Extensive reading materials on reserve, including

Section 12: Intro to Devices Extensive reading materials on reserve, including Robert F. Pierret, Semiconductor Device Fundamentals EE143 Ali Javey

Bond Model of Electrons and Holes Si Si Si Si Si Si Si Si Si Silicon crystal in a two-dimensional representation. Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si When an electron breaks loose and becomes a conduction electron, a hole is also created. EE143 Ali Javey

Semiconductors, Insulators, and Conductors E c E g=1.1 ev E c Ev E g= 9 ev E v Top of conduction band empty filled E c Si, Semiconductor SiO 2, insulator Conductor Totally filled bands and totally empty bands do not allow current flow. (Just as there is no motion of liquid in a totally filled or totally empty bottle.) Metal conduction band is half-filled. Semiconductors have lower E G s than insulators and can be doped EE143 Ali Javey

electron - Bottom of conduction band Intrinsic Carriers Energy gap =1.12 ev hole + Top of valence band n (electron conc) = p (hole conc) = n i EE143 Ali Javey

Dopants in Silicon Si Si Si Si Si Si Si As Si Si B Si Si Si Si Si Si Si As, a Group V element, introduces conduction electrons and creates N-type silicon, and is called a donor. B, a Group III element, introduces holes and creates P-type silicon, and is called an acceptor. EE143 Ali Javey

Types of charges in semiconductors Hole Electron Mobile Charge Carriers they contribute to current flow with electric field is applied. Ionized Immobile Charges Donor Ionized Acceptor they DO NOT contribute to current flow with electric field is applied. However, they affect the local electric field EE143 Ali Javey

Fermi Function The Probability of an Energy State Being Occupied by an Electron 1 E = f is called the Fermi energy or f ( E) ( E E f ) / kt 1+ e the Fermi level. Boltzmann approximation: ( E E f ) kt E f E) e ( E E f ) kt f ( E) e ( E E f >> kt E f + 3kT E f E E f + 2kT ( E f E ) kt E f + kt E f E f kt E f 2kT E f 3kT ( E f E ) kt f ( E) 1 e ( ) kt f ( E ) 1 e E E f << kt 0.5 1 f(e) EE143 Ali Javey

Electron and Hole Concentrations n = N c e ( E E F C ) / kt N c is called the effective density of states. p = N v e ( E E V F ) / kt N v is called the effective density of states of the valence band. Remember: the closer E f moves up to E c c,, the larger n is; the closer E f moves down to E v, the larger p is. For Si, N c = 2.8 10 19 cm -3 and N v = 1.04 10 19 cm -3. EE143 Ali Javey

Shifting the Fermi Level EE143 Ali Javey

Quantitative Relationships n: electron concentration (cm -3 ) p : hole concentration (cm -3 ) N D : donor concentration (cm -3 ) N A : acceptor concentration (cm -3 ) Assume completely ionized to form N + D - and N A 1) Charge neutrality condition: N D + p = N A + n 2) Law of Mass Action : n p = n 2 i What happens when one doping species dominates? EE143 Ali Javey

General Effects of Doping on n and p I. N N >> n (i.e., N-type) d a i n = N d N a p = n 2 i n If N d >> N a, n = Nd and 2 p = n i N d II. N N >> a d n i (i.e., P-type) p = n = N a N n 2 i p d If N >>, a N d p = N a and n = 2 i n i N a EE143 Ali Javey

Carrier Drift When an electric field is applied to a semiconductor, mobile carriers will be accelerated by the electrostatic force. This force superimposes on the random thermal motion of carriers: 3 2 1 4 electron E =0 5 5 3 4 2 E 1 electron E.g. Electrons drift in the direction opposite to the E-field Current flows Average drift velocity = v = μ E EE143 Ali Javey Carrier mobility

Carrier Mobility Mobile carriers are always in random thermal motion. If no electric field is applied, the average current in any direction is zero. Mobility is reduced by 1) collisions with the vibrating atoms phonon scattering 2) deflection by ionized impurity atoms Coulombic scattering - B- - As+ - - Si EE143 Ali Javey

Total Mobility s -1 ) -1 Mobi ility (cm 2 V - 1600 1400 1200 Electrons 1000 800 600 400 200 Holes 1 1 = + τ τ τ 1 = μ phonon 1 + 1 impurity 1 μ phonon μ impurity 0 1E14 1E15 1E16 1E17 1E18 1E19 1E20 N + -3 a N d (cm ) Total Impurity Concenration (atoms cm -3 ) EE143 Ali Javey

Conductivity and Resistivity J p,drift = qpv = qpμ p E J n drift = qnv = qnμ n E n,drift q q μ n J drift =J n,drift +J p,drift = σ E =(qnμ n +qpμ p )E conductivity of a semiconductor is σ =qnμ n +qpμ p Resistivity, ρ = 1/ σ EE143 Ali Javey

Relationship between Resistivity and Dopant Density TY cm -3 DOPANT DENSI N-type P-type RESISTIVITY (Ω cm) ρ = 1/σ EE143 Ali Javey

W I + V Material with resistivity ρ L _ Sheet Resistance L t R = ρ Wt R s is the resistance when W = L R s ρ t = R s L W (in ohms/square) if ρ is independent of depth x R s value for a given conductive layer (e.g. doped Si, metals) in IC or MEMS technology is used for design and layout of resistors for estimating values of parasitic resistance in a device or circuit EE143 Ali Javey

Diffusion Current Particles diffuse from higher concentration to lower concentration locations. EE143 Ali Javey

J n, diffusion = qd Diffusion Current n dn dx J p, diffusion = qd p dp dx D is called the diffusion constant. Signs explained: n p x x EE143 Ali Javey

Generation/Recombination Processes Recombination continues until excess carriers = 0. Time constant of decay is called recombination lifetime EE143 Ali Javey

Continuity Equations Combining all the carrier actions: n n n n t = t + t + + drift diff t thermalr G Now, by the definition of current, we know: n t others n n J J Nx Ny J Nz t + 1 t = q 1 x + y + z = drift ( diff ) q J N Since a change in carrier concentration must occur from a net current Therefore, we can compactly write the continuity equation as: n n n = 1 J N + + t q t thermalr G t other p t = 1 q J P + EE143 Ali Javey p t thermalr G + p t other

PN Junctions Donors N-type P-type I V + I V N P Reverse bias Forward bias diode symbol A PN junction is present in almost every semiconductor device. EE143 Ali Javey

Energy Band Diagram and Depletion Layer N-region P-region (a) E f E c (b) E c E f E v (c) E v E c E f E v n 0 and p 0 in the depletion layer (d) Neutral N-region Depletion layer Neutral P-region E c d E f bi 2 q ni E v φ = kt ln N N a EE143 Ali Javey

Qualitative Electrostatics Band diagram Built in-potential From ε=-dv/dx EE143 Ali Javey

Depletion-Layer Model N eut ra l Region N Depletion Layer Neutral Region P On the P-side of the depletion layer, ρ = qn a x n 0 x p ρ d E qn = a dx ε s qn d x n qnn a x p x a a qn 1 qn p E ( x ) = x + C = ( x x ) ε s ε s E E On the N-side, ρ = qn d d qn x = + ε s x x n n 0 x ( ) ( x x ) p E EE143 Ali Javey

Effect of Bias on Electrostatics EE143 Ali Javey

Current Flow - Qualitative EE143 Ali Javey

PN Diode IV Characteristics I = qv kt I0( e 1) I 0 = Aqn 2 i L D p p N d + Dn L N n a I = I + r = 0 A qn i W dep τ dep EE143 Ali Javey

Solar Cells light N short circuit P Isc I Dark IV Eq.(4.9.4) - 0 0.7 V V Ec Ev + (a) Isc Solar Cell IV Eq.(4.12.1) Maximum power-output (b)

p-i-n Photodiodes Only electron-hole pairs generated in depletion region (or near depletion region) contribute to current Only light absorbed in depletion region contributes to generation Stretch depletion region Can also operate near avalanche to amplify signal

Light Emitting Diodes (LEDs) LEDs are typically made of compound semiconductors Why not Si

MOS Capacitors MOS: Metal-Oxide-Semiconductor V g V g metal gate gate SiO 2 N + SiO 2 N + Si body P-body MOS capacitor MOS transistor EE143 Ali Javey

Ideal MOS Capacitor Oxide has zero charge, and no current can pass through it. No charge centers are present in the oxide or at the oxidesemiconductor interface. Semiconductor is uniformly doped Φ M = Φ S = χ +(E C E F ) FB

Ideal MOS Capacitor Ideal MOS Capacitor At Equilibrium:

Ideal MOS Capacitor Under Bias Let us ground the semiconductor and start applying different voltages, V G, to the gate V G can be positive, negative or zero with respect to the semiconductor E F,metal E F,semiconductor = qv G Since oxide has no charge (it s an insulator with no Since oxide has no charge (it s an insulator with no available carriers or dopants), d E oxide / dx = ρ/ε = 0; meaning that the E-field inside the oxide is constant.

Inversion condition If we continue to increase the positive gate voltage, the bands at the semiconductor bends more strongly. At sufficiently high voltage, E i can be below E F indicating large concentration of electrons in the conduction band. We say the material near the surface is inverted. The inverted layer is not gotten by chemical doping, but by applying E-field. Where did we get the electrons from? When E i (surface) E i (bulk) = 2 [E F E i (bulk)], the condition is start of inversion, and the voltage V G applied to gate is called V T (threshold voltage). For V G > V T, the Si surface is inverted.

Ideal MOS Capacitor n-type Si

Electrostatic potential, φ(x) Define a new term, φ(x) taken to be the potential inside the semiconductor at a given point x. [The symbol φ instead of V used in MOS work to avoid confusion with externally applied voltage, V] 1 φ( x) = [ Ei (bulk) Ei q ( x)] Potential at any point x φ S = 1 q [ E i (bulk) E i (surface)] Surface potential φ F = 1 q [ E i(bulk) E F ] φ F related to doping concentration φ F > 0 means p-type φ F < 0 means n-type

Electrostatic potential φ S is positive if the bands bend\.? φ S = 2φ F at the depletion-inversion transition point (threshold voltage)

Charge Density - Accumulation p-type silicon accumulation condition V G < 0 G M O S p-si The accumulation charges in the semiconductor are., and appear close to the surface and fall-off rapidly as x increases. One can assume that the free carrier concentration at the oxide-semiconductor interface is a δ-function. Accumulation of holes x Charge on metal = Q M Charge on semiconductor = (charge on metal) Q Accumulation = Q M

Charge Density - Depletion p-type Si, depletion condition The depletion charges in Si are immobile ions - results in depletion layer similar to that in pn V junction or Schottky diode. G > 0 M O S p-si q N A A W = Q M ( ) (+) If surface potential is φ s, then the depletion layer width W will be Q M w Depletion of holes W = 2εε qn Si A φ S Does this equation look familiar?

p-type Si, strong inversion Charge Density - Inversion M O V G >>0 Once inversion charges appear, they remain close to the surface since they are.. Any additional voltage to the Q M w gate results in extra Q M in gate and get compensated by extra inversion Depletion of electrons in holes semiconductor. S p-si Inversion electrons: δ-function-like So, the depletion width does not change during inversion. Electrons appear as δ- function near the surface. Maximum depletion layer width W = W T

MOS C-V characteristics The measured MOS capacitance (called gate capacitance) varies with the applied gate voltage A very powerful diagnostic tool for identifying threshold voltage, oxide thickness, substrate doping concentration, and flat band voltage. It also tells you how close to an ideal MOSC your structure is. Measurement of C-V characteristics Apply any dc bias, and superimpose a small (15 mv) ac pp y y p p ( ) signal (typically 1 khz 1 MHz)

Consider p-type Si under accumulation. V G < 0. Looks similar to parallel plate capacitor. C-V: under accumulation V G < 0 G M O S p-si Accumulation of holes C G = C ox where C ox = (ε ox A) ) / x ox x C G is constant as a function of V G

C-V: under depletion Depletion condition: V G > 0 V G >0 M O S p-type Si C G is C ox in series with C s where C s can be defined as semiconductor capacitance Q M C o W C s Depletion of holes C ox = ε ox A / x ox C s = ε Si A / W C G = C ox C s / (C ox + C S ) x 2ε W = qn Si A φ where φ s is surface potential s C G decreases with increasing V G

C-V: under inversion (high frequency) V G = V T and V G > V T Inversion condition φ s = 2 φ F V G >>0 W = W 2ε Si T = 2 q NA At high frequency, inversion electrons are not able to respond to ac voltage. C ox = ε ox A / x ox φ C s = ε Si A / W T C G (ω ) = C ox C s /(C ox + C S ) F Q M C G will be constant for V G V T M O C o x S W p-si Depletion of holes Inversion electrons δ- function C s

C-V: under inversion (low frequency) At low frequency, the inversion electrons will be able to respond to the ac voltage. So, the gate capacitance will be equal to the oxide capacitance (similar to a parallel plate capacitance). C G (ω 0) = C ox = ε ox A / x ox C ox C low frequency high h frequency V fb V t accumulation depletion inversion V g C G increases for V G V T until it reaches C ox Ideal MOSC (p-type Si)

The First Transistor

1956 Physics Nobel Prize

Invention of the Field-Effect Transistor In 1935, a British patent was issued to Oskar Heil. A working MOSFET was not demonstrated until 1955.

Today s MOSFET Technology Gate oxides as thin as 1.2 nm can be manufactured reproducibly. Gate o des as t as. ca be a u actu ed ep oduc b y. Large tunneling current through the oxide limits oxide-thickness reduction.

Introduction to the MOSFET Basic MOSFET structure and IV characteristics

Introduction to the MOSFET Two ways of representing a MOSFET:

Complementary MOSFETs (CMOS) NFET PFET When V g = V dd, the NFET is on and the PFET is off. When V g = 0, the PFET is on and the NFET is off.

CMOS (Complementary MOS) Inverter V dd PFET S V in NFET D D S 0V C: V out 0V etc.) capacitance (of interconnect,

Qualitative discussion: n-mosfet V G > V T ; V DS 0 I D increases with V DS V G > V T ; V DS small, > 0 I D increases with V DS, but rate of increase decreases. V G > V T T; V DS pinch-off I D reaches a saturation value, I D,sat The V DS value is called V DS,sat V G > V T ; V DS > V DS,sat I D does not increase further, saturation region.

Threshold voltage for NMOS and PMOS When V G = V T, φ s = 2 φ F ; we get expression for V T. V ε 2q N 2 φ Si A T = φf + xox 2 εox εsi F Ideal n-channel (p-silicon) device both terms positive V T ε 2 N = 2φ + Si q D F xox 2 φf εox εsi Ideal p-channel (n-silicon) device both terms negative ε Si / ε ox = = 11.9 / 3.9 3

How to Measure the V T of a MOSFET T I ds V ds = 10mV V gs V t is measured by extrapolating the I ds versus V gs (at low V ds ) curve to I ds = 0. V t I dsat W = Coxe( Vgs Vt ) μnsv L ds V gs V t

Quantitative I D -V DS Relationships 1 st attempt Square Law I D = Zμ L n C ox V ( DS V V ) V G T DS 2 2 < V ; DS < DS, sat V G > V T 0 V I D will increase as V DS is increased, but when V G V DS = V T, pinch-off occurs, and current saturates when V DS is increased further. This value of V DS is called V DS,sat. i.e., V DS,sat = V G V T and the current when V DS = V DS,sat is called I DS,sat. I D,sat Z μc ( V V ) 2 = ox G T D V DS, sat 2 L V > ; V G > V T Here, C ox is the oxide capacitance per unit area, C ox = ε ox / x ox

I D -V DS characteristics expected from a long channel (ΔL << L) MOSFET (n-channel), for various values of V G

I -V characteristics for n-mosfet D DS Linear region Saturation region

N-channel MOSFET Layout (Top View) 4 lithography steps are required: 1. active area 2. gate electrode 3. contacts 4. metal interconnects EE143 Ali Javey

Simple NMOS Process Flow 1) Thermal oxidation (~10 nm pad oxide ) 2) Silicon-nitride (Si 3N 4 4) deposition by CVD (~40nm) 3) Active-area definition (lithography & etch) 4) Boron ion implantation ( channel stop implant) EE143 Ali Javey

5) Thermal oxidation to grow oxide in field regions 6) Si 3 N 4 & pad oxide removal 7) Thermal oxidation ( gate oxide ) 8) Poly-Si deposition by CVD 9) Poly-Si gate-electrode patterning g( (litho. & etch) Simple NMOS Process Flow 10) P or As ion implantation to form n+ source and drain regions Top view of masks EE143 Ali Javey

Simple NMOS Process Flow 11) SiO 2 CVD Top view of masks 12) Contact definition (litho. & etch) 13) Al deposition by sputtering 14) Al patterning by litho. & etch to form interconnects t EE143 Ali Javey