Interpretación de la Información

As m entioned previously, the extrem ely high m obility obtained in m odulation-doped h ete ro stru ctu res arises from th e se p aratio n betw een the p a re n t ions an d th e carriers by building a spacer lay er betw een th e carrier channel an d th e donor supply layer.

At th e heterojunction, electrons from the d opant tra n sfe r across the interface to th e lower lying b an d edge of th e neighbouring sem iconductor w hich is sp atially sep ara ted from th e ionised p a re n t donors. The electron m obility in th e channel is considerably enhanced w hen com pared to the m obility in a bu lk m ateria l of equivalent carrier concentration because of the reduction in ionised im p u rity scattering. Hence, th e m odulation-doped h e tero stru ctu re h as th e g reater advantage a t lower te m p e ra tu re s where, in regularly-doped sem iconductors, carrier sc atterin g by ionised im p u rities prevails. This advantage is som ew hat reduced a t h ig h er te m p e ra tu re s due to phonon scattering.

The following discussion will consider various scatterin g m echanism s p re se n t w ith in a b u lk non-polar elem en tal sem iconductor such as Si an d Ge; i) Phonon scattering: L attice vibrations d istu rb th e m otion of th e electrons. The v ib ratio n s m ay be rep resen ted by acoustic an d non-polar optical phonons by w hich electrons are scattered. The phonon population a n d hence th e ir sc atterin g ra te increases w ith tem p eratu re. Therefore, a t OK, no phonons are p resen t. Acoustic phonons become im p o rtan t above about 1.5K, w h ereas non­ polar optical phonons occur above 80K.

are scattered from th e vicinity of one conduction b an d m inim um to an o th er m inim um .

iii) A lloy scattering for crystals: The alloy scatterin g process h a s to be ta k e n into account in Sii.^Ge^ alloys. The random d istrib u tio n of Ge atom s in th e alloy gives rise to p o ten tial fluctuations, causing scatterin g of the mobile carriers.

No system atic m obility investigations on bulk Si^Goi.^ alloys have been done so far, because all research into Si^.^Ge^ alloys is m ainly concentrated on stra in e d layers in 2D system s. All th e above m entioned sc atterin g m echanism s are not only p resen t in the bu lk sem iconductor m aterial, b u t m ore or less influence th e tra n sp o rt behaviour of the c arriers in a 2D system , as well. B ut pseudom orphical grow th an d s tra in a lte r th e cry stal stru c tu re an d th u s the physical p roperties of such a system . C onsequently, existing scatterin g m echanism s have to be modified an d additional ones have to be ta k e n into account for th e calculation of th e carrier m obilities for a 2D Si/Si^.^Ge^ h etero stru ctu res:

iv) Rem ote im p u rity scattering: S catterin g of electrons by th e Coulomb p o ten tials of th e rem ote ionised im p u rities in th e Sii.^Ge^ supply layer is the dom inant source of scatterin g in m odulation-doped stru c tu re s a t low tem p era tu re . U sually th e ir influence on the 2DEG is reduced by adding an undoped spacer layer as m entioned earlier. Some general sta te m e n ts can be m ade about th is scatterin g process: As the Coulomb in teractio n follows an inverse-square law, th e scatterin g ra te would be expect to show a sim ilar dependence on th e sep aratio n betw een th e w ell an d donor regions, i.e. on the spacer lay er thickness. T heoretical studies of th e m obility dependence on spacer th ick n ess in m odulation-doped Si/Sii.^Ge^ have been done by S te rn et

al. [20]. They have obtained th e following conclusion th a t it h as been reasonable to expect th a t hig h er m obilities m ight be realised by using thicker spacer layers. Don Monroe e t al. [24] have estim ated th e rem ote im p u rity scatterin g lim ited m obility a t 4.2K as 1 7 0 ,0 0 0 cm ^ for a spacer thickness of 150Â giving ng=5xl0^^cm^. The o th er side, its contribution to th e so far experim entally realised hole m obilities is negligibly sm all. Only for very high hole m obilities >10®cmW s do th e rem ote im p u rities theoretically become im p o rtan t in th e calculations.

v) B ackground im purity scattering: The im p u rities in th e nom inally undoped Si channel region of a h etero stru ctu re are a source of electron scatterin g in m odulation-doped stru ctu res. The purpose of th e m odulation-doping technique is to se p ara te th e carriers in the channel from th e dopant in supply layer. Practically, th is is not possible due to grow th affects such as segregation of the dopant an d germ anium , an d th e incorporation of im p u rities from the grow th cham ber, leading to u n in ten tio n al doping in th e channel. The resu ltin g background im p u rity scatterin g effects th e electron m obihty alread y a t ra th e r m odest densities, w hile th e h m it for th e hole m obihties ag ain is too high to see its significance in experim ents.

vi) Interface roughness scattering: One or two m onolayers a t the heterojunction should be considered as a tra n sitio n region betw een th e Si and Sii.xGe^ layers. Moreover, in ap p ro p riate grow th conditions can cause grow th by 3D islands, leading to a n o n p lan ar interface. T his interface roughness in q u an tu m wells is usually considered as a random m odulation of th e w idth of a q u an tu m well. The roughness of th e interface betw een Si an d Sii.^Ge^ h a s a g reat influence on th e mobility. However, m odern advanced grow th techniques such as MBE or MOCVD, m ake it possible to grow epilayers of high quality

interfaces w ith negligible interface roughness sc atterin g effects,

vii) Threading dislocation scattering: T hreading dislocations in th e channel, w hich are strongly dependent on th e density of th e m isfit dislocations, cause th is scatterin g process. T h read in g dislocation densities as low as 10® cm^ can be rea h se d w ith p re se n t grow th techniques, an d th e h m it set by th is scatterin g m echanism exceeds by fa r the h ig h est electron(5xl0® cm ^’^s‘^)[25] an d hole m obihtes(2xl0^cm ^'^s'^)[26] achieved so far, an d th u s th rea d in g dislocation sc atterin g can be neglected.

A discussion of th e factors lim iting th e m obihty in our sam ples will be given in ch ap ter 4.