Two-dimensional electron gas of very high mobility in planar doped heterostructures

HAL Id: jpa-00210651

https://hal.archives-ouvertes.fr/jpa-00210651

Submitted on 1 Jan 1987

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Two-dimensional electron gas of very high mobility in planar doped heterostructures

B. Etienne, E. Paris

To cite this version:

B. Etienne, E. Paris. Two-dimensional electron gas of very high mobility in planar doped heterostruc-

tures. Journal de Physique, 1987, 48 (12), pp.2049-2052. �10.1051/jphys:0198700480120204900�. �jpa-

00210651�

Two-dimensional electron _gas of _very high mobility ⁱⁿ planar doped

heterostructures

B. Etienne and E. Paris

Laboratoire de Microstructures et de Microélectronique (L2M), Centre National de la Recherche Scientifique (CNRS), ¹⁹⁶ Av. Henri Ravera, ⁹²²²⁰ Bagneux, ^France (Regu ^{le f4 aolit} 1987, rivisi le 21 octobre 1987, accept ^{le 26 octobre} 1987)

Résumé.2014 Nous montrons comment optimiser la réduction de la diffusion par les impuretés ^ionisées

introduites dans les hétérostructures à modulation de dopage. ^Ceci peut être obtenu _par une nouvelle

conception ^du dopage de la barrière : celle-ci comprend deux monocouches de dopage planaire séparées

par ^une couche non dopée. ^{Nous avons vérifié cette} prédiction ^{dans des} hétérojonctions GaAs/GaAlAs

et obtenu des mobilités électroniques très élevées atteignant 3, 7 106 cm2 V-1 s-1 _pour une densité

surfacique d’électrons de 1, 8 ^x 1011 cm-2.

Abstract.2014 We demonstrate how it is possible ^to optimize the reduction of remote ionized impurity scattering in modulation doped heterostructures. This can be obtained by ^{a novel} implementation

of the doping in the barrier using ^two planar doped layers separated by ^a large spacer. We have verified this prediction ⁱⁿ GaAs/GaAlAs heterojunctions and obtained in preliminary ^studies very high

mobilities reaching ^a peak ^{value of 3.7} 106cm2V-1s-1 at a sheet electron density ^{of 1.8 x} 1011 cm-2.

Classification

Physics ^Abstracts

72.20F - 73.40K - 68.55B

The doping modulation of GaAs/GaAlAs ^het-

erojunctions, ^{i.e. the} spatial separation ^between

the intentionally introduced impurities (in ^the

GaAlAs barrier) and the free charge ^carriers (at

the interface in the GaAs channel), ^{has led to}

the obtention of quasi two-dimensional electron gas of high mobility ^{at low} temperature [1]. ^Un-

der transverse intense magnetic ^field fascinating quantum physical properties ^{of such} nearly per- fect 2D electron _gas have been observed (the

fractional quantum ^Hall effect) [2] ^{or may be ex-}

pected (the Wigner crystallization). ^{It is there-}

fore quite challenging ^to attempt ^to improve ^the

electron mobility ^{in these} structures, ^{in which} remarkable _progress has already been obtained and in which the ultimate limit is surprisingly

not accurately ^{known now.}

Further progress may be expected currently along ^two directions. First the steady improve-

ment of epitaxy conditions (higher purity ^{of the} products, ^better growth procedure) has allowed

recently the obtention of record electronic mobil-

ities : p ^{= 3.1 x 10s cm2V-1s-1} with electron

sheet density ^{ng = 3 x 1011 cm-2 at 4K} by ^Har-

ris et at. [3] ^{and u = 5 x} 106 CM2V-lS-1 with ns = 1.5 x 1011 cm-2 at 1K by English et ^at. [4].

Second an analysis ^{of the} physical processes lim-

iting ^the mobility ^{and a} resulting optimization ^of

the structure might also still lead to mobility ^im- provement. ^We present in this letter a way of do-

ing this and the results of preliminary transport

measurements. We obtain _very repeatedly ^elec-

tron mobilities in excess of 2 x 106 cm2 V -1 s-1 at 4K with peak ^values of it = 2.5 X 106 cm2V-1s-1 with ns = 1.7 x 1011 cm-2 at 4K (JJ ^{= 3.7 x 106}

cm2 V -1 s-1 with _ns =1.8 x 1011 cm- 2 at 1. 5K in another heterojunction) in conditions of epitaxy

which we think are more easily attainable than those reported in references [3] ^and [4] (concern-

ing ^{the basic} pressure of the growth chamber,

the residual background doping ^{of the} layers ^and

the number of growth required before the obtan- tion of heterostructures with _very high ^electron

mobility)

In modulation doped heterostructures of

good quality ^the dependence of the electron mo-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198700480120204900

2050

bility p ^{at low} temperature ^{with 2D} electron den-

sity ^ns (y proportional ^to ns l2, ^see _below) proves that _u is limited by ^ionized impurity scattering

(refer ^to Fig.la ^{for a} sketch of the structure and of its most important elements). ^{When p} > 10e

cm2 IV ^{sec was} obtained, ^{it was not so clear un-}

til recently ^whether the dominant mobility ^limi-

tation came from background ^{or remote ionized} impurity (i.e. ^{either residual} impurities ^{in the}

channel or doping impurities ^{in the} barrier). ^The

report by ^{Harris et al.} [5] ^{of an increase of mo-} bility concomitant with unchanged transferred

charge density solely by increasing the thickness of the doped ^GaAlAs layer provided ^{in our} opin-

ion strong ^{evidence that :} i) ^{the mobility is lim-}

ited rather by ^{remote ionized} impurity ^scatter- ing ^{even for} quite large spacer thickness and low residual doping ^{of the GaAs} channel, ii) ^{the im-} purities ionized because of surface depletion ^can-

not be in fast ignored ⁱⁿ any realistic estima- tion of total ionized impurity scattering. Higher

electron mobility is therefore to be expected by putting ^{them far} away from the electron _gas.

Fig.l- Sketch of the conduction band energy profile

of the heterostructure. (a) Conventional bulk doping

of the barrier : d1 ^{is the} spacer, d is the distance from the heterointerface to the middle point ^{of the} region depleted by charge ^transfer. (b) ^{Planar doping in}

two layers bl ^and 82 separated by ^a spacer d2. ^The

cap layer of GaAs is also shown..

This second point ^{is most} important ^once

it has been realized that the electrical charge

needed for surface depletion, because of the pin- ning of the Fermi level ^at the surface ^at roughly

mid forbidden _gap [6], ^{is much} larger ^{than the} charge transferred into the 2D electron _{gas :} typ- ically = ^{6 x 1012 CM-2 if} put ^at 200 as from the surface for the former, ^{versus * 2 x 1011 cm-2 for}

the latter. Starting ^{from the} general expression

of the screened Coulomb interaction between Ni

ionized charge ^centres per surface unity ^situated

at distance di ^{from an electron} gas of Fermi wave

vector kf [7], ^{it can} be deduced after some alge-

bra that, in the limit kF di > > 1, the electron mo-

bility ^is approximately proportional ^to k3 cPi IN¡

or equivalently ^to n. i INi (the electron den-

sity ^n. being ^{related to the Fermi wave vector} kF by ns ⁼ k 2 /2H ^{for a 2D system at} OK). ^This

settles the figures ^{in order to obtain a reduction}

of the ionized impurity scattering : ^{the donors}

ionized for surface depletion, being roughly ³⁰

times more numerous than those needed for the formation of the 2D electron _gas, the former should ideally ^be placed ^more than three times farther _away from the heterointerface than the latter. Therefore we chose to divide the usual

one piece doped layer in the barrier (Fig.1a) ^into

two parts : ^{one close to the} surface, ^{the other}

close to the heterointerface. These two doped layers ^{are thus} separated by ^{a second} spacer d2 much larger ^than the well established _spacer d1

between the electron _gas and the nearest inten-

tionally introduced donors.

Next, ^{as noticed} by ^Stern [8], the transferred

charge density ^{ns is} solely determined (for given

barrier height) by the distance d between the het- erointerface and the centre of the depleted doped layer (the ^result is in fact rigourously ^true only

in the case of absence of electrical charge ^{in the}

spacer). ^{Using the planar} doping technique [9],

we are in this _way able to obtain this distance d to correspond nearly completely ^to spacer d1.

This helps again ^to increase the mobility ^because

for ^a given ^{n. and a} given Ni ^{in the} doped layer transferring ^{electrons to the 2D} gas (Ni ^{may be}

larger ^{than ns in} spite ^{of overall} charge ^neutral- ity because of possible impurity compensation)

we can afford ^{now a} larger spacer dl. ^This pla-

nar doping technique ^{can be used as well for the}

other doped layer ^{because of the} high ^carrier

sheet density ^{which can} be obtained with this

growth technique ^at very close proximity ^{to the}

surface of the sample [10].

For all these reasons we believe that ^a nearly complete optimization ^{of the barrier} doping ⁱⁿ

a modulation doped heterostructure can be _ap-

proached by ^a design ^{of the structure} correspond-

ing ^to figure 1b : the barrier comprises ^{now two} planar doped layers b1 (~ ^{2 x 1011} cm-2), ⁸² (~ 6 ^{x 10’2} cm-2) ^{and two spacers di and d2.}

The heterostructures are obtained by ^molec-

ular beam epitaxy. ^{A detailed} report ^{of the} growth procedure ^{will be} given elsewhere. Our

system ^{is a Riber 2300. The basic} pressure of the

growth chamber, which is warmed _up ^{at room} temperature every night, ^{is 10-1° torr before} growth. ^The structures studied here have been obtained a short time after reloading ^{of the As}

cells (they ^are between the 5th and the 20th epi- layers). ^In references [3] ^and [4] ^{it seems that}

the continuous chamber cooling (resulting ^{in a}

lower basic _pressure of the chamber) and the im- provement ^{of the} quality ^{of the} epilayers ^{after a} large ^{number of} growths ^{over an extended} pe- riod of time are major points. ^{In our case the}

net residual doping ^{of the} GaAs is in the low 1014 cm-3 _range with a compensation ^{ratio of 3}

as estimated from the temperature dependance

of the electronic mobility ^of slightly ^Si doped

10 pm thick GaAs epilayers.Thus ^our growth

conditions are rather common and we estimate therefore that the increase of the electron mobil-

ity ^{observed in this work is rather a matter of} optimization ^{of the structure.}

The Al composition of the barrier is around 32 % . This composition ^{and the} quality ^{of the}

GaAs channel have been verified by photolumi-

nescence at low temperature. ^The dopant ^{is sil-}

icon. The carrier density ^{and electron} mobility

are obtained by conventional four point ^{Hall ef-}

fect and Van der Pauw measurements between

room and liquid ^He temperature ^on square pieces

of samples. ^{The ohmic contacts are obtained} by ^In diffusion and _very good quality ^is easily

achieved in spite ^{of the} large spacer d2. Light ^il-

lumination (at wavelength ^below the GaAs bar- rier band gap) ^{is used to increase} slightly ^the charge density and this effect is persistent ^{in the}

dark. The corresponding increase of the mobil-

...

ity is proportional ^to ng ^as expected ^{from the}

relation given ^above between > ^{and ns.}

With the conventional structures (Fig.la)

we obtain electronic mobilities at 4K around 106 cm2V-1s-1 for ns around 2.5 ^x 1011 cm-2 and for a spacer thickness d1 ^{in the} 400-600 k _range.

With the new structures (Fig.lb) ^{we have ob-}

tained repeatedly mobilities in excess of 2 x 106 cm2V-’s-’ for _ns around 1.7 x 1011 cm- 2 ^and

spacer thickness di ^{in the} 750-1000 A _range.

At present ^{time our} best values are 2.5 x 106 cm2V-1 s-1 for _ns ⁼ 1.7 x 1011 cm-2 at 4K and d1 ^{= 1000} A and 3.7 x 106 cm2V-1 s-1 for

ns = 1.8 x 1011 CM-2 at 1.5K and d1 ^{= 800} A. A

figure ^{of merit of} modulation doped heterojunc-

tions being given by ^the ratiou/n. 3/2 the ^interest

of the new implementation of the barrier doping

is clear.

In order to test more quantitatively ^the pro-

posed ^ideas concerning the minimization of re-

mote ionized impurity scattering, ^{we have com-} pared ^the following ^{series of} heterojunctions.

They ^{all have the same} spacer thickness di ^of

750 A. Four heterojunctions have been grown with the new structures (Fig.lb) and spacer thickness d2 varying ^{between 0 and 1800} as, ^the

fifth is _grown with the conventional structure us-

ing ^bulk doping (Fig.la). ^The thickness of the

doped ^GaAlAs layer of this last heterojunction

is 500 A and chosen in order to have the same

amount of Si atoms as in the planar doped layer 82 of the others. Slight variations of n. between the different heterojunctions ^have been corrected in the presentation of the results (Fig.2) ^{in or-}

der to compare the structures for the same 2D

charge density of the 2D electron _gas chosen to be _{ns =} 1.5 x 1011 CM-2 . The large increase of electronic mobility (by ^{a factor of} 3.3) ^{which is}

observed demonstrates the interest of the het- erostructures with a second _spacer d2 ^{in addition}

to dl.

Fig.2.- 4K electronic Hall mobilities (normalized ^at

ns = 1.5 x 1011 cm-2) ^{for a series of} heterojunctions

(d1 ^{= 750} A). ^{Left part} conventional bulk doping ^of 500 A of the barrier. Right part : effett of the increase of _spacer d2 thickness in planar doped structures.

Thus ^we have put forward in this study ^how

a large increase of electron mobility ^{at low tem-}

perature ⁱⁿ modulation doped GaAs/GaAlAs ^he-

2052

terojunctions ^{could be} expected by optimizing

the doping of the barrier in order to reduce ^as much as possible ^{the remote ionized} impurity scattering.

We have proposed ^a design ^{of the GaAIAs}

barrier doping ^{that fits} ideally well this analy- sis, using ^two planar doped layers separated by

a large spacer. We have proved the effective in- terest of this structure by ^a study ^of the electron

mobility ^{in a series of} heterojunctions ^{in which}

the thickness of this new additional _spacer layer

is varied. The striking improvement ^demonstra-

ted here is expected ^to be fundamental in the at-

tempt ^to realizing nearly perfect ^{2D electron} gas of _very high Jl Ins /2 ratio needed for further _pro- gress in quantum transport ^studies.

We would like to thank V. Thierry-Mieg ^who

has been involved in the study ^of planar doping of GaAIAs, ^Y. Lagadec, ^F. Mollot, ^R. Planel with whom we are sharing the molecular beam expi-

taxy system ^{and J. Rosiu for in contact studies}

and preliriiinary electrical characterization.

References

[1] STÖRMER, H.L., Surf. ^{Sci. 132} (1982) ^519.

[2] TSUI, D.C., STÖRMER, ^{H.L. and} GOSSARD, A.C., Phys. Rev. Lett. 48 (1982) ^1559.

[3] HARRIS, J.J., FOXON, C.T., BARNHAM, K.W.J., LACKLISON, D.E., HEWETT, ^J.

and WHITE, C., J. Appl. Phys. ⁶¹ (1987)

1219.

[4] ENGLISH, J.H., GOSSARD, A.C., STÖRMER,

H.L. and BALDWIN, K.W., Appl. Phys.

Lett. 50 (1987) ^1826.

[5] HARRIS, J.J., FOXON, C.T., LACKLISON,

D.E. and BARNHAM, K.W.J., Superlattices

Microstructures 2 (1986) ^563.

[6] ^{see for instance ILEGEMS,} M. in The Tech-

nology ^and Physics of Molecular Beam Epi- taxy, ^edited by ^{E.H.C. Parker} (Plenum

Press, London) ^{1985, p.83} and references therein.

[7] ANDO, T., FOWLER, ^{A.B. and} STERN, F.,

Rev. Mod. Phys. ⁵⁴ (1982) ^437.

[8] STERN, F., Appl. Phys. ^{Lett. 43} (1983)

974.

[9] WOOD, C.E.C., METZE, G., BERRY, ^{J. and} EASTMAN, L.F., ^J. Appl. Phys. ⁵¹ (1980)

383.

[10] PLOOG, K., ^J. Crystal ^{Growth 81} (1987) ³⁰⁴

and references therein.