Electron Density Effects in the Modulation Spectroscopy of Strained and Lattice-Matched InGaAs/InAlAs/InP HEMTs.
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nm undoped In 0.52 A10 .48 As / 20 nm n-type Ino.52A10. 48As donor / L, undoped 1n0 .52A10 .48 As spacer / (L.) InGal_,As channel/ 1 pm undoped Ii0.52Alo.4sAs buffer / S.I. InP (100) substrate. The Indium composition was x = 0.6 and 0.65 for the strained and x = 0.53 for the lattice-matched samples. The channel width L. had values between 10 and 100 nm. For all samples presented below, the n-type doping in both donor and contact layers was 4x 1018 cm-3. However, due to the different x and L, values, and, primarily due to different spacer widths L,, the electron density in the channel was different for each one of the samples investigated. Prior to Hall and optical measurements, the top contact layer was removed by wet etching. The changes AT/T in the transmittivity, induced by an AC laser light (' 1 mW), were detected by using a cooled InSb photodiode and analysed by standard lock-in 6 techniques. Details of the experimental arrangement are given elsewhere . Description of the Phototransmittance Spectra
The Phototransmittance spectra of the samples investigated are shown in Figures 1(a) and 1(b). The spectral position of each one of the optical transitions depends on many parameters such as x, L,, n, and strain. The hh-Ih energy splitting AE seen in Fig. 1(a), is a combined effect of strain and quantum confinement. The latter contributes the same amount for every x value since all samples have the same L. and similar electron densities. The increase of splitting with x is a result of increasing of the compressive strain due to lattice mismatch Aa/a equal to 4.7 x 10- 3 (x = 0.6) and 8.2 x 10-3(X = 0.65). By assuming coherent strain 6 with values c -_ -(Al/a), the contribution to the splitting AEt, = 2b(1+2C 12 /Cll)c becomes 33 and 57 mV for x = 0.6 and x = 0.65, respectively. Since the splitting associated with quantum confinement AEq, is about 20 mV (as measured from the lattice-matched 53 meV for x = 0.6 and sample 682), the total splitting will be AE = AEqc + AEstr 77 meV for x = 0.65 which are identical with the measured values from the spectra of samples 694 and 683, respectively. In conclusion, the hh-Ih splittings indicate coherently strained heterostructures, free of misfit dislocations. As the electron density increases to higher values, the lh transition is not resolved and the signal has the tendency to broaden (see Fig. 1(b)), developing a high energy tail. In sample 790, only the 21h optical transition is resolved, since the the ground state transition llh is quenched due to conduction band filling effects, originating from the high electron density present in the structure. RESULTS AND DISCUSSION The Model The spectra were analysed according to the formulae 6T/T - -L6L, and al - o(1 - fe). V Here, c 0 is the absorption coefficient for the undoped case and does not depend explicitly on n,. For the doped case, however, the absorption coefficient c, must account for the effects of a degenerate electron gas through the Fermi-filling factor fe[tt(n,)]. 2 The changes 6a in the absorption coefficient can
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