Investigation of the quantum confinement effects in Ge dots by electrical measurements

Applied Surface Science 225 (2004) 281–286

Investigation of the quantum confinement effects in Ge dots by electrical measurements X.Y. Maa,b,*, Sh. H. Huanga, Y. Chena, F. Lua a

Surface Physics Laboratory, Fudan University, Shanghai 200433, PR China Department of Physics, Shaoxing College of Arts and Sciences, Institute of Photoelectrical Materials, Shaoxing 312000, Zhejiang Prov., PR China

b

Received 22 May 2003; accepted 14 October 2003

Abstract The quantum confinement effects of Ge quantum-dots (QDs) grown by molecular beam epitaxy (MBE) are investigated by capacitance–voltage (C–V), admittance spectroscopy, and deep level transient spectroscopy (DLTS). The potential height of hole in the Ge dot obtained by C–V intercept, admittance spectroscopy and DLTS are 0.335, 0.341, and 0.338 eV, respectively. The DLTS method is also used to observe the changes of hole concentration, activation energy (Ea), and capture cross-section with filling time duration (tp) and bias voltage. The results show that the hole concentration in the Ge quantum-dots is a function of the pulse duration (tp) and reversed bias voltage, the activation energy and capture cross-section decrease with the increasing filling time duration due to the Coulomb charging effect. # 2003 Elsevier B.V. All rights reserved. PACS: 68.35.Dv; 68.55.Ln; 61.72.Tt; 61.80.Jh Keywords: Ge QD; C–V; Admittance spectroscopy; Deep level transient spectroscopy; Hole potential height DE

1. Introduction The quantum-dot (QD) structures based on Ge/Si heterojunction are very promising for photodetector and photo wave-guild devices. For example, comparing to quantum well infrared photodetectors (QWIP), the efficiency may be further enhanced in quantumdot infrared photodetectors (QDIPs), where the confinement potential is three-dimensional [1]. For building such QD devices, it is very important to completely understand the energy band diagram [2–4]. Optical methods of investigation are usually * Corresponding author. Tel.: þ86-575-8062252. E-mail address: [email protected] (X.Y. Ma).

applied to examine the electronic structure of such heterostructures. However, it can also be studied using electrical measurements. Recently, as a fundamental technique for band structure and deep level studies, capacitance–voltage (C–V), admittance spectroscopy and deep level transition spectroscopy (DLTS) have been applied to study Ge QDs [5–7]. This paper outlines how C–V intercept of a semiconductor heterostructure, admittance spectroscopy, and DLTS are used to measure the hole potential and how DLTS is used to investigate the hole capture kinetics of Ge QDs embedded in a Si matrix. Besides, the activation energy of the confined levels in Ge QDs and its apparent capture cross-section for holes are determined from standard DLTS Arrhenius plots of

0169-4332/$ – see front matter # 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2003.10.032

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ln ðep =T 2 Þ  1=kT, and the results of energy and capture cross-section with filling time duration (tp) have also been presented.

2. The principles of the measurements 2.1. The C–V intercept method for determination hole potential height in Ge dot C–V method allows for measuring the carrier concentration of semiconductor side for a Schottky diode. Considering the stored charge QVR in the junction and its cross-sectional area A, on which there is an externally applied reverse voltage VR, the small signal capacitance CVR can be expressed as CVR

  1 2eeN 1=2 ¼ A 2 Vbi þ VR

(1)

where e is the permittivity of the semiconductor, Vbi the built-in potential of the metal–Si junction, and N is the doped concentration in the semiconductor. For the Ge quantum-dot studied, the band diagram under applied bias is shown in Fig. 1. The energy band discontinuities at the junction between Si and Ge layers may result in redistribution of carriers at the interface. We assume Si semiconductor is uniformly 2 spatially doped. The total capacitance CVR at the reverse bias VR can be expressed as   2 2 CVR ¼ (2) ðVbi þ VR Þ eeðNA  PGe ÞA2 Vbi is the built-in potential of the Schottky barrier with Ge/Si quantum-dot, NA the dopant concentration in Si, and PGe is the carrier concentration in Ge dot. Using Eq. (2), we can determine the built-in potential Vbi at bias VR.

Metal

Si

eVb1

Ge

Si EVsi-EF ∆E eVd eVb2

EF

Fig. 1. The energy band diagram of Ge/Si quantum-dot.

2.2. Admittance spectroscopy Admittance spectroscopy is also used to study the energy level structure of the QDs quantitatively. According to the thermal emission theory [8]:   Eai (3) ei ¼ aT 2 exp  kT where a is temperature-independent constants, ei the hole emission rate in Ge dot, T the temperature, k the Boltzmann constant, and Ea is the activation energy of ith holes emitting from QDs with respect to Si valence band edge (i.e. the difference between the energy level of emitted hole and the valence band edge of Si barrier). The carrier population in the Ge dot changes with applied bias, and the conductance, G, changes with the hole emission rate from QDs. The conductance of the sample can be described by the hole emission theory. Due to the strong temperature dependence of the hole emission rate, G changes with temperature. The conductance will get a maximum value when the emission rate equals the frequency at some temperature Tm. Under multiple frequency, the peak of G shifts to higher temperatures with increasing measurement frequency. We may get a set of (ei, Tm) for different frequencies, the activation energy Eai of the confined levels in the dot can be deduced from the slope of an Arrhenius plot of ln ðo=T 2 Þ  1=kT. The hole potential height DE can be determined by the activation energy from the ground level of the dot DE ¼ Ea1

(4)

2.3. Deep level transient spectroscopy (DLTS) The Ge QD can be viewed as a giant point trap, which captures and emits carriers in the same way as a deep level trap. The thermal emission of captured charge carriers during measurements of the DLTS spectra gives information about the energy barrier height between a level in the Ge QD and the edge of Si valence band. The DLTS measurements were carried out under filling pulse time duration (tp) as short as 1 ms possible. With a reversed pulse bias applied on the sample and in the pulse period, holes fill the QD levels. Then QD levels emits after the pulses, the capacitance of the sample exponentially decreases with time: CðtÞ ¼ Cð0Þ expðep tÞ

(5)

X.Y. Ma et al. / Applied Surface Science 225 (2004) 281–286

240 Capacitance (pF)

The emission rate of holes is expressed as Eq. (3), where Eai is also the activation energy of the ith hole emitting from the dot. The values of ei as a function of temperature can be obtained in the DLTS measurement. The activation energy Eai can be determined from the Arrhenius ln ðep =T 2 Þ  1=kT plot. Similar to Admittance spectroscopy method, the hole potential height can be determined by Eq. (4).

283

200

160

120

3. Experiment

-4

-3

-2

-1

0

1

Reverse Bias (V)

The sample investigated in this article consists of one layer of Ge quantum-dots grown by the molecular beam epitaxy (MBE) on p-type Si(1 0 0) wafers with the resistivity of about 0.1 O cm. The growth temperature was kept at 500 8C and the growth rates were ˚ /s for Si and Ge, respectively. The Ge 1 and 0.2 A quantum-dot layer was formed by the self-assembly via the Stranski–Krastanov growth mode. A 200 nm B-doped (2  1016 cm2) Si buffer layer was grown on the substrate firstly, then followed a 1.4 nm thick Ge QD layer, finally capped with a 320 nm B-doped (2  1016 cm2) Si layer. The sample was structurally characterized using in situ reflection high-energy electron diffraction (RHEED) and cross-section transmission electron microscopic (TEM). The island of Ge is about 2 nm in height and 13 nm in diameter. The area density of the dots is in the range of 108– 109 cm2. The sample was then fabricated into an Schottky diode structure with an Al electrode at the front-side and an ohmic contact at the backside. The diameter of the Al electrode is about 0.9 mm. Capacitance–voltage and the admittance spectroscopy were performed at a multi frequency LCR meter HP4275A. DLTS measurements were done with high frequency capacitance meter Boonton 72BD and special computer control and process system within the temperature range of 77–300 K.

4. Results and discussion 4.1. C–V results The capacitance–voltage characteristic of the sample measured under the bias 3 to 0.3 V is shown in

Fig. 2. The C–V curve under reverse bias voltage.

Fig. 2. There is a platform in C–V curve in the bias region of 0 to 1.5 V, which indicates that the boundary of space charge region is located at the quantumdot layer where the large concentration of confined holes blocks the further extension of space charge region. As the reverse bias voltage increases above 1.5 V, the space charge region extends over the dot layer so the holes in the dot are completely pumped out. The Schottky potential region will extend in the Si cap layer when we apply a small positive bias to the sample. As the positive bias is decreased to 0 V (Fig. 2), the Schottky potential region will arrive at the edge of the Si/Ge junction and then meet the Si/Ge space charge region. Here, the total built-in potential is the sum of the Schottky built-in potential and the Si/ Ge built-in potential. Up to now, the carriers in the Ge dot have not been pumped out and PGe does not change in the forward bias region. Therefore, the term (NA  PGe ) in Eq. (2) can be considered as a constant 2 and CVR depends on VR only. If we extrapolate this linear relation to the voltage axis, it gives an intercept that we denote as Vb1. According to above analysis, the Schottky built-in potential equals to Vb1. If we denote Vd as the built in potential of Ge/Si heterostructure and the total built-in potential as Vb0 at bias 0 V, we may have a relation: Vb0 ¼ Vb1 þ Vd

(6)

Decreasing the bias continuously, it becomes reverse bias, the Schottky potential region will pass the Ge dot and over the Ge/Si buffer space charge region. For large applied reverse bias VR nearby

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2.0 V (see Fig. 2), the carriers PGe in Ge dot are completely pumped out, and the total built-in potential becomes Vb2 (Fig. 1). Similarly, we obtain the relation: Vb2 ¼ Vb0 þ Vd 2 In here, the evaluation of CVR becomes   2 2 ¼ CVR ðVb2 þ VR Þ eeNA A2

(7)

(8)

2 Thus, Cbi is linearly dependent on VR, and the intercept value on the voltage axis will give the magnitude of the total built-in potential Vb2. Putting the Eq. (6) into Eq. (7), we have Vb2 ¼ Vb0 þ VD ¼ Vb1 þ 2VD . Therefore, the hole potential height of Ge dot is given by (see Fig. 1)

1 DE ¼ eVD þ ðEVSi  EF Þ ¼ eðVb2  Vb1 Þ 2 NA þ kT ln NVSi

(9)

where ðEVSi  EF Þ is the energy difference between Fermi energy and the valence band edge for p-Si. At room temperature, the acceptor impurity is completely ionized. NVSi is the effective state density of the valence bands of Si. The corresponding dependencies of (1/C2)–VR of nearby 0 and 2.0 V measured by C–V show in Figs. 3 and 4, respectively. From Figs. 3 and 4, we get the values of Vb1 ¼ 0:351 V and Vb2 ¼ 0:70 V. The given dopant concentration in Si is 2  1016 , and NVSi ¼ 1:1  1019 cm3. According to Eq. (9), the hole potential height in the dot DE ¼ 0:335 eV.

Fig. 3. The (1/C2)–VR dependence nearby bias 0 V, which eVb1 can be determined by extrapolating applied bias VR.

Fig. 4. The (1/C2)–VR dependence nearby 2.0 V, which eVb2 can be determined by extrapolating applied bias VR.

4.2. Admittance spectroscopy result Admittance spectroscopy measurement of temperature dependence is completed to the sample under various frequencies at bias 0.5 V. The result is shown in Fig. 5. With increasing applied frequency, the corresponding peaks shift to high temperature. The activation energy obtained from Arrhenius ln ðo=T 2 Þ  1=kT is 0.341 eVat bias 0.5 V. At weak field, the activation energy of 0.341 eV can be considered as emitting energy of hole from the ground state of the dot. According to Eq. (4), the hole potential height of the ground state in Ge dot DE ¼ 0:341 eV. 4.3. DLTS spectroscopy results DLTS measurements of temperature dependence are performed to the sample at various filling time

Fig. 5. Admittance spectroscopy temperature dependence of the sample at various frequencies.

X.Y. Ma et al. / Applied Surface Science 225 (2004) 281–286

Fig. 6. DLTS temperature dependence of the sample at various filling time duration (tp).

durations (tp) (Fig. 6). The maximum amplitude of the DLTS in quantum-dot also shows a feature of saturation for increasing tp. It arrives at saturation at tp ¼ 15 ms, because the maximum amplitudes of the DLTS signal (DC) of tp ¼ 15 ms and 1 ms overlap, indicating that hole concentration in the QD arrives at saturation. The data of activation energy and capture cross-section at vary tp obtained by Arrhenius ln ðep =T 2 Þ  1=kT are presented in Table 1. The values of activation energy decrease with increasing tp. The reason is that there are discrete energy levels in a QD and a Coulomb charge effect. The activation energy a mount to Ea ¼ 0:338 and 0.225 eV when the pulse duration was fixed at tp ¼ 5 and 15 ms, respectively. This value of activation energy of 5 ms is higher than that of 15 ms. A phenomenological explanation can be provided on the analysis of the capture kinetics of the dot. For long tp, the hole concentration in the dot is higher than that of the short tp, Coulomb repulsive effect will appear and oppose the arrival of holes. For shorter (tp) values, a lower concentration of holes is confined in the dot. Therefore, the activation energy is

285

higher. The capture cross-section was found to be two orders of magnitude higher at tp ¼ 5 ms (5:2  1015 cm2) than that measured at tp ¼ 15 ms (4:0  1017 cm2). Accordingly, the reduction in capture cross-section with filling time (tp) also can be attributed to Coulomb repulsive effect. It is clear that the first hole is in Ge dot when tp ¼ 5 ms. The activation energy of tp ¼ 5 ms can be considered as the hole potential height of the ground state DE ¼ Ea1 ¼ 0:338 eV. This value agrees with the value 0.335 eV measured by C–V and 0.341 eV obtained by admittance spectroscopy measurement. The reason that the value 0.335 eV from C–V measurement is smaller than the other two values 0.338 and 0.341 eV is that C–V measurement is a direct measurement method and the other two methods are indirect measurements, in which we made some approximations. Fig. 7 shows the DLTS signals at various reversed bias voltages. We find that the peaks shift to higher temperature and the peaks become broad gradually with the increasing reverse bias. The amplitude of the peaks increases initially, then decrease with the enhanced reverse bias, so there is a maximum value. This behavior is related to the carrier concentration of the dot. The carriers concentration can be identified by the position of Fermi energy level, it moves toward Si valence band with increasing reverse bias across more energy levels and detecting hole emission from deeper levels of the dot. The area of the DLTS peak corresponds to hole concentration in the dots. The amplitude of DLTS peaks will arrive at a maximum when

Table 1 Activation energy (Ea) and capture cross-section (s) of the Ge QD with the various filling time duration (tp) tp (ms) 5 8 10 12 15

Ea(eV) 0.338 0.312 0.286 0.261 0.225

s(cm2) 5.2 1.2 8.5 3.5 4.0

    

Tpeak(K) 15

10 1015 1016 1016 1017

135 140 155

Fig. 7. The DLTS signals of the sample at various reversed bias voltages.

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Fermi level pass over the total levels of the QD at a certain reverse bias. On the other hand, the tunneling probability of hole increase with the applied bias, so the amplitude of DLTS peaks will decrease with increase of reverse bias. Accordingly, the DLTS peaks shift to high temperature, and the peaks become broad gradually. Above all, C–V intercept method, admittance spectroscopy and DLTS measurements all can be used to measure the quantum confined effects. The hole potential height measured by them are very well in agreement. But C–V is more complex than admittance spectroscopy and DLTS. Admittance spectroscopy and DLTS are very similar in principle of measurements. DLTS cannot only study the Coulomb charging effects at varying pulse duration, but also can investigate the tunneling effects under varying bias.

energy and capture cross-section decrease with the increasing value of tp. The maximum of the peaks of DLTS signals shift to higher temperature and the peaks become broad gradually with the increased reverse bias. It is attributed to Coulomb repulsive effect, the variation of the carrier population and the tunneling effect in Ge quantum-dot.

Acknowledgements This work was supported by the special funds for Major State Basic Research Project No. G2001CB3095 of China, the Commission of Science and Technology of Shanghai, and the National Natural Science Foundation of China.

References 5. Conclusions The C–V intercept method, admittance spectroscopy, and DLTS measurements have been applied to investigate the quantum confinement effect. They give hole potential height in the Ge quantum-dot 0.335, 0.341, and 0.338 eV in this paper, respectively. The values are very consistent. Deep level transient spectroscopy technique also has been used to investigate the hole capture process and concentrations changes of Ge QD. Variations of activation energy and capture cross-section with the filling time and reverse bias voltage are observed. Both activation

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