Field dependence of surface mobility at n-n heterojunction interface

86

NOTES

Solid-State

Electronics

pp. 86-88.

Field

Pergamon Press 1965. Printed in Great Britain

dependence

of surface

n-n heterojunction (Receiwd

mobility

Vol.

8,

at

interface

25 June 1964)

MEASUREMENTS of field-effect interface conductance have recently been reported by ESAKI and others in GeeGaAs n-n heterojunctions.(l) Their results gave direct evidence for the existence of an electron accumulation layer on the Ge-side at the interface as suggested by the model proposed by SHOCKLEY@) and ANDERSON.(~)In the present work, similar measurements were performed at 77°K on both Ge-GaAs and Ge-GaAss.sPa.l n-?z heterojunctions, attention being paid particularly to the field dependence of the surface mobility. =Zn electric field range of 10”-3 x 105 V/cm was investigated. It was found that the electron mobility in Ge at the interface depends on the field. But the dependence is weaker than that which would be expected for a purely diffuse scattering process. c4) Germanium of lOl’-101s cm -3 donors was deposited epitaxially on 1016-5 x 101s cm-s GaAs and 1017-Z x 1017 cm-s GaAss.sPs.1 substrates. The latter material was used for the purpose of achieving higher field, since the barrier height existed in the pair Ge-GaAsa.sPa.1 was relatively large.(s) Heterojunctions made from these deposits exhibited ideal characteristics in the sense that surface states played no important role.(s,s) the interface structure could be Therefore, approximated by a space charge in GaAs (or GaAss.sPa.1) which supported the voltage and a surface charge in Ge, in which the electron mobility was measured. If the mobility is assumed to vary with field by the expression to = aE-k, the a.c. conductance as measured between two contacts on the Ge-side can be shown to be G L.C. = Uv&c.(l - k)( W/L)(El/c2@,9)k ’ C1+k, where C, the capacitance per unit area, is varied by varying the bias across the junction. W/L is the geometrical width to length ratio of the Ge contacts and vu.,. the voltage applied between them. or and l2 are the dielectric constants of Ge and the substrates respectively. The exponent K should be

a function of E in general, being 0 at zero field. Experimentally, K was assumed fixed for each limited field range and its value was determined from the facts that a plot of G,.,. vs. Cl+k should be linear and, when extrapolated, should pass through the origin. The linearity relation if used alone as a criterion in determining K would lead to ambiguity, since k varied slowly with E and only a small range of E could be achieved for each substrate doping N,n. 2.4,

/ 1.62 E -”

P

“0_

,

,

/

/

/-

,’

0.8

/ Oo

FIG. 1. A.C.

04

conductance

08

I.2

lOI c:/*(forad)3’2 vs. three-halves

I.6

capacitance.

Figure 1 is a plot of G,.,, vs. Cy”, where CT is the total capacitance. The three halves dependence indicated that k = 0.5, thus f~ varied with l/Eli* over the field range (1.6-2.3)x 105 V/cm as calculated from E = (cz/q)(qN~/C). The substrate for this unit was GaAss.sPs.1 with No = 2 x 1017 cm--s. The junction area was 7.2 x lo-4 cm* and the geometrical factor had a value equivalent to L/W = 0.75, both of which were typical in our units. Knowing vd.,. = 50 mV as used in our experiments, the value of a was evaluated from the slope according to the above expression. The mobility could then be obtained as a function of the electric field. The d.c. conductance, taking the field dependence of mobility into account, is given by Gd.c. = Go+

~(W/L)(~~)“(~~~NO)~-“/C~-~,

where Go is the bulk conductance. Such measurements, however, lack a criterion in determining k, and were used only as a check on the a.c. measurements. Using K = 0.5 as obtained before, C&e.

87

NOTES

2.3I3r

I I.00 IO+ CT

FIG.

2. D.C.

I&

-1 I.10

(farad?‘*

conductance vs. reciprocal capacitance.

square-root

is plotted vs. C;liz as shown in Fig. 2 for the same unit. The value of a evaluated in this case was 1.43 x 105 crns/zjWa set as compared to 1 a36 x 105 found from a.c. measurements. The good agreement clearly verified the reality of the effect of field on the surface mobility. Measurements at lower fields were made on substrates with lower dopings. It was found that the value of k was decreased with decreasing field. The absolute magnitude of mobility scattered somewhat due to the inevitably different growing conditions from run to run. But the optimum p

chosen from the best unit of each group was found to increase with decreasing field. These results gave further evidence to a field dependent mobility. Figure 3 shows these results, where the optimum mobilities obtained at specified No are superimposed and plotted as a function of E. The value of k increased from 0.1 to 0.2, 0.33 and 0.5. Normalised mobility ~],uo with pug = 500 cm2jV set was actually used in this plot, ~0 being found at still lower field (E < 104 V/cm) where no field dependence of mobility was observed. A theoretical curve of diffuse scattering in a uniform field is drawn in this figure for comparison.@) In view of the complications that may arise from nonuniform field, non-spherical energy surfaces and probably non-Boltzmann statistics in our case, it does not seem appropriate at the present stage to attempt any quantitative determination of the scattering mechanism. The results of this work, as exhibited in Fig. 3, show the kind of field dependence of mobility at the heterojunction interface. The large deviation of the data from the theoretical curve clearly indicates that the scattering is not completely diffuse and some degree of specularity must be involved. are due to L. ESAKI for helpful discussions, M. BERKENBLIT for growing the germanium and J. CUMMINGS for fabricating the samples.

Acknowledgements-Thanks

IBM Watson Research Center Yorktown Heights, New York

L. L. CHANG

Notation Field effect a.c. conductance (mho) Gd.c. Field effect d.c. conductance (mho) Bulk d.c. conductance (mho) Go vd.c. d.c. voltage applied across Ge-contacts (V) Capacitance per unit area (Ficms) C Total capacitance (F) CT Substrate (GaAs or GaAsa.gPs.1) donor conND centration (cme3) Electron surface mobility in Ge at interface P (cmz/Vsec) Electric field in Ge at interface (V/cm) E W,'L Geometrical width to length ratio of Ge-contacts El, 63 Dielectric constants of Ge and the substrate G B.C.

E (V/cm) FIG. 3. Electron mobility at heterojunction interface vs. electric field. Substrates are GaAs with ND = 101s cm-a (+), 5 x lOIs and GaAsa.sP0.l with ND = lW7( x), 2 x lW7( 0). A theoretical diffuse-scattering curve is drawn for comparison.

(F/cm) a, k Q

Coefficients defined as p = aE-” Electronic charge (1.6 x lo-19 C)

1. L.

References ESAKI, W. E. HOWARDand .I. HEER, Appl. Phys. Lett. 4, 3 (1964); Int Ccnf. Solid Surface., dence, June (1964).

Provi-

2. W.

SHOCKLEY, US Patent 2,.569,347. (Sept. 25, 1951). 3. R. L. ANDERSON, Solid-State Electron. 5, 341 (1962). 4. J. R. SCHRIEFFER,Phys. Rev. 97, 641 (1955). 5. L. L. CHANG, to be published.

Solid-State

Pergamon

Electronics pp. M-90.

Printed

Press 1965.

in Great

Vol.

8,

Britain

Calculation of high-frequency characteristics of thin-film transistors (Received

30 June 1964)

THE HIGH-FREQUENCY behaviour of field-effect transistors is frequently judged by the value of the gain-bandwidth product g,/C, which constitutes a kind of reciprocal dielectric relaxation time (RC time) for the structure composed of the conducting channel between source and drain and the controlling gate. SHOCKLEY(~) gives a rough estimate of the RC time for his unipolar fieldeffect transistor starting from a so called gradual whereas WEIMER@) (see also approximation, BORKAN and WEIMRR(3)) presents an expression for the gain-bandwidth product to be used for his thin-film transistor (TFT). In this last transistor the p-n junction known from Shockley’s fieldeffect transistor is replaced by an insulating layer separating the gate and the conducting channel. There is a close connexion, which reduces in some cases to an identity, between the gain-bandwidth product and the reciprocal transit time of the charge carriers.

Dielectric

FIG. 1. Longitudinal

In the aforementioned analyses the electronic device is not considered in any detail and no serious account is therefore taken of the distribution of the capacitance and the conductance in the interior of the transistor. It is the aim of this and a following note to present the most important formulae obtained by means of a theory which does take these distributed conductance and capacitance into account and which therefore constitutes an extension of the theories presented by Shockley and Borkan and Weimer to high frequencies. The present note deals with the thin-film transistor. The most important assumptions introduced by Weimer and Borkan and Weimer are: (1) Thickness of insulating layer between gate and channel is large with respect to thickness of channel so that the potential drop between gate and channel is restricted nearly entirely to the dielectric of the capacitor. As a result the capacitance between gate and channel may be considered as constant. (2) Width of entire configuration is large compared with source-drain distance so that a twodimensional theory may be applied. The current 1(x; t) in the n-type channel is given by (see Fig. 1)

I(x;t)=

-?

No+--

Cg[Vg(t)- V(x; t)]

i

(I

i

1

--v(n; c’x

t),

(1) in which p: electron mobility; 4: absolute value of electron charge; L: source-drain distance; No: total number of charge carriers originally present minus number of traps; C,: gate-channel capacitance; IS-~(~): gate potential taken with respect to the source; V(I(S; t): potential at a point of the

V(x;W

cross section

I

Wf)

of thin-film

transistor.