Supplemental material for
Femtosecond upconverted photocurrent spectroscopy
of InAs quantum nanostructures
Yasuhiro Yamada1, David M. Tex1,2, Itaru Kamiya3, and Yoshihiko Kanemitsu1,2,a)
1
Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan
2
Japan Science and Technology Agency, CREST, Uji, Kyoto 611-0011, Japan
3
Toyota Technological Institute, Nagoya, Aichi 468-8511, Japan
a)
kanemitu@scl.kyoto-u.ac.jp
Contents:
1. Sample structures and fundamental properties of QWIs
2. Principles of FEC spectroscopy
1
1. Sample structures and fundamental properties of QWIs
It is widely known that different InAs quantum structures appear during epitaxial
growth of InAs on GaAs or AlxGa1-xAs because of the large lattice mismatch. After the
formation of the two-dimensional (2D) wetting layer, which is a monolayer (ML) thick
film, 2D disk-like structures with heights of two or three MLs are formed with additional
supply of InAs (also called quantum well islands; QWIs) [S1]. When the deposition
amount of InAs exceeds the critical value typically equivalent to 1.7 MLs, the majority
of the islands transform into quantum dots [S2]. The sample used in this study was
prepared by molecular beam epitaxy under conditions identical to the conditions
described in our previous publication [S3,S4] (corresponding to Sample C in Ref. S4).
The sample structure is schematically shown in Fig. S1.
This sample has been investigated in detail in our previous publications by means of
static photoluminescence (PL) and photocurrent (PC) excitation spectroscopy [S3,S4].
Based on these researches, we have determined the temperature-dependent resonance
energy of InAs QD, 2ML-QWI, 3ML-QWI, and WL in the AlGaAs barrier, as illustrated
in Fig. S1. The assignment of the 2-and 3-ML peak energies was confirmed by comparing
the peak positions with those obtained from an eight-band k-p calculation [S4]. For
instance, the resonance energy for 2-ML QWIs at room temperature is 1.37 eV, and QD
resonance energy widely ranges below 1.25 eV. The QWI and QD resonance energies
show blueshifts with a decrease of temperature. By performing the time-resolved
measurements on this specific same sample, we are able to directly verify the
upconversion process, supported by the previous studies. It is considered that these InAs
quantum structures are randomly distributed in the InAs layer according to the PL and PC
imaging spectroscopy [S5]. As confirmed by atomic force microscopy, the QD density
was several fold larger than QWI density in an uncapped sample [S4] and the micro-PLE
and PC measurements suggest that energy transfer occurs from QWI to deep QD states
[S5].
As described in the main text, the Auger process is responsible for upconversion in
QWIs, and carriers are excited to the barrier’s higher energy state when multiple carriers
are photogenerated in a QWI. This process results in charge migration to the surrounding
AlxGa1-xAs.
2
InAs
GaAs
AlGaAs
WL
Conduction
Band
2ML-QWI
3ML-QWI
QD
Valence
Band
FIG. S1 Schematic description of the sample structure and the energy diagram.
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2. Principles of FEC spectroscopy
von der Linde proposed FEC spectroscopy as a convenient and cost-effective
measurement method for ultrafast PL measurements [S6]. In FEC, two femtosecond
pulses are focused on a sample. In the present study, a mechanical chopper modulates the
laser pulses at different frequencies (f1 and f2). Using a lock-in amplifier, the frequency
difference component (|f1-f2|) of the total PL (or PC) intensity as a function of the time
delay (t) between the first and second pulses is detected. Therefore, the FEC intensity
corresponds to a variation of the PL (or PC) due to the temporal overlap of photocarriers
induced by pump and probe excitation.
Here, we consider the relationship between the FEC profile and the photoexcited
carrier dynamics. For a carrier lifetime such that << t [as shown in Fig. S2(a)], there
is no temporal overlap between carriers induced by the first and second pulses. In this
case, the total PL (or PC) is a simple sum of the contribution from the first and second
∞
∞
pulses, i.e., ∫0 𝑛(𝑁1 , 𝜏)𝑑𝜏 + ∫0 𝑛(𝑁2 , 𝜏)𝑑𝜏 (see Fig. S2(a)), and the FEC signal intensity
should be 0 by definition. Here, n(N,t) represents the carrier density at time t after the
initial carrier density N induced by photoexcitation at time 0. N1 and N2 are the initial
photocarrier densities generated by the first and second pulses. Conversely, when ~ t,
temporal overlap between carriers generated by the first and second pulses occurs, and
this overlap results in a variation in the total PL (or PC) intensity because of the nonlinear
interaction between carriers. If we assume that the PL (or PC) intensity is proportional to
∞
𝑡
the carrier density, the total PL (or PC) is written as ∫0 𝑛(𝑁1 , 𝜏)𝑑𝜏 + ∫0 𝑛(𝑁2 +
𝑛(𝑁1 , 𝑡), 𝜏)𝑑𝜏 which corresponds to the integrated value of the carrier density over time
(see Fig. S2(b)). Therefore, the FEC signal intensity, corresponding to a variation of the
PL (or PC) due to the temporal overlap of photocarriers, becomes
∞
∞
∞
𝑡
FEC∝ ∫0 𝑛(𝑁1 , 𝜏)𝑑𝜏 + ∫0 𝑛(𝑁2 , 𝜏)𝑑𝜏 − ∫0 𝑛(𝑁1 , 𝜏)𝑑𝜏 − ∫0 𝑛(𝑁2 + 𝑛(𝑁1 , 𝑡), 𝜏)𝑑𝜏
(S1).
When N1 << N2, we obtain the following approximation:
∞ 𝑛(𝑛(𝑁1 𝑡),𝜏)
FEC ∝ 𝑛(𝑁1 , 𝑡) ∫0 {
𝑛(𝑁1 𝑡)
−
𝜕𝑛(𝑁2 ,𝜏)
𝜕𝑁
} 𝑑𝜏 (for t > 0)
∞
∞
(S2).
In this derivation, we used ∫0 𝑛(𝑛(𝑁1 , 𝑡), 𝜏)𝑑𝜏 = ∫𝑡 𝑛(𝑁1 , 𝜏)𝑑𝜏 and the approximation
𝑛(𝑁2 + 𝑛(𝑁1 , 𝑡), 𝜏) ≅ 𝑛(𝑁2, 𝜏) + 𝑛(𝑁1 , 𝑡)
𝜕𝑛(𝑁2 ,𝜏)
𝜕𝑁
.
4
If we assume weak nonlinearity, (i.e., n(N,t)=A1(t)N + A2(t)N2 +…), the FEC signal is
approximately FEC ∝ n(N1,t)N2.
According to Eq. (S2), the FEC signal intensity is zero when n(N,t) depends linearly
on N, and positive (negative) FEC signal corresponds to sublinear (superlinear)
excitation-intensity dependence. We have confirmed in our experiment that the FEC
decay profile is independent of the second-pulse fluence (N2), as can be inferred from Eq.
(S2), implying that our assumption to derive Eq.(S2) is valid in our experimental
condition.
We emphasize that the nonlinearity of the excitation-intensity dependence is essential
for the FEC measurement. However, the physical mechanism that causes this nonlinearity
has no influence on the validity of the FEC spectroscopy.
FIG. S2 Decay dynamics of carrier density under excitation by first and second pulses for
(a)t>>carrier lifetime and (b) t~ carrier lifetime.
References
[S1] R. Heitz, T. R. Ramachandran, A. Kalburge, Q. Xie, I. Mukhametzhanov, P. Chen,
and A. Madhukar, Phys. Rev. Lett. 78, 4071 (1997).
[S2] D. Leonard, M. Krishnamurthy, C. M. Reaves, S. P. Denbaars, and P. Petroff, Appl.
Phys. Lett. 63, 3203 (1993).
5
[S3] D. M. Tex and I. Kamiya, Phys. Rev. B 83, 081309(R) (2011).
[S4] D. M. Tex, I. Kamiya, and Y. Kanemitsu, Phys. Rev. B 87, 245305 (2013).
[S5] D. M. Tex, T. Ihara, I. Kamiya, and Y. Kanemitsu, Phys. Rev. B 89, 125301 (2014).
[S6] D. von der Linde, J. Kuhl, and E. Rosengart, J. Lumin. 24–25, 675 (1981).
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