Work function measurements on germanium by thermionic emission

Surface Science 69 (1977) 428-436 0 North-Holland Publishing Company

WORK FUNCTION MEASUREMENTS

ON GERMANIUM BY THERMIONIC

EMISSION N. TALLAJ and M. BUYLE-BODIN Laboratoire d’Electronique *, INPG, Ecole Nationale Sup&ieure d’Electronique et de RadioklectricitP de Grenoble, 23, avenue des Martyrs, 39031 Grenoble-Cedex, France Received 3 March 1977; manuscript received in final form 11 July 1977

In the present paper, we report the results of experiments carried out to determine the effect of surface states on the work function of intrinsic, germanium crystals. This investigation is realised by using the Thermionic Emission Theory at the intrinsic temperature range T (from 900 to 1050 K). The “apparent work function” $J*, obtained from the experimental In(i$T*) versus l/T curves, is found different from the Richardson-Dushman equation one: “the true work fucntion” @ This difference is mainly due to the work function and electron reflection coefficient dependence on temperature. ~5is deduced from @* and from RD modified equation taking into account the semiconductor case. The value of @varies with T: from 3.97 to 4.16 eV. These results are compared with those obtained, by several authors, using other techniques. We present an analysis of these results taking into consideration the effect of surface states shifts on the surface barrier height, and on the work function consequently.

1. Introduction

The thermionic emission method had been used, by several authors [l-3], to determine the work function of conductors, which can be deduced, experimentally, by using the well-known RD (Richardson-Dushman) equation:

is =A,(1

- r,)T* exp(-q$/kr)

,

(1)

where i, is the saturated current density emitted from a conductor at temperature T; A,-, is a universal constant of value 120 A cm-* deg-*; r, is the reflection coefficient for incident electron; and $ is the work function. In the case of semiconductors, the assumptions which were made during the derivation of eq. (1) [l] are no longer available, particularly at high temperatures, and the following factors must be taken into account. (1) The temperature dependence of the Fermi level is larger than for conductors. (2) The presence of discrete charges in impurity levels and in surface states of semiconductor ensures that the surface properties are different from those of the bulk. * Equipe de recherche associhe au CNRS, No. 659. 428

IV. Tullaj,M. Buyle-Bodin / Workfunction measurements on Ge

429

(3) The temperature dependence of the electron reflection coefficient is not neglected. (4) The effective mass of electron m* in eq. fl), has to be considered (m* = 1.6 nae for Ge, where m. is the mass of electron in vacuum). A0 becomes: = 120 A cm-= degW2

(2)

However, we admit that A remains constant, since the temperature influence on m* is negligible. The Schottky lowering of the barrier may be neglected in our case, because the applied field is kept as low as 1 V/cm (see eq. (2)). Linear Richardson an Schottky plots have been shown by Esaki [4] and Bachmann et al. [S] on silicon. No work is published on germanium. In this paper, we report the results of experiments carried out to determine the work function, taking into account the factors mentioned above for ge~~ium. This investigation is based on the determination of Cp*and the resolution of RD modified equation. Our main discussion covers the dependence of temperature and surface states shifts effect on the work function (see section 4). However, these “preliminary” measurements allow us furthermore, to illustrate the influence of ambient gas on the lon~tu~~ conduction of germanium [6].

vacuum pump Fig. 1. Experimental assembly and circuit measurements: (A) germanium sample, (B) quartz sample-holder, (C) tungsten whiskers, (D) copper tub, (E) tantalum anode.

430

N. Tallaj, M. Buyle-Bodin

2. Experimental

/ Work function

measurements

on Ge

procedure

The measurements were performed on an intrinsic germanium sample with the dimensions of (20 X 3 X 1) mm3, and about 50 ohm cm resistivity. The emitted surface has a (111) orientation, it was polished, etched in CPs, rinsed, and then neutralized.The arrangement of elements in the experimental vacuum chamber and the circuit measurement are indicated in fig. 1. The germanium sample A is put on a quartz sample-holder B, which constitutes a parallelopipedic tub with ten holes for tantalum electrod furation and their pressure readjustment. The contacts (1 to 4) serve for longitudinal conductivity measurement, u, which allows to deduce the sample’s temperature. This temperature is compared with that indicated by a chromel-alumel thermocouple (placed at one side of the sample). The contact 5 serves for current emission measurement. Tungsten wiskers C passing through a copper tub D served to lead the heater ac current. The tantalum anode E is placed parallel to the sample with a rotation and translation adjusting system. The whole is placed in a vacuum chamber which is thoroughly evacuated and tipped off at a pressure of low6 Torr. Under such “contaminated” pressures we succeed to determine, in parallel, the influence of ambient gas on the longitudinal conduction. The emitted current is detected by a digital electrometer (Keithley) which has a current noise below 2 X lo-” A. However, an unreductable current noise of about IO-l4 A is observed with our screened circuit measurement (see fig. 1).

3. Experimental

results

3.1. The apparent work function After etching, the sample is placed in the vacuum chamber and heated at a high temperature for many hours. The a(T) curve [6] is compared with the theoretical one obtained by Morin and Maita [7]. The results are in agreement with theory. However, a temperature variation of about 5 K is noted. We can deduce, from o(T) curves, the variation of Forbidden gap with temperature, considering that the mobility changes with temperature [8]. The usefulness of this deduction is discussed in section 4. Before the work function measurements of germanium, we tested the circuit for measuring the well-known function of tantalum, which serves for our experiment, as an anode. We obtained a work function value of 4.18 eV which, in general, is in agreement with that currently found in litterature [9]. The experimental ln(iS/T2) versus l/T curves, for two germanium samples (1, 2) (which have at room temperature, a resistivity of 50 and 60 R cm respectively), are shown in fig. 2. The slope of the plot gives @*;the apparent work function that is: K -d‘* = -4 d(l/T)

[ln(iJT*]

,

N. T&aj, M. B&e-Bodin

/ Work function measurements on Ge

431

is/T2(A/cm2 deg*)

10-l

3O-1

03/T(K-') 039

1

1.1

Fig. 2. The experimental ln(&/?“*) versus l/T curves: (A) sample No. 1; (0)sample No. 2.

and the intercept of the ln(i,/T2) versus l/T plot on the l/r axis is used to determine A *, “the apparent emission constant”. A * may be shown to be related to the constant A by [l] : - re) .

A = A* exp[(~d#/d~~/~]~(l

(4)

Table 1 reports our results on @*and A* for two the germanium samples. 3.2. RD modified equation and Cp We shah look for a solution on the general RD equation with Q,and T only, taking into account the factors mentioned in section 1. The saturated zero-field current density i, must obey the RD equation (1); the substituting of (3) in (1) gives:

cb=O’+T22!+kT2~. dT

q(1 -r,>

dT

(9

In this expression, we consider the temperature dependence of work function and electron reflection coefficient. To resolve eq. (S), we use the quantum electron reflection theory from the sur-

IV. Tallaj, M. B&e-&din

432

1 Work function

measurements

on Ge

Table 1 The apparent work function and the apparent emission constant values of two germanium samples Sample No.

cp* (eV)

A * (A cmW2 degm2) _...

1

2.896

7.26

2

2.792

1.45 ---~-

_..

_

__-.-

GteV)

re

4,l

1.725

4

0.720

3,

950

1000

1050

T(K)

Fig. 3. The true work function and the electron reflection variation with ‘Z’for two germanium samples: (A) sample No. 1; (0) sample No. 2.

N. Tallaj. M. Buyle-Bodin

/ Work function

measurements

face. With the Schrodinger equation and its solutions vacuum, r, can be expressed as [lo] : ?-,(T, @>=

1-4(g2 [$z(y’]

The substitution

of r, and dr,/dT

on Ge

433

for the semiconductor

.

and the

(6)

in eq. (5) gives: (7)

The integration constant, CY,is determined by experimental considerations. The value of 4 versus T curves has been plotted by means of a computer (see fig. 3). We notice that 4 increases with temperature. It varies from 3.97 to 4.16 eV in the temperature range (900 to 1050 K) for the sample No. 1, and from 3.92 to 4.10 eV for the sample No. 2. We present in fig. 3 the variations of r, with T. The value of r, is deduced from eq. (6) once @Jdetermined for a given temperature T. We note that re decreases when the temperature increases. Furthermore, the value of r, is important compared with unity. 3.3. Estimation of experimental error The error in the experimental eq. (1) we then get:

value will be estimated

approximately

by deriving

If the true current emitted is 10% larger or smaller than the assumed one, and the precision of the determination of T is about l%, we get: A$/$ = 0.012 , and @ will decrease or increase of about 0.048 eV. Hence, the uncertainty current emitted has relatively little influence on the results.

of the

4. Discussion 4.1. Results analysis The variation with temperature, of the work function which is observed, will be attributed to the slow surface states perturbation. In fact, we can express, in general, the work function as (fig. 4): ‘$=x-qT”,+ub,

(9)

N. Tallaj, &I.Buyle-B&in / Work function measurements on Ge

434

Eg(eV)

0,54

0,53

3,80

0,52

3,75

0,51ii

900

950

1000

1050

Fig. 4. Energy level diagram for an intrinsic germanium in the presence of acceptor-like. Ei is the intrinsic level, and the variations of forbidden gap, (x - q VS) and re with temperature: C&‘X Co) (x - q V,)(T).

(a)

where x is the electron affinity, V, is the potential barrier height, and ub is the energy separation between the Fermi level and the conduction band edge in the bulk. (In our case ub = Es/2 for intrinsic mater@ where Es is the forbidden gap.) In the temperature range (900-1050 K): - The lon~tudin~ conductivity measurement and the concentration of intrinsic carriers caIcuIation, ailow to deduce the variation 6 vb: 6 v,, = 4 6Ea = 3 [Es( 1050) - E&900)]

(10)

,

this variation is equal to O.Ol5 eV. - The work function variation value S# is about 0.20 eV. Thus, we can neglect SEg compared with Sgi, the work function S@=S(x

- 4VS/,)+

Such a change of @observed experimentally,

variation is then: UI)

may be due to a variation of both x

N. Tallaj,M. Buyle-Bodin / Workfunction measurements on Ge

435

and I’,. A change of electron affinity is due to a layer of absorbed dipoles [ 111. On the other hand, electron transition between acceptor or donor species (positive or negative adsorbed ions), and the semiconductor may occur by thermoionic emission over the potential barrier, by tunnelling through it, or by some combination of the two processes [12]. Here, such processes would explain the changes in barrier height following the surface contamination by the ambient gas at a pressure of 10m6 Torr. In fact, we have shown [6], that the conductivity of the sample increases after evacuation to a pressure of 1O-5-1O-6 Torr since most of the slow states on ordinary surfaces consist of ions adsorbed from the surrounding ambient gas. The surface states density in the space-charge region increases which gives rise to a change of the potential barrier height [lo]. A such change is accelerated by heating due to the relaxation time enhancement [ 121. The work function increases consequently. We think, meanwhile that the electron affinity variation is small compared with 6 I’,, since no layer of adsorbed dipoles exists [ 111. 4.2. Comparison with other experiments Several works have been published concerning the work function measurements of germanium. These works were based on either a contact potential difference CPD [14], or photoemission [15], measurements. Parallel to this, there are many papers on work function measurements of silicon using CPD [ 141, photoemission [ 161, and thermoionic emission [4,5]. Table 2 shows their results as well as those presented in this paper. Dillon and Farnsworth [14] obtained the work function &~o 4.5 eV on germanium and 4.48 eV on silicon by the CPD method. Haneman [15] obtained a @Ph value of about 4.66-4.80 eV on germanium, whereas Allen and Gobeli [16] obtained 4.82 eV on silicon, all using the photoemission on silicon, Bachmann et al. [5] obtained a $Th value of 4.03 eV, and Esaki [4] obtained 4.02 eV. We observe (see table 2) that at high temperature, like in silicon, the value of @is

Table 2 Summary

of results

obtained

by different

SC

Technique,

Ge(ll1)

CPD [14] Photoemission Thermoemission

[ 151

CPD [ 14) Photoemission Thermoemission

[ 161

Si(ll1)

method

workers

on the work function

Temperature

(K)

of Ge and Si @ (eV)

300 300 900-1050

4.50 4.75 No. 1 4.07 No. 2 4.01

300 300 1373-1623 1284-1664

4.48 4.83 4.02 4.05

0.05 0.05

[4] [5]

436

N. Tallaj, M. Buyle-Bodin

/ Work function

measurements

on Ge

less than that at room temperature. Furthermore, the relative values with temperature are comparable for germanium and silicon. The difference of work function $cPD - @Thcomes out of the fact that: (a) the energy gap decreases with temperature, and (b) the surface states effect is more important at high temperature [ 171. On the other hand, we can explain the difference @ph - 4CPD by the fact that @it, is the threshold of the photoemission process which is given by the sum of the electron affinity x, and the energy gap Eg (see fig. 4). Hence $ph does not correspond to the true work function.

5. Summary The results of experiments covering the work function and electron reflection coefficient of germanium dependence, on temperature have been presented. It shows once more that the experimental value of work function is smaller than that of the RD equation. We have shown that the value of @increases with temperature range T (900 to 1050 K). This variation is mainly due to surface barrier height shifts and its dependence on temperature. The part of surface states on work function has been pointed out. Since this is the first reported study of thermoionic emission from intrinsic germanium surfaces, we think that a better interpretation must await further and more refined experimentation and theoretical consideration. It does appear that some very careful measurements along these lines may provide much useful information.

References [l] J.C. Rivikre, in: Solid State Surface Science, Ed. M. Green (Dekker, New York, 1969). [2] V.L. Stout, Thermionic Emission and Thermionic Power Generation, in: Thermoelectricity, Ed. P.H. Egli (Wiley, New York, 1958). [3] E.B. Hensley, J. Appl. Phys. 32 (1961) 301. [4] L. Esaki, J. Phys. Sot. Japan 8 (1953) 347. [S] R. Bachmann, G. Busch and A.H. Madjid, Surface Sci. 2 (1964) 396. [6] N. TalIaj, Vide, les Couches Minces 186 (1977) 20. [7] F.J. Morin and J.P. Maita, Phys. Rev. 94 (1954) 1525. [8] G. Kamarinos and M. Diouri, Phys. Status Solidi (a) 32 (1975) KlOl. [9] B.J. Hopkins and J.C. Riviere, Brit. J. Appl. Phys. 15 (1964) 941. [lo] N. TaIlaj and M. Buyle-Bodin, Accepted communication, 7th IVC and 3rd ICSS, Vienne, 1977. [ 111 G. Heiland and P. Handler, J. Appl. Phys. 30 (1959) 446. [ 121 S.R. Morrison, Phys. Rev. 102 (1956) 1297. [13] N. Tallaj, 38me cycle thesis, INP Grenoble (1973); G. Kamarinos, N. TaIlaj and P. Viktorovitch, Elect. Fis. Appl. 17, No. l-2, (1974). [14] J.A. Dillon and H.E. Farnsworth, J. Appl. Phys. 28 (1957) 174. 1151 D. Haneman, Phys. Chem. Solids 11 (1959) 205. 1161 F.G. AIlen and G.W. Gobeli, Phys. Rev. 127 (1962) 150. [ 171 V.I. Lyashenko and N.S. Chernaya, Soviet Phys.-Solid State 1 (1959) 921.