S.Sze., Physics of Semiconductor Devices. John Wiley and Sons, 1981.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....affecting the highest derivatives is widely met in mathematical models of physical or chemical processes. In particular, as Poisson s equation for the electrostatic potential it is a constituent of the so called drift diffusion model which describes the behaviour of semiconductor devices (see [25], for example) The model is used extensively in semiconductor device modelling (see [22] for instance) Under suitable continuity and compatibility conditions on the data, a unique solution u(P ) of the problem (1) exists (see [11] for details) Furthermore, for 1 problem (1) is singularly ....

S. Sze, Physics of semiconductor devices, Wiley, New York, 1969.

....After the annealing, the off current stays about the same, but the subthreshold slope is improved to 65mV decade. Another effect of the annealing is that the on current is increased by almost 15 times. From the subthreshold slope, we can analyze the quality of the oxide silicon interface [6]: Dit = 60mV (Cit Cd) Cox (1) where Dit is the interface trap density, Cd is the depletion capacitance, Cox is the gate oxide capacitance, and Cit is the capacitance caused by the trapped charges at the oxide silicon interface. Cit = q Dit (2) where q is the single electron charge and is ....

S.Sze, "Physics of Semiconductor Devices," John Wiley and Sons,Inc.NewYork,NY,1981,pp.251.

....collection e#ciency (CCE) for photon interactions immediately below the oxide layer between the strips due to a distortion of the electric field. Positive charges are accumulated in the interface between oxide and silicon, and these attract electrons in the silicon resulting in a space charge [100]. The e#ect from this space charge of electrons is that the potential increases between the electrodes. In the resulting absence of a field gradient that drift charges towards the electrodes, they have to di#use out from these regions leading to charge losses and reduced pulse 0.14 0.80 2.01 ....

S. Sze. Physics of semiconductor devices. New York: Wiley, 1981.

....silicon due to high level impurity doping. W bem and W bcol are the limit of the neutral base from emitter and collector at zero biasing and n ie (T) represents the effective doping profile of intrinsic carriers given by E i ie Gbgn e T n T n = 3) Using the Einstein relation [3] and the mobility temperature variation, the mean diffusion constant D nb N E nb nb T T D T D 0 0 ) 4) where E N is the temperature exponent. The temperature variation of the Gummel number can be written as E G W W T T N dx T x N ....

S.M. Sze, "Physics of Semiconductor Devices", 2nd edition, 1981 John Wiley & Sons, Inc.

....With a nonlinear 1D Poisson solver we have first computed the value of n s at equilibrium as a function of E pin (Fig. 2A) in order to obtain the value of E pin corresponding to the measured n s (E pin 0. 855 eV) Such a value is well within the range of values for E pin found in the literature [4]. The corresponding electric field at the surface is E = 0.772 MV cm 1 . We have then computed the sheet electron density in the 2DEG as a function of the gate voltage for different values of the etching depth (Fig. 2B) an etching depth of 1 nm corresponds to a shift of about 70 mV for the ....

S. Sze, Physics of Semiconductor Devices (Wiley, New York, 1981) pp. 270--279.

....it is sufficient to model it as a single additional layer. Usually the doping profile of the p well is known. For the calculation of the average resistivity one has to take into account that the carrier mobility depends on doping concentration due to additional scattering at ionised impurities [9]. Simulations show that using several layers to describe the changing doping concentration leads to the same result. It can be seen in Figure 1 that the electric field near the injection point has a simple 1 r relationship which is similar to a field of a single layer halfspace with r r ....

S. M. Sze. Physics of Semiconductor Devices. John Wiley & Sons, New York, 2 edition, 1981.

....forward bias the p n junction momentarily, it is not likely that the significant minority carrier injection will occur since the voltage drop below 0 is only a half of or 300 mV. Furthermore, the amount of charge injected is too small (50 fC) to sustain a large current that can initiate a latch up [36]. IV. MULTIPHASE CLOCK GENERATION AND RECOVERY The previous section described parallel combinations of transmitters and receivers that achieve high aggregate bitrate while operating at low clock frequency. Timing to select each transmitter and receiver is controlled by the clocks with equally ....

S. M. Sze, Physics of Semiconductor Devices, 2nd ed. New York: Wiley, 1981.

....lengths below the space charge region of the pn junction. n is the minority carrier concentration in the region below the space charge region, relative to the equilibrium concentration n that would be obtained in an infinite bulk layer. The transport of these carriers is described by the equation [6]: 1) With the electron generation rate, being the diffusion coefficient of the electrons in the doped layer, is the electrical field along the axis (i.e. the direction perpendicular to the surface) is the electrical field along the axis (i.e. the direction parallel to the surface ....

....field in the region below the space charge region is negligible, 1) can be approached by (3) In the simulations discussed below, all parameters are taken as follows: is about cm at the GaAs bandgap ( nm) the mobility of electrons in doped Si is 1500 cm V s, cm s, s, and equals 3. 11 mm [6]. When a light source at nm can be used, increases to cm . We used diffusion equation (3) to calculate numerically the minority carrier profile below the space charge region of the PN junctions of an SML detector. For a periodicity of the detector fingers of 2 m, we will compare the analytical ....

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S. M. Sze, Physics of Semiconductor Devices, 2nd ed. New York: Wiley, 1981.

....is commonly used for discussing the basic characteristics of a thyristor is the two transistor analogue. In this model, the thyristor, a four layer p n p n device, is represented by a pnp transistor and an npn transistor with the base electrodes connected to the respective other transistor [2]. A similar scheme can be set up for analysing the bistable behaviour in the bipolar double barrier structure with alloyed n emitter (Fig. 4b) In this scheme, the transistors are replaced by a three terminal node. The pnp transistor is transposed into a node for electrons, and the npn transistor ....

S.M. Sze, Physics of Semiconductor Devices, 2nd ed., Wiley, New York, 1981, p. 190.

....APPENDIX A. GP0 MOSFET Models Here we describe the MOSFET large and small signal models used in our method. The model, which we refer to as GP0, is essentially the standard long channel square law model described in, 3] and [41] This model can be inadequate for short channel transistors [70] [91] in which case better models can be developed that still allow optimization via geometric programming (see the Appendix, Section B) 1) Large Signal Models: Correct operation of the op amp requires all transistors to be in saturation. For an NMOS transistor this means (47) When the NMOS ....

S. M. Sze, Physics of Semiconductor Devices, 2nd ed. New York: Wiley, 1981.

....and plot the absorption coefficient, a, by using (4) A typical result is presented in figure 4. The intersection of the tangent to the a(l) curve with the horizontal axis leads to l g 551 nm. Accordingly, the band gap of GaP is found to be E g 2. 25 eV in good agreement with the literature [3, 4]. CALCULATED ABSORPTION COEFFICIENT USING THE DATA FROM FIGURE 3 B) EMISSION OF LIGHT The above mentioned physics course is also concerned with emission of light and the students should be well prepared for this subject. If the conduction band is filled with more than an equilibrium ....

....MO prediction of (8) but it will be seen in the next paragraph that the agreement is reasonable. The correct spectral line shape for band to band transitions can be calculated by a convolution integral over the density of states and the Fermidistribution functions of the electrons and holes [4]. This leads indeed to a better agreement between theory and experiment but is much too complicated for students at that stage. The quantitative description of the bandwidth is determined by the FWHM definition (full width at half maximum) The application of a generally accepted definition by ....

Sze, S.M., Physics of Semiconductor Devices, Wiley, New York, 2

....of the overall current response. The photo generated carriers in the N well and inside the junction have to travel only a short distance and yield as a consequence a fast current response. The minority carrier distribution as a function of time can be obtained by solving the di#usion equation [4]. However, almost no electric field is present in the p substrate. This allows us to simplify the di#usion equation to #n p #t = D n #x D n #y # n g(t, y)e #x , 1) with n p being the minority carrier concentration in the region under the N well, relative to the ....

....being 2m and a reverse bias voltage of 3.3 V. In this simulations all parameters are taken as follows: # is about 7 cm 1 at the GaAs bandgap (# = 825 nm) the mobility of electrons ( n )inpdoped Si is 1500 cm V s, D n = 38.8 cm s, # n = 2.5 10 3 s, and L n equals 3. 11 mm [4]. When a light source at # = 600 nm can be used, # increases to 4 3 cm 1 . The immediate region was first illuminated during 5 ps after t o and the total structure was monitored further up to t o 400 ps. Some obtained minoritycarrier profiles are shown in Fig. 2. It should be noted that ....

S. M. Sze, "Physics of semiconductor devices", Second Edition, John Wiley & Sons, 1981.

....comments. 38 A MOSFET models In this section we describe the MOSFET large and small signal models used in our method. The model is very similar to the standard long channel square law model described in, e.g. 83, 84] This model can be inadequate for short channel transistors (see, e.g. [85, 86]) in which case better models can be developed that still allow optimization via geometric programming; see x7.5. PMOS NMOS D D G G S S I D I D Figure 11: Transistor symbols A.1 Large signal models Correct operation of the op amp requires all transistors to be in saturation. For an NMOS ....

S. M. Sze. Physics of Semiconductor Devices. John Wiley & Sons, 2nd. edition, 1981.

....r [2] which models the impact of neutral base recombination on output resistance can be reliably extracted only for a range of V cb where avalanche breakdown does not dominate variations in base current. Usually a linear dependence of base current reduction on the square root of V cb is assumed [3] for the range of V cb where neutral base recombination dominates over avalanche breakdown. Although neutral base recombination is significant enough [4] to have a nonnegligible impact on the small signal output resistance in SiGe HBT s typical of those now in use in analog circuits, the actual ....

....and D. Harame, Neutral base recombination in advanced SiGe HBT s and its impact on the temperature characteristics of precision analog circuits, in IEDM Tech. Dig. 1995, pp. 755 756. 2] P. Gray and R. Meyer, Analysis and Design of Analog Integrated Circuits. New York: Wiley, 1993, 3rd ed. [3] Z. Shafi, C. Gibbings, P. Ashburn, I. Post, C. Tuppen, and D. Godfrey, The importance of neutral base recombination in compromising the gain of Si SiGe heterojunction bipolar transistors, IEEE Trans. Electron Devices, vol. 38, pp. 1973 1976, Aug. 1991. IEEE TRANSACTIONS ON ELECTRON DEVICES, ....

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S. M. Sze, Physics of Semiconductor Devices. New York: Wiley, 1969, p. 40.

.... t C x D 1 x D . 14) accounts for scattering in the source channel and drain channel barriers. Recall that y C is the thickness of the inversion layer which is uniform from source to drain under the assumed weak inversion conditions. We can estimate the thickness of the inversion layer from [Sze81] y C k B T q F S = 1 qN A aC ox 2 k B T q j S k B T q ( 1 2 , 15) where F S is the normal electric field at the surface, and a = 2k S e 0 L D 1 C ox (16) with L D = 2k S e 0 k B T q 2 N A (17) being the extrinsic Debye length. Finally, using the channel ....

....aC ox 2 k B T q ( n i N A 2 1 e qV D k B T ( e qj S k B T qj S k B T ( 1 2 . 18) Our result for the subthreshold drain current should now be compared with the standard results based on diffusion theory . Equation (18) is identical to the conventional result (e.g. Ref [Sze81]) except for the replacement, Confidential Draft 9 June 3, 1996 D n L u inj t C 2X . 19) The conventional expression could break down for an extremely short channel, if the diffusion velocity, D n L exceeds the thermal velocity. In the scattering theory, a ballistic MOSFET would have a ....

S.M. Sze, Physics of Semiconductor Devices, 2nd Ed., John Wiley and Sons, New York, 1981, p.446.

....when using one of these models, despite the fact that all models predict a quite similar DeltaE g for this particular density. The overestimation of the gain increases with the underestimation of the BGN in the emitter, since the former is proportional to n base =pem exp( Gamma DeltaE g =kB T ) [11]. High injection levels giving rise to plasma induced BGN also occur in photo conductive switches, concentrator solar cells, and power devices operated in the on state. In case of a neutral plasma we may distinguish between two situations: a symmetrical electronhole (e h) plasma (e.g. by laser ....

S. M. Sze, Physics of Semiconductor Devices, John Wiley and Sons, 2nd ed., New York (1981).

....Fermi level is located within the allowed bands themselves and causes a depletion layer width only of the order of 10 nm. This distance corresponds to the potential barrier width the electrons have to tunnel from the conduction band on the n side to the valence band on the p side of the junction [71]. Currently available semiconductor fabrication technology allowed the introduction of a double barrier structure for resonant tunneling [71] The photonic tunneling results are in agreement with the predictions of quantum mechanics. 31 Thus we conclude, that the intrinsic tunneling time for ....

.... to the potential barrier width the electrons have to tunnel from the conduction band on the n side to the valence band on the p side of the junction [71] Currently available semiconductor fabrication technology allowed the introduction of a double barrier structure for resonant tunneling [71]. The photonic tunneling results are in agreement with the predictions of quantum mechanics. 31 Thus we conclude, that the intrinsic tunneling time for electrons will also be determined by the available quantum mechanical calculations. That means, the utmost dynamical specification of a device ....

S.M.Sze, `Physics of Semiconductor Devices', Sec. Edition, John Wiley and Sons, New York (1981)

....degeneracy and change the curvature of the bands in the vicinity of the Gammapoint. Since it is nearly impossible to calculate the consequences of this effect on the tunneling 6 probability (see [38] for an attempt) we will use the value of the light hole mass (m lh = 0:16 m 0 ) in our model [39, 40]. Inserting (12) 13) and Boltzmann factors for f c;v (l) into (9) and (10) gives for the field enhancement factors g n (F (x) P l0 (l Gamma S) 2 exp n Gamma l h 0 2 kT o I l (z) P i=x;y;z q h Theta i;k F i E t Gammalh 0 h Theta i;k j 3 P l E t h 0 (l Gamma ....

S. M. Sze, Physics of Semiconductor Devices, 2nd ed. New York: Wiley 1981

....of the tunneling mass with ND = 1:9 Theta 10 18 cm Gamma3 , c) variation of the barrier height with ND = 1:7 Theta 10 18 cm Gamma3 , d) effect of a change in the metal Fermi energy and effective mass with ND = 1:9 Theta 10 18 cm Gamma3 . for the contacts) Phi B = 0:50 eV [31], mM = m 0 , and E F;M = 11:7 eV . In Fig. 11a the doping concentration was varied from (1:7 Gamma 1:9) Theta 10 18 cm Gamma3 showing its strong influence on the tunneling current. The best fit is achieved with a value between (1:8 Gamma 1:9) Theta 10 18 cm Gamma3 which agrees well ....

S. M. Sze. Physics of Semiconductor Devices. John Wiley & Sons, New York - Chichester - Brisbane - Toronto - Singapore, 1981. 26

....reflects the DOS near the conduction band edge. The minimum of the differential conductance corresponds to the minimum in the DOS. Beyond this minimum, the tunnel barrier becomes smaller, leading to an increase in the tunnel probability and hence in the differential conductance. 11 12 13 14 15 16 17 0.65 0.66 0.67 0.68 0.69 0.70 Impurity band 15.9 mV Intersection of conduction and impurity band 12.7 mV DC Voltage [mV] Fig. 3. Detailed measurement of the dI dV versus VDC characteristic between 11 and 17 mV at 4.2 K (low bias range of Fig. 2) The real DOS deviates ....

....Fermi energy F and the scaling factor g. The scaling factor is obtained by fitting the measured DOS to the intrinsic DOS at high energies far away from the conduction band edge. As mentioned above, the Fermi energy is 12.7 mV and a value of VB = 0. 8 V is chosen for the Au n Si contact [14] In Figure 5, we varied the remaining parameter Eo between 55 and 65 meV, using VB = 0.8 V and F = 12.7 meV. The calculated DOS is most consistent with the intrinsic DOS at medium energies, if we chose Eo 60 meV. The mathematical approach used in this work is based on Ref. 5 and relies on ....

S.M. Sze, Physics of Semiconductor Devices, 2nd ed. (John Wiley, Singapore, 1981), p. 206.

....have included it in our model via the subtracted current in (1) Obviously, this leakage current should be modeled as a function of both carrier number and temperature [23] preferably via a simple analytical expression. An obvious choice would be the well known formulation of thermionic emission [68]. In this case, the leakage current density is proportional to where is a constant that characterizes the emission s exponential temperature dependence. A similar expression can be derived for heterojunction leakage if we assume that it is proportional to the carrier density immediately outside ....

S. M. Sze, Physics of Semiconductor Devices, 2nd. ed. New York: Wiley, 1981.

....different empirical BGN models. Adapted from Ref. 17] Application of different empirical BGN models has a tremendous effect on the simulated current gain, which is for an npn transistor proportional to n base =pem exp( Gamma DeltaE g =kB T ) where DeltaE g denotes the BGN in the emitter [18]. From a theoretical point of view BGN results from many body effects and from potential fluctuations caused by the disordered impurities. In addition, electron hole plasmas can modify the electron impurity interaction. 3.1 Doping Induced Rigid Shift of the Band Edges The main contribution to ....

S. M. Sze, Physics of Semiconductor Devices. John Wiley and Sons, 2nd ed., New York, 1981

....resistance, and decrease very slowly with temperature. III. Contact Resistance Model For contacts to heavily doped (N 10 17 cm 3 ) n and p type Si, tunneling is the dominant carrier transport mechanism [4 5] and the contact resistance is known to vary exponentially with the factor (B #N) [6], where B is dependent on the barrier height f b , and the tunneling effective mass, and N is the impurity doping concentration at the metal semiconductor interface. The temperature and dopant concentration dependent contact resistance to n and p Si can be expressed as RTH BT N c n n n ( ....

S. M. Sze, Physics of Semiconductor Devices, Wiley, pp. 305, 1981.

....approach for adjusting the parameters of a semiconductor to t a given, ideal IVC. Their work has its focus on testing di erent approaches to solve numerically the least squares problem. In standard applications a working point, i.e. a certain voltage current pair, for the device is xed [14]. Thus, in this paper we consider the modi ed design question: Is it possible to gain an ampli ed current at the working point only by a slight change of the doping pro le We give an positive answer to this question by means of an optimal control problem for the DD. The focus on the DD is due ....

....Debye length of the device and n ; p denote the carrier mobilities. The total current Optimal Control of the Drift Di usion Model 3 density is given by J = Jn J p : 1. 1f) Note that for the sake of simplicity we assume constant mobilities and that no generation recombination processes occur [14]. Inserting the relations for the current densities into the continuity equations yields the system n div(n rV ) 0; 1.2a) p div(p rV ) 0; 1.2b) 2 V = n p C; 1.2c) which will be considered in the following. To get a well posed problem, system (1.2) has to be supplemented with ....

S. M. Sze. Physics of Semiconductor Devices. Wiley, New York, second edition, 1981.

....metal and semiconductor, a positive charge is distributed all over the depletion layer, near the semiconductor surface. This induces a potential barrier, the built in potential V bi , which depends on the metal work function, the electron affinity of the semiconductor and the doping profile (see [34] chapter 5 for more details) When a bias is applied to the structure, the value of the built inpotential strongly influences the current flowing through the device. We assume the diode consists of a one dimensional N type semiconductor of length L in the x direction. The distribution function f ....

....0 and L are at thermo dynamical equilibrium (i.e. Maxwellians with respect to k) N 0 = MC exp( Gamma q Phi b kBT ) ND exp( Gamma qV bi kB T ) 2. 6) is the equilibrium density at x = 0, MC the effective density of states at the conduction band, MC = 2 m kB T 2h 2 3 2 , see [34]) V bi is the built in potential, which gives the potential difference between the bottoms of the conduction band at x = 0 and x = L. Its definition (2.6) assumes that neutrality holds at the ohmic contact x = L. Phi b is the barrier height, which depends on the metal work function Phi m and ....

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S.M. Sze, Physics of semiconductor devices, Wiley, New York, 2 nd edition, (1981).

....switch every cycle. Consequently, CMOS domino circuits increase the operating temperature faster than static CMOS gates. Also, the noise margin of a CMOS domino circuit strongly depends on the transistor threshold voltage. As the temperature increases, the transistor threshold voltage decreases [Sze 81] As a result, the noise margin of a CMOS domino circuit decreases as the operating temperature increases. Consequently, resistive shorts with large resistance, which cannot be detected at normal operating voltage and room temperature (25 o C) may fail when the operating temperature increases ....

Sze, S.M., Physics of Semiconductor Devices, 2nd Edition, pp. 451-453, John Wiley & Sons, Inc., 1981.

....that is 1.5 for SiO 2 and 2 for Si 3 N 4 , which determines a difference in reflectance [3] 4. Temperature effects 4.1. Temperature dependence of the dark current Before irradiation the bulk current is due to the thermal generation of carriers and the temperature dependence can be described by [4]: I B T 3=2 Delta e GammaE G=2KT (6) where EG is the energy of the forbidden gap in silicon, which is about 1.2 eV. 3 V(V) 1 10 10 2 10 3 0 25 50 75 100 125 150 175 200 (a) BA) V(V) M 1 10 10 2 10 3 0 25 50 75 100 125 150 175 200 (b) BC) V(V) 1 10 10 2 10 3 0 20 40 60 80 ....

....can be described by a linear fit. 4.2. Temperature dependence of the gain Figure 7(a) shows the gain as a function of bias voltage at different temperatures. The gain of an APD decreases with increasing temperature. For these devices the avalanche region is usually described by the formula [4]: M(V) 1 1 Gamma (V=V b ) n (7) where V b is the breakdown voltage and n is a coefficient to be determined experimentally. Both V b and n depend on the temperature and this dependence is linear to a first approximation. Usually the temperature dependence of the gain around the working point ....

S. M. Sze, Physics of semiconductor devices. Wiley and Sons (New York) 1981.

....of the forward biased PINdiode were measured. Each point was measured 100 times. This takes about 2 seconds for each point. Fig. 3, 4 and 5 show the measurements and the corresponding standard deviations. The measured PIN diode characteristic clearly differs from the Shockley diode model [15]: 24) where , and represent the potential across the junction, the threshold voltage and the saturation current respectively. Two different non linear models are used to model the diode characteristic. Fig. 3. Measured and estimated DC characteristics of a forward bias PIN diode. The model, based ....

Sze S.M., "Physics of Semiconductor Devices.", John Wiley & Sons, New York, 1981.

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S.Sze., Physics of Semiconductor Devices. John Wiley and Sons, 1981.

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S. M. Sze, Physics of Semiconductor Devices, Wiley, 1981.

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S. M. Sze, Physics of Semiconductor Devices, 2nd ed. New York: Wiley, 1981.

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Sze S.M. Physics of Semiconductor Devices, Wiley, New York, (1981)

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S. M. Sze, Physics of Semiconductor Devices. Wiley, New York, 2 ed., 1981.

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S.Sze., Physics of Semiconductor Devices. John Wiley and Sons, 1981.

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S. M. Sze, Physics of Semiconductor Devices. Wiley, New York, 2 ed., 1981.

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S. M. Sze, Physics of semiconductor devices, 2 ed. New York: John Wiley & Sons, 1981.

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S. M. Sze, Physics of Semiconductor Devices. Wiley, New York, 2 nd ed., 1981.

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S. M. Sze, Physics of Semiconductor Devices. Wiley, New York, 2 ed., 1981.

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S.Sze., Physics of Semiconductor Devices. John Wiley and Sons, 1981.

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S. M. Sze, "Physics of Semiconductor Devices," J. Wiley, NewYork, 1981, p. 261.

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S. M. Sze, Physics of Semiconductor Devices. New York: Wiley, 1981.

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Sze, S.: Physics of Semiconductor Devices. John Wiley & Sons, Inc., 1981.

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S. M. Sze, Physics of Semiconductor Devices, Second Edition, John Wiley and Sons, 1981. 183

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. S.M. Sze, Physics of Semiconductor Devices (Wiley, New York 1981)

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S. M. Sze, Physics of Semiconductor Devices, 2nd ed. New York: Wiley, 1981.

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S. M. Sze, "Physics of semiconductor devices", Second Edition, John Wiley & Sons, 1981.

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S. M. Sze, Physics of Semiconductor Devices (Wiley, New York, 1981).

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S. M. Sze. Physics of Semiconductor Devices. John Wiley & Sons, 2nd. edition, 1981.

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S. M. Sze, Physics of Semiconductor Devices, John Wiley & Sons, Inc., 1981.

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S. Sze, Physics of Semiconductor Devices, 2nd ed., John Wiley and Sons, 1981.

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