新穎光電半導體材料、奈米微細結構及其元件構造之光學特性研究

新穎光電半導體材料、奈米微細結構及其元件構造之光學 特性研究

研究成果報告(精簡版)

計 畫 類 別 ： 個別型

計 畫 編 號 ： NSC 97-2221-E-011-131-

執 行 期 間 ： 97 年 08 月 01 日至 98 年 10 月 31 日 執 行 單 位 ： 國立臺灣科技大學電子工程系

計 畫 主 持 人 ： 黃鶯聲

計畫參與人員： 博士班研究生-兼任助理人員：吳俊德

處 理 方 式 ： 本計畫可公開查詢

中 華 民 國 98 年 11 月 13 日

□期中進度報告

新穎光電半導體材料、奈米微細結構及其元件構造之光學特性 研究

Optical Characterization of Novel Optoelectronic Semiconductor Materials, Nanostructures and Device Structures

計 畫 類 別 ： ■ 個 別 型 計 畫 □ 整 合 型 計 畫 計 畫 編 號 ： NSC 97 － 2221 － E － 011 － 131 － 執行期間： 97 年 08 月 01 日 至 98 年 10 月 31 日

計 畫 主 持 人 ： 黃 鶯 聲

計 畫 參 與 人 員 ： 吳 俊 德 、 蔡 欣 利 、 林 智 偉 、 林 沿 志 、 洪 筱 芸

成果報告類型（依經費核定清單規定繳交）：■精簡報告 □完整報告

本 成 果 報 告 包 括 以 下 應 繳 交 之 附 件 ：

□ 赴 國 外 出 差 或 研 習 心 得 報 告 一 份

□ 赴 大 陸 地 區 出 差 或 研 習 心 得 報 告 一 份

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□ 國際合作研究計畫國外研究報告書一份

處理方式：除產學合作研究計畫、提升產業技術及人才培育研究計畫、列管計畫 及下列情形者外，得立即公開查詢

□涉及專利或其他智慧財產權，□一年□二年後可公開查詢

執 行 單 位 ： 國 立 台 灣 科 技 大 學 電 子 工 程 所

中 華 民 國 9 8 年 1 1 月 1 2 日

本報告利用各種不同光學量測技術，包括電場調制、壓電調制、光子調制、表面光電 壓、光激發光譜及拉曼散射等量測技術，來研究新穎光電半導體材料(例如:寬能隙 II-VI 族半

導體、含銻氮 III-V 族半導體以及砷化鎵/鍺異質結構太陽電池材料)、低維度奈米微細結構

(InGaAs/GaAs 量子井、GaAInNP/GaAs 第二型量子井、InGaAsP 多重量子井、II-VI 族半導體 多重量子井以及 GaAsSb/GaAs 多重量子井)以及過渡金屬硫屬化合物 (ReSe

、WS

)之光學特 性。此外也探討元件構造之半導體元件之光學特性(例如: II-VI 族半導體材料非對稱耦合量子 井以及磷砷化銦鎵多重量子井)。

藉由比較各種不同調制方式的譜線藉以瞭解光學調制機制。配合理論計算，探討半導體 能帶或激發態之躍遷情形，以瞭解其異質接面狀態及其奈米微細結構和合金成分；分析譜線 的半高寬度，以鑑定其界面品質及特性，並探討可能影響的因素。同時將研究其各個躍遷訊 號和電場隨溫度的變化情形，以充掌握各種外加參數對元件品質及性能之影響,進而提昇元件 的性能。

關鍵詞：調制光譜，表面光電壓，拉曼散射，寬能隙 II-VI 族半導體，量子井，多重量子井，

非對稱耦合量子井，過渡金屬硫屬化合物

二、 英文摘要

Modulation spectroscopy and surface photovoltage spectroscopy （ SPS ） are powerful techniques for studying and characterizing the properties of bulk semiconductors, low dimensional nanostructure systems, and actual device structures. We present a detailed study of semiconductors including GaAs/Ge, GaAsSbN, II-VI wide bandgap semiconductors（ZnMgSe, ZnCdSe, ZnBeCdSe, ZnBeMgSe ） , semiconductor nanostructures （ Type-II QW, QW ） by using various modulation techniques including electric field modulation, piezomodulation , photomodulation, SPS, and Raman scattering.

The detailed study of the temperature evolution and electric field dependent of the optical transitions on bulk semiconductors, low dimensional nanostructure systems have been carried out.

The sharp, derivative like features will be fit and the origins of the various spectral features are identified by comparison with the theoretical calculation.

Keyword: Modulation spectroscopy, surface photovoltage spectroscopy, Raman scattering, II-VI wide

bandgap semiconductors, QW, MQW, ACQW

近來光電半導體材料、元件及低維度半導體奈米微細結構蓬勃發展、普遍受學界及產業 界重視。國內產業界更大量投資 MOCVD 及 MBE 設備從事 LED、LCD 面板、雷射二極體、

高效率太陽能電池以及光檢測器等光電元件，HBT 及 pHEMT 等高頻快速元件結構之磊晶成

長，並有多家廠商從事元件製造，為新興高科技產業之一。然除 LED 外，大部份元件良率有

待改進。光電半導體材料系統式樣多，結構複雜需凝聚各種背景研究人力及研究生投入研發

工作。從 1964 年起，迄今調制光譜被證明是研究半導體及其微細結構相當有力的工具。近年

來更用於實際元件（如：Solar Cell、HBT、PHEMT，LD、RCLED、VCSEL、MOS 等）結構 及量子線、量子井、量子點等低維度奈米結構之光學特性的探討，為一方便使用有效的非破 壞性鑑定方法。此類量測技術用於基本學理探討及實用元件品改善等均極富潛力，在國內外 普遍受到重視，但要分析此複雜的譜線須要足夠的專門知識，本實驗室目前已具有相當的分 析能力，然更深入瞭解譜線的來源及機制，仍是重要的課題。本計劃擬以調制光譜及表面光 電壓光譜量測技術研究新穎光電半導體低維度微細結構與元件之光學特性。

四、 研究方法

調制光譜量測技術係將待測樣品的外在物理量（如溫度、壓力、電場或磁場）做微小的 週期性改變，或是不改變待測樣品之條件，僅將量測系統（如入射光波長）做微小的週期性 變化，因而得到微分形式的譜線。此具微分形式的特性，可抑除背景信號及雜訊，使許多難 以分辨的微細結構得以清晰分辨，能靈敏地檢測材料特性，如量子井束縛能階間的躍遷能 量，合金成份、材料均勻度、內建電場強度、界面品質、深階缺陷及其活化能（activation energy ） 等 均 可 分 析 求 得 。 調 制 光 譜 與 常 見 的 穿 透 （ 吸 收 ） 、 反 射 、Photoluminescence

（PL）、Photoluminescence excitation（PLE）等量測技術是相輔相成的，互相比較量測結果 可增加對樣品本質的認識及對調制機制的瞭解。因其譜線為微分形式，訊息較傳統光譜清晰

且豐富。分析調制光譜可以靈敏地檢測出能譜的結構位置，其準確度可達 1 meV。由調制光

譜可得到的訊息和 PLE 相近。但 PLE 深受激發雷射光源的限制，量測範圍有限。PL 譜線則

在分析樣品所含雜質、缺陷有獨到之處，但難以觀察異質結構或量子侷限效應造成較高能階 的子帶間躍遷現象。而調制光譜正可補其不足。壓電調制光譜在分辨重電洞和輕電洞躍遷方

面是相當便捷的方法，而且可以避免產生在電場調制時，常因 FKO 現象而使譜線難以分析的

情形。透過各種不同調制的方法，收集到豐富而完整的光學特性，可以對樣品的品質、結構

有精確的認識，有助於改良光電元件的設計及製造技術。

得到量測樣品的躍遷訊號，將上述量測技術與調制光譜相互比較，得以更有效研究半導體細 微結構及元件結構之特性。

五、 成果報告內容 研究計畫相關成果：

1. Chan, C. H., J. D. Wu, Y. S. Huang, Y. K. Su, and K. K. Tiong, “Temperature dependent surface photovoltage spectroscopy characterization of highly strained InGaAs/GaAs double quantum well structures grown by metal organic vapor phase epitaxy”, J. Appl. Phys., Vol. 106, pp. 043523- 1~043523-5 (2009).

2. Wu, J. D., J. W. Lin, Y. S. Huang, W. O. Charles, A. Shen, Q. Zhang

and M. C. Tamargo,

“Characterization of a Zn

Cd

Se/Zn

Cd

Mg

Se multiple quantum well structure for midinfrared device applications by contactless electroreflectance and Fourier transform infrared spectroscopy”, J. Phys. D: Appl. Phys., Vol. 42, pp.165102-1~165102-4 (2009).

3. Wu, J. D., Y. S. Huang, G. Brammertz, and K. K. Tiong, “Optical characterization of thin epitaxial GaAs films on Ge substrate”, J. Appl. Phys., Vol. 106, pp. 023505-1~023505-5 (2009).

4. Ho, C. H., J. S. Li, Y. J. Chen, C. C. Wu, Y. S. Huang, and K. K. Tiong, “Optical anisotropy of near band-edge transitions in zinc oxide nanostructures”, J. Alloys Compd., Vol. 480, pp. 50~53 (2009).

5. Liang, C. H. Y. H. Chan, K. K. Tiong, Y. S. Huang, Y. M. Chen, D. O. Dumcenco, and C. H. Ho,

“Optical anisotropic of Au-doped ReS

Crystals”, J. Alloys Compd., Vol. 480, pp.94~96 (2009).

6. Dumcenco, D. O., W. Y. Huang, Y. S. Huang, and K. K. Tiong, “Anisotropic optical characteristics of Au-doped rhenium diselenide single crystals”, J. Alloys Compd., Vol. 480, pp.

104~106 (2009).

7. Sitarek, P., H. P. Hsu, Y. S. Huang, J. M. Lin, H. H. Lin, and K. K. Tiong, “Optical studies of type I GaAs

Sb

/GaAs multiple quantum well structures”, J. Appl. Phys., Vol. 105, pp. 123523- 1~123523-4 (2009).

8. Dumcenco D. O., C. T. Huang, Y. S. Huang, F. Firszt, S. Łęgowski, H. Męczyńska, A. Marasek, K. K. Tiong, “Optical characterization of Zn

Be

Mn

Se mixed crystals”, Phys. Rev. B, Vol.

79, pp. 235209-1~ 235209-8 (2009).

9. Lin, D. Y., W. C. Lin, F. L. Wu, J. S. Wu, Y. T. Pan, S. L. Lee and Y. S. Huang, “Investigations

of interdiffusion in InGaAsP multiple-quantum-well structures by photoreflectance”, phys. stat.

II band alignment at the ordered GaInNP to GaAs heterointerface”, phys. stat. sol. (a), Vol. 206, pp. 803~807 (2009).

11. Hsu, H. P., Y. N. Huang, Y. S. Huang, Y. T. Lin, T. C. Ma, H. H. Lin, K. K. Tiong, P. Sitarek, and J. Misiewicz, “Piezoreflectance and photoreflectance study of annealing effects on GaAs

Sb

and GaAs

Sb

N

films on GaAs grown by gas-source molecular beam epitaxy”, phys. stat. sol. (a), Vol. 206, pp. 830~835 (2009).

12. Ho, C. H., S. T. Wang, Y. S. Huang, and K. K. Tiong, “Structural and luminescent property of gallium chalcogenides GaSe

S

Layer compounds”, J. Mater. Sci. - Mater. Electron., Vol. 20, pp.

S207~S210 (2009).

13. Liang, C. H., K. K. Tiong, Y. S. Huang, D. Dumcenco and C. H. Ho, “In-plane anisotropic electrical and optical properties of gold–doped rhenium disulphide”, J. Mater. Sci. - Mater.

Electron., Vol. 20, pp. S476~S479 (2009).

14. Dumcenco, D. O., Y. S. Huang, F. Firszt, S. Łęgowski, H. Męczyńska, A. Marasek, K.

Strzałkowski, W. Paszkowicz, K. K. Tiong, and C. H. Hsieh, “Temperature dependent electromodulation characterization of Zn

Be

Mg

Se mixed crystals”, J. Appl. Phys., Vol. 104, pp. 073528-1~073528-6 (2008).

15. Dumcenco, D. O., Y. S. Huang, C. H. Liang, and K. K. Tiong, “Optical characterization of Au- doped rhenium diselenide single crystals”, J. Appl. Phys., Vol. 104, pp. 063501-1~063501-6 (2008).

16. Dumcenco, D. O., H. P. Hsu, Y. S. Huang, C. H. Liang, K. K. Tiong, and C. H. Du, “Optical properties of tungsten disulfide single crystals doped with gold”, Mater. Chem. Phys., Vol. 111, pp. 475-479 (2008).

17. Firszt, F., S. Łęgowski, H. Męczyńska, C. T. Huang, H. P. Hsu, and Y. S. Huang, “Localization of excited carriers in Zn

Mg

Se and Zn

Mg

Cd

Se solid solutions”, J. Korean Phys. Soc., Vol.

53, pp. 13-18 (2008).

18. Hsu, H. P., D. O. Dumcenco, C. T. Huang, Y. S. Huang, F. Firszt, S. Łęgowski, H. Męczyńska, K.

Strzałkowski, A. Marasek, and K. K. Tiong “Photoluminescence and electromodulation spectroscopy characterization of Zn

Mg

Se and Zn

Be

Mg

Se mixed crystals”, J.

Korean Phys. Soc., Vol. 53, pp. 71-76 (2008).

19. Hsu, H. P., T. W. Chung, Y. S. Huang, F. Firszt, S. Łęgowski, H. Męczyńska, A. Marasek, K.

Strzałkowski, K. K. Tiong, and M. Muñoz, “Optical characterization of Zn

Be

Mn

Se

mixed crystals”, J. Korean Phys. Soc., Vol. 53, pp. 77-82 (2008).

本期計劃中， II-VI 族半導體單晶樣品主要與波蘭 Institute of Physics, N. Copernicus University 的 Firszt 教授合作，同時 III-V 族含銻之量子點與量子井低微度奈米結構則與台灣 大 學 林 浩 雄 教 授 及 成 功 大 學 蘇 炎 坤 教 授 合 作 ， 並 且 II-VI 族 寬 能 隙 ZnCdSe 薄 膜 、 ZnCdSe/ZnCdMgSe 非對稱耦合量子井（Asymmetric Coupled Quantum Well, ACQW）結構、

含 Be 之 II-VI 族新穎材料及低維度結構（如量子井，量子點）則與紐約市立大學 M. C.

Tamargo 教授合作。

本計劃進行期間總共發表與計劃相關論文 19 篇（詳見附錄），成果豐碩。計畫進度與 原計畫書所預期目標相符、在本計劃所預期之目標為探討半導體能帶或激發態之躍遷情形，

以瞭解其異質接面狀態及其奈米微細結構和合金成分；分析譜線的半高寬度，以鑑定其界面 品質及特性，並探討可能影響的因素。同時將研究其各個躍遷訊號和電場隨溫度的變化情 形，以充掌握各種外加參數對元件品質及性能之影響,進而提昇元件的性能。並擬將此技術發 展成為非接觸及非破壞性元件構造與品質鑑定之有利工具。本計劃之研究成果均發表於知名 SCI 學術期刊中，研究成果可供相關元件特性模擬及設計者參考，具應用價值。

七、 參考文獻

1. Lyakh, A., P. Zory, D. Wasserman, G. Shu, C. Gmachl, M. D’Souza, D. Botez, and D. Bour,

“Narrow stripe-width, low-ridge high power quantum cascade lasers,” Appl. Phys. Lett. 90, 141102 (2007).

2. Lu, H., A. Shen, M. Mounz, M. C. Tamargo, W. Charles, I. Yokomizo, Y. Gong, G. F. Neumark, K. J. Franz, and C. Gmachl, “Study of intersubband transitions of Zn

Cd

Se/Zn

Cd

Mg

Se multiple quantum wells grown by molecular beam epitaxy for midinfrared device applications,” J. Vac. Sci. Technol. B 25, 1103 (2007).

3. M. Adachi, K. Ando, T. Abe, N. Inoue, A. Urata, S. Tsutsumi, Y. Hashimoto, H. Kasada, K Katayama, and T. Nakamura, “Slow-mode degradation mechanism and its control in new bright and long-lived ZnSe white LEDs,” phys. stat. sol. (b) 243, 943 (2006).

4. D. S. Jiang, Y. H. Qu, H. Q. Ni, D. H. Wu, Y. Q. Xu, and Z. C. Niu, “Optical properties of InGaAs/GaAs quantum wells grown by Sb-assisted molecular beam epitaxy,” J. Cryst. Growth 288, 12 (2006).

5. R. Kudrawiec, M. Gladysiewicz, J. Misiewicz, H. B. Yuen, S. R. Bank, M. A. Wistey, H. P. Bae,

and J. S. Harris, “Interband transitions in GaN

As

Sb

/GaAs (0<x<0.11) single quantum

wells studied by contactless electroreflectance spectroscopy,” Phys. Rev. B 73, 245413 (2006).

1054 (2005).

7. L. Wu, S. Iyer, K. Nunna, J. Li, S. Bharatan, W. Collis, and K. Matney, “MBE growth and properties of GaAsSbN/GaAs single quantum wells,” J. Cryst, Growth 279, 293 (2005).

8. S. H. Park, “Electronic and optical properties of 1.3 μm GaAsSbN/GaAs quantum well lasers,” J.

Appl. Phys. 100, 043113 (2006).

9. Y. X. Dang, W. J. Fan, S. T. Ng, S. Wicaksono, S. F. Yoon, and D. H. Zhang, “Study of interdiffusion in GaAsSbN/GaAs quantum well structure by ten-band k‧p method,” J. Appl.

Phys. 98, 026102 (2005).

10. Y. Kawamura, T. Kakagawa, and N. Inoue, “Lasing characteristics of InGaAsSbN quantum well laser diodes at 2-μm-wavelength region grown on InP substrates,” Jpn. J. Appl. Phys. 44, 6000 (2005).

11. S. Wicaksono, S. F. Yoon, K. H. Tan, W. K. Cheah, “Concomitant incorporation of antimony and nitrogen in GaAsSbN lattice-matched to GaAs,” J. Cryst. Growth 274, 355 (2005).

12. S. Wicaksono, S. F. Yoon, W. K. Loke, K. H. Tan, K. L. Lew, M. Zegaoui, J. P. Vilcot, D.

Decoster, J. Chazelas, “Effect of growth temperature on defect states of GaAsSbN intrinsic layer in GaAs/GaAsSbN/GaAs photodiode for 1.3 μm application,” J. Appl. Phys. 102, 044505 (2007).

13. K. Nunna, S. Lyer, L. Wu, J. Li, S. Bharatan, X. Wei, R. T. Senger, and K. K. Bajaj, “Nitrogen incorporation and optical studies of GaAsSbN/GaAs single quantum well heterostructures,” J.

Appl. Phys. 102, 053106 (2007).

14. D. P. Xu, J. Y. T. Huang, J. Park, L. J. Mawst, T. F. Kuechm, X. Song, and S. E. Babcock,

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191909 (2007).

Temperature dependent surface photovoltage spectroscopy characterization of highly strained InGaAs/GaAs double quantum well structures grown by metal organic vapor phase epitaxy

C. H. Chan,¹J. D. Wu,²Y. S. Huang,^2,a兲 Y. K. Su,³and K. K. Tiong⁴

1Department of Information Management, St. John’s University, Tamsui 251, Taiwan

2Department of Electronic Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan

3Department of Electrical Engineering and Institute of Microelectronics, Advanced Optoelectronic Technology Center, National Cheng Kung University, Tainan 701, Taiwan

4Department of Electrical Engineering, National Taiwan Ocean University, Keelung 202, Taiwan 共Received 4 June 2009; accepted 22 July 2009; published online 28 August 2009兲

Highly strained InxGa_1−xAs/GaAs double quantum well 共DQW兲 structures grown by metal organic vapor phase epitaxy with different In compositions are investigated by surface photovoltage spectroscopy共SPS兲 in the temperature range 20–300 K. A lineshape fit of spectral features in the differential surface photovoltage 共SPV兲 spectra determines the transition energies accurately. A comprehensive analysis of the anomalous phenomena appearing in lower temperature SPV spectra enable us to evaluate directly the band lineup of DQW and to remove the ambiguity in the identification of spectral features. The process of separation of carriers within the QW with possible capture by the interface defect traps plays an important role for phase change in SPV signal in the vicinity of light-hole related feature at low temperature. The results demonstrate the considerable diagnostic values of the SPS technique for characterizing these highly strained DQW structures.

© 2009 American Institute of Physics.关DOI:10.1063/1.3208053兴

I. INTRODUCTION

Highly strained InGaAs/GaAs quantum wells 共QWs兲 have the advantages of a simple structure, a well developed fabrication technique, and good optical properties among the research efforts being carried out to extend the emission wavelength of GaAs-based materials system to 1.3 ␮^{m for} application as light sources in wide area networks. Ryu et al.¹ and Salomonsson et al.² reported the development of vertical cavity surface emitting lasers operating around 1220 nm. The In content must be increased in order to extend the use of these devices to the long-wavelength region for opti- cal communication applications. However, pseudomorphic growth of the InGaAs layer on GaAs is limited not only by the generation of misfit dislocations but also by a transition from a two- to three-dimensional growth mode at higher In content.³ Strained InGaAs QWs with In content exceeding 40% have been reported by using only conventional sources made by metal organic vapor phase epitaxy 共MOVPE兲.⁴ Various spectroscopic techniques have been widely used to investigate strained InGaAs QWs to obtain complementary information associated with the growth of QWs. In particu- lar, the surface photovoltage spectroscopy 共SPS兲 technique can provide more information about QWs than the routinely used photoluminescence technique even at room temperature.⁵ SPS has been well established as a powerful technique for studying electronic states of semiconductors.⁶ However, to date, very little is known about the influence of In composition on the optical properties of highly strained In_xGa_1−xAs/GaAs QWs grown by MOVPE using SPS.^7,8

In this work, we report a systematic temperature- dependent SPS characterization of four InGaAs/GaAs double quantum well 共DQW兲 structures in the temperature range between 20 and 300 K. A comprehensive analysis of the anomalous phenomena appearing in lower temperature sur- face photovoltage 共SPV兲 spectra enables us to evaluate di- rectly the band lineup of DQW structures.

II. EXPERIMENT

The InGaAs/GaAs DQW structures were grown on n⁺ GaAs共100兲 substrates using MOVPE in an Aixtron 200 hori- zontal reactor with gas-foil rotation. Four samples with In compositions of 39.5%, 41%, 42.5%, and 44% were studied and designated as samples A, B, C, and D, respectively. The structure of the DQW contained a 500 nm GaAs buffer layer and two periods of InGaAs/GaAs共85 Å/300 Å兲 DQWs. Pre- cursors used for the InGaAs DQW were trimethylindium 共TMIn兲, triethylgallium 共TEGa兲, and tertiarybutylarsine 共TBAs兲. The growth temperatures of the buffer layer and DQWs were 725 and 475 ° C, respectively. The thicknesses of the well and barrier, and the composition of indium in the InGaAs layer were determined by high-resolution x-ray dif- fraction measurements with a Bede D1 four-crystal diffrac- tometer.

In the SPS measurement, the SPV was measured be- tween the sample and a reference metal grid electrode in a capacitive manner as a function of the photon energy of the probe beam. A soft contact mode was used to enhance the photovoltage signals.⁹ This method consisted of placing a thin indium wire around the edge of the sample surface with the metal grid pressing lightly on top. The illumination sys-

a兲Electronic mail: [email protected].

0021-8979/2009/106共4兲/043523/5/$25.00 106, 043523-1 © 2009 American Institute of Physics

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tem consisted of a 150 W quartz-halogen lamp chopped at 200 Hz and a grating monochromator. A beam splitter was placed in the path of the incident light. The intensity of this radiation was monitored by a pyroelectric detector and was kept constant by a stepping motor connected to a variable neutral density filter, which was also placed in the path of the incident beam. The incident light intensity was maintained at a constant level of ⬃10⁻⁵ W/cm². The photovoltage spec- trum on the metal grid was measured with a copper plate as the ground electrode, using a buffer circuit. The in-phase signal, measured with respect to the light modulation, re- corded from a dual phase lock-in amplifier was taken as the SPV signal. For temperature-dependent SPV measurements, a closed-cycle cryogenic refrigerator equipped with a digital thermometer controller was used. The measurements were recorded over a temperature range 20–300 K with a tempera- ture stability of 0.5 K or better.

III. RESULTS AND DISCUSSION

Figure1共a兲depicts the SPV spectra of samples A–D at room temperature. Several spectral features are clearly vis- ible for all samples, which are governed by absorption in the QW region. The sharp peak nature observed in the funda- mental transition suggests the transition to be excitonic. In order to determine the transition energy precisely, the differ- ential SPV 共DSPV兲 spectra with respect to the photon en- ergy, as shown in Fig.1共b兲, are fitted to the first derivative of a Lorentzian-type function proposed by Aspnes,¹⁰ which is appropriate for excitonic transitions in QW structures.^11,12 The evaluated peak position is marked by an arrow. The notation mnH共L兲 labeled in the figure denotes transitions be- tween the mth conduction electron and nth heavy共light兲-hole sublevels. As expected, the spectral features undergo signifi- cant energetic redshifts with an increase in indium content due to the reduction in the bandgap energy of the InGaAs layer. For the prominent 11H feature, the transition energy and the spectral broadening parameter of sample A are evalu- ated to be 1.039 eV and 10 meV, respectively. The corre- sponding values for samples B–D are 1.024 eV and 13 meV,

1.012 eV and 29 meV, and 0.994 eV and 29 meV, respec- tively. Note that the sharpness and the exciton enhancement of the 11H transition for samples A and B are clearly visible, reflecting the higher homogeneity of the InGaAs layer. In contrast, a drastic increase in the values of the spectral broadening parameter is observed for samples C and D. The possible origins for inhomogeneous broadening are the pres- ence of In clusters and/or fluctuations in the In composition at the QW interfaces, which leads to a loss of sharpness of the 11H transition. A relatively weak spectral intensity for a parity forbidden 12H transition is also observed in the DSPV spectra关see Fig.1共b兲兴. The relaxation of the selection rule is most likely due to the distortion of the symmetry of the wave functions in the presence of built-in electric field in the QWs.

The 11L transition is attributed to type-II absorption between light holes 共LHs兲 in the GaAs layer and electrons in the strained InGaAs layer and will be explored below.

Displayed in Figs. 2共a兲–2共d兲 are the experimental SPV spectra of samples A–D at several temperatures between 20 and 300 K. As is the case for general semiconductor proper- ties, all QW-related transitions show a redshift with an in- crease in temperature. Comparing to the higher temperature spectra, a distinct difference for the 11L feature could be noticed for temperature below 100 K. The 11L feature shows a significant phase difference of the signal for temperature below 100 K. This observation indicates that the character- istic of the 11L feature is different from that of the other spectral features. A most probable explanation is that the

FIG. 1. 共a兲 Room temperature SPV spectra of InxGa_1−xAs/GaAs DQW samples A–D with 39.5%, 41%, 42.5%, and 44% In contents, respectively.

共b兲 The DSPV spectra of InxGa_1−xAs/GaAs DQW samples 共dashed curve兲 and the first-derivative Lorentzian lineshape fit共solid curve兲. The obtained values of the various interband transition energies are shown by arrows.

FIG. 2. Temperature dependence of SPV spectra for four InxGa_1−xAs/GaAs DQW samples with different In contents:共a兲 x=0.395, 共b兲 x=0.41, 共c兲 x

= 0.425, and共d兲 x=0.44. Clearly, a reversal of the spectral lineshape of 11L transition occurs below⬃100 K and the dashed line is a guide to the eye.

For comparison, the 11H transition is also shown.

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difference in the band configuration for heavy hole共HH兲 and LH bands is due to band splitting introduced by a highly compressive strain, thereby causing the LH valence band to form a type-II configuration and the HH and LH to be con- fined in different regions of the QWs共see Fig.3兲.

The SPV signal S of a QW structure in the energy region below the band gap of the substrate can be described as^8,13

S⬀␣QW共h␯兲 ⫻ 关fe共h␯^,T兲d1+ f_h共h␯^,T兲d2兴. 共1兲 The first term in Eq. 共1兲, ␣QW共h␯兲, refers to the absorption coefficient in the QW as a function of photon energy and fe共h␯, T兲 关fh共h␯, T兲兴 is the escape efficiency of the generated electrons共holes兲 from the QW followed by a further separa- tion in the electric field over the effective distance d₁ 共d2兲, with d₁ being the effective distance between QW and sub- strate and d₂ is the effective distance between QW and sur- face. The latter term, fe共h␯, T兲 关fh共h␯, T兲兴, is strongly tem- perature dependent. Three processes of charge separation can be envisaged after carrier generation by photoexcitation in- side the QW.¹⁴These are共a兲 thermal emission of carriers out of the well followed by field separation, 共b兲 tunneling of carriers through the potential barrier followed by field sepa- ration, and 共c兲 separation of carriers within the QW with possible capture by the interface defect traps. We argue that the third process plays an important role for phase change in SPV signal in the vicinity of LH-related feature. However, we focus only on the qualitative analysis here. These three processes have different excess carrier lifetimes and can lead

temperature, the conduction electrons with higher mobility are expected to play a major role in the SPV. At lower tem- perature, the contribution from the thermal escape process and trapped carriers by the localized defect states within the QW are expected to depreciate significantly, and the tunnel- ing effect is treated as the dominant mechanism contributing to the SPV. Compared to the HH-related features, there could be significant field assisted tunneling for the LH-related tran- sition. This means that at low temperatures, the LHs rather than the conduction electrons become a dominant compo- nent. The different mechanisms responsible for the high and low temperature SPVs lead to a phase change in the SPV signal at the vicinity of 11L transition for temperature below 100 K. The above analysis shows that the band configuration is of mixed type, i.e., conduction-HH band is type I and conduction-LH band is type II. This facilitates the identifica- tion in the origins of all optical transitions.

When grown on a GaAs buffer, the InGaAs layers sub- strain a biaxial in-plane compression and a corresponding extension along the 关001兴 growth direction. Since the GaAs buffer is much thicker than the InGaAs layers, the biaxial strain␧ is given by

␧ =a_GaAs− a_InGaAs

a_InGaAs , 共2兲

where a_InGaAsand a_GaAs are the lattice constants of the In- GaAs and GaAs, respectively. The former is obtained by a linear interpolation between the lattice constants of InAs and GaAs. This strain alters the band structure of the InGaAs/

GaAs DQW. The strain-dependence conduction 共C兲 to heavy-共HH兲 and light-共LH兲 energy gaps is thus¹⁵

E₀^C,HH= E₀共InGaAs兲 +␦^EH−␦^ES, 共3a兲 E₀^C,LH= E₀共InGaAs兲 +␦^EH+␦^ES−共␦^ES兲²

2⌬0

. 共3b兲

In Eqs. 共3a兲 and 共3b兲, E0共InGaAs兲 is the unstrained direct band gap of the InGaAs and ⌬0 is the spin-orbit splitting.

The quantities of hydrostatic-pressure shift␦^EHand uniaxial stress-induced valence-band splitting ␦^ESare given by¹⁵

␦^EH= 2a关共C₁₁– C₁₂兲/C₁₁兴␧, 共4a兲

␦^ES= b关共C11+ 2C₁₂兲/C11兴␧. 共4b兲 The parameters a and b are the interband hydrostatic- pressure and uniaxial deformation potentials, respectively, and the Cij are the elastic-stiffness constants. The LH va- lence band has a nonlinear strain dependence because of the

TABLE I. The material parameters used in calculating the stress-dependent band gaps in In_xGa_1−xAs.

Material

al

共Å兲

a 共eV兲

b 共eV兲

C₁₁ 共10¹¹ dyn/cm²兲

C₁₂ 共10¹¹ dyn/cm²兲

GaAs 5.6533^a ⫺9.8^b ⫺1.76^b 11.88^a 5.32^a

InAs 6.0584^a ⫺5.8^b ⫺1.8^b 8.33^a 4.53^a

aReference18.

bReference19.

FIG. 3. Possible escape mechanisms for photogenerated carriers out the QW and SPV generation.共a兲 Thermal emission and carrier separation. 共b兲 Field- assisted tunneling emission and carrier separation, and 共c兲 separation of photogenerated carriers within the QW. The solid共dotted兲 line indicates the potential profile of the HH 共LH兲 band, along with the observed optical transitions.

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strain-induced coupling with the spin-orbit-split band.¹⁵ Since for InGaAs/GaAs ␧⬍0, the effect of the lattice mis- match strain is to increase the energy gap of the InGaAs 共hydrostatic-pressure component兲 and split the degeneracy of the valence-band edge at the center of the Brillouin zone, so that the HH band moves up and the LH band moves down, relative to the unstressed valence band.

To investigate the nature of the observed spectral fea- tures and to explain their dependence on In composition, we have solved the one dimensional Schrödinger equation for finite QWs based on the envelope function approximation¹⁶ including the effects of strain.¹⁷ The values of the various strain-related parameters used in the calculation are listed in Table I.^18,19 A linear interpolation was used for the InxGa_1−xAs values. The energy gaps and masses employed are given as follows:¹⁸

E₀共InxGa_1−xAs兲 = E0共GaAs兲 − 1.53x + 0.45x²eV

at 300 K, 共5a兲

⌬0= 0.341 − 0.09x + 0.14x² eV, 共5b兲

m_C^ⴱ=共0.0665 − 0.044x兲m0, 共6a兲

m_HH^ⴱ =共0.45 − 0.07x兲m0, 共6b兲

m_LH^ⴱ =共0.094 − 0.062x兲m0, 共6c兲 where m₀is the free-electron mass. The value of the strained conduction band offset ratio Q_c=⌬Ec/共⌬Ec+⌬Ev兲 is used as an adjustable parameter. The exciton binding energies are estimated to be 5 meV in a variational approach²⁰ and are assumed to be the same for all the transitions except 11L.

The 11L is considered to be a cross-directional real-space transition with little excitonic behavior so that the binding energy is neglected in our case. The value of Q_creported by other groups was varied in the range 0.6–0.81.^21–23TableII lists the experimental results and theoretical calculation for the four samples. In this study, we have obtained the best agreement between experiments and theoretical calculations for Qc=共67⫾2兲%.

IV. CONCLUSION

In conclusion, we have performed a detailed temperature-dependent SPS investigation of highly strained InxGa_1−xAs/GaAs DQW structures grown by MOVPE with different In compositions共0.395ⱕxⱕ0.44兲 in the tempera-

ture range 20–300 K. The interband transition energies are determined via a lineshape fit to DSPV spectra and exhibit a redshift with increasing In composition. A considerable in- crease in the spectral linewidth for higher In composition samples results from the presence of In clusters and/or fluc- tuations in the In composition at the QW interfaces. A com- prehensive analysis of the anomalous phenomena, which ap- peared in lower temperature SPV spectra enables us to determine the band lineup of DQW structures. The process of separation of carriers within the QW with possible capture by the interface defect traps plays an important role for phase change in SPV signal in the vicinity of LH-related feature at low temperature. Numerical calculations for excitonic transi- tion energies, with Qc=共67⫾2兲%, are in good agreement with the experimental results. The results demonstrate the considerable diagnostic values of the SPS technique for char- acterizing these highly strained DQW structures.

ACKNOWLEDGMENTS

The authors acknowledge the financial support from the National Council of Taiwan under Project No. NSC97-2215- E-011-002.

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19Semiconductors, Intrinsic Properties of Group IV Elements and III-V, II-VI for highly strained InxGa_1−xAs/GaAs DQW structures at 300 K.

Transitions

Samples

A共x=0.395兲 B共x=0.41兲 C共x=0.425兲 D共x=0.44兲

Expt. Calc. Expt. Calc. Expt. Calc. Expt. Calc.

11H 1.039 1.038 1.024 1.023 1.012 1.010 0.994 0.996

12H 1.069 1.070 1.059 1.057 1.045 1.043 1.028 1.030

11L 1.176 1.174 1.166 1.166 1.158 1.158 1.146 1.144

22H 1.212 1. 219 1.201 1.208 1.192 1.197 1.182 1.186

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Characterization of a

Zn _x Cd _{1 −x} Se / Zn _x
Cd _y
Mg _{1 −x}
−y
Se multiple quantum well structure for mid-infrared device applications by

contactless electroreflectance and Fourier transform infrared spectroscopy

J D Wu

, J W Lin

, Y S Huang

, W O Charles

, A Shen

, Q Zhang

and M C Tamargo

1Department of Electronic Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan

2Department of Electrical Engineering, The City College and The Graduate Center of CUNY, New York, NY 10031, USA

3Department of Physics, The City College and The Graduate Center of CUNY, New York, NY 10031, USA

4Department of Chemistry, The City College and The Graduate Center of CUNY, New York, NY 10031, USA

E-mail:[email protected]

Received 13 April 2009, in final form 7 July 2009 Published 31 July 2009

Online atstacks.iop.org/JPhysD/42/165102 Abstract

Contactless electroreflectance (CER) and Fourier transform infrared (FTIR) spectroscopy were used to study the intersubband transitions of a ZnxCd1−xSe/Znx
Cdy
Mg_1−x
−y
Se multiple quantum well (MQW) structure grown by molecular beam epitaxy for mid-infrared device applications. The CER spectrum revealed a wide range of possible optical transitions in the MQW structure. The ground state transition was assigned by comparison with the

photoluminescence emission signal taken from the same structure. A comprehensive analysis of the CER spectrum led to the identification of various interband transitions. The

intersubband transitions were estimated and confirmed by FTIR measurements. The results demonstrate the potential of using CER as a complementary technique for the contactless and nondestructive characterization of the wide band gap II–VI MQW structures for mid-IR intersubband device applications.

(Some figures in this article are in colour only in the electronic version)

1. Introduction

Devices that are based on intersubband (ISB) transitions, such as quantum well infrared photodetectors and quantum cascade lasers, are of considerable interest due to their potential

5 Author to whom any correspondence should be addressed.

advantages over devices based on interband (IB) transition in the infrared range [1–3]. ISB devices are usually made of multiple quantum well (MQW) structures and need a large band discontinuity to achieve operation at shorter wavelengths and higher temperatures. MQW structures made of wide band gap II–VI materials ZnxCd1−xSe/Znx
Cdy
Mg_1−x
−y
Se are promising candidates for short-wave mid-infrared ISB device

0022-3727/09/165102+04$30.00 1 © 2009 IOP Publishing Ltd Printed in the UK

In this work we report a detailed study of the IB transitions from a ZnxCd_1−xSe/Znx
Cdy
Mg_1−x
−y
Se MQW structure fabricated by molecular beam epitaxy (MBE) at room temperature (RT) using contactless electroreflectance (CER).

CER has been proven to be extremely useful in the investigation and characterization of semiconductor microstructures [7–9].

The derivative nature of CER spectra suppresses uninteresting background effects and greatly enhances the precision of IB transition energies. CER enabled us to observe a wide range of IB transitions besides the fundamental (E1–H1) transition as photoluminescence (PL) usually does. The comparison of experimental data and theoretical analysis based on the envelope function approximation [10,11] allowed us to identify the features present in the CER spectrum. Therefore, the ISB transition energies could be estimated. Our study showed that by using CER we can accurately determine the ISB transition energies, and the results are confirmed by ISB absorption measured by Fourier transform infrared (FTIR) spectroscopy. The results demonstrate the potential for contactless and nondestructive characterization of the wide band gap II–VI MQW structures for mid-IR ISB devices by CER.

2. Experimental

2.1. Sample growth by MBE

The MQW structure was grown by MBE on (0 0 1) semi- insulating InP in a dual-chamber Riber 2300P system. After deoxidation of the InP substrate in the III–V chamber, a 0.25 µm thick InGaAs buffer was grown at 400^◦C. The sample was then transferred via vacuum modules to the II–VI chamber where it was heated to 200^◦C. At this temperature, the InGaAs surface was exposed to a Zn flux for 40 s, then a 9 nm ZnCdSe buffer layer was grown. These steps for adjusting the III–V and II–VI interface are known to improve the material quality of the epitaxial layers [12,13]. At the end of this low temperature growth, the substrate temperature was raised to 300^◦C to grow the II–VI MQW structure. The layer structure of the MQW sample is shown in figure1. To ensure the lattice matching of both the ZnxCd_1−xSe wells and the Znx
Cdy
Mg_1−x
−y
Se barriers to the InP substrate, two Zn cells were employed. The sample consists of 30 periods of ZnxCd_1−xSe/Znx
Cdy
Mg_1−x
−y
Se MQWs. The nominal ZnxCd_1−xSe well thickness was 25 Å. The well had the lattice-matched composition, x = 0.46, and was doped with Cl (using ZnCl2as dopant source) to 2× 10¹⁸cm⁻³. The Znx
Cdy
Mg_1−x
−y
Se barrier thickness was about 130 Å. The Zn and Cd contents in the Znx
Cdy
Mg_1−x
−y
Se barrier were x
= 0.24 and y
= 0.25, respectively, corresponding to a band gap of about 2.9 eV at RT. The MQWs were sandwiched between a 0.3 µm bottom and a 0.1 µm cap ZnxCd_1−xSe layers. The growth rate and doping concentration were determined from separate calibration layers. These layers were also grown to optimize the growth conditions. The results obtained from double-crystal x-ray diffraction rocking curve

Figure 1. Schematic layer structures of the investigated MQW sample.

measurement indicate the excellent structural quality of the sample.

2.2. Characterization techniques

The CER measurements were carried out at RT from 1.9 to 3.2 eV. In the CER experiment an ac modulating voltage (∼1 kV at 200 Hz) was applied between a front wire grid electrode and a second electrode consisting of a metal plate.

These two electrodes were separated by an insulating spacer in such a manner that there was a very thin layer (∼0.1 mm) of air (or vacuum) between the front surface of the sample and the front electrode. Thus, there is no direct contact with the front surface of the sample. The probe beam enters through the front wire grid. The radiation from a 150 W xenon arc lamp filtered by a 0.25 m monochromator provided the monochromatic light. The reflected light was detected by an UV-enhanced silicon photodiode. The dc output of this photodiode was maintained constant by a servomechanism of a variable neutral density filter. A dual-phase lock-in amplifier was used to measure the detected signals. Multiple scans over a given photon energy range were programmed until a desired signal-to-noise level was attained with the computer controlled data acquisition procedure. PL spectra were excited using the 325 nm line (∼50 mW) of a He–Cd laser.

The luminescence signals were analysed using a Jobin-Yvon

‘TRIAX 550’ spectrometer equipped with a ‘SIMPHONY’

charge coupled device (CCD) camera. For ISB absorption measurements, the sample was polished to a multiple-pass waveguide geometry with parallel 45^◦facets. The absorption measurements were performed at RT using a Nicolet Nexus- 870 FTIR spectrometer equipped with a liquid-nitrogen-cooled HgCdTe detector.

3. Results and discussion

The CER spectrum of the MQW sample is shown in figure2.

The dotted curve is the CER spectrum measured at RT. The solid curves are least-squares fits to a derivative Lorentzian lineshape function of the form [7–9]

R

R = Re

j=1

A_je^ij

E− Ej + ij

_−n

, (1)

2

1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 Expt.

Fit

Photon Energy(eV)

PL Intensity (a.u.)

∆ ∆ R/R (a.u.)

PL E0(ZnCdSe)

E1H1

E₀(ZnCdMgSe) E2H2

E0+_∆

0(ZnCdSe) E1L1

x2

Figure 2. The experimental CER (dotted line) data at RT of a MQW structure. The full curve is the least-squares fit to equation (1). The PL emission measured at RT, used to identify the E1–H1 transition, is also shown.

Table 1. Experimental and calculated transition energies of the ZnxCd1−xSe/Znx
Cdy
Mg_1−x
−y
Se MQW structure.

ZnCdSe/ZnCdMgSe MQW Theory (eV) Experiment (eV) IB transitions (Qc= 0.75 ± 0.05, (±0.005)

Lw= 23 Å)

E0(ZnCdSe) 2.073

E0+
0(ZnCdSe) 2.520

E1–H1 2.318± 0.002 2.313

E1–L1 2.370± 0.007 2.368

E2–H2 2.853± 0.004 2.837

E0(ZnCdMgSe) 2.930

ISB transition FTIR

E1–E2 400± 20 meV 376± 5 meV

where Aj and j are the amplitude and phase of the lineshape, Ej and j are the energy and broadening parameters of the transitions and the value of n depends on the origin of transitions. n = 2.5 is appropriate for M₀ type three-dimensional critical point IB transitions and n = 2 is appropriate for the bounded transitions. Our experimental signatures for E0(ZnCdSe), E0+
0(ZnCdSe) and E0(ZnCdMgSe) are more consistent with n= 2.5, while the features originating from MQW IB transitions have better fit with n= 2. The arrows in figure2indicate all the energy values of the transitions resulting from the fit. These values are also presented in table1. The notation En–H(L)m represents the transition from the nth conduction subband to the mth valence subband of heavy (H) or light (L) hole character, respectively.

Assignment of the transitions was done according to the following considerations. The feature at 2.93± 0.005 eV was assigned to the Zn0.24Cd0.25Mg0.51Se barrier by comparison with the 77 K PL emission of the calibration layer, which was observed at 3.0 eV, considering that the thermal energy shift from 77 K to RT is about 70 meV. The signals at 2.073±0.005 and 2.52± 0.005 eV were assigned to the E0 and E0 +
0

transitions of the Zn0.46Cd0.54Se grown lattice matched to the InP substrate according to a previous report [14]. Comparing the PL emission spectrum at RT, included in figure2 and in

2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 0.5

0.6 0.7

0.8 E1H1 E1L1 E2H2

Conduction Band Offset

Photon Energy (eV)

Figure 3. Energies of the transitions determined by the envelope function approximation versus conduction band offset. The dotted vertical lines indicate the experimentally determined energies of the various CER features from the MQW.

table1, the CER transition at 2.319± 0.005 eV is assigned to the E1–H1 transition.

To complete the identification of the CER features, a theoretical calculation based on the envelope function approximation, considering that the quantum well was doped, was performed [10,11]. We have used various relevant parameters (energy gaps, effective masses) of Zn0.46Cd0.54Se/Zn0.24Cd0.25Mg0.51Se listed in [4]. The well width (L_w) was assumed to be 23 Å. In order to evaluate the conduction band offset, Q_c =
Ec/
E_g, we have also compared the experimental and theoretical results as illustrated in figure 3. The dotted vertical lines indicate the experimentally determined energies of the various CER features from the MQW (see figure2). The shaded regions around these vertical lines represent the experimental error in evaluating the respective energies. The solid lines indicate the calculated results from various En–H(L)m transitions as a function of Q_c. These transitions correspond to the symmetry allowed (n = m) ones. As shown in figure 3, the best agreement between the calculated and the experimental values for all the transitions was found for Qc = 0.75 ± 0.05. The obtained value of Qcis slightly smaller than that of the previous report on ZnxCd_1−xSe/Znx
Cdy
Mg_1−x
−y
Se single quantum well (Q_c = 0.82 ± 0.02) by Muˇnoz et al [4]. However, the predicted values of ISB transitions with the obtained Qcby this study show better agreement with the experimental data obtained from the FTIR measurements on similar structures reported by Lu et al [6]. As seen in figures 2 and 3, and table1, there is good overall agreement. From these data, the E1–E2 transition can be estimated to be 400 meV.

The predicted value of the E1–E2 transition was confirmed by the FTIR measurements. The absorbance for the sample is obtained by taking the negative logarithm of P -polarized transmittance over S-polarized transmittance. The normalized absorbance of the sample is shown in figure4. An absorption peak at 376 meV (3.30 µm) is clearly observed and it is strongly polarization dependent. The full width at half maxima (FWHM) is 29± 3 meV and the ratio of
E/Epeak

is of the order of 10%, a signature of bound-to-bound transition, as usually observed in the conventional III–V semiconductors [15]. Comparison between the FTIR result 3

300 350 400 450 3

3.5 RT FTIR

4

Photon Energy (meV)

Normalized Absorbance

Expt.

Fit Emax= 376 5 meV

FWHM = 29 3 meV

Figure 4. ISB absorption (dashed line) measured by FTIR at RT and lineshape fit (solid line) for the MQW structure. The inset indicates the multiple-pass geometry used in the measurements.

(376 meV) and the CER prediction (400 meV) indicates good agreement. These results indicate that CER may be used to accurately predict ISB transition energies of device-like structures while the results of FTIR directly represent the properties of ISB transition devices [6]. CER has been demonstrated to be a good complementary technique, as compared with the FTIR absorption which requires complex sample preparation, for characterization of the wide band gap II–VI MQW structures for mid-IR ISB device applications.

4. Summary

In summary, a Zn0.46Cd0.54Se/Zn0.24Cd0.25Mg0.51Se MQW structure was grown by a dual-chamber MBE system and has excellent material quality, which is consistent with the requirements of mid-infrared ISB devices. Using CER and theoretical envelope function approximation calculations, the ground state and higher order transitions were observed and identified. Based on the current result, the E1–E2 ISB transition energy was estimated as 400 meV. This value was confirmed by FTIR absorption measurements, which showed

agreement between these two techniques shows that CER can be used as a complementary technique to investigate structural, optical and electronic properties of these complex structures, including prediction of the ISB transition energy.

Acknowledgments

This work was supported by the National Science Council of Taiwan under Project No 97-2221-E-011-131 and NASA Grant No NCC-1-03009, NSF Grant No EEC-0540832 through MIRTHE-ERC and the Center for Analysis of Structures and Interfaces (CASI).

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