COLD CATHODE ELECTRON EMISSION DUE TO CHANGING ELECTRIC FIELDS So far it has been established that emission from a cold MgO cathode is merely due to high electric

3. The Design of the X-ray Tube and the MgO Cold Cathode

3.2.5. COLD CATHODE ELECTRON EMISSION DUE TO CHANGING ELECTRIC FIELDS So far it has been established that emission from a cold MgO cathode is merely due to high electric

S5000~----~---=~~---~~

>

"'-

Q) C)

-

(0

Q

>

MgO dz

84080.79 V

Vacuum

Thickness

Equilibrium state without charges

Fig. 3.2.4: Equilibrium potentials with and without surface charges.

3.2.5. COLD CATHODE ELECTRON EMISSION DUE TO CHANGING ELECTRIC FIELDS

the MgO layer. According to Elliott [IS] equation 3.2.7 may also be expressed in the form of the following equation:

p= Na E

I--

r

Na EO

(3.2.S)

Thus under the restrictions of this analysis the polarization P ^IS linearly proportional to the macroscopic field [IS] . For this reason one may write

(3.2.9)

in which Xe is a dimensionless constant, called the dielectric susceptibility, and is given by Na

(3.2.10)

Xe = Na

l-y-

&0

where

r

is a constant. According to Elliott [IS] the flux density in the material is

(3.2.11) The relative dielectric constant Kr can be expressed using the following relation [16]:

&

K _r =-=I+X _e (3.2.12)

&0

where E is the permittivity of the dielectric and Eo is the permittivity of space. Therefore, with the relative dielectric constant for MgO being 9.65, Xe is easily computed using equation 3.2.12 and is found to be equal to 9.65. From equation 3.2.9 we can therefore express the volume density of dipole moments for MgO also in the form of equation 3.2.13:

P = (2,5· S.S54xl0-¹² F.m-^I) . E

2.214xlO-¹¹ • E (3.2.13)

Using equations 3.2.11 and 3.2.13 one can now relate a changing electric field 8EJat to a magnetic field and the motion of charges, or better still a current, within a dielectric medium. If a dielectric material is considered at the microscopic level to consist of an aggregation of charged particles, then the free-space Maxwell's equation, also known as Ampere's law,

(3.2.14)

is applicable, with jt ⁼ j + jb representing the total current density due to motions of both primary charges j and the bound charges (jb) within the dielectric. R. S. Elliott [18] goes on to show that

and therefore

• • • •

D

=

co E+ P

=

Co E+ j ^{t -} j

With the dielectric material being nonmagnetic as in the case of MgO we can then also express Maxwell's equation (equation 3.2.14) in the form

(3.2.15)

Substituting equation 3.2.11 into equation 3.2.15 one obtains

(3.2.16) From equation 3.2.16 it can be seen that the changing electric field 8Etat and the current density j have the same signs, which means that in order for a current to be emitted from the MgO layer of the cathode, i.e. in order for j to be a positive quantity, 8E/8t would obviously have to be positive (see Figure 3.2.5 and 3.2.6). According to Young [31] if one takes the electric field E as a vector quantity, then it is equal to -V/d, where V to the voltage applied across a medium of length d. Thus in order to produce electric fields with positive gradients across the 85 kV X-ray tube a pulsed X-ray tube power supply has to be used, that generates a saw tooth waveform with voltage pulses, that have negative slopes (see Figure 3.2.6). At the same time V x B in equation 3.2.16 shows that a circular magnetic field arises around the current present in the dielectric medium as a result of the electric field gradient 8Etat. It is also important to note, that equation 3.2.16 also explains why current emission can take place in the case of a constant electric field across the MgO film provided that the emission is initiated by a starter mechanism. With E having a constant value 8E/8t becomes 0, so that equation 3.2.16 can be reduced to

(3.2.17) From equation 3.2.17 one can deduce, that if the initial current emission from the cathode is equal to zero or if no starter mechanism is applied to the cathode under a constant electric field, then no magnetic field will be able to develop within the MgO layer of the cathode. Hence no current emission will be able to take place. However, as long as the condition that a nonzero initial current is provided is fulfilled, a magnetic field will be able to develop, even though 8E/8t = 0, and a constant current equal to the initial current will develop. Equation 3.2.16 is therefore in perfect agreement with the observations made by Dagfish [9] and ShroffT2], that in order to cause electron emission form a cold cathode under a constant electric field it is necessary to create an initial current from the cold cathode by an external starter mechanism. All in all it can therefore be seen, that the starter mechanisms mentioned above for constant electric fields become completely

redundant for cold cathode X-ray tubes, if a changing electric field is introduced by applying pulsed voltages across the tube.

~

^NiO

I"

C»

j VAC

-

^!'I:I

^{... jM9O~}

^~

iii _C»

.Q _::I . "

CI) MgO 0 s::

C»

4

E

^MQO

_{E ~8C} «

~ u ₄

Z

I

I

_Vacuum

MgO

Fig. 3.2.5: Graphic representation of X-ray tube dielectric layers and the directions of the electric field E and the current density j across them.

85kV

o

_{tl = 0.003 sec}

Time

Fig. 3.2.6: Voltage waveform of an 85 kV X-ray power supply with negative gradient.

3.2.6. DETERMINATION OF CURRENT EMISSION FROM THE MgO COLD CATHODE

In order to determine theoretical values for currents produced by the MgO cold cathode it is necessary to determine the conductivity a of MgO at room temperature (293 OK). The previous sections have shown that the total field enhanced secondary emission is caused by an intense electric field in the magnesium oxide film. This is a direct result of the formation of positive surface charges. It is therefore sufficient to merely consider the electron emission properties of MgO, since an equilibrium between the charging of the MgO surface and recombination with charges from the nickel substrate of the cathode is established during the electron emissive process [6]. The MgO sample to be measured for its conductivity was prepared as follows:

Magnesium oxide (MgO light) was mixed in a one-to-one ratio with magnesium carbonate (MgC03), where 2g of each substance were used. This mixture was then rolled in 15 cm³ of amyl acetate and then diluted in 15 cm³ of I-propanol. The magnesium oxide cathode was prepared using this MgO.MgC03 mixture as it promised the highest emission rate according to measurements made by Shroff [2] (see figure 5.10, of this section). The amyl acetate and 1- propanol mixtures were employed as binders for the MgO.MgC03powder as suggested by Daglish [9]. In this way it was possible to spray the final mixture onto a surface. Once applied to an insulating ceramic surface the amyl acetate and I-propanol mixture was then allowed to evaporate from the MgO.MgC03 mixture by heating the prepared sample to a temperature of 40°C for an hour in a vacuum oven under a pressure of 10-4 Torr.

The conductivity of the MgO. MgC03 mixture was then determined experimentally using the four point method. By connecting a current source across a 3mm long MgO slab of cross sectional area A

=

(0.4xl0-³ m) . (3xlO-³ m)

=

1.2xlO-⁶ m^2, as illustrated in Figure 3.2.7, a potential difference of rp

=

27 V was measured at an applied current of 10 ~A. By applying these values in equation 3.2.18 [16] the conductivity a ofMgO was found to be 9.26xlO-4 S m-I.

1GpAl

MgO Sample

Insulating Surface

Fig. 3.2.7: Measurement of the conductivity of MgO using the four point method.

rp = I (J·A

I (3.2.18)

Using a 111 Hz 85 kV power supply to operate the X-ray tube (see Figure 3.2.8 for voltage waveform) an expression for the power supply voltage output and hence the electric fields across the tube can be found. The equation for one voltage pulse of 0.003 sec duration across the entire tube (see equation 3.1.2, Section 3.1.2), i.e. the NiO-MgO-vacuurn structure, is

-8.5 x 10⁴

V(t)

=

t + 8.5 X 10⁴ Volts

0.003 (3.2.19)

In section 3.2.4 it was found that V2, the voltage across the magnesium oxide film, was 15.73 V when a voltage of 85 kV was applied across the tube. Therefore the voltage waveform across the MgO layer will have the same shape as that provided by the power supply (see Figure 3.2.8).

However, the potential across the MgO film will peak at 15.73 V (see Section 3.2.4) rather than 85 kV while for the NiO layer the peak will be at 1.279x 1 0-² V. Thus the potentials developing inside the MgO and NiO layers during one pulse can be expressed using equations 3.2.20a and 3.2.20b:

-15.73

VMgO(t)

=

t+15.73 Volts

0.003 (3.2.20a)

-1.279 X 10-²

VNiO(t)

=

t+1.279 ^X 10-² Volts

0.003 (3.2.20b)

Therefore E2 from section 3.2.4, namely the electric field across the MgO layer, can now be expressed as

- 15.73

- -t+ 15.73 0.005

--=..:...::c.::..::=--_ _ _

=

1 ^X 10-⁴

-5.243 x 10⁷ t + 1.573 x 10⁵ V m-^l (3.2.21a)

and EI, the electric field across the NiO layer, can be written as

- l.279 x 10-² t + l.279 X 10-² 0.003

-~=..::~---=---

=

I X 10-⁷

-4.263 X 10⁷ t + l.279 X 105 V m-^I (3.2.21b)

where the values for

V;

and V₂ are taken from equation 5.20 and d] = 1 xl 0-⁷ m and d2 = 1 X 1 0-4 m are the thicknesses of the NiO and MgO layers respectively. Keeping in mind that the current density j = ( j E, the current density j emitted by the MgO film can be obtained by substituting the electric field E by E2 in equation 3.2.22:

(3.2.22)

The total current ifield emitted due to the electric field in the MgO layer into the vacuum of the X- ray tube by the cathode can be computed by multiplying the total surface area A of the MgO cathode by j. With the cathode having an outer radius of 0.014 m and an inner radius of 0.006 m, its surface area A is found to be equal to 1.256x 10-4 m². Therefore the time dependent field current

i field becomes

-6.098t + 0.018 Amperes (3.2.23a)

This relation is plotted in Figure 3.2.9 below illustrating how the current emitted during a single pulse by the MgO cold cathode decays with a negative electric field gradient BE/Bt according to the method described above.

al C')

::: to

>

o

o

85kV

-df dV

0.003 sec time ^{0.009 sec}

Fig. 3.2.8: Voltage waveform of a 111Hz 85 kV X-ray power supply with a 33,33% duty cycle.

o 0.CXX)5 0.001 0.0015 0.002 0.0025 0.003 0.0035

time (sec)

Fig. 3.2.9: Chart of current ijieu(t) emitted by MgO cold cathode during one voltage pulse.

The voltage waveform is shown in fig. 5.8.

j(mA cm-2 )

15r---~---~

10~---~+---~

5 -------~--~---~

D1 C1 ~1 ^{F1 A1} E1

I .I.

, ..

25 50 75 100% MgC02

... &

. ,

i I

,

100% 75 50 25 0

MgO

Fig. 3.2.10: Current density of emitted electrons versus cold cathode composition [2)

According to Figure 3.2.10 a maximum electron emission current density can be obtained, if MgO is mixed with MgC03 in a one-to-one weight ratio, so that a current emission density of 15 mAcm-² can be obtained [2]. This implies that a MgO cathode of 1.4 cm outside and 0.6 em inside diameter would be capable of providing current densities of up to 19 rnA cm-^2. It can be seen, that the maximum cathode current ifield

=

18.295 rnA, or alternatively the emitted current density j =

14.566 rnA em-^2, calculated using equation 3.2.23a, which is plotted in Figure 3.2.10, is somewhat lower than that measured by Shroff [2] (see Figure 3.2.10). However, one can say that the above two predictions (see Figure 3.2.9 and 3.2.10) are roughly in agreement with each other, whereby the total maximum emitted current ifield = 19 rnA predicted by Shroff differs only by 3.88 % from the current value of 18.295 rnA predicted by equation 3.2.23a. As in the case of the average power supply output current iAVE (see Section 3.1.2) the average field current iave,jieldCan be obtained from equation 3.2.23a as follows:

f

I, ^{-6.098t + 0.018}

. -=.0 _ _ _

=

⁰

=

lave.field

= -"---

t2 t2

[ ] 0.003

-3.049(2 + 0.018t

°

0.009

=

3.048xlO-³ Amperes

=

3.048 rnA; (3.2.23b)

In conclusion we can see that electron emission from a MgO cold cathode can neither be attributed to the Schottky effect nor can it be explained via the Fowler-Nordheim relation (equation 3.2.5). At temperatures as high as 1100 OK a MgO cathode with a surface area of 1.256 cm² would be capable of providing a negligible current of only 9.411xl0-⁵ rnA (see Table 3.2.2, section 3.2.3), which leads us to exclude the possibility of the Schottky effect taking place in the cold cathode under the influence of a high electric field. At the same time one can see, that any value calculated for the emitted current density j using the Fowler-Nordheim equation approaches zero. This result would indicate that no current would be emitted from a MgO cold cathode under the influence of high electric fields, which, however, is not the case according to experimental observations [2,3 ... 13]. With Maxwell's third law, or Ampere's law, however, it is evident that not only will a current pass through a dielectric medium provided a changing electric field is present across it, but that this is primarily due to a circular magnetic field, namely V x B , that builds up in the dielectric layers of the cold cathode. Even if a constant electric field is applied across the dielectric medium, MgO in our case, a constant current will develop across the material together with a rotating magnetic field provided an initial current is present at the start of the emission process.

3.2.7. ADDITIONAL ELECTRON EMISSION DUE TO X-IRRADIATION OF THE

CATHODE

From the end-window tube construction described in Chapter 3.1 (see Figure 3.l.1) one can see, that, once electrons have struck the target surface of the tube, the X-ray photons thus produced will not only leave through the window of the tube to irradiate a given specimen, but will also strike the surface of the cold cathode thus exciting further electrons in the nickel substrate of the MgO cathode. However, instead of falling back into their shells causing further X-ray photons to be emitted from the cathode itself, the electrons will, under the influence of the electric fields present in the NiO, MgO and vacuum layers of the tube, be able to travel all the way to the target [56]. As a result of this more electrons will be emitted from the cathode in addition to those being emitted solely under the influence of the electric fields mentioned above. In Figure 3.2.11 we can see how the cathode is positioned with respect the target face of the tube. In the figure one can clearly see that the cathode itself will receive X-radiation from the target [56].

Mgo Cathode W -Target

~-- ~ -e--- ~ ---, ^/

to detector ~

. / ^~

X-ray Window

~

){-I3Y phO'lons:

produced at target

e- ~

electron beam tl3velling from cathode

Fig. 3.2.11: Position ofthe MgO cold cathode with respect to the target/anode face ofthe tube [56].

According to R. H. Fowler [23] photoemission of electrons from a material can be considered as directly proportional to the photon energy incident on the surface of the material. Obviously it is this photon energy, be it in the form of visible or ultraviolet light, X-ray or radioactive radiation and so on, that causes electrons to be photoemitted from a given material. When a specimen is subjected to a bombardment of highly energetic electrons, X -rays will be produced from the specimen. This type of excitation is referred to as electron excitation, and the intensity of a Kline resulting from such an interaction between the electrons and the specimen can be expressed in terms of equation 3.2.24:

(3.2.24) where I ^K is the intensity of a specific K line or the spectral intensity distribution of the primary radiation, V_K is the K-excitation potential (kV), V can be either the peak or the constant X-ray tube potential in kV, i is the X-ray tube current (rnA) and Pis a constant equal to 1.7 [24]. The quantity (V - V_{K )} is the over potential or overvoltage, while the exponent is a constant which has a value typically between 1.5 and 2. From equation 3.2.24 we can therefore see, that

I K

is directly proportional to the tube current i. If we take this current to represent the photoemitted electrons described earlier it follows, that the K line intensity I K of nickel is also directly proportional to the amount of electrons emitted from the nickel substrate of the cold cathode as a result of X-rays from the target striking it. Hence

(3.2.25) where i is the X-ray tube current. In order to determine how much photocurrent is produced by the cold cathode and therefore how high the total tube current i

=

i _p ^ho _to + ifi _{e '} ld where i _field is the

current emitted due to the field alone (see Figure 3.2.9, section 3.2.6), is it is necessary to calculate the fluorescence intensities of the fluorescent X-radiation emitted from nickel assuming that no electric fields are present and therefore no electrons are emitted. In the treatment of this problem it will also be assumed, that the X-rays emitted from the target of the X-ray tube will completely pass through the thin and porous MgO and NiO layers of the cathode causing emission of photoelectrons from its nickel sleeve. The intensities calculated in this manner will then be directly related to the total tube current i , which arises from the combined effect of the X -irradiation of the nickel substrate of the cathode and the high electric fields present in the dielectric layers of the tube i.e. the NiO, MgO and vacuum layers. In Section 3.2.11 of this chapter an idealised case be presented, in which it is assumed that all the electrons excited and removed from their atomic shells will be accelerated through the high electric fields present in the vacuum space of the tube towards the anode rather than undergo processes of recombination. The symbols that will be used in the intensity calculations in this section are illustrated in Table 3.2.3.

3.2.8. DEFINITION OF PRIMARY, SECONDARY AND TERTIARY FLUORESCENCE