Channel hot carrier effects in n-MOSFET devices of advanced submicron CMOS technologies

Microelectronics Reliability 47 (2007) 552–558 www.elsevier.com/locate/microrel

Introductory Invited Paper

Channel hot carrier effects in n-MOSFET devices of advanced submicron CMOS technologies Giuseppe La Rosa *, Stewart E. Rauch III IBM Systems and Technology Group, Technology Collaboration Solutions, USA Available online 9 April 2007

Abstract A review of the channel hot carrier (CHC) mechanism and its effects on n-MOSFET devices of deep submicron CMOS bulk technologies is presented. Even with power supply reduction (Vsupply  1.0 V) CHC effects still limit aggressive transistor scaling. In this work it is shown that the ‘‘Lucky Electron Model’’ picture is not adequate to describe carrier heating under quasi ballistic transport. A more general physical picture is proposed, in which the driving force of the hot carrier damage is the ‘‘carrier dominant energy’’ determined by the energy convolution of the effective interface states generation (ISG) cross section (SIT(E)) and the electron energy distribution function (EEDF) at given bias stress conditions. Both the CHC LEM and the energy driven approximations are derived. The latter is shown to be more adequate to describe the CHC degradation with supply voltage reduction. This approach allows an experimental quantification of SIT(E).  2007 Published by Elsevier Ltd.

1. Introduction Recently the modeling of channel hot carriers, defined as carriers which gain substantial kinetic energy in excess of the average thermal energy, has been considered one of the most challenging tasks posed by MOSFET scaling, mainly because of the strict reliability constraints the presence of energetic carriers applies to CMOS technology development. The difficulty of this task derives from the quasi ballistic transport experienced in MOSFETs of advanced CMOS technologies. In this case the strongly non-equilibrium nature of hot carrier transport makes the simple equilibrium or quasi-equilibrium lucky electron model (LEM) not physically sound and often oversimplistic. In the case of n-MOSFET transistors a key information for a suitable modeling approach of the CHC degradation is a detailed knowledge EEDF and its relation to the Interface States (SIT) and impact ionization (SII) cross sections. To the best of our knowledge, the CHC dominant energy picture [1] provides the first phenomenological CHC modeling approach which takes into account both the depen*

Corresponding author.

0026-2714/$ - see front matter  2007 Published by Elsevier Ltd. doi:10.1016/j.microrel.2007.01.031

dence of the EEDF on the activation of energy gaining mechanisms such as e–e scattering during stress as well the SII and SIT carrier energy dependence. In addition to an overview of LEM picture, the fundamental aspects of the n-MOSFET dominant energy CHC model will be reviewed in the following sections. In particular the energy driven approximation is proposed to describe the CHC reliability of n-MOSFETs in low voltage applications (Vdd  1 V). 2. Experimental To experimentally demonstrate the energy driven concept and the SIT energy dependence, n-MOSFET devices from two bulk CMOS technology nodes were used. These two device types are: (1) a 1.2 V (90 nm node) device with a nominal LPOLY (gate poly length)  60 nm, and a gate oxide thickness of 1.3 nm, and (2) a 1.8 V (180 nm node) device with a nominal Leff (electrical channel length) = 120 nm, and a gate thickness of 3.5 nm. Our database includes a range of channel lengths, as well as a large number of stress conditions, varying both VGS and Vds. All the experiments were run at 30 C.

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2.1. Overview of lucky electron model picture Historically the lucky electron model (LEM) is one of the first attempts to analyze hot carrier effects in devices [2,26], here we describe one of its simplest form: the effective temperature model (ETM) which is based on the following two assumptions: • Electrons while traveling in the pinch off region of the device reach locally a quasi-thermal equilibrium between carrier energy distributions (f(E)) and local maximum electric field (Fmax). In this case f(E) is a Maxwellian distribution with an effective temperature Te determined by Fmax through the relation: kT e ¼ qkF max

ð1Þ

where k in the electron mean free path. • The CHC damage is due to ‘‘Lucky Carriers’’ who have enough kinetic energy to surmount the SiO2/Si barrier height (Ec P UB  (3.2 eV)). In addition electrons with kinetic energy larger than UII (EG/q) (impact ionization threshold) can produce e–h pairs contributing to the substrate current Isx. Under these conditions ETM predicts the following relations between the substrate (Isx) and gate (Ig) currents: I sx / I d  expðUII =kT e Þ I g / CðF max Þ  I d  expðUB =kT e Þ  UB =UII Ig I sx ¼ CðF max Þ  Id Id

ð2Þ

where Te is given by (1). The collecting efficiency of the gate C(Fmax) is a slow function of Fmax and being associated to barrier lowering. An experimental verification of the correlation expressed by (2) is given in [26]. The linearity of the curves (Fig. 1) suggests that Isx and Ig are generated by car-

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riers part of the same Fmax heated EEDF. A key consequence of the LEM picture is that the worst case CHC condition is the one corresponding to the maximum impact ionization ratio (Isx/Id) as given by "  U =U #n DI cp DI d I d I sx IT II / / t ð3Þ DN IT / I cp Id W Id The observation that no dramatic reduction of CHC damage has been measured even at Vds values smaller than the threshold energies questions the validity of the LEM picture. Further questioning on the LEM validity comes from the consideration that with advanced CMOS scaling ballistic carrier transport will produce no localized field thermalization of carrier in the channel pinch off region and other carrier heating mechanism (e–e scattering, secondary II, etc.) are more effective than electric field carrier heating [8–10]. 2.2. CHC dominant energy picture We will introduce the CHC dominant energy picture by describing the case of CHC induced impact ionization (II) phenomena. The effective II rate is approximately determined by the product: Z 1 I sx / F ðI s Þ  f ðEÞ  S II ðEÞdE ð4Þ Id Ec where SII is the II cross section and f(E) is the electron energy distribution function (EEDF). F(Is) is a function of the source current. As seen in [3,4] F ðI s Þ ¼ I 2s (quadratic regime) or Is (linear regime) depending on the contribution of the e–e scattering. There are several formulations of the II cross section [8,15,19], we adopt the simple Kamakura formula [15]: S II ðEÞ ¼ AðE  EG Þ

4:6

ð5Þ

where EG is the band gap energy (1.1 eV). The integrand f(E) · SII(E) will generally peak at one or more energy points. We will call these energy values ‘‘dominant energy’’ points when at these points f(E) · SII(E) has the maximum contribution to II rate. We denote these dominant energy points qVeff. Under these conditions we can use the following approximation: Z 1 X f ðEÞ  S II ðEÞdE  f ðqV ieff Þ  S II ðqV ieff Þ ð6Þ Ec

i

In these cases the II rate is mainly dependent on the effective voltage V ieff which, in turns, are functions of the bias conditions at stress. Mathematically V ieff are the solutions of the following equation: d ln f d ln S II ¼ dE dE Fig. 1. Correlation between Ig and Isx for different values of Vg–Vd. Leff = 0.15 lm, Tox = 75 A.

ð7Þ

A dominant energy point is defined by the ‘knee’ points (points of high curvature) of either ln(f) or ln(SII).

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In this work we consider two approximations of interest where (6) is valid: the electric field (Fmax) and energy (qVeff) driven approximation. The electric field driven approximation assumes that the knee points of the ln(SII) function determine the dominant energy points. The energy driven approximation [1] assumes that the knee points of ln(f) defines the dominant II rate energy points. We will describe both the E field and dominant energy driven approximation in the case of II rate. A similar integral as given by (4) can be used to estimate the ISG rate. In this case: Z 1 oN IT / F ðI s Þ  f ðEÞ  S IT ðEÞdE ð8Þ ot Ec where SIT is the effective ISG cross section. Similarly as in the II case, the dominant energy points (qVeff) are solutions of the equation: d ln f d ln S IT ¼ dE dE

ð9Þ

2.3. II Rate under the electric field driven approximation This approximation is valid for long channel n-MOSFET operated at high power supply voltages (Vdd) such that the overlap integrand (6) is maximized by EEDF population part of the high electric field (Fmax) region, where carrier heating is controlled by (1). Under these conditions this approximation corresponds to the LEM picture. Fig. 2 gives a graphical description. In the region of maximum value of the overlap integrand the EEDF can be approximated by the Maxwellian distribution: f ðEÞ / eE=qkF max

ð10Þ

ð11Þ

where p = 4.6. The dominant energies points (qVeff) are weak functions of bias conditions and are controlled by Fmax. In this case the CHC carrier bias dependencies are due almost solely to the changes of the EEDF slope with lateral electric field in the channel pinch off region. By integrating (4), it is easy to demonstrate that the II ratio (rII = Isx/Id) is given by rII / GðF max Þ  expðEG =qkF max Þ

ð12Þ

where G(Fmax) is obtained from the integration in (4). Eq. (12) suggests that the electric field driven approximation is equivalent to the LEM description.

2.4. II Under the energy driven approximation (linear regime) To describe this approximation we consider an EEDF having only a thermal tail (base EEDF). In this case the II rate is equal to (4) where F(Is) = Is (linear regime). Many authors [6–10] have shown that the EEDF has a significant knee near the maximum energy available from the steep potential drop at the drain. This is approximately the potential drop (Vds–Vdsat) from the drain (Vds) to the channel pinch-off point (Vdsat). As seen from Fig. 3 the carrier energy point (qVeff) at which the overlap integral has its maximum value is generally distinguished from the carrier energy value corresponding to the knee of the EEDF (q(Vdd–Vdsat)). At sufficiently low Vdd it is expected, however, that Veff  (Vdd  Vdsat). This implies that EEDF knee determines the dominant energy point (qVeff) and the II rate dependencies are due primarily to the energy dependence of the effective SII cross section, through the bias dependence of Veff. Under these conditions the field dependence of the EEDF is secondary. Assuming no contribution from e–e scattering, the II rate (rII), measured as Isx/Id, is given by rII / B  S II ðqV eff Þ

ð13Þ

Low Fmax

f(E) f(E)* SII (E )

2

4

6

E (Carrier energy) (eV) Fig. 2. A graphical representation of the Fmax field driven CHC carrier approximation applied to the II rate.

10-6

qVeff

SII(E) Carrier Heating due to F max Thermal Tail

10-4

High Fmax

10-2

f (E)

SII(E) Slope ≈ 1/qλF max

10-2

f(E)

10-10 10-8 10-6 10-4

0

1

1

and log (f(E)) has no knees. Its slope (1/qkFmax) is controlled by the maximum lateral electric field (Fmax) in the channel pinch off region. For given bias conditions, only one dominant energy point (qVeff) is found, corresponding to the maximum value of the II rate, and is controlled by the curvature of the SII cross section in this region. Assuming that SII(E) follows the Kamakura formula [15] we get:

qV eff ¼ EG þ pqkF max

0

qVeff ≈ q(Vdd-Vdsat)

≈ q(Vdd-Vdsat) q(Veff)

f(E) f(E)*SII(E) 2

4

6

E (Carrier energy) (eV) Fig. 3. A graphical representation of the dominant energy driven CHC applied to II. SII is given by Kamakura formula (SII  (E  EG)4.6).

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2.5. Estimate of Veff under the energy driven approximation Under the energy driven approximation Veff is basically equal to the effective potential drop from channel to drain. We assume: V eff ¼ V 0 þ V ds  V dsat

ð14Þ

where V0 is the added potential due to halo [17,18], and/or ‘source function’, (total expected to be on the order of several hundred mV), while Vdsat is the pinch-off voltage. Rauch et al. give in [28] the regime within which Veff  Vdd  Vdsat under the condition of a base EEDF having a thermal tail with slope (1/nkT) (E > qVeff) and LEM Maxwell distribution following (1) for E 6 qVeff. EG þ pnkT 6 qV eff 6 EG =ð1  ðpk=lÞÞ

ð15Þ

where l = pinch off region length, p is defined in (5). Using an approximate equation from Taur and Ning [21], V dsat ¼

2ðV GS  V T Þ=m qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi GS V T Þ 1 þ 1 þ 2ðV mF C ðLLS Þ

ð16Þ

with FC is the critical electric field for velocity saturation, L = Lpoly or Leff, LS = length of velocity saturated region, and m = body effect coefficient. VT is the initial (before stress) VT measured in saturation at stress conditions. Table 1 gives the estimated values of the parameters used for Vdsat calculation in the technologies under investigation. The parameters V0 and LS are treated as constants, even though in general both may be functions of Vds and L [16]. Additionally for device 1, LS may contain an extra length due to the gate poly overlap (LPOLY–Leff). For these reasons, and because of the approximate nature of Eq. (8), these LS values may be somewhat different from the actual lengths of the high field regions. 2.6. Evidence of the validity of energy driven approximation Fig. 4 shows rII, the impact ionization ratio, measured as Isx/Id at stress conditions before stress as a function of Veff estimated from (14). n-MOSFET devices of both technologies were investigated. To avoid e–e scattering effects (observed at lower Vds and higher VGS), this analysis was restricted to the bias stress conditions for which VGS < 0.85Vds (in this case F(Is) = Is, linear region). Because the data sets for the two device types are almost overlapping and each contains a large numbers of points, they are separated on the plot by a factor of two. The measured data follow the energy driven prediction, Eq. (13), Table 1 Values of the parameters used to calculate Vdsat Technology

FC (mV/nm)

m

V0 (V)

LS (nm)

1 2

3.0 3.0

1.2 1.2

0.29 0.22

45 60

Fig. 4. Measured impact ionization ratio, rII, for device type 1, and 2 versus calculated Veff. Lines: impact ionization scattering rate, SII, calculated from [15].

almost exactly, for VEFF < 2.7 V. Although the values for V0 are here somewhat arbitrary, and were adjusted to achieve a good fit, the fact that the expected slope and shape of the Kamakura’s SII function can be reproduced so well independently of device scaling, and for reasonable parameter values, must be viewed as an experimental verification of the energy driven model. This also provides justification for extending this approach to the following experimental determination of the SIT carrier energy dependence. 2.7. CHC modeling under the energy driven approximation Given the similar mathematical formulation, a description equivalent to the one for II (4) can be given for the Interface States Generation rate as well under the energy driven approximation. Similarly to the LEM we assume that the CHC damage in n-MOSFET transistors is due to Interface States Generation (NIT) by breaking of the SI–H bond according to the electro chemical reaction:  SiAH þ e $ Si þ H

ð17Þ

Hot electrons (e) break the Si–H bond to produce the Si* trivalent silicon atom (NIT) and the H diffusing species (H*). This reaction is assumed to be reversible, meaning that the unpassivated bond S* can be repassivated by H* recombination. Under the energy driven approximation  the rate of bond breaking ðdNdtIT B:B Þ is given by:  dN IT  / F ðI s Þ  S IT ðqV eff Þ ð18Þ dt B:B where F(Is) = Is (linear regime) and I 2S (quadratic regime) in absence or presence of the e–e scattering contribution. The value of qVeff associated to the maximum ISG is expected to be similar as for the II since they are both determined by the knee of the same EEDF at a given bias stress condition. In the case of ISG contributed by the knee of the EEDF associated to a thermal tail V eff = Veff. In the case of e–e scattering being dominant a second, weaker knee is observed in the EEDF (see Fig. 5). This

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where DH*, XH* are respectively the H* effective diffusion constant and diffusion length at the stress temperature. W is the device channel width. Following the same physical arguments as in [2], it is easy to show that the total number of interface states (DNIT) generated during the stress time t is  n F ðI s ÞS IT ðqV eff Þ t ð23Þ DN it ¼ H  W

Fig. 5. A representation of ISG damage rates incorporating an e–e scattering tail to the EEDF. The first peak of SIT(E)f(E) is the ‘linear regime’ due to electrons in the base distribution, and the second peak is the ‘quadratic regime’ due to the e–e scattering induced tail.

knee corresponds to almost twice the energy value of the energy knee point (Veff) associated to the thermal tail. Following the same argument, we expect that e–e scattering contributes with another maximum of the ISG rate at a dominant energy point around V eff  2V eff [6,7,11–13], (and an even weaker knee at somewhat below 3 Veff, etc., which will be neglected here). Adding e–e scattering effects to the EEDF and assuming (as yet) hypothetical ISG cross section SIT will result in something like that shown in Fig. 5. The e–e scattering induced dominant energy (the second peak) is approximately a constant multiple mEE (=E2/E1) of qVeff. Since it tracks with Veff, this is also an energy driven situation. In summary we have  dN IT  / I s  S IT ðqV eff Þ ð19Þ dt B:B in the linear regime controlled by the knee of the base EEDF and  dN IT  / I 2s  S IT ðqmEE V eff Þ ð20Þ dt B:B in the quadratic region. To develop a CHC model based on the dominant energy approximation assume that the ISG generation results from a balance between Nit generation and repassivation (H* recombination) controlled by the following two equations. The net rate of interface states generation dN IT K ¼  F ðI S Þ  S IT ðqV eff Þ  BNIT N H ð0Þ W dt

ð21Þ

The term BNITNH*(0) is associated to the H* recombination which proportional to the initial H* concentration at the interface (NH*(0)). The net rate ISG is also associated to the rate of H* diffusing away from SiO2/Si interface dN IT ¼ DH N H ð0Þ=X H dt

ð22Þ

where n is the time slope of the order of 0.5. H is a technology constant. The above formula represents a universal formulation of the CHC model under the energy driven approximation. In this case the CHC bias dependence is contained in the energy dependence of SIT through V eff . Once the functional dependence on SIT on V eff is estimated, then it is possible to model the NIT increase under given bias stress conditions. Assuming that SIT(E) is independent from the technology under consideration, during a reliability technology qualification it is sufficient to estimate the constant H to fully characterize the CHC dependence. The total end of life DNIT increase can be estimated once Is and V eff is known at use conditions. In the following paragraph we are giving an estimate of SIT dependence on electron energy assuming (23) holds. 2.8. Estimate of SIT under the CHC energy driven approximation The increase in Interface States density (DNIT) induced by the CHC stress corresponds to a selected n-MOSFET parameter shift of interest (Ion, Gmax etc) to which typically a maximum target shift is associated with a corresponding lifetime s. From (23) in the case of the energy driven approximation the ISG lifetime (sIT) is given by 1=sIT / C  I s  S IT ðqV eff Þ

ð24Þ

in the linear regime, and 1=sIT / D  I 2s  S IT ðqmE V eff Þ

ð25Þ

in e–e scattering assisted quadratic regime. While the best measure of ISG from I–V characteristics would seem to be D(1/gmlin, max) [4,20], the parameter D(1/ION) (where ION = ID @ VGS = Vds = technology power supply voltage) proved to be much more robust over the entire range of stress conditions and channel lengths in the database. However, this damage metric displayed additional channel length (L) and threshold voltage (VT) dependencies. These were normalized out by using this definition for sIT (ISG lifetime): lifetime to 5% shift of the parameter ( )1  b L ðV tech  V t Þ ð26Þ DI ON Lnom A value of b = 1.2 seemed to work well for both device types. Vtech = technology voltage = 1.2 and 1.8 V for device types 1 and 2, respectively. The Vt value used was the saturated Vt measured at time 0 (before stress).

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Fig. 6. Proposed ISG cross section, SIT (solid line), compared to experimental data via Eqs. (10b) and (10c).

From Eqs. (24) and (25) it is possible to estimate the SIT dependence on qV eff once the Interface States lifetime sIT is estimated in both linear and quadratic regimes. Fig. 6, shows the inverse of normalized extracted interface states lifetime (1/(sITIs) and ð1=sIT I 2s Þ in the linear and quadratic regime respectively) as function of the qVeff from both the mid and high Vg CHC stresses carried over in this study. In this case the linear and quadratic dependencies are stitched together into a single energy axis in the following way E = available energy = qVeff for linear regime data, and qmEEVeff for quadratic regime data. The parameter mEE was given the value 1.8, suggested by simulation. The arbitrary constants C and D for each technology are then adjusted to overlap the data sets onto a single curve. This curve represents an experimentally measured dependence of the SIT(E) function, which can be fit to the following empirical form S IT / expðaEÞ;

E 6 UIT þ p=a p

/ ðE  UIT Þ ;

E > UIT þ p=a

ð27Þ

with the following parameter values /IT ¼ 1:6 eV;

p ¼ 14;

a ¼ 11 eV1 :

As demonstrated in Fig. 6, this model allows for a nearly universal description of hot carrier behavior for n-MOSFET devices at or below the 180 nm technology node. Notice that the estimated SIT does not have a threshold energy contrary to what assumed in the LEM picture. 2.9. Similarities between of SIT (CHC) to z (TDDB) The measured SIT function is extremely ‘‘soft’’ – that is, there is no sharp ‘‘knee’’ point. In addition no actual threshold energy is observed down to E < 1.9 eV contrary to what assumed in the LEM picture. One possible explanation of this soft cross section may be the multiple pathways to H desorption [22–24]. However, no structure that would relate to multiple-energy thresholds is seen. Two possible mechanisms reported in the literature would tend to ‘‘smear’’ out any structure, and may contribute to the

Fig. 7. Defect generation efficiency as function of anode carrier energy [27,28]. Symbols correspond to experimental results and the solid line is a fit to a power law f / (EMAX)38. In red and green we represent the SIT(E) extracted from the CHC experiments. (For interpretation of the references in colour in this figure legend, the reader is referred to the web version of this article.)

observed exponential tail. These are bond energy-dispersion due to SiO2 disorder, and multiple vibrational excitation [25]. The major effect of the multiple vibrational excitations may be to lower the energy needed for a single large-energy interaction to generate an interface state [25]. This would result in a very complex, and perhaps ‘‘soft,’’ cross section, due to the complexity of the defect creation. In this picture, the SIT function proposed here must be considered an effective ISG cross section for hydrogen desorption. An indirect evidence of the mechanisms involved in the ISG during CHC stress given by the work by Sune et al. [27,28]. Fig. 7 suggests some similarities between the SIT extracted from the CHC stresses (red and green symbols) under the energy driven approximation and the TDDB defect generation efficiency (f) calculated from the QBD stressed. The authors, assuming the Hydrogen release model picture, suggest single electron assisted Si–H breaking from the 6r ! 6r* for high E values, while, at sufficiently low energy, they attribute the bond breaking to multi-vibronic excitations. In the TDDB case the carrier energy (E) is the electron energy gained at the anode. This similarity between two independent ways of measuring the ISG cross section may be an indication of a common origin. Of course more investigations are needed to confirm these conclusions.

3. Conclusions The dominant energy approximation has been demonstrated to be adequate to describe the CHC degradation in advanced submicron technologies (1.2 and 2 V technologies). This approximation fully explains the measured

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impact ionization rate at mid Vgs in agreement with observed SII energy dependence. In addition an effective interface states cross section (SIT) has been estimated in the energy region 1.8–5.5 eV for the first time from CHC stresses. This experimental measured ISG cross section is very ‘soft’, with no observed energy thresholds. However, SIT is steeper below 3 eV. Similarities with defect generation efficiency calculated from TDDB QBD data give some insights on the physical nature of the interface state generation from SI–H bond breaking. References [1] Rauch III SE, La Rosa G. The energy driven paradigm of n-MOSFET hot carrier effects. In: Proceedings of IRPS 2005; 2005, p. 708–9. [2] Hu CM, Tam SC, Hsu FC, Ko PK, Chan TY, Terril KW. Hotelectron induced MOSFET degradation – model, monitor, and improvement. IEEE Trans Electron Dev 1985;32(2):375–85. [3] Rauch SE, Guarin FJ, La Rosa G. Impact of e–e scattering to the hot carrier degradation of deep sub-micron n-MOSFETs. IEEE Electron Dev Lett 1998;19(12):463–5. [4] Rauch III SE, La Rosa G, Guarin FJ. Role of e–e scattering in the enhancement of channel hot carrier degradation of deep sub-micron n-MOSFETs at high Vgs conditions. IEEE Trans Dev Mater Reliab 2001;1(2):113–9. [6] Jakumeit J, Ravaioli U. Influence of electron–electron scattering on the hot electron distribution in ultra-short Si-MOSFETs. Physica B 2002;314(1–4):363–6. [7] Chang MY, Dyke DW, Leung CC, Childs PA. Modeling of gate currents in MOSFETs operating at low drain voltages. Proc ESSDERC 1996;96:263–5. [8] Bude J, Mastrapasqua M. Impact ionization and distribution functions in sub-micron n-MOSFET technologies. IEEE Electron Dev Lett 1995;16(10):439–41. [9] Venturi F, Sangiorgi E, Ricco B. The impact of voltage scaling on electron heating and device performance of submicrometer MOSFET’s. IEEE Trans Electron Dev 1991;38(8):1895–904. [10] Childs PA, Dyke DW. Hot carrier quasi-ballistic transport in semiconductor devices. Solid State Electron 2004;48:765–72. [11] Childs PA, Leung CC. A one-dimensional solution of the Boltzmann transport equation including electron–electron interactions. J Appl Phys 1996;79(1):222–7.

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