Porous silicon formatio A quantum wire effect

V. Lehmann and U. Gijsele
A quantum
wire effect
School of Engineering, Duke University, Durham, North Carolina 27706
(Received 13 March 1990; acceptedfor publication 25 November 1990) Porous silicon layers grown on nondegenerated p-type silicon electrodesin hydrohuoric acid electrolytes are translucent for visible light, which is equivalent to an increasedband gap compared to bulk silicon. It will be shown that a two-dimensional quantum confinement (quantum wire) in the very narrow walls between the pores not only explains the change in band-gap energy but may also be the key to better understanding the dissolution mechanism that leads to porous silicon formation. The formation of porous silicon layers (PSLs) on silicon electrodesin hydrofluoric acid electrolytes under anodic bias was first described by Uhlir' and Turner.' The properties of porous silicon layers were studied intensively becauseof their potential use in producing silicon layers fully isolated by porous oxidized silicon (FIPOS) .3 The diameter of PSL pores or channels was found to range from 1 up to 100 nm associatedwith porosities of 20-80%. The channels in nondegenerated p-type silicon were found to be the smallest (typically around 2 nm)."' The formation mechanism itself and especially the reason why the walls betweenthe pores are so remarkably resistant against further chemical attack of the electrolyte are still poorly understood. For the smaller ones of the dimensions mentioned above, semiconductors show specific quantum effects due to geometrical constraints7*"In this letter we will show that formation of PSL on nondegenerated p-type silicon is a self-adjusting processdue to a geometrical quantum well or wire effect associatedwith the thin silicon walls remaining between the pores. In our experiments all porous silicon layers were grown in a 1:l (98 wt.% ethanol: 48 wt.% HF) electrolyte using a power supply working as a current source and a Pt working electrode. The sampleswere kept in the dark during PSL formation. In order to measurethe optical absorption of PSL it was necessaryto fabricate layers of about 100 pm separatedfrom the substrate. PSL on single crystalline silicon (5 R cm boron doped, polished surface) was grown in a setup similar to the one used by Turner2 (55 mA/cm2, 45 min). The PSL can be easily separatedfrom the silicon substrate by reducing the electrolyte concentration to 1 wt.% aqueousHF and electropolishing (at 100 mA/cm2 for 10 s). The PSL ( 110pm thickness) has to be kept under water or ethanol becausein air it will easily break, disintegrate into small pieces, and curl up to small loops of approximately 500 pm diameter during drying. Porous silicon layers grown on lightly doped substratesappear to be translucent from dark red to light orange in color after separation from the substrate. The porosity of this layer is high enough (600 m2/cm3)5 to be etched significantly even in pure water (observedby H, evolution). A changein color from red to orange to yellow is observableduring this etching. It was not possibleto separatePSL grown on a degeneratedp + -type silicon sample from the substrate with the electropolishing procedure described above. Therefore a stripe-shapedsilicon sample ( 10 mm x 100 mmx 500 pm, 0.01 fi cm p type) was slightly beveledby grinding (minimum thickness: 109pm, 0.7"beveling angle). The thinned end of the beveledstripe was immersed into a beaker filled with the electrolyte (for 30 min at a current density of 55 mA/cm2). PSL grows on both sides of the stripe. Consequently, the remaining silicon substrate inbetween the growing porous silicon layers becomesthinner and thinner, until it is finally totally transformed into porous silicon. In contrast to PSL on lightly doped substrates, no obvious change in the optical appearance (compared to the substrate itself) was found for PSL grown on the degenerated substrate. The PSL samples ( 110 pm grown on p-type, 150 pm grown on p ' -type substrate) and a lightly doped singlecrystal silicon reference sample (40 pm) were clamped between two 500 [lrn quartz plates under wet conditions and illuminated with monochromatic light (Bausch & Lomb monochromator, 675 grooves/mm) while the intensity of the transmitted light was measured using a germanium detector. The measuredvalues were compared to the ones measuredfor two wet quartz plates only. No corrections were made for the reflections caused by the samples. In order to understand the PSL formation it is necessary to deal with the dissolution chemistry of silicon anodically biased in hydrofluoric acid. A silicon surface is known to be virtually inert against attack of hydrofluoric acid at low pH values, which corresponds to low OH concentrations.'If the silicon is under anodic bias, PSL formation is observedas long as the reaction is limited by the charge supply of the electrode and not by ionic diffusion in the electrolyte. This condition is fulfilled for current densitiesbelow a I3F concentration dependent,critical current density Jpst,." The inner surface of PSL was found to be covered with hydrogen." From these facts and observations of charge transfer ratios at silicon electrodes in hydrofluoric acid, which will be discussed in detail elsewhere,t2 the dissolution mechanism shown in Fig. 1 has been derived. For PSL formation it is essential that a silicon surface saturated by hydrogen is virtually inert against further attack of fluoride ions as long as no electronic holes (h + ) are availableat the silicon electrodebecausethe electronegativity of H is about that of Si and the induced polarization is low. 1:f a hole (h + ) reaches the surface nu-