Basic Device Equations and Models

Before further characterizing the trapped charge behaviors, we should first understand the basic operating principle and related models of SONOS-type memory. In this section, we will first introduce the basic operating principle of SONOS. Then, we discuss the e-field of each ONO film for program/erase and the transient currents under different trap location assumptions. From these e-field and transient current models, we can obtain the relation between e-field and transient current. This information can help us further understand the trapped charge behaviors.

2.1.1 Basic Operating Principle [1.3,1.6]

The storage principle of non-volatile memory devices can be simplified as the charges (QT) are trapped in the gate insulator of a MOSFET, as illustrated in Fig. 2.1(a). The trapped charges will change the threshold voltage (V_T) of MOSFET and provide two distinct states (0 for erased state and 1 for programmed state), as illustrated in Fig. 2.1(b). Based on the basic theory of the MOSFET, its V_T can be given by

0

2 ^{I D T}

T F ms I

I I I

Q Q Q

V d

C C

φ φ ε ε

= + − − − (2-1)

where φF is the Fermi-potential of the semiconductor at the surface, φms is the work function difference between the gate and the bulk material, Q_I is the fixed charge at the silicon/

insulator interface, QD is the charge in the silicon depletion layer, QT is the charge stored in the gate insulator at a distance dI from the gate,CIis the capacitance of the insulator layer, εI

is the dielectric constant of the insulator, and ε0 is the permittivity of free space. Therefore, the VT shift (∆VT) caused by the QT is given by

0 T

T I

I

V Q d

∆ = −ε ε (2-2) Negative Q_T (electron) will cause positive ∆V_T while positive Q_T (hole) will cause negative

∆VT.

Applying an appropriate gate voltage (Vread) which is between two possible VT’s, as illustrated in Fig. 2.1(b), the stored information can be detected. The detected current is high for erased state but low for programmed state, so that we can easily distinguish the stored states.

2.1.2 Electric Field Model

The ONO energy band diagram of SONOS-type memory under zero bias is shown in Fig.

2.2. T_Box is the bottom oxide (B.O.) thickness, T_N is the nitride thickness, and T_Tox is the top oxide (T.O.) thickness. The conduction band offset between oxide and nitride is about 1.05eV, and the valence band offset between oxide and nitride is about to 2.85eV [2.1].

Under positive gate bias (VG), the ONO energy band diagram bends, as illustrated in Fig.

2.3(a). The voltage drop on total ONO is equal to V_G if we ignore the voltage drops on Si-sub and gate. Therefore, the B.O. e-field (EBox) and the T.O. e-field (ETox) can be easily calculated by

G

Box Tox

E E V

= = EOT (2-3) where the EOT is the equivalent oxide thickness of total ONO. Since there is no charge at nitride/B.O. interface, from continuity equation [2.2]: εoxEBO ﹣εNEN = 0, we can obtain the nitride e-field (EN).

ox ox G

N Box

N N

E E V

EOT

ε ε

ε ε

= = ⋅ (2-4)

where εox and εN is the dielectric constant of oxide and nitride, respectively. From Eq. (2-4), we can know that the material with higher dielectric constant (k) has lower e-field. That is why high-k materials have been proposed to replace the T.O. of SONOS memory to reduce the gate injection and release the erase saturation [2.3-2.4].

If there are charges in the nitride, the e-field of ONO will change. For example, the trapped electrons (holes) at nitride/B.O. interface will cause decreased (increased) EBox but

increased (decreased) EN, as illustrate in Fig. 2.3(b). Fortunately, the changed e-fields can be simply calculated based on continuity equation and voltage conservation. From Eq. (2-2), the charges trapped in nitride can be extracted from ∆VT according to

0

In order to simplify this subject, we first consider three cases: (a) charges at the B.O./nitride interface, (b) charges at the T.O./nitride interface, and (c) charges at the center of nitride.

(a) Charges at the B.O./nitride interface:

Since there is Q_T at B.O./nitride interface, and there is no charge at T.O./nitride interface, the continuity equation gives us

oxEBox NEN QT From voltage conservation, the summation of voltage drop on each ONO film is equal to the external gate bias.

(b) Charges at the T.O./nitride interface:

Since there is no charge at B.O./nitride interface, and there is Q_T at T.O./nitride interface, the continuity equation gives us

oxEBox NEN 0

(c) Charges at the center of nitride:

The ONO energy band diagram for charges at the center of nitride is shown in Fig. 2.4.

The nitride is divided into two equal parts. The bottom nitride e-field is E_N1 while the top

The voltage conservation consists of four films.

From the results of three cases, we find that they can be simplified as one general case:

the trapped charges locate at x from B.O./nitride interface, as illustrated in Fig. 2.5(a), and the e-field of each film can be calculated by

G T

where EOTQG is the equivalent oxide thickness of the distance from QT to gate. It should be noted that the E_Box is independent of charge location. On the other hand, for the ONO energy band diagram under negative gate bias, as shown in Fig. 2.5(b), we can follow the same procedure as positive gate bias, but total voltage drop on ONO should be equal to V_G . The e-fields can be simplified as

G T charge location (x) can be summarized as Table 2.1.

2.1.3 Transient Current Model

If we assume all the injected charges are trapped in the nitride and contribute to ∆VT, we can extract the transient hole current or electron current directly from ∆VT. From Eq. (2-5),

The transient injection current during programming or erasing can be expressed as

0 ox

Using Eq.(2-34) and Eqs. in Table 2.1, we can further plot the J vs. E curves of SONOS-type devices. For memory devices, the J vs. E curves can give us a lot of information. For example, compare with theoretical Eqs., we can make sure the detailed transport mechanisms; compare the current and e-field criteria, we can further optimize the operation window.

In this dissertation, we used J vs. E curves to confirm the charge location. Moreover, we also proposed a systematic method to distinguish the erase mechanisms of SONOS-type devices based on the comparison of J vs. E curves.