terpretation of the IA for NIR probe as combination of bleaching and an additional

absorption components will be presented in the next section.

Figure 4.9b shows the IA decay with NIR probe; two regions can be distinguished:

Figure 4.9: The comparison of IA dynamics for the undoped and co-doped samples

excited by the photon energy of 3.1 eV. a): The IA dynamics for VIS probe is

normalized at the maximum, the co-doped sample shows a slightly faster decay than

the undoped one, the �tting curves for these traces are also shown. b): The IA

dynamics for the NIR probe normalized around t = 200 ps. A clear di�erence between

the two dynamics can be seen for t < 200 ps. For t > 200 ps, the dynamics for both

materials are similar.

• 0 - 200 ps: the undoped sample shows a faster IA decay, with its ampli-

tude reducing 2 times, while that of the co-doped one decreases around 1.5

times. We propose that in this time window, the co-doped sample exhibits

both the additional absorption as well as bleaching, which slows down the

experimentally measured dynamics. A more detailed discussion will be given

later.


• After 200 ps: the IA decay dynamics of both materials becomes comparable,

with that of the undoped sample being slightly slower.

In order to understand why the IA dynamics for the co-doped sample might be

di�erent for VIS and NIR probe ranges, we note the following:

• The probe pulse might induce both interband and intraband transitions - see

�gure 4.10a. Upon a pump energy of 3.1 eV, carriers are initially excited into

the conduction band. A subsequent probe might induce the linear absorp-

tion (interband transition) as well as the free-carrier absorption (intraband

transition), if the probe energy is larger than bandgap.

Figure 4.10: The transitions of electron in transient absorption in a co-doped NC

a): the pump energy is high enough to excite the carrier to the conduction band

(blue arrow), the VIS probe might cause both interband and intraband transitions

(pink arrows) if its energy is larger than the band gap, and/or between impurity

levels (black arrows). b): The NIR probe beam with incident intensity I0 is absorbed

by the sample, the transmitted intensity is Ino pumpprobe . c): The NC is excited by the

pump, the hot carrier cools down to the band edge, the NIR probe with the same

energy as bandgap can not induce the interband transition because the level at the

conduction band edge is occupied, the probe is not absorbed and its intensity is higher

than Ino pumpprobe ; consequently IA < 0. This process is called bleaching.

• The processes which might take place in the co-doped sample upon NIR probe

are illustrated in �gures 4.10b and 4.10c. The pump beam creates a free carrier

in the conduction band and the probe might excite the free carrier to a higher



level (interband transition), or promote another carrier from the valence band

if its energy is high enough. The lower energy probe can also excite a carrier

at a donor or an acceptor level. When only the probe is applied, the initial

intensity I0 is absorbed by the NC and the transmitted beam has a lower

intensity (Ino pumprobe ). However, if the probe pulse is preceded by a pump, then

the lowest states in the conduction band as well as some dopant states might be

occupied, and consequently, the probe absorption in the range of the bandgap

energy will be bleached. In this case, the probe intensity I0 is not changed,

and the IA amplitude, as calculated by equation 2.13, appears to be negative.

Figure 4.11: The interpretation of the IA dynamics for the co-doped sample with NIR

probe upon the excitation energy of 3.1 eV. The grey trace relates to experimental

IA dynamics with VIS probe, and the red curve is experimental data of IA dynamics

obtained with the NIR probe. The violet trace is the di�erence between the red curve

and the grey one, and represents the bleaching of the probe absorption. The �tting

of the bleach is shown with the same colour as the experimental data.

In the view of the above, a di�erent procedure is used to model the IA decay dy-

namics for the co-doped sample, as illustrated in �gure 4.11 for transients measured

with the pump energy of 3.1 eV. The IA for VIS probe (grey trace) and for NIR (red

trace) are normalized at 200 ps. The �rst trace stands for the free carrier absorp-

tion, and is �tted by a function consisting of a single and a stretched exponential

component with lifetimes of 750 and 0.5 ps, respectively. The bleaching component

is obtained by subtracting the IA transient measured with the VIS probe from that

obtained for the NIR probe; the bleaching dynamics can be �tted by two single

exponent components, with the lifetimes of 1 and 12 ps.


4.3.4 Comparision of carrier generation quantum yield as deter-

mined from photoluminescence and induced absorption

Figure 4.12: a): The procedure to calculate the relative PL QY of the co-doped sample

from the IA measurements for a pump energy of 2.48 eV (see the text for details)

in measurements of series 2. b): The dependence of IA amplitude at 3 ps for the

co-doped sample on the number of absorbed photons. The error bars are calculated

by the same method as in �gure 4.3.

In �gure 4.3, CM is investigated in terms of the amplitude of IA at the tail of

IA dynamics for the �rst series of measurements (series 1). However the A-to-B

ratios are almost similar for all excitation energies (see �gure 4.8), which implies

that CM can be investigated by the amplitude at any point of the IA dynamics

trace. In �gure 4.12a, the amplitudes of IA at a time delay of 3 ps are shown

as function of the number of absorbed photons for a pump energy of 2.48 eV in

series 2. The �tting line for this dependence is expected to pass through the origin.

Because of the error bars, the possible �tting lines are in the shadowed area. The

slopes of the lines can be determined at the black vertical line, for the number of

absorbed photons of 6 × 1014. The lines with lowest and highest slope intersect

with the black line at UL and UH , respectively. The average amplitude is the

average value of UA = (UL + UH)/2. The average �tting line connects UA and the

origin of coordinate system. The relative quantum yield for this pump energy is

UA ± ∆U, where ∆U=UH - UA. Figure 4.12b presents results obtained with the

same method applied for various excitation energies. The slopes of the �tting lines

present the relative free-carrier generation yield for individual excitation energies.

As can be seen, the carrier generation yield increases with the excitation energy.

As discussed before, the PL QY is proportional to the free carrier generation yield,

as determined from IA measurements. The relative PL QY from measurements of



Figure 4.13: a) and b) CM in the co-doped and undoped materials investigated by

IA (from both series 1 and series 2) and PL QY, displayed in absolute and reduced

energy scales, respectively. PL QY gradients of the samples in the absolute energy

scale are quite similar. c) and d) the spectral shifts for the two samples shown in

absolute and reduced energy scales, respectively [123].

series 1 is calculated by the same method (not shown). In �gure 4.13a, the relative

PL QY is aligned with the absolute value over a large range of excitation energies.

For the undoped Si NCs, the agreement of PL QY between setup in �gure 2.1 and

IA has been reported in reference [72]. In the current research, PL QY of the co-

doped sample is multiplied 4 times to get to the same scale as that of the undoped

sample. The PL QY of both samples feature an initial growth with the gradient

for the undoped sample being higher than that of the co-doped one. These samples

show a similar dependence on the excitation energy; an initial growth is followed by

a stability range, and then by an onset of a steep increase.

Because the CM in the undoped materials relates to the optical bandgap, the same

might hold for the co-doped sample. In �gure 4.13a and b, the QY data for both

samples are represented. From those, we note the following:

• PL QY of both the undoped and co-doped sample shows a positive gradient


in the low excitation energy range, followed by a stability range; subsequently

a sharp increase appears around 3Eg.

• The gradient of the initial increase of PL QY of the undoped sample is higher

than that of the co-doped one.

• PL QY of the undoped sample starts stabilizing around 2Eg, but for the co-

doped one, the stability appears above 2.5 Eg.

In the past, CM has been investigated also by the spectral shift of PL [123]. The

PL spectral shifts of the two samples are shown in the absolute scale (panel c) and

reduced energy scale (panel d). Those show, again, a similar behaviour: the blueshift

appears in the low excitation energy range, followed by spectral stabilization in the

middle range, and �nally a blueshift is found for the highest energies. In the reduced

energy scale, blue PL spectral shift �nishes at the excitation energy of around 1.7

times of the bandgap for both samples. The blue shift of the co-doped sample re-

appears at around 3.5 times of the bandgap energy, with a high gradient.

In order to investigate the nature of CM in co-doped Si NCs, we divide the excitation

energy into two regions:

4.3.4.1 The high excitation range, Eexc > 2.5 eV

For the undoped Si NCs, a step-like enhancement of PL QY by SSQC has been found,

and could be simulated by the SSQC [105], by integrating multiples of PL spectra.

A similar SSQC estimation is possible for the co-doped sample. Figure 4.14a shows

the SSQC estimation. In �gure 4.14b, the log-normal �tting for a PL spectrum

of the co-doped sample as obtained for an excitation energy of 2.1 eV, normalized

at the peak of the PL spectrum, called 1 PL, is shown �rst. The spectrum called

2 PL is produced through doubling the PL energies, while maintaining the same

integrated intensity. The same method is applied for other spectra, until 5 times of

the emitted energy (5 PL). The integration of these PL spectra is shown in panel

a), here the result is normalized by the integration of 1 PL. The initial value for

PL QY is set at 1 unit for the excitation energies below twice the bandgap, called

the baseline of PL QY. The photon energy is shifted by 0.05 eV., representing an

activation energy, similar to the scenario used for the undoped NCs.

In order to understand the nature of CM in the co-doped samples, we propose

a model, called �the mix�. Since doping introduces additional energy levels to the

�undoped� Si NCs, then the CMmechanism might be partly controlled by II occuring

on the band states of pure Si NCs, called �intrinsic� II and leading to the SSQC

process. The dopant levels might introduce an additional channel of II called co-

doped II. In mix model, PL QY of co-doped Si NCs is in�uenced by both II types

mentioned above. The relevant simulation result is shown in �gure 4.15a. Four



Figure 4.14: Explanation for the SSQC estimation from the PL spectra. a): the

SSQC estimation obtained by integration of multiple PL spectra. b): the �tting of

a PL spectrum of the co-doped sample (1 PL) upon an excitation of 2.1 eV. The

multiplication of emitted energy, including 2, 3, 4 and 5 times are shown together,

the PL intensities of all multiples of the PL spectra are normalized for the same

integral.

types of datasets are shown together within the same energy region, the SSQC

estimation is already shown in �gure 4.14, and the PL QY of the undoped sample is

used as a reference. In the model, the PL QY of the co-doped sample includes the

SSQC estimation (see �gure 4.14) and a 40 % contribution of II proceeding by the

band-states of Si NCs, unrelated to doping. The PL QY of the co-doped sample is

magni�ed 5 times to align with the simulation from the mix model. The results can

be well accounted for with the proposed model.

The �mix model� is schematically illustrated in �gure 4.15b. A co-doped Si NC (at

the center of the panel) is excited by a high energy photon, and a hot carrier is

created. The excess energy can be transferred to the neighbour in terms of SSQC,

as for undoped Si NCs. Loosing excess energy, the hot carrier relaxes to the band

edge, and subsequently to the donor level and recombines with the hole on the


Figure 4.15: a) and b): 4 di�erent datasets related to PL QY of the co-doped Si NCs;

the simulation with the mix model showing a good agreement with the experimental

data. c): Schematic illustration of the mechanism invoked in the mix model of the

CM in co-doped Si NCs: the excess energy of hot carrier in the excited co-doped Si

NCs might be transferred to its neighbours, and this amount of energy might excite

either an electron in the band state (SSQC) or an electron in the dopant states

(co-doped II).

acceptor level, emitting a NIR photon. The same process also appears in the NC

excited through the SSQC. Besides, the excess energy of the excited NC might be

transferred to two closest NCs by means of the II on dopant levels, increasing PL

QY.

4.3.4.2 The low excitation range, Eexc < 2.5 eV

For the low excitation range, the PL QY can not be measured with an integrat-

ing sphere due to the experimental constraints. Therefore the results from the IA

measurements in this range are used to compare with the SSQC model. The agree-

ment between the two datasets in �gure 4.16 suggests that the dopant-related II is

the dominant process in this excitation energy range, and that CM in this case pro-

ceeds via the SSQC process, which is also consistent with the excitation-independent

A-to-B ratio in the IA dynamics, as illustrated in �gure 4.8 and discussed before.

4.4. Conclusions 77

Figure 4.16: Comparison between the PL QY estimated from IA measurement and

from the SSQC estimation for the co-doped sample. The relatively good agreement

suggests that in the low excitation energy range, SSQC takes place for the co-doped

Si NCs. PL QY increase is controlled by the SSQC e�ect proceeding via the dopant

related levels, i.e. is governed by the optical bandgap responsible for PL.

4.4 Conclusions

The �rst �ngerprint of CM has been found in co-doped Si NCs with the energy

threshold between 1.5 and 2.4 times of the average optical bandgap of an ensemble,

and the nature of this process is similar to the SSQC process in undoped Si NCs.

In the high excitation energy range, the CM in the co-doped Si NCs is proposed

to be controlled by the previously identi�ed SSQC II process, which in this case

can proceed also via donor and acceptor states induced by doping. In the IA decay

dynamics, bleaching is observed; this is proposed to originate from state-�lling e�ects

at band-edge states responsible for PL. The latter result provides new insights into

microscopic origin of PL in co-doped Si NCs.

uva-dare (digital academic repository) different ... · figure 4.1: a): the dshifter of pl spctrea...

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