Physical Electronics Test 2
forward bias voltage pn junction
(+p, n-) everything basically decreases(junction voltager and transition region narrows) w reverse bias>wforward boas
true electric field of semiconductor of holes and electrons after they diffuse and acheive equilibrium
(nonunifrom compistion - varied gradually from one end to the other) assumed on positive test charges
current density at equilibrium for holes and electrons
0
eV to Joules
1 eV = 1.6E-19J eV/q = Volts (EMF) because eV = 20e*5 Volts
explain the eneergy band diagram for a pn junction at equilibrium constants, qvbi, transistion region, charge, potential energy, electric field, impurities, and the work function (which way does the electric field travel?) all bounderies? where does the qvbi occur?
1) electric field created (non neutralized donors on n side and nonneutralized acceptors on p side with non neautralized meaning there are no free electrons or holes to neutralize the charge) *2)Evac, Ec, Ev, parallel and lamda, gamma, Eg constant* 3)an electron escaping from the bottom of the conduction band in the n region to the vacuum level on the right side must overcome the electrostatic potential of the built-in field in addition to the electron affinity of the material. *4) space charge region - contains non neutralized impurity ions on both sides depending on concentration of impurties, * *5) depletion or transition region is depleted of carriers so ignore concentration(middle), known as w* *6) charge same on each side with opposide signs* *7)qVBi exists where qVbi = phip-phin (built in voltage) where the phis are the work functions taken as positive or difference in fermi levels* 8)This implies that the potential energy barrier is the same for electrons as for holes. 9)for equal doping levels, the width of the space charge region is the same on each side of the junction. For unequal doping levels most of the space charge region is on the side with the lighter doping. 10)qvbi increases with increased doping and is mostly across the more lightly doped region *11) E = 1/q dEvac/dx, with max at x0* travels left to right to due to ionized donor electrons filling in holes *12) phi n<phip* *13)easier for electrons to go from n side to p side, leaves ionized donors, and acceptors accept to become ionized (- stationary charges) and creates electric field from left side to right side , and because of work function difference, the electric field must reach equilibrium to balance each other* *14) jn = jp = 0 at equilibrium* Ei also curves with Ec and ev, only thing constant is Ef
concentration (n, deeltan, ni, units)
1/cm^3
What is Nc? units
1/cm^3 Nc = effective density of states in the conduction band 1/cm^3how many electrons can conduct1/cm^3
what is angstrom and how do you write it?
1A = 1E-10 m, but write as 100E-8 to get into cm
depletion region he uses
2 is out because it is squared phis = 2phif?
pn homojunction vs pn heterojunction
A pn homojunction (often called simply a pn junction) consists of a single crystal of a given semiconductor in which the doping level changes from p type to n type at some boundary. The term homojunction implies that the junction is between two regions of the same material (e.g., silicon), as opposed to the term heterojunction in which the junction is between two different semiconductors (for example, Ge and Si).
steps for band diagram for nonuniform semiconductor in equilibrium vs electrical neutral *dont really need to worry about steps*
Assume electrical neutrality in every macroscopic region. 2. Using the vacuum level as a reference, i.e., with Evac constant with position, draw the energy band diagram taking the electron affinity and band gap into account. 3. From a knowledge of the net doping, find the Fermi level with respect to the appropriate band edge (EV for p-type, EC for n-type material). 4. Adjust (tilt) the neutrality band diagram such that the Fermi level is at constant energy, keeping electron affinity and band gap constant.
what happens to the energy band diagram when a voltage is applied across it? what is the voltage measurement?
By convention the applied voltage is measured from p side to n side, or with the n side as a reference. Thus, the diode is forward biased if Va is positive, and reverse biased if Va is negative. junction voltage Vj = Vbi - Va where Vbi = phip-phin greatest Vj at x0 or the metallurgical point
how do you measure the capacitance of a mos capacitor?
Cs is the semiconductor depletion region capacatance
Capacitance formulas explained capaciatance for n channel or p substrate Capacitor what is the total capciatnace for two capacitors in series?
D = distance between plates because of the dielectric Es = Ers E0 where Ers given in the textbook for silicon Ei = Eri E0, where Eri of Si02 is for the oxide, then Eri = 3.9 E0 = 8.85-14(F/cm^2) Cd = Cs = EsE0/wm Ci = Cox
direct vs indirect semiconductor
Direct means that the minimum in the conduction band is at the same value of K as the maximum in the valence band, here at K = 0. Thus, the transition results from the direct interaction of a photon with an electron. Direct gap materials are generally efficient emitters and absorbers of optical energy because it is easy for electrons to move between the conduction band and valence band without having to acquire or give off K An electron cannot go from one band to the other simply by absorbing a photon of energy close to the band gap because the photon cannot supply adequate wave vector. The electron needs to acquire both energy and wave vector to make the transition in indirect materials. Illuminating a semiconductor with photons of energy greater than the band gap produces hole-electron pairs. Since photons have little wave vector, this produces a near-vertical transition in the electron E-K diagram for a direct gap semiconductor. For an indirect gap semiconductor a phonon is required to furnish the change in wave vector required by the electron transition, making optical transitions less probable in indirect materials.
how does flux and drift/diffusion current density travel in an electric field?
E runs form positive to negative, so drift current flux of holes goes to negative, and flux of electrons go to positive hole and electron current density go in the same direction in an electric field due to the same signs (qnun+qpup)E diffusion flux for holes and electrons go in same direction (negative side of the electric field) and Jp goes to negaitve side, since Jp = -qFn and Jn goes to positive, because Jn =-qFn
reverse bias voltage pn junction
Ec and Ev increase due to constant band gap built in voltage increases xp+xn increase, so w or depletion region, increases aswell p side is negative, so higher potential for electrons, n side is more positive, lower potential energy for the electrons junction voltage increases and depletion region is wider as more uncompensated charges become uncovered
ntype vs ptype for nondegenerate semiconductors what about fermi levels? important equations
Ef>Ei = n type(doNor), ef is closer to ec n0 = Nd when Nd>ni if still nondegenerate, p0 = ni^2/n0 n = doNor - positively charged Ef<Ei = p type(accePtor) Ef is closer to ev p0 = Na when Na>ni p = accePtor - negatively charged Ef = Ei = intrinsic and n0 = p0 = ni^2 in intrinsc only REMEMBER ni is given if you use the n0 = nd if n type, you cant find Na basically nondegenerate means the band gap does not decrease, or fermi level is at least 2.3 kt away from either band
difference between flux and current density
Flux is the presence of a force field in a specified physical medium, or the flow of energy through a surface current density - number of charges passing through a unit cross sectional area per unit time (same thing just with charges)
continuity equations for electrons vs holes
Gn = generation rate Rn = recombiniation rate Gn = gthermal (phonon induced) + Goptical(photon) + Gother(trapping) Rn = deltan/Tn (minority carrier lifetime) where n = n0 + deltaN or delta p/tn where Jn =-qFn and is total electron current density(diffusion and drift velocity) Fn- electron flux density change in electron and hole concentrations vs time
doping mobility, un and up
IF NOT SILICON, un and up are different!!!
what is important about equilibrium systems?
In a system at equilibrium, the Fermi level is at constant energy jn = jp = 0
Energy difference between conduction band edge and the Fermi level in the neutral region on the n side of the junction (5.06) & Energy difference between the Fermi level and the top of the valence band in the neutral region on the p side of the junction (5.08) what is they are degeneratly doped? REVIEW*
ND' and ND can be used interchangable basically just the distaznce between conduction band and fermi level on n side and distance between valance band and fermi on p side
what is the net doping profiles, and when is it a p type or ntype?
Nd' = Nd-Na Na' = Na-Nd ptype when Na>Nd Ntype when Nd>Na
energy band daigram for nonuniformly doped semiconductor (NA decreases with distance) and convenient method to draw energy band diagram at equilibrium *dont worry about steps* Nd'?
Neutrality exists in every macroscopic region. Nd' = Nd-Na (ionized donors) Na' = Na -Nd in this example, the net acceptor rate decreases from left to right, so it is noniform but just a function of distance Assume electrical neutrality in every macroscopic region. 2. Using the vacuum level as a reference, i.e., with Evac constant with position, draw the energy band diagram taking the electron affinity and band gap into account. 3. From a knowledge of the net doping, find the Fermi level with respect to the appropriate band edge (EV for p-type, EC for n-type material). 4. Adjust (tilt) the neutrality band diagram such that the Fermi level is at constant energy, keeping electron affinity and band gap constant.
what is the electron current density as a function of x and where x = xp
Note that the electron current density decreases exponentially with x on the p side. But since the total current must remain constant, the hole current increases by the same amount
what does it mean for a surface region to be inverted?
Notice that for this example, at equilibrium (Figure 7.1d), the Fermi level actually crosses the intrinsic level. This means that, while the substrate is doped p type, near its surface it is effectively n type. The Fermi level near the surface is closer to the conduction band edge than to the valence band edge. At the interface, there is a higher concentration of electrons than holes because of the band bending. The Si surface region is not only depleted, it is inverted
what is Nv?
Nv = effective density of a state in the top of valence band 1/cm^3 constant
What is the MOSFET energy band diagram at equilibrium and under neutrality? where is the VBi? what are the work functions? what forms?
PhiS = Evac - Efp PhiG = Evac - Echannel uppdercase Phis(not ializices) are energies in eV where lowercase phi are potentials in volts forms weak p type since Ei is above Ef right side is the bulk side channel is the left side?
three ways qvbi can be expressed where is it on the graph?
Phip - phin = Ecp - Ecn basically higher conduction band - lower conduction band
What assumptions are made for long channel model?
Qch = channel charger per unit area or mobil charges that carry current Id = small signal drain current
formulas for Qd, Qm, and Qs
Qd = charge per unit area of depletion region
what is poissons equation, and what is the depletion approximation?
Qv is the charge per unit volume at a given position x so only integrating in those two regions
resistance formula
R = pL/A resistivity*length/area (ohms)
what is a mossfet and what is it made out of?
The gate material in these devices was originally a metal (aluminum) and the insulator was silicon dioxide (SiO2). That is the origin of the term metaloxide- semiconductor field-effect transistor, or MOSFET. For ease of fabrication and reproducibility, however, a current practice is to use degenerately doped polycrystalline Si (poly-Si), which is highly conductive, instead of metal for the gate (although in modern MOSFETs with very short channels, metals are often used). In n-channel devices, n+ poly-Si is used for the gates, and p+ poly-Si is used for p-channel devices. Silicon dioxide was historically used for the insulator, but now nitrogen is often incorporated into the SiO2 to better passivate the bulk Si surface, increase the dielectric constant, and thus improve device performance. This silicon oxynitride layer is SiOxNy or SiON.
What is impurity band scattering?
The above two scattering mechanisms, ionized impurity scattering and phonon scattering, apply to both minority carriers and majority carriers. There is an additional scattering mechanism associated with majority carriers traveling within the dopant impurity states. As discussed in Chapter 2, with increased doping the states associated with the dopant atoms overlap in space and energy to form an impurity band extending from the bottom of the normal conduction band EC0 into the normally forbidden band. This impurity bandwidth increases with increased doping.
long chanel model of mosfet defintion
This is the simplest model, called the long-channel model, and it predicts the general form of the ID-VDS characteristics. It is useful for obtaining insight into the general behavior of MOSFETs
What is the second step in a pn junction? *REVIEW*
Upon contact between the two materials,3 electrons flow (diffuse) from the n-type semiconductor to the p-type semiconductor because there are more quasi-free electrons on the n side than on the p side. As the electrons move toward the p-type region, they leave behind ionized donors (charged positively) that are locked into the crystal lattice. At the same time, holes flow from the p semiconductor to the n semiconductor, leaving behind negatively charged acceptors. This separation of charges sets up an electric field, as shown in Figure 5.3. This is the situation at equilibrium At equilibrium there is no net current, so Jn = Jp = 0 and the Fermi levels are equalized. A built-in field ℰ is generated in what is referred to as the transition region. In the transition region, the field produces a drift current for electrons that at every position exactly compensates for the diffusion current caused by the electron concentration gradient. A similar balance of hole drift and diffusion currents exists.
what is the applied voltage to the metal? explain each term
V = Vi + phis Vi = voltage drop across insulator phis = voltage drop in the semiconductor Vi = -Qs/Ci
diode current under forward bias REVIEW! units J0 = I0 in this case how to find the applied voltage?
Va = applied voltage book has I=I0 *e^qva/Kt when Va>>> kt/q this is derived from 5.81 in the book make sure you divide by the q to get both units to volts (Is = I0?) mutiply by the area A for I0 which is the same as the last one because current density is a/m^2 whereas curent is A
What is phis and phif, and how do you acheive strong inversion?
Vgs - gate source voltage VDS - drain source voltage phis = surface potential where phif is difference between ferm level and intrinsic level larger phif means larger p type
total current density on forward bias (combination of Jn at xn and Jp at xp) - basically can be broken up! REVIEW (relates to next question) current in a forward bias when J0 = I0 HOW SHOULD YOU ACTUALLY WRITE IT? explain majority and minority carriers
We also agreed by Assumption 3 that the drift of minority carriers was neglible, so on either side of the junction the total current of the minority carriers is due to diffusion. Therefore both electron and hole currents are continuous across the transition region and at any point in the transition region, as shown in Figure 5.20c. The total current anywhere between xn and xp is given by the sums of the diffusion currents from either side of the junction: so if pn0 > np0, you can use the table, so in this case, n type is majority and p type coefficents are minority, where we use ND as reference, ///////if np0, p type is majority and us Na if va is in volts, divide by q to get Va/(kt/q) to put all in volts mutiply by the area when finding I0
What are the total carreir concentrations including excess carriers after equillibrium is disturbed? review the names REVIEW!! (n0 is at equilibrium, n is just electron concentratiojn) *HOW MANY EXCESS HOLE CONCRETAION IS THE EXCESS ELECTRON CONCNENTRAITON IS 10^17 WHEN A SAMPLE IS ILLUMINATED AND WHY?*
When light shines on a semiconductor, equilibrium is disturbed. When a given photon is absorbed, an extra electron (beyond the equilibrium number) is produced in the conduction band, and an extra hole is simultaneously produced in the valence band. An electron-hole pair is thus produced for every photon that is absorbed. These electrons and holes are termed excess carriers—excess above the equilibrium concentrations. The excess electron concentration is Δn and the excess hole concentration is Δp. The total carrier concentrations are the equilibrium values plus the excess concentrations: when illuminated, deltan = deltap because for each electron to the conduction band leaves a hole in the valence band
diffusion length for holes and electrons
average distance an electron diffuses before it recombinrs Where Ln is the minority carrier (electron) diffusion length. It is the average distance that an electron in the p-side-neutral can travel before recombine with a hole (majority carrier)
rise time and fall time of delta n in nonequilibrium(steady state excess carrier concentration)
basically it takes time to reach stead state carrier concentration when the light is turned on replace with p and Tp for p type
two types of conductivity
change in conductivity at the darfuce is using the delta n or photoconducitiity
what is the hole and electron mobility? (units)
cm^2/(V*s)
electron concetration as a function of x
decays exponentially with positiion from its value at the edge of the junction
doping notations
degeneratly doped side is where the fermi level is the conduction band therefore, for p^+n, depletion region = Na or if n^+p, depletion region is Np pn is both nondegenerately if p+n, then lightly doped side is Nd' and vice versa
what is Eb? energy barrier height, and how do you solve for it?
deltap = Ef - Evbulk smaller Eb means stronger n type Electron concentration at the surface or at the channel, ns oxide voltage at the threshold
What are the Einstein relations? units?
dn = cm^2/s un = cm^2/vs kt=ev kt/q=v
What is the first step in drawing a junction band diagram? (work?)
draw the eleectrically neautral state (energy band before they are in conctact) (work function)phi = Evac- Ef, electron affinity, ionization energy etc
What is the drift current density in a semiconductor? units of eachWHAT
drift = A/m^2 *E = electric field* p = resistivity= ohm cm sigma =conductivity= seimens/cm J = I/Area also
What are the two ways electrons can move? what is required for both?
drift velocity - electric feild applied creates movement of electrons towards positive direction diffusion current - process of mobile particles moving from region of high concentration to regions of low concentrations(gradient change), where temperature gives energy for movment (gradient and temperature
what is the pn junction of ion implementation? what is x0?
electric field is max at x0, and junction voltage is max as well nd = na, net doping is 0
emmision of an electron
electron loses energy and gives off the excess energy as a photon
enhancment/depletion nfet and pfets REVIEW
enahncement is normally off channel, being enhanced by th voltage depletion is normally on witht the channel n channel has n type ground and source and p type subtrate p channel has p type ground and source and n type subtrate
what is epsilon when silicon is used?
epsilon is E*Er 8.85E-14*11.8
What is the electron and hole diffusion current density?
flux density * charge of the electron Fn = flux density (electron) Dn = diffusion coefficeint for electrons DP = diffusion coefficent
What are the minority and majority mobilities? how do you use them? how do you read it? ***How about for intrinsic?*!!!!!!!!!! what is majority and minority? page 133 for dn and dp page 151 for Ln and Lp
if it is N type, use un majority at given ND and up minoirty at given ND if it is P type, use up majority at given NA and un minority at given NA intrinsic, then up and un are majority! and assume at 10^15 ? (furthest left) doping increases, the mobilit decreases 10,20,30... 100, 200 ,300 ... 1000,2000,3000... 10000,20000,300000....
how does depletion region act for heavily doped n side and lightly doped p side
if n side is greater doped, wp > wn because doping concenretation of donor on n side is greater than acceptor on p side if p side is greater doped, wn> wp because doping on accpetors on p side is greater than donors on n side
what is the depletion region on the n and p side? formulas
if nd is larger on n side, then wp is the larger depletion region verifying the smaller width with larger concnetration
what is qi for nonideal mosfet? what to remember about qi?!!!!!!
if qi is given with qcol/cm^2, multiply by the charge q?, where the q is 1.6E-19
excess carrier electron concentration and hole concetration under forward bias in general
injected excess decreases exponetially with x whereas hole increass Let Δnp represent the excess electron concentration on the p side and Δpn represent the excess hole concentration on the n side
What are the two types of scattering? Explain them
ionized impurity - N types(+) and P types(-) usually have a charge when ionized. These charged atoms cause deflections of electrons or holes approaching the impurity lattice phonon - as the temperature increases causes more vibrations which is more movement in front of electron paths which cause collisions
forward vs reverse bias band diagrams, what to notice?
it goes from p to n type, NOTICE THE SIDES
What is the forward bais current?
little recombination, recombination current is from right to left; tunneling current occurs when electrons move through a barrier that they classically shouldn't be able to move through
what is the depletion region look like for n+p junction width, or wm units?
meters, use wm!!!
minority concentration for holes on n side and electrons on p side (THIS IS UNDER NO VOLTAGE)
minority = majority of the other side * the constant e^-qvbi
what is wn and wp and total width of nondegenerate semiconductor? (Depletion region) when is w equal to each for degenerate as well?
n side and p side junction width E = 8.85 E-12 (E0) Vj = Vbi - Va
what is the quasi fermi levels? how to calculate them? what are the regular fermi levels? what is the difference? REVIEW use quasi which is the bottom when he asks you too
n type - efn-Ei p type - Ei - efp basically for nonequilibrium materials - aka light is shined on them Efn = Ei+kT ln(n/ni) Efp = Ei-kT ln(p/ni) use n and p!! not n0/po!!!
how do you determine which type of channel you have? look at NFET and PFDET
n type subtrate, or body, means you have the two p type sides which gives as the drain and source, which means you have p type channel p type substrate, or body, means you have two n types drains and sources which means you have n type channel
what is the threshold in terms of flatband voltage? WHAT DO YOU NEED TO REMEMBER ABOUT USING THIS EQUATION?
n+ poly-Si is used for the gates, and p+ poly-Si is used for p-channel devices, so signs will have to be ajdusted according to eariler item, given his example was p type channel with n type subtrate, this top one is the original, qd is always minus, the internal equation is where the sign comes in
how do positive and negative voltages affect the p type semiconductor?
negative voltage is negative slope positive voltage is positive slope
nn0, np0, pn0, pp0
nn0-equilibrium concentration of electrons in n-material=ND (nd' and nd are interchangable) np0-equilibrium concentration of electrons in p type=ni^2/Na' pn0-equilibrium concentration of holes in n-type material=ni^2/Nd' pp0-equilibrium concentration of holes in p-type material=NA all cm^3(-1)
What is the reverse bias current?
not much current to begin with(Graph) genaration current from left to right voltage and EF increases if doping is high, tunneling happens (tunneling current) low doping,
what happens when positive and negative voltages are applied to the gate?
notice is positive so thats why the direction is the same as the applied voltage
photoconductivity vs conductivity in the dark
or sigma(t) = q deltaN(t)(un +up) when deltaN = deltaP photoconducvtivity is when it is illuminated
Resistivity and Conductivity relationship
p = 1/sigma
VFB for ideal vs nonideal mosfet, or Vfb also signs for phims, Qi, Qd, 2phi, for n type or p type channel! Vthreshold equaiton is also on here
p silicon for p substrate and n silicon for n substrate
what is the Vbi, or built in potential of a MOSFET?
phi ox aand phi s are in voltas
what is phif and when is a semiconductor inverted?
phif = Ei-Ef (can be Ei or Ef!!!) 2phi f = phis phif = kt/q ln(NDA/ni)
ideal mosfet vs nonideal mosfet with regards to phims NOTE IDEAL VS NONIDEAL MOSFET TRAITS
phims = 0 and Qi = 0 for ideal MOSFET, whatever the substrate is the p Si or n Si used
what is phims?
phims is equal to the flatband voltage
voltage and current relationship in a pn junction
positive = va positive on p side with respect to n side(forward bias) va negative on n side (reverse bias)
minoirty carrier concentration at xn and xp under forward bias
remember, you can express in volts of v / kt
what is the depletion region(transition)width and relationship to xn and xp?
same as space charge, depletion or transition region; to be w = xn, then it is an n+p because it will be degeneratly doped
what is the hole and electron conductivity? (units) WHAT?
seimens/*cm* un = -vdn/E
what is a nonhomegenous semiconductor?
so far, we have examined homogeneous semiconductors. By homogeneous we mean that the entire semiconductor is made of the same material and doped uniformly. Examples of the other case, nonhomogeneous semiconductors, are semiconductors whose doping varies with position or where the semiconductor composition varies.
labels of silicon based mosfet (REVIEW!)
source and drain are relative t ox is usually SiO2, and is the insulator or dieletric layer
What is the drift velocity and mobility for electrons with scattering?
t = t-t0
What is the drift velocity and mobility for holes with scattering?
t=t-t0
final continuity equations
tao = minority carrier electron lifetime basically when you have a well defined carreir lifetime
excess carrier concentration as a function of x derivation for where x extends from the smples illiuminate surface to the infinitely long bulk
the picture is under forward bias equations 5.47 - 5.56 derive under equilibrium on page 256
what happens when two materials are joined together?
they are electrically neutral, but they are not stable (changes once they come into contact) By electrical neutrality, we mean that in any macroscopic region, the concentration of negative charge in the region equals the positive charge concentration, two differnt materials have fermi levels match when combined at equilibrium A is a little p type, B is a strong P-type
forward bias on pn junction
w is shorter, electrons on n side go to p side and goes to neutral region after depletion region as it diffuses to the right, it goes to 0 at infinity, and holes do the same thing
How does mobility act with temperature?
with increasing temperature, lattice scattering mobility decreases becaused increase phonon vibration causes increased scattering with increasing temperture, mobility ionized impurity mobility decreases because the speeds of the carrier particles are increased which leads to less reflection creating less scattering
minority carrier concentration lfetime graph or Tn Tp!!!
write all as 10^-5 not 10E-5!!!!!!!
what is xn and xp?
xn = boundary of depletion region on n side xp =boundary of dpletion region on p side
What is the total mobility of scattering? What does it resemble? How do you interpret it?
you know that the small value takes precedent same formula as parallel resistors
what approximations are used in the step -junction model of this pn junction?
• The doping profile is a step function. - n side, nd - na is a constant, p side na - nd is a constant • All impurities are ionized. electron concenctration on n side = n0 =Nd' hole concentration on p side = p0 = N'a • Impurity-induced bandgap- narrowing effects are neglected